This document summarizes and explains the phenomenon of quantum capacitor behavior at a metal-liquid interface. Specifically:
1) Above a critical solute concentration, the differential capacitance (C-V) curve shows plateaus where the capacitance does not change over a voltage range. This "anomalous" behavior is not explained by classical models of adlayer formation.
2) The author proposes a model where electrons become trapped in surface states at the interface, acting as a quantum capacitor. When the surface state band is filled, it completely screens the metal charge, resulting in a constant differential capacitance.
3) Mathematical analysis of the model shows that the capacitance depends only on properties of the thin confining layer
This document provides an overview of interfacial electrochemistry. It discusses how interfaces form boundaries between different phases of matter and influence interactions with the environment due to changed atomic structures. Most electrochemical events occur at interfaces, making interfacial electrochemistry important. When two dissimilar materials contact, charge separation occurs across the interface, creating an interfacial potential difference. The document also describes models of the electrical double layer that forms at electrode-electrolyte interfaces, such as the Helmholtz-Perrin and Gouy-Chapman models.
The document reports on an experiment to investigate the variation of conductance with temperature in electrolytes. It describes using ZnSO4 and CuSO4 solutions with Zn and Cu electrodes, respectively. Readings of current, voltage, resistance, and conductance were taken at increasing temperature intervals. The results show that the conductance of both electrolytes increased with rising temperature, in accordance with expected behavior. The document provides the aim, apparatus, procedure, observations, graphs, and conclusion of the experiment.
1st Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document provides an overview of key concepts in electrochemistry. It discusses how dry cells generate electricity through a chemical reaction that converts chemical energy to electrical energy. Electrolysis is described as breaking down an electrolyte through the passage of electricity, converting electrical energy to chemical energy. The document also covers electrical conduction through metallic conductors and electrolytic solutions, resistance and conductance, and the relationships between conductivity, molar conductivity, concentration, and volume for electrolytic solutions.
This document contains a project proposal that examines generating electricity from fruits. The proposal outlines using different fruits as electrolytes in a circuit with copper and zinc electrodes. It summarizes the chemistry behind how redox reactions produce electricity and the relationship between pH and acidity. The objectives are to analyze how fruit freshness affects voltage and pH, and determine which fruits produce the highest voltage based on pH readings. The methodology describes taking pH readings of various fruits and measuring the voltage, current, and time an LED lights when the fruits are used in a circuit with the electrodes. The expected results are that more acidic fruits will generate electricity for a longer time.
This document describes a student project to study how the EMF (electromotive force) of a Daniel cell is affected by various factors. The student will measure the EMF under different concentrations of reactants, temperatures, and electrode areas. A Daniel cell works by converting the chemical energy of a redox reaction between zinc and copper into electrical energy. The student outlines the objective, introduces the Daniel cell, describes the required materials and procedure, and presents observations and conclusions regarding how the EMF changes with concentration, temperature, and electrode area.
Physical chemistry of soil for PG studentsP.K. Mani
The document summarizes the Stern model of the electrical double layer at electrode-electrolyte interfaces. The Stern model proposes that the double layer consists of two parts - an inner compact layer where ions are firmly adsorbed, and an outer diffuse layer where ions are scattered in solution. The potential drops linearly within the compact layer and exponentially within the diffuse layer. The Stern model implies that there are two potential drops and that the interface can be represented as two capacitors in series. At high electrolyte concentrations, the diffuse layer is compressed and the interface capacity is equal to the compact layer capacity alone.
2nd Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document discusses the variation of conductivity and molar conductivity with concentration for strong and weak electrolytes. It explains that conductivity decreases with decreasing concentration as there are fewer ions to carry current. Molar conductivity initially increases with dilution as more ions are produced, but levels off for strong electrolytes at infinite dilution. In contrast, molar conductivity does not linearly depend on concentration for weak electrolytes. Kohlrausch's law is introduced to calculate the molar conductivity at infinite dilution for weak electrolytes based on that of their dissociated ions. The document also outlines the process for measuring conductivity using a conductivity cell and Wheatstone bridge.
The electrical double layer theory deals with the distribution of ions that occurs at the interface between a charged solid surface (such as a colloid) in contact with an aqueous electrolyte solution. The theory proposes that ions of the opposite charge are attracted to the solid surface (known as the potential determining ions), forming a tightly bound layer, giving the surface a net positive or negative charge. Nearby, counter ions of the opposite charge form a diffuse layer in the solution. The difference in electric potential between the charged surface and the neutral point in the diffuse layer is known as the Nernst potential. The electrical double layer consists of a fixed Stern layer near the surface and a diffuse layer extending into the solution.
This document provides an overview of interfacial electrochemistry. It discusses how interfaces form boundaries between different phases of matter and influence interactions with the environment due to changed atomic structures. Most electrochemical events occur at interfaces, making interfacial electrochemistry important. When two dissimilar materials contact, charge separation occurs across the interface, creating an interfacial potential difference. The document also describes models of the electrical double layer that forms at electrode-electrolyte interfaces, such as the Helmholtz-Perrin and Gouy-Chapman models.
The document reports on an experiment to investigate the variation of conductance with temperature in electrolytes. It describes using ZnSO4 and CuSO4 solutions with Zn and Cu electrodes, respectively. Readings of current, voltage, resistance, and conductance were taken at increasing temperature intervals. The results show that the conductance of both electrolytes increased with rising temperature, in accordance with expected behavior. The document provides the aim, apparatus, procedure, observations, graphs, and conclusion of the experiment.
1st Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document provides an overview of key concepts in electrochemistry. It discusses how dry cells generate electricity through a chemical reaction that converts chemical energy to electrical energy. Electrolysis is described as breaking down an electrolyte through the passage of electricity, converting electrical energy to chemical energy. The document also covers electrical conduction through metallic conductors and electrolytic solutions, resistance and conductance, and the relationships between conductivity, molar conductivity, concentration, and volume for electrolytic solutions.
This document contains a project proposal that examines generating electricity from fruits. The proposal outlines using different fruits as electrolytes in a circuit with copper and zinc electrodes. It summarizes the chemistry behind how redox reactions produce electricity and the relationship between pH and acidity. The objectives are to analyze how fruit freshness affects voltage and pH, and determine which fruits produce the highest voltage based on pH readings. The methodology describes taking pH readings of various fruits and measuring the voltage, current, and time an LED lights when the fruits are used in a circuit with the electrodes. The expected results are that more acidic fruits will generate electricity for a longer time.
This document describes a student project to study how the EMF (electromotive force) of a Daniel cell is affected by various factors. The student will measure the EMF under different concentrations of reactants, temperatures, and electrode areas. A Daniel cell works by converting the chemical energy of a redox reaction between zinc and copper into electrical energy. The student outlines the objective, introduces the Daniel cell, describes the required materials and procedure, and presents observations and conclusions regarding how the EMF changes with concentration, temperature, and electrode area.
Physical chemistry of soil for PG studentsP.K. Mani
The document summarizes the Stern model of the electrical double layer at electrode-electrolyte interfaces. The Stern model proposes that the double layer consists of two parts - an inner compact layer where ions are firmly adsorbed, and an outer diffuse layer where ions are scattered in solution. The potential drops linearly within the compact layer and exponentially within the diffuse layer. The Stern model implies that there are two potential drops and that the interface can be represented as two capacitors in series. At high electrolyte concentrations, the diffuse layer is compressed and the interface capacity is equal to the compact layer capacity alone.
2nd Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document discusses the variation of conductivity and molar conductivity with concentration for strong and weak electrolytes. It explains that conductivity decreases with decreasing concentration as there are fewer ions to carry current. Molar conductivity initially increases with dilution as more ions are produced, but levels off for strong electrolytes at infinite dilution. In contrast, molar conductivity does not linearly depend on concentration for weak electrolytes. Kohlrausch's law is introduced to calculate the molar conductivity at infinite dilution for weak electrolytes based on that of their dissociated ions. The document also outlines the process for measuring conductivity using a conductivity cell and Wheatstone bridge.
The electrical double layer theory deals with the distribution of ions that occurs at the interface between a charged solid surface (such as a colloid) in contact with an aqueous electrolyte solution. The theory proposes that ions of the opposite charge are attracted to the solid surface (known as the potential determining ions), forming a tightly bound layer, giving the surface a net positive or negative charge. Nearby, counter ions of the opposite charge form a diffuse layer in the solution. The difference in electric potential between the charged surface and the neutral point in the diffuse layer is known as the Nernst potential. The electrical double layer consists of a fixed Stern layer near the surface and a diffuse layer extending into the solution.
F.Sc. Part 1 Chemistry.Ch.10.Test (Malik Xufyan)Malik Xufyan
The document contains information about chemistry test series books published by Malik Xufyan of JIAS Academy, Jhang Institute for Advanced Studies. It lists the titles of 9 books covering chemistry courses from 9th class to F.Sc. Part II, which are available in both chapter-wise and board paper-wise test series formats. It also provides the contact information of the publisher.
5th Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
1) A galvanic cell consists of two half-cells separated by a salt bridge. At the interface between a metal electrode and solution, there is a potential difference called the electrode potential. The overall potential of the cell is called the electromotive force (emf).
2) The standard cell potential is the sum of the standard electrode potentials measured under standard conditions (1M concentrations, 1 atm pressure, 25°C). The Nernst equation relates the cell potential to concentrations and allows calculations of cell and electrode potentials.
3) The maximum work a galvanic cell can perform is equal to the negative of the change in Gibbs free energy of the cell reaction. The standard cell potential is directly
4th Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document discusses quantitative aspects of electrolysis and galvanic cells. It provides formulas for calculating moles and mass of products formed during electrolysis based on current, time, and mole ratio. It explains that the mass of substances produced in two cells connected in series is related by the mole ratio and molar mass. It also describes the components and functioning of a galvanic cell, including the half cells, electrodes, salt bridge, and how to write the overall cell reaction.
Coagulation and flocculation are essential processes used in water and wastewater treatment that involve destabilizing colloidal particles in water. Common coagulants used are aluminum sulfate, ferric chloride, and polyaluminum chloride. There are four main mechanisms for destabilizing colloids - double layer compression, charge neutralization, enmeshment in a precipitate, and interparticle bridging. The efficiency of coagulation-flocculation depends on factors like coagulant dosage, pH, mixing conditions, and flocculation time.
This document discusses bioelectrochemistry and membrane potentials. It introduces how electrochemistry studies ions and electrodes in biological systems. Cells are surrounded by membranes made of phospholipids that contain uneven distributions of ions like potassium, sodium, and chloride. This ion gradient across the cell membrane generates a resting membrane potential. Ions can cross the membrane through permeability or active transport via sodium-potassium pumps. The difference in ion concentrations, not the ions themselves, cause the membrane potential. Protein adsorption on metal electrodes is also examined as a model for interfacial electron transfer in biological systems.
Magnetoresistance anomalies in (Ga,Mn)As epilayers with perpendicular magneti...Oleg Maksimov
This document summarizes magnetoresistance anomalies observed in tensile-strained (Ga,Mn)As epilayers with perpendicular magnetic anisotropy. The researchers observed "spikes" in the longitudinal magnetoresistance that are antisymmetric with respect to the direction of the magnetic field. These anomalies occur during magnetization reversal and are accompanied by a change in sign of the anomalous Hall effect. Angular sweeps of the magnetic field reveal that the anomalies have an antisymmetric dependence on the helicity of the field sweep. The data suggest that the antisymmetric anomalies originate from anomalous Hall effect contributions to the longitudinal resistance when domain walls are located between the voltage probes.
EXPLAINS WHAT IS AN ELECTRICAL DOUBLE LAYER AND HOW IT FORMS
INCLUDES DISTRIBUTION OF IONS AROUND A PARTICLE OF SUSPENSION
HOW THE IONS GET ADSORBED ON THE SURFACE OF SUSPENDED PARTICLE AND HOW IT AFFECTS DISTRIBUTION OF REST OF THE IONS IN THE LIQUID PHASE
EXPLAIN DIFFERENT POTENTIALS ACROSS
ZETA POTENTIAL NERNST POTENTIAL ETC.
ELECTRO CHEMISTRY l electrolytic cell std 12 lec 1MAYURI SOMPURA
This document discusses electrochemistry and different types of electrochemical cells. It explains that in an electrolytic cell, electrical energy is used to drive a non-spontaneous redox reaction to produce a chemical energy output. The cathode is where reduction occurs through electron gain, and the anode is where oxidation occurs through electron loss. An electrolytic solution contains molecules bound by ionic bonds that allow conduction when an electrical current is applied to the cell.
CONTENTS
Electrochemistry: definition & importance
Conductors: metallic & electrolytic conduction,
Electrolytes, Electrochemical cell & electrolytic cell
A simple electrochemical cell: Galvanic cell or (Daniell Cell)
Cell reaction, cell representation, Salt bridge & its use,
Electrode potential, standard electrode potential, SHE,
Standard cell potential or standard electromotive force of a cell
Electrochemical series (Standard reduction potential values)
Nernst Equation, Relationship with Standard cell potential with Gibbs energy & also equilibrium constant
Resistance (R) & conductance (G) of a solution of an electrolyte
Conductivity (k) of solution, Cell constant (G*) & their units,
Molar conductivity (Λm) & its variation with concentration & temperature,
Debye Huckel Onsager equation & Limiting molar conductivity,
Kohlrausch’s law & its application & numerical problems.
Electrolytic cells & electrolysis.
Some examples of electrolysis of electrolytes in molten / aq. state.
Faraday’s laws of electrolysis: First & second law- numerical problems. Corrosion, Electrochemical theory of rusting.
Prevention of rusting.
This document analyzes quantitative X-ray absorption and emission spectroscopic data to understand the electronic structures of Cu2S and CuS. It finds that Cu2S has a significant amount of Cu2+ sites and some Cu0 centers, which contributes to its electrical conductivity. CuS is shown to have tetrahedral Cu2+ and trigonal Cu1+ sites arranged in crystal planes with alternating charge densities, which may enable its photoluminescence properties. A quantitative molecular orbital approach is able to solve the complicated electronic structures of these materials and correlate them to important physical properties.
Juornal of Physics Condensed Matter - Article IRossen Hristov
This document summarizes a study that investigated the mobility of counterions condensed on carboxymethyl cellulose (CMC) polymer chains adsorbed onto alumina colloid particles. Previous studies using electro-optical techniques reported that condensed counterions are mobile in alternating electric fields. However, the current study uses an amplitude approach, measuring particle polarizability at increasing CMC concentration rather than frequency dependence. Results indicate condensed counterions do not contribute to particle polarization at 1 kHz, suggesting they are immobile in sinusoidal fields up to 0.5 kV/cm and 1 kHz. Comparison of polarizability and electrophoretic mobility supports the conclusion that condensed counterions are immobilized on the CMC chains.
3rd Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document summarizes key aspects of electrochemistry including:
1) An electrochemical cell consists of two electrodes immersed in an electrolyte that allows ionic conduction. Oxidation occurs at the anode and reduction at the cathode.
2) There are two types of cells - electrolytic cells use an external power source to drive nonspontaneous reactions, while galvanic/voltaic cells generate power from spontaneous reactions.
3) The electrolysis of molten NaCl produces chlorine gas at the anode and deposits metallic sodium at the cathode, while electrolysis of aqueous NaCl produces hydrogen and chlorine gas due to the lower standard potentials of sodium and chlorine ions compared to water.
WHILE UPLOADING SOME CHANGES ARE HAPPENED IN FRONT PAGE.I FACED MANY PROBLEMS TO COMPLETE THIS PROJECT.BECAUSE NO ONE HAD DONE THIS PROJECT BEFORE SO, IN ORDER TO AVOID OTHERS TO FACE SAME PROBLEM WHICH I FACED KEPT THIS EXAMPLE WHICH HELP YOU ALL.HOPE IT WILL HELPS YOU.
This document discusses introducing electronegative guests into the skutterudite CoSb3 framework to form inclusion compounds. It finds that sulfur (S) and selenium (Se) can stably fill the framework when charge compensation via tellurium substitution is used. The strong covalent bonding between the electronegative guests (S and Se) and the host framework leads to unique localized "cluster vibrations" that significantly reduce the thermal conductivity compared to systems with electropositive guests or without guests. Very low lattice thermal conductivity values around 1.5 W m-1K-1 are achieved with S-filled CoSb3, promising for thermoelectric applications.
Efficient production of negative hydrogen ions in RF plasma by using a self-b...IJERA Editor
Volume production of negative hydrogen ions is established efficiently in a pure hydrogen RF discharge plasma by using a self-biased grid electrode for production of low electron-temperature and high density plasma. Using this electrode both high and low electron temperature plasmas are produced in the regions separated by the grid electrode in the chamber, in which the electron temperature in the downstream region is controlled by the mesh size and plasma production parameters. The production rate of negative ions depends strongly on the electron temperature varied by the RF input power and hydrogen pressure. In the case of the grid electrode with the 5 mesh/in., the negative hydrogen ions are produced effectively in the downstream region in the hydrogen pressure range of 0.9 −2.7 Pa. In addition, the production rate of the negative ion 퐻 − raises from 62 % to 87 % at 0.9 Pa by changing the RF power from 20 W to 80W.
1. Electrochemistry deals with the production of electricity from chemical reactions and use of electricity to cause non-spontaneous reactions.
2. Conductors are classified as metallic conductors which allow current by electron movement and electrolytic conductors which allow current through dissolved or molten state with chemical decomposition.
3. Electrolytes are classified as strong which completely dissociate and weak which partially dissociate. Conductivity is directly proportional to concentration and inversely proportional to length.
6th Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
The document discusses reference electrodes and the standard hydrogen electrode (SHE) used in electrochemistry. It then summarizes different types of galvanic cells, including primary cells like dry cells that cannot be recharged, and secondary cells like lead-acid batteries that can. Specifically, it describes the construction, reactions, and uses of the common dry cell, which contains a zinc anode, manganese dioxide and carbon cathode, and a moist paste electrolyte.
F.Sc. Part 1 Chemistry.Ch.10.Test (Malik Xufyan)Malik Xufyan
The document contains information about chemistry test series books published by Malik Xufyan of JIAS Academy, Jhang Institute for Advanced Studies. It lists the titles of 9 books covering chemistry courses from 9th class to F.Sc. Part II, which are available in both chapter-wise and board paper-wise test series formats. It also provides the contact information of the publisher.
5th Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
1) A galvanic cell consists of two half-cells separated by a salt bridge. At the interface between a metal electrode and solution, there is a potential difference called the electrode potential. The overall potential of the cell is called the electromotive force (emf).
2) The standard cell potential is the sum of the standard electrode potentials measured under standard conditions (1M concentrations, 1 atm pressure, 25°C). The Nernst equation relates the cell potential to concentrations and allows calculations of cell and electrode potentials.
3) The maximum work a galvanic cell can perform is equal to the negative of the change in Gibbs free energy of the cell reaction. The standard cell potential is directly
4th Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document discusses quantitative aspects of electrolysis and galvanic cells. It provides formulas for calculating moles and mass of products formed during electrolysis based on current, time, and mole ratio. It explains that the mass of substances produced in two cells connected in series is related by the mole ratio and molar mass. It also describes the components and functioning of a galvanic cell, including the half cells, electrodes, salt bridge, and how to write the overall cell reaction.
Coagulation and flocculation are essential processes used in water and wastewater treatment that involve destabilizing colloidal particles in water. Common coagulants used are aluminum sulfate, ferric chloride, and polyaluminum chloride. There are four main mechanisms for destabilizing colloids - double layer compression, charge neutralization, enmeshment in a precipitate, and interparticle bridging. The efficiency of coagulation-flocculation depends on factors like coagulant dosage, pH, mixing conditions, and flocculation time.
This document discusses bioelectrochemistry and membrane potentials. It introduces how electrochemistry studies ions and electrodes in biological systems. Cells are surrounded by membranes made of phospholipids that contain uneven distributions of ions like potassium, sodium, and chloride. This ion gradient across the cell membrane generates a resting membrane potential. Ions can cross the membrane through permeability or active transport via sodium-potassium pumps. The difference in ion concentrations, not the ions themselves, cause the membrane potential. Protein adsorption on metal electrodes is also examined as a model for interfacial electron transfer in biological systems.
Magnetoresistance anomalies in (Ga,Mn)As epilayers with perpendicular magneti...Oleg Maksimov
This document summarizes magnetoresistance anomalies observed in tensile-strained (Ga,Mn)As epilayers with perpendicular magnetic anisotropy. The researchers observed "spikes" in the longitudinal magnetoresistance that are antisymmetric with respect to the direction of the magnetic field. These anomalies occur during magnetization reversal and are accompanied by a change in sign of the anomalous Hall effect. Angular sweeps of the magnetic field reveal that the anomalies have an antisymmetric dependence on the helicity of the field sweep. The data suggest that the antisymmetric anomalies originate from anomalous Hall effect contributions to the longitudinal resistance when domain walls are located between the voltage probes.
EXPLAINS WHAT IS AN ELECTRICAL DOUBLE LAYER AND HOW IT FORMS
INCLUDES DISTRIBUTION OF IONS AROUND A PARTICLE OF SUSPENSION
HOW THE IONS GET ADSORBED ON THE SURFACE OF SUSPENDED PARTICLE AND HOW IT AFFECTS DISTRIBUTION OF REST OF THE IONS IN THE LIQUID PHASE
EXPLAIN DIFFERENT POTENTIALS ACROSS
ZETA POTENTIAL NERNST POTENTIAL ETC.
ELECTRO CHEMISTRY l electrolytic cell std 12 lec 1MAYURI SOMPURA
This document discusses electrochemistry and different types of electrochemical cells. It explains that in an electrolytic cell, electrical energy is used to drive a non-spontaneous redox reaction to produce a chemical energy output. The cathode is where reduction occurs through electron gain, and the anode is where oxidation occurs through electron loss. An electrolytic solution contains molecules bound by ionic bonds that allow conduction when an electrical current is applied to the cell.
CONTENTS
Electrochemistry: definition & importance
Conductors: metallic & electrolytic conduction,
Electrolytes, Electrochemical cell & electrolytic cell
A simple electrochemical cell: Galvanic cell or (Daniell Cell)
Cell reaction, cell representation, Salt bridge & its use,
Electrode potential, standard electrode potential, SHE,
Standard cell potential or standard electromotive force of a cell
Electrochemical series (Standard reduction potential values)
Nernst Equation, Relationship with Standard cell potential with Gibbs energy & also equilibrium constant
Resistance (R) & conductance (G) of a solution of an electrolyte
Conductivity (k) of solution, Cell constant (G*) & their units,
Molar conductivity (Λm) & its variation with concentration & temperature,
Debye Huckel Onsager equation & Limiting molar conductivity,
Kohlrausch’s law & its application & numerical problems.
Electrolytic cells & electrolysis.
Some examples of electrolysis of electrolytes in molten / aq. state.
Faraday’s laws of electrolysis: First & second law- numerical problems. Corrosion, Electrochemical theory of rusting.
Prevention of rusting.
This document analyzes quantitative X-ray absorption and emission spectroscopic data to understand the electronic structures of Cu2S and CuS. It finds that Cu2S has a significant amount of Cu2+ sites and some Cu0 centers, which contributes to its electrical conductivity. CuS is shown to have tetrahedral Cu2+ and trigonal Cu1+ sites arranged in crystal planes with alternating charge densities, which may enable its photoluminescence properties. A quantitative molecular orbital approach is able to solve the complicated electronic structures of these materials and correlate them to important physical properties.
Juornal of Physics Condensed Matter - Article IRossen Hristov
This document summarizes a study that investigated the mobility of counterions condensed on carboxymethyl cellulose (CMC) polymer chains adsorbed onto alumina colloid particles. Previous studies using electro-optical techniques reported that condensed counterions are mobile in alternating electric fields. However, the current study uses an amplitude approach, measuring particle polarizability at increasing CMC concentration rather than frequency dependence. Results indicate condensed counterions do not contribute to particle polarization at 1 kHz, suggesting they are immobile in sinusoidal fields up to 0.5 kV/cm and 1 kHz. Comparison of polarizability and electrophoretic mobility supports the conclusion that condensed counterions are immobilized on the CMC chains.
3rd Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
This document summarizes key aspects of electrochemistry including:
1) An electrochemical cell consists of two electrodes immersed in an electrolyte that allows ionic conduction. Oxidation occurs at the anode and reduction at the cathode.
2) There are two types of cells - electrolytic cells use an external power source to drive nonspontaneous reactions, while galvanic/voltaic cells generate power from spontaneous reactions.
3) The electrolysis of molten NaCl produces chlorine gas at the anode and deposits metallic sodium at the cathode, while electrolysis of aqueous NaCl produces hydrogen and chlorine gas due to the lower standard potentials of sodium and chlorine ions compared to water.
WHILE UPLOADING SOME CHANGES ARE HAPPENED IN FRONT PAGE.I FACED MANY PROBLEMS TO COMPLETE THIS PROJECT.BECAUSE NO ONE HAD DONE THIS PROJECT BEFORE SO, IN ORDER TO AVOID OTHERS TO FACE SAME PROBLEM WHICH I FACED KEPT THIS EXAMPLE WHICH HELP YOU ALL.HOPE IT WILL HELPS YOU.
This document discusses introducing electronegative guests into the skutterudite CoSb3 framework to form inclusion compounds. It finds that sulfur (S) and selenium (Se) can stably fill the framework when charge compensation via tellurium substitution is used. The strong covalent bonding between the electronegative guests (S and Se) and the host framework leads to unique localized "cluster vibrations" that significantly reduce the thermal conductivity compared to systems with electropositive guests or without guests. Very low lattice thermal conductivity values around 1.5 W m-1K-1 are achieved with S-filled CoSb3, promising for thermoelectric applications.
Efficient production of negative hydrogen ions in RF plasma by using a self-b...IJERA Editor
Volume production of negative hydrogen ions is established efficiently in a pure hydrogen RF discharge plasma by using a self-biased grid electrode for production of low electron-temperature and high density plasma. Using this electrode both high and low electron temperature plasmas are produced in the regions separated by the grid electrode in the chamber, in which the electron temperature in the downstream region is controlled by the mesh size and plasma production parameters. The production rate of negative ions depends strongly on the electron temperature varied by the RF input power and hydrogen pressure. In the case of the grid electrode with the 5 mesh/in., the negative hydrogen ions are produced effectively in the downstream region in the hydrogen pressure range of 0.9 −2.7 Pa. In addition, the production rate of the negative ion 퐻 − raises from 62 % to 87 % at 0.9 Pa by changing the RF power from 20 W to 80W.
1. Electrochemistry deals with the production of electricity from chemical reactions and use of electricity to cause non-spontaneous reactions.
2. Conductors are classified as metallic conductors which allow current by electron movement and electrolytic conductors which allow current through dissolved or molten state with chemical decomposition.
3. Electrolytes are classified as strong which completely dissociate and weak which partially dissociate. Conductivity is directly proportional to concentration and inversely proportional to length.
6th Lecture on Electrochemistry | Chemistry Part I | 12th StdAnsari Usama
The document discusses reference electrodes and the standard hydrogen electrode (SHE) used in electrochemistry. It then summarizes different types of galvanic cells, including primary cells like dry cells that cannot be recharged, and secondary cells like lead-acid batteries that can. Specifically, it describes the construction, reactions, and uses of the common dry cell, which contains a zinc anode, manganese dioxide and carbon cathode, and a moist paste electrolyte.
Dokumen tersebut membahas tentang mata pelajaran Pendidikan Kewarganegaraan yang bertujuan membentuk warga negara Indonesia yang memahami dan mampu melaksanakan hak dan kewajibannya sesuai dengan Pancasila dan UUD 1945. Mata pelajaran ini mencakup berbagai aspek seperti persatuan bangsa, hukum dan HAM, sistem pemerintahan, demokrasi, serta hubungan internasional."
Dokumen tersebut membahas tentang ketentuan kriteria ketuntasan minimal (KKM) dalam Kurikulum Tingkat Satuan Pendidikan (KTSP), termasuk proses penetapan KKM, format KKM, dan teknik penilaian hasil belajar.
The document summarizes 4 theoretical problems and 1 experimental problem from the 1971 International Physics Olympiad held in Sofia, Bulgaria. The theoretical problems involve calculating the acceleration of blocks on an inclined prism, determining the mass of hydrogen in a sealed system using changes in mercury levels, calculating the total energy stored in a circuit of batteries and capacitors, and finding the relative velocity of images of a fish moving in an aquarium. The experimental problem involves constructing a circuit using a DC source, ammeter, voltmeter and rheostat to plot power, resistance and efficiency.
1) A spacecraft measures the redshift of photons emitted from the surface of a star to determine the star's mass M and radius R. As it approaches the star, it measures the velocity needed for resonant absorption of photons by He+ ions.
2) The experimental data gives the velocity needed for resonance at different distances from the star. This data is plotted to determine M and R graphically.
3) In addition to gravitational redshift, the emitted photons will experience a small relativistic frequency shift due to the recoil of the emitting atom. This effect is much smaller than the gravitational redshift.
The document discusses several physics concepts:
1) Light interference from two slits and diffraction gratings, showing how the intensity of light varies with angle due to interference.
2) Seismic wave propagation through the Earth, describing how travel times vary with angle depending on the wave path through the mantle or core.
3) Vibrations of coupled harmonic oscillators arranged in linear chains, showing the normal mode solutions and frequency distributions that arise.
1. The document discusses orbital parameters of a binary star system. It provides the orbital period, radii, and velocities of the two stars.
2. Doppler shift formulas are used to calculate the orbital velocities of the stars based on differences between maximum and minimum observed wavelengths from the stars.
3. Gravitational force equations are used to calculate the masses of the stars based on their orbital radii and velocities.
The document provides instructions for a 5-hour theoretical physics competition with 3 questions. It details formatting requirements for working out the questions, including labeling pages with question number, page number, and total pages used. It also provides instructions for arranging the completed pages in proper order at the end. The first theoretical question is about vibrational modes in a linear crystal lattice model and includes parts on deriving the equation of motion, solving for mode frequencies and wave numbers, calculating average phonon energy, determining total crystal energy, and relating heat capacity to temperature. The second question considers a "rail gun" device constructed by a young man to launch himself across a strait to reach his love within 11 seconds. It involves deriving acceleration, calculating
This document outlines strategies for creating linkable content assets for boring or regulated industries. It suggests focusing on data and facts related to the industry rather than just content. Specific ideas include creating guides on industry-related topics like office hacks or finance industry trends. For regulated industries, it recommends using approved data sources to create interactive charts and maps. The goal is to establish yourself as a resource by answering people's questions about the industry through helpful, shareable assets.
Lo que no se dice de la nueva planta de monsanto en córdoba- Informes 1 y 2Ramón Copa
Lo que no se dice de la nueva planta de Monsanto en Córdoba
Las semillas transgénicas para la Planta de Malvinas Argentinas
Los promotores de la instalación de Monsanto en Malvinas Argentinas argumentan que la planta no generara contaminación al ser una “procesadora de semillas”; tratan de ocultar el carácter tóxico de la misma detrás de la simbólicamente apreciada concepción de “semilla” que tienen todos en general. También intentan esconder los poderosos venenos con que trataran a esas semillas, y sobretodo buscan disimular en qué han convertido a esas semillas de maíz manipuladas por Monsanto, la empresa más siniestra e inescrupulosa entre todas las multinacionales.
Para divulgar esta información, la Red de Médicos de Pueblos Fumigados emite este primer Informe sobre la nueva semilla que se procesará en la planta, utilizando la información que ha podido ser obtenida hasta este momento con mucha dificultad. En poco tiempo emitiremos un 2º Informe sobre el proceso de tratamiento de las semillas en el proyectado establecimiento.
This document summarizes the key electrical properties of metals and semiconductors. It discusses Ohm's law and how electrical conductivity in metals is influenced by drift velocity and current density. It also explains how resistivity is related to temperature in metals. For semiconductors, it describes the band structure of insulators, metals and semiconductors and how conductivity varies with intrinsic carrier concentration and temperature in intrinsic semiconductors. It then discusses the effects of doping on carrier concentrations and conductivity in n-type and p-type extrinsic semiconductors. Finally, it provides an overview of compound semiconductors made of two or three elements.
- The document discusses an undergraduate investigation using point contact spectroscopy (PCS) to study quantum criticality in materials. PCS has traditionally been used to determine scattering information in metals and energy gaps in superconductors. A recent theory suggests PCS may also detect non-Fermi liquid behavior associated with quantum criticality.
- The investigation began by using PCS to study the superconductor FeTe0.55Se0.45 to establish ballistic contacts. It then aimed to use PCS to search for signatures of quantum fluctuations in the quantum critical material YFe2Al10 above the superconductor's critical temperature. This may provide evidence for detecting quantum critical behavior through PCS.
This document describes an experiment to observe and record the surface plasmon resonance (SPR) curve for a thin metal film. Light from a laser is shone through a glass prism onto the metal film at varying angles of incidence. The intensity of the reflected light is recorded versus the angle to generate the SPR curve. Surface plasmons are quantum phenomena that can be excited at the metal-air interface by photons and decay back into photons. The SPR curve depends on the dielectric constant of the metal film and its thickness. Matching the wavevector of incident light to that of surface plasmons requires increasing the wavevector by passing light through a higher index material like glass before it reaches the metal film.
Electrical Measurements for Semiconducting DevicesYogesh Patil
The document discusses electrical measurements for semiconducting devices. It describes current-voltage (I-V) characteristics and capacitance-voltage (C-V) characteristics, which are important for understanding the performance of solar cells and other semiconductor applications. The I-V characteristics provide information about the ideality factor and barrier potential of devices like diodes and solar cells. C-V measurements allow determining parameters like doping concentration and flat band potential. Understanding these electrical measurements is key to improving the efficiency of devices using heterojunctions of wide bandgap semiconductors.
This document discusses how laser tweezers can trap neutral atoms by exploiting the atom's polarizability. It provides a classical explanation in four parts: (1) a polarized atom experiences a restoring force at the focus of a laser beam where the electric field strength peaks; (2) absorption of photons along the beam direction results in a longitudinal force; (3) modeling the atom's polarizability shows the real part peaks at a frequency slightly below the natural frequency; (4) tight focusing is required to ensure the radial trapping force exceeds the longitudinal force, with a calculated optimum f-number provided.
Stillwell_ Strongly coupled electronic, magnetic, and lattice degrees of free...Ryan Stillwell, Ph.D.
This document summarizes research on the ferromagnetic compound LaCo5 under high pressure. X-ray diffraction measurements show an anisotropic lattice collapse of the c axis near 10 GPa, consistent with theoretical predictions. High-pressure magnetotransport measurements reveal changes in the Hall effect signatures near 10 GPa, providing the first experimental evidence of changes in the electronic and magnetic properties associated with the predicted magnetoelastic collapse. The coupling of structural, electronic, and magnetic behaviors in LaCo5 under pressure substantiates the theoretical model of an electronic topological transition driving the magnetoelastic collapse.
The Effect of High Zeta Potentials on the Flow Hydrodynamics in Parallel-Plat...CSCJournals
This paper investigates the effect of the EDL at the solid-liquid interface on the liquid flow through a micro-channel formed by two parallel plates. The complete Poisson-Boltzmann equation (without the frequently used linear approximation) was solved analytically in order to determine the EDL field near the solid-liquid interface. The momentum equation was solved analytically taking into consideration the electrical body force resulting from the EDL field. Effects of the channel size and the strength of the zeta-potential on the electrostatic potential, the streaming potential, the velocity profile, the volume flow rate, and the apparent viscosity are presented and discussed. Results of the present analysis, which are based on the complete Poisson-Boltzmann equation, are compared with a simplified analysis that used a linear approximation of the Poisson-Boltzmann equation.
Semiconductors have properties between conductors and insulators due to their small energy band gap. Band theory explains the allowed energy levels for electrons in solids. Intrinsic semiconductors have few charge carriers that are generated thermally, while extrinsic semiconductors have impurities that generate majority carriers. The Hall effect demonstrates the behavior of charge carriers in a magnetic field and can determine carrier type and concentration. Semiconductors are used widely in electronic devices like diodes, transistors, sensors and solar cells due to their small size, low power needs, and long lifespan.
Electronic Devices and Circuits by Dr. R.Prakash Raorachurivlsi
This document provides an overview of electronic devices and circuits in 5 units:
1. PN junction diodes, tunnel diodes, varactor diodes, and photo diodes.
2. Rectifiers, filters, and voltage regulation using zener diodes.
3. Bipolar junction transistors, characteristics, configurations, and transistor amplifiers.
4. Transistor biasing and stabilization techniques.
5. Field effect transistors including JFETs, MOSFETs, and FET amplifiers.
This chapter discusses electric current and resistance. It defines current as the rate of flow of electric charge and introduces concepts like current density and drift velocity. Ohm's law is examined at both the microscopic and macroscopic levels. The chapter establishes relationships between current, voltage, resistance, resistivity, and conductivity. It also discusses how materials can be ohmic or non-ohmic and explores how resistance and resistivity are calculated for different objects. Electrical energy and power delivered by a battery through a resistor are also summarized.
This document summarizes an experiment on electrowetting of poly(ethylene terephthalate) (PET) films. The researchers measured how applying a voltage between a water drop and a rear electrode affected the contact angle of the water drop on the PET film. They found that voltages up to 200V could decrease the contact angle by over 30 degrees. At higher voltages, the contact angle reached a saturation point and did not decrease further. The decrease in contact angle was irreversible, likely due to modification of the PET polymer near the contact line where the electric field was strongest. The researchers also investigated how aqueous solutions of salts and polymers were affected by the applied voltage.
This document provides an overview of intrinsic and extrinsic semiconductors. It begins with an introduction to crystalline solids and classifications of solids as conductors, insulators, or semiconductors. It then discusses intrinsic semiconductors, how increasing temperature generates electron-hole pairs, and how conductivity increases with temperature. Extrinsic or doped semiconductors are introduced, including n-type and p-type semiconductors created by adding donor or acceptor impurities. The document explains how doping increases the number of charge carriers and conductivity.
This document discusses electrical conductivity in various materials. It begins by explaining that metals are good conductors due to their large number of free electrons. Semiconductors have lower conductivity than metals due to their lower concentration of free charge carriers. Conductivity in nonmetals like ionic crystals and glasses depends on mobile charges like electrons and ions. The document then discusses how conductivity varies with temperature in nonmetals. It also covers the skin effect in conductors at high frequencies and conductivity considerations in thin metal films. The document concludes by discussing copper interconnects in microelectronics.
The document discusses electric fields and electric dipoles. It defines the electric field as a vector field generated by electric charges that acts upon other charges. Electric field lines are introduced to visualize electric fields, with higher density of lines indicating stronger fields. Dipoles, such as water molecules, have a built-in electric polarity due to unequal charge distribution. When placed in an external electric field, dipoles experience a torque attempting to align them with the field but do not experience a net force. Microwave ovens work by using an oscillating electric field to cause the rotation of polar water molecules in food, generating heat through molecular collisions.
Electromagnetic dissociation of Co and Au targets by a 10.2 GeV_nLars Ewell
The document describes the theory behind electromagnetic dissociation (ED) of nuclei by relativistic heavy ions. It discusses how the virtual photon approach of Weizsacker, Williams and Fermi can be used to model the Lorentz contracted electromagnetic fields of the projectile nucleus as pulses of photons interacting with the target nucleus. Approximations are made treating both nuclei as point particles to calculate the electric and magnetic fields in the laboratory frame. This allows relating the ED cross sections to real photonuclear cross sections.
This document discusses dielectrics and their properties. It introduces dielectrics as materials that can store electric charge and energy with minimal heat loss. The document discusses how a capacitor's capacitance depends on the dielectric material between its plates, including the dielectric constant which measures a material's ability to concentrate electrostatic lines of flux. It also examines polarization in insulators when an electric field is applied and defines related terms like permittivity, dielectric constant, and loss tangent.
1 c -users_haider_app_data_local_temp_npse36cMudassir Ali
The document summarizes the operation of a Schottky diode. It begins by explaining that a Schottky diode uses a metal-semiconductor junction rather than a PN junction. Rectification occurs due to differences in work functions rather than doping profiles. It then discusses the ideal characteristics of a Schottky junction in terms of band diagrams and depletion widths. The document proceeds to describe how applied voltages affect the junction. It concludes by noting some deviations from ideal behavior including Schottky barrier lowering, surface imperfections, tunneling effects, and series resistance.
Dielectric Dilemma 1901.10805 v2 feb 4 2019Bob Eisenberg
A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications. The dilemma can be partially resolved by a rederivation of conservation of current, where current is defined now to include the epolarization of the vacuumf ..0 .......... Conserveration of current becomes Kirchoff's current law with this definition, in the one dimensional circuits of our electronic technology. With this definition, Kirchoff's laws are valid whenever Maxwell's equations are valid, explaining why those laws reliably describe circuits that switch in nanoseconds.
Paragraf pertama membahas tentang Anisa, siswa terpandai di kelasnya yang humoris dan gemar membaca. Paragraf berikutnya membahas tentang kriteria bahan pembelajaran sastra untuk kelas rendah yaitu keterbacaan dan kesesuaian. Paragraf terakhir menjelaskan tentang struktur bahasa Indonesia baku yang ditunjukkan pada suatu kalimat contoh.
Dokumen tersebut berisi soal-soal ujian untuk mengetahui tingkat pemahaman siswa tentang berbagai konsep pendidikan seperti teori belajar, strategi pembelajaran, penilaian hasil belajar, dan penerapan kurikulum 2013. Soal-soal tersebut mencakup 32 pertanyaan pilihan ganda.
Teks tersebut berisi 17 pertanyaan mengenai situasi dan tanggapan yang tepat bagi seorang guru dalam berbagai kondisi. Ringkasannya adalah: Teks tersebut memberikan opsi-opsi tanggapan yang tepat bagi seorang guru dalam menghadapi berbagai situasi sehari-hari di sekolah seperti menangani konflik antar siswa, menilai prestasi belajar siswa, serta menjalankan tugas sebagai guru dan petugas tata tertib
Teks tersebut membahas tentang kompetensi pedagogik, sosial, dan kepribadian yang harus dimiliki seorang guru. Beberapa poin penting yang diangkat antara lain terlibat aktif dalam perencanaan program sekolah, membantu peserta didik yang kurang mampu, serta mengutamakan keselamatan diri dan orang lain dalam menjalankan tugas.
Teks tersebut membahas berbagai soal tentang sosial dan kepribadian, model pembelajaran, penanganan masalah siswa, dan tugas seorang guru. Secara garis besar, teks tersebut memberikan saran agar guru dapat menangani berbagai situasi dengan bijak, adil, dan melibatkan semua pihak terkait.
Teks tersebut berisi soal-soal untuk mengetahui sikap dan tanggapan seseorang dalam berbagai situasi. Soal-soal tersebut meliputi berbagai topik seperti tanggung jawab sebagai PNS, tanggapan terhadap kesalahan, kerjasama tim, dan kerahasiaan informasi.
Teks tersebut membahas mengenai kecenderungan wisatawan Indonesia untuk berlibur ke luar negeri daripada mengunjungi objek wisata di dalam negeri. Hal ini disebabkan oleh beberapa faktor seperti daya tarik objek wisata luar negeri, keterbatasan sarana transportasi dan fasilitas pariwisata di dalam negeri, serta mahalnya biaya. Teks ini juga menyebutkan peningkatan jumlah wisatawan Indonesia yang berkunjung ke luar neger
1. Menggali informasi dari guru dan peserta didik secara terpisah. Kemudian, dengan kesepakatan bersama mengajak dialog keduanya agar keduanya dapat saling memahami.
2. Semua peserta didik dengan prestasi tinggi maupun rendah sama-sama memiliki kebutuhan untuk memelihara motivasi belajar mereka, tetapi bentuk dan strateginya yang berbeda.
3. Sudah menjadi kewajiban guru untuk mengatasi masalah belajar
Dokumen tersebut membahas mengenai perkembangan kognitif peserta didik, perkembangan sosial-emosional, perkembangan moral, kesulitan belajar siswa, teori belajar, dan perencanaan pelaksanaan pembelajaran. Dokumen ini memberikan penjelasan mengenai berbagai aspek perkembangan peserta didik dan prinsip-prinsip dasar dalam merencanakan dan melaksanakan pembelajaran.
Dokumen tersebut berisi soal latihan mengenai perkembangan kognitif, sosial-emosional, dan moral peserta didik. Juga membahas teori belajar, perencanaan pembelajaran, dan kesulitan belajar siswa. Terdiri dari 31 pertanyaan pilihan ganda.
Dokumen tersebut berisi kumpulan soal tes formatif dan sumatif untuk mata pelajaran kompetensi pedagogi. Soal-soal tersebut mencakup pengertian pengukuran, penilaian, tes, dan evaluasi serta mata pelajaran lainnya seperti perencanaan pembelajaran, strategi pembelajaran, dan pengelolaan kelas.
Buku ini berisi ringkasan singkat mengenai kisi-kisi soal Ujian Kompetensi Mahasiswa Pendidikan Profesi Guru (UKMPPG) Program Studi Pendidikan Guru Sekolah Dasar (PGSD) tahun 2017. Terdiri dari kisi-kisi soal untuk kompetensi pedagogik dan profesional mata ujian Bahasa Indonesia, Matematika, IPA, IPS, dan PPKn beserta indikator esensialnya.
Dokumen tersebut berisi paket soal untuk tes kemampuan verbal, kuantitatif, dan logika yang terdiri dari 75 soal pilihan ganda. Soal meliputi materi seperti analogi, hitungan matematika, deret bilangan, persentase, dan logika.
Teks tersebut merupakan soal tes yang terdiri dari 5 subtes yaitu: 1) Padanan kata, 2) Lawan kata, 3) Pemahaman wacana, 4) Deret angka, dan 5) Aritmetika dan konsep aljabar. Subtes tersebut berisi soal-soal pilihan ganda untuk mengetahui kemampuan verbal, kuantitatif, dan logika peserta ujian.
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor IvaniukFwdays
At this talk we will discuss DDoS protection tools and best practices, discuss network architectures and what AWS has to offer. Also, we will look into one of the largest DDoS attacks on Ukrainian infrastructure that happened in February 2022. We'll see, what techniques helped to keep the web resources available for Ukrainians and how AWS improved DDoS protection for all customers based on Ukraine experience
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
Main news related to the CCS TSI 2023 (2023/1695)Jakub Marek
An English 🇬🇧 translation of a presentation to the speech I gave about the main changes brought by CCS TSI 2023 at the biggest Czech conference on Communications and signalling systems on Railways, which was held in Clarion Hotel Olomouc from 7th to 9th November 2023 (konferenceszt.cz). Attended by around 500 participants and 200 on-line followers.
The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
Monitoring and Managing Anomaly Detection on OpenShift.pdfTosin Akinosho
Monitoring and Managing Anomaly Detection on OpenShift
Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
- Step-by-step guide on deploying anomaly detection models on edge devices using ArgoCD.
5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
- Overview of Jupyter Notebooks, an open-source web application for creating and sharing documents with live code, equations, visualizations, and narrative text.
12. Jupyter Notebooks with Code Examples
- Hands-on examples and code snippets in Jupyter Notebooks to help you implement and test anomaly detection models.
Essentials of Automations: Exploring Attributes & Automation ParametersSafe Software
Building automations in FME Flow can save time, money, and help businesses scale by eliminating data silos and providing data to stakeholders in real-time. One essential component to orchestrating complex automations is the use of attributes & automation parameters (both formerly known as “keys”). In fact, it’s unlikely you’ll ever build an Automation without using these components, but what exactly are they?
Attributes & automation parameters enable the automation author to pass data values from one automation component to the next. During this webinar, our FME Flow Specialists will cover leveraging the three types of these output attributes & parameters in FME Flow: Event, Custom, and Automation. As a bonus, they’ll also be making use of the Split-Merge Block functionality.
You’ll leave this webinar with a better understanding of how to maximize the potential of automations by making use of attributes & automation parameters, with the ultimate goal of setting your enterprise integration workflows up on autopilot.
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/how-axelera-ai-uses-digital-compute-in-memory-to-deliver-fast-and-energy-efficient-computer-vision-a-presentation-from-axelera-ai/
Bram Verhoef, Head of Machine Learning at Axelera AI, presents the “How Axelera AI Uses Digital Compute-in-memory to Deliver Fast and Energy-efficient Computer Vision” tutorial at the May 2024 Embedded Vision Summit.
As artificial intelligence inference transitions from cloud environments to edge locations, computer vision applications achieve heightened responsiveness, reliability and privacy. This migration, however, introduces the challenge of operating within the stringent confines of resource constraints typical at the edge, including small form factors, low energy budgets and diminished memory and computational capacities. Axelera AI addresses these challenges through an innovative approach of performing digital computations within memory itself. This technique facilitates the realization of high-performance, energy-efficient and cost-effective computer vision capabilities at the thin and thick edge, extending the frontier of what is achievable with current technologies.
In this presentation, Verhoef unveils his company’s pioneering chip technology and demonstrates its capacity to deliver exceptional frames-per-second performance across a range of standard computer vision networks typical of applications in security, surveillance and the industrial sector. This shows that advanced computer vision can be accessible and efficient, even at the very edge of our technological ecosystem.
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
What is an RPA CoE? Session 1 – CoE VisionDianaGray10
In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems
Taking AI to the Next Level in Manufacturing.pdfssuserfac0301
Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
6. Ideas and approaches to help build your organization's AI strategy.
How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?
Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
2. at xϭ0, the wave function may have a noncontinuous deriva-
tive. By integrating the Schro¨dinger equation in a neighbor-
hood of the origin, the derivative difference is6
ប2
2m
͓⌽2Ј͑0͒Ϫ⌽1Ј͑0͔͒ϩ␣⌽͑0͒ϭ0, ͑1͒
where, as shown in Fig. 4, ␣ represents the strength of the ␦
function at the origin, and is, for a thin layer, the product of
the potential well and its spatial extension.
We are interested in charge accumulation at the interface.
Then, we look for electron bound eigenstates. These eigen-
states ͑in this particular problem there is only one͒ must have
negative total energy E. If they did not, they would be delo-
calized states. As in the case of transmission and reflection
through a potential step, if 0ϽEϽV0 then the electron is
delocalized for xϽ0 and confined within a small region for
xϾ0. If, on the other hand, V0ϽE, then the electron state is
delocalized for all x. In the case of a potential step ͑that is,
our problem with ␣ϭ0͒, there cannot be states completely
confined around xϭ0, since for EϽ0 the only solution to the
Schro¨dinger equation would be ⌽ϵ0. However, nontrivial
solutions can exist when ␣ 0. Thus we search for exponen-
tial solutions decaying away from the origin and with
EϽ0:
⌽1͑x͒ϭAex
, ͑2͒
⌽2͑x͒ϭAeϪx
, ͑3͒
EϭϪ
ប2
2
2m
, ͑4͒
EϭVϪ
ប2
2
2m
, ͑5͒
where and are real constants.
We next define a new parameter, , to simplify the nota-
tion:
ϭͱ2mV
ប2 sinh , ͑6͒
Fig. 1. Typical differential interfacial capacitance of mercury in contact
with aqueous solution of guanidinium nitrate for concentrations below
0.3 M.
Fig. 2. Typical differential interfacial capacitance of mercury in contact
with aqueous solution of guanidinium nitrate for concentrations above
0.3 M.
Fig. 3. Diagram of the system show-
ing the metal, the electrolyte, the thin
layer, and the electron wave function.
602 602Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
3. ϭͱ2mV
ប2 cosh . ͑7͒
From these definitions and Eqs. ͑4͒ and ͑5͒, one obtains the
state given by
ϭ
1
2
log
2m␣2
ប2
V
. ͑8͒
Let Q1 and Q2 be the net charges to the left and to the
right of the interface, respectively.
Then
Q1ϭe ͵Ϫϱ
0
͉⌽1͑x͉͒2
dxϭ
eA2
2
, ͑9͒
where the normalization constant A is obtained by requiring
that
͵Ϫϱ
0
͉⌽1͑x͉͒2
dxϩ ͵0
ϩϱ
͉⌽2͑x͉͒2
dxϭ1:
A2
ϭ2
V
␣
cosh  sinh . ͑10͒
In the previous expression, we have made use of the fact
that Eq. ͑1͒ is equivalent to ϩϭ2ma/ប2
.
Then
Q1ϭ
e
ϩ
. ͑11͒
And, similarly
Q2ϭ
e
ϩ
. ͑12͒
The charge at the interface capacitor can now be evaluated
QcϭQ1ϪQ2ϭe
Ϫ
ϩ
ϭe
ប2
V
2m␣2 . ͑13͒
The capacitance, CϭdQc /dV, is
Cϭ
eប2
2m␣2 , ͑14͒
which is a constant that depends only on the properties of the
layer through the parameter ␣.
Thus by simply adding a small confining layer at the in-
terface, it is possible to explain the flat characteristics of the
total capacitance. As the external voltage in the electrolytic
cell changes, the thin layer may appear or disappear, thus
creating ‘‘normal’’ C–V regions, and flat ones.
ACKNOWLEDGMENTS
I would like to thank Dr. Steven J. Eppell and Dr. Lesser
Blum for useful comments. The National Cancer Institute
through Grant No. CA77796-01 has financially supported
this work.
a͒
Electronic mail: zypman@ymail.yu.edu
1
E. Budevski, G. Staikov, and W. J. Lorenz, Electrochemical Phase For-
mation and Growth ͑Wiley, New York, 1996͒, pp. 200–210.
2
Wolfgang Lorenz, ‘‘The rate of absorption and of two-dimensional asso-
ciation of fatty acids at the mercury-electrolyte interface,’’ Z. Elektro-
chem. 62 ͑1͒, 192–199 ͑1958͒.
3
M. V. Sangaranarayanan and S. K. Rangarajan, ‘‘Adsorption-isotherms for
neutral organic-compounds—A hierarchy in modeling,’’ J. Electroanal.
Chem. Interfacial Electrochem. 176 ͑1-2͒, 45–64 ͑1984͒.
4
M. V. Sangaranarayanan and S. K. Rangarajan, ‘‘Adsorption-isotherms—
microscopic modeling,’’ J. Electroanal. Chem. Interfacial Electrochem.
176 ͑1-2͒, 119–137 ͑1984͒.
5
T. Wandlowski, G. Jameson, and R. De Levie, ‘‘Two-Dimensional Con-
densation of Guadinidium Nitrate at the Mercury-Water Interface,’’ J.
Phys. Chem. 97 ͑39͒, 10119–10126 ͑1993͒.
6
C. Cohen-Tannoudji, Bernard Diu, and Frank Laloe¨, Quantum Mechanics
͑Wiley, New York, Paris, 1977͒, Vol. 1, p. 87.
Fig. 4. Potential function representing
the metal, the interface, and the elec-
trolyte.
603 603Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
5. eliminating the absorption at the resonance frequency and
therefore creating electromagnetically induced transparency,
as shown in the problems given here.
II. PROBLEMS
A. Coherent population trapping
The key to keeping the group velocity at the vicinity of a
resonance frequency meaningful lies in the properties of the
laser-dressed atomic cloud. Without such an effect, absorp-
tion would be too strong to have any transmitted light.
Consider that each atom in the medium has three levels.
The presence of a coupling ͑dressing͒ laser (cӍ2Ϫ1)
and a probe laser (Ӎ2Ϫ0) causes a mixing of the three
levels, ͉0͘, ͉1͘, and ͉2͘.
The Hamiltonian of such a system is
HϭH0ϩH1 . ͑11͒
Here the unperturbed Hamiltonian H0 is given by
͗l͉H0͉lЈ͘ϭបl␦llЈ , ͑12͒
with l, lЈϭ0,1, 2. The perturbation H1 is restricted to be
͗l͉H1͉lЈ͘ϭ͗lЈ͉H1͉l͘*ϭប⍀llЈeϪillЈt
, ͑13͒
with llЈϭlϪlЈ and ⍀llϭ⍀01ϭ⍀10ϭ0. Note that 2
Ͼ1Ͼ0ϭ0 and l0ϭl . This is a so-called ‘‘⌳’’ system
with the highest level coupled to two lower levels.
For the Hamiltonian given, find the time-dependent wave
function
͉͑t͒͘ϭ͚lϭ0
2
cl͑t͉͒l͘, ͑14͒
if ͉(0)͘ϭc0(0)͉0͘ϩc1(0)͉1͘ with ͉c0(0)͉2
ϩ͉c1(0)͉2
ϭ1.
Discuss the condition for c2(t)ϵ0 and its implication.
B. Electromagnetically induced transparency
If we define a density matrix
͑t͒ϭ͉͑t͒͗͑͘t͉͒, ͑15͒
whose diagonal elements are the probabilities of occupying
specific states and off-diagonal elements represent the tran-
sition rates between two given states, we have
iប
ץ
ץt
ϭ͓H,͔, ͑16͒
from the Schro¨dinger equation. The interactions between at-
oms in the cloud can cause a finite linewidth and decay of
each level, which can be accounted for by a relaxation ma-
trix:
͗l͉⌫͉lЈ͘ϭ2␥l␦llЈ , ͑17͒
and change Eq. ͑16͒ into
iប
ץ
ץt
ϭ͓H,͔Ϫ
iប
2
͑⌫ϩ⌫͒. ͑18͒
Assuming that only the dominant decaying factor is nonzero,
that is, ␥2ϭ␥ and ␥0,1ϭ0, and that the atom is in the ground
state at tϭ0, show that
⑀͑͒ϭ⑀0ͫ1ϩ
d͑Ϫ2͒
R
2
/4Ϫ͑Ϫ2͒2
Ϫi␥͑Ϫ2͒ͬ, ͑19͒
where dϭna͉p20͉2
/ប⑀0 with ͉p20͉ being the coupling dipole
strength between ͉2͘ and ͉0͘ and Rϭ2͉⍀21͉ the Rabi angu-
lar frequency between ͉2͘ and ͉1͘.
C. The slowest light
In the recent experiment, Hau and co-workers have suc-
cessfully reduced the group velocity of light in a cold, laser-
dressed sodium atom cloud to 1 mile per hour ͑0.45 m/s͒.1
Each sodium atom can be approximated well by a three-level
system. Assume that the permittivity of such a laser-dressed
atom cloud is given by Eq. ͑19͒ and the frequency of the
probe laser (/2) is near the resonance frequency ͑2/2
Ӎ5.1ϫ1014
Hz for sodium atom͒. Estimate the number den-
sity of the atom cloud needed in order to have vg
Ӎ0.45 m/s. Assume that the Rabi angular frequency is about
Rϭ3.5ϫ107
rad/s and the coupling dipole strength is about
͉p20͉Ӎ2.5ϫ10Ϫ29
C m.
III. SOLUTIONS
A. Coherent population trapping
From the time-dependent Schro¨dinger equation
iប
ץ͉͑t͒͘
ץt
ϭH͉͑t͒͘, ͑20͒
we have
ic˙0͑t͒ϭ0c0͑t͒ϩ⍀20ei2t
c2͑t͒, ͑21͒
ic˙1͑t͒ϭ1c1͑t͒ϩ⍀21ei21t
c2͑t͒, ͑22͒
ic˙2͑t͒ϭ2c2͑t͒ϩ⍀02eϪi2t
c0͑t͒ϩ⍀12eϪi21t
c1͑t͒.
͑23͒
If we redefine the coefficients by
cl͑t͒ϭeϪilt
bl͑t͒, ͑24͒
the equation set is simplified to
ib˙ 0͑t͒ϭ⍀20b2͑t͒, ͑25͒
ib˙ 1͑t͒ϭ⍀21b2͑t͒, ͑26͒
ib˙ 2͑t͒ϭ⍀02b0͑t͒ϩ⍀12b1͑t͒. ͑27͒
Multiplying Eq. ͑25͒ with ⍀02 and Eq. ͑26͒ with ⍀12 and
adding them together, and substituting the resulting equation
into Eq. ͑27͒ after taking one more time derivative, we ob-
tain
b¨ 2͑t͒ϭϪ͉͑⍀20͉2
ϩ͉⍀21͉2
͒b2͑t͒. ͑28͒
We have used ⍀02ϭ⍀20* and ⍀12ϭ⍀21* . So we have
b2͑t͒ϭAei⍀t
ϩBeϪi⍀t
, ͑29͒
with ⍀ϭͱ͉⍀20͉2
ϩ͉⍀21͉2
. Taking the initial condition
b2(0)ϭc2(0)ϭ0, we arrive at
b2͑t͒ϭC sin ⍀t, ͑30͒
with C being a constant. Substituting this result back into
Eqs. ͑25͒ and ͑26͒, we have
b0͑t͒ϭ͓c0͑0͒Ϫ␣͔cos ⍀tϩ␣, ͑31͒
b1͑t͒ϭ͓c1͑0͒Ϫ͔cos ⍀tϩ, ͑32͒
where ␣ and  are constants constrained by
605 605Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
6. ⍀02␣ϩ⍀12ϭ0. ͑33͒
We have used the initial conditions b0(0)ϭc0(0) and
b1(0)ϭc1(0). The coefficient C is given by
Cϭ
i
⍀
͓⍀02c0͑0͒ϩ⍀12c1͑0͔͒. ͑34͒
If c0(0) and c1(0) are such that Cϵ0, we have c2(t)ϵ0 all
the time. A typical case is ͉⍀02͉ϭ͉⍀12͉ and ͉c0(0)͉
ϭ͉c1(0)͉ϭ1/&, with the total phase difference between the
two terms being . So the state ͉2͘ will stay empty and the
atoms are trapped in the lower states. The effect of such a
coherent population trapping is that the absorption or emis-
sion of light is completely eliminated.
B. Electromagnetically induced transparency
Consider that the traveling ͑probing͒ laser is described by
a time-dependent electric field E(t)ϭE0eϪit
with very
close to 2 . The perturbation from such a field is
͗2͉H1͉0͘ϭϪ͗2͉p͉0͘E0eϪit
ϭប⍀20eϪit
, ͑35͒
where p is the dipole moment induced by the field. Now if
we examine the density matrix elements between two states,
llЈϭ͗l͉͉lЈ͘, we have
i
ץ20
ץt
ϭ͑2Ϫi␥͒20ϩ⍀21eϪi21t
10
ϩ⍀20eϪit
͑00Ϫ22͒, ͑36͒
i
ץ10
ץt
ϭ110ϩ⍀12eϪi12t
20Ϫ⍀20eϪi2t
12 . ͑37͒
We have used
͚lϭ0
2
͉l͗͘l͉ϭ1 ͑38͒
in deriving the above equations. We can then replace 00 ,
22 , and 12 by their values at tϭ0, that is, 00ϭ1, 22ϭ0,
and 12ϭ0, and change a variable with 10ϭ10eϪi21t
, be-
cause we are only looking for the linear solution. Then we
have
i
ץ20
ץt
ϭ͑2Ϫi␥͒20ϩ⍀2110ϩ⍀20eϪit
, ͑39͒
i
ץ10
ץt
ϭ210ϩ⍀1220 . ͑40͒
This equation set resembles a harmonic oscillator under
damping and driving forces. The steady solutions are there-
fore given by
20͑t͒ϭAeϪit
, ͑41͒
10͑t͒ϭBeϪit
. ͑42͒
Substituting the above solutions into the equations, we obtain
Aϭ
⍀20͑Ϫ2͒
͑Ϫ2ϩi␥͒͑Ϫ2͒Ϫ͉⍀21͉2 . ͑43͒
Because 20 represents the dipole transition rate between ͉2͘
and 0͘, the polarization of the system is given by P
ϭna20p02ϭ(⑀Ϫ⑀0)E(t) with p02ϭ͗0͉p͉2͘ϭp20* . Then we
reach Eq. ͑19͒.
C. The slowest light
We know that the group velocity is given by
vgϭ
d
dk
ϭ
c
nϩ͑dn/d͒
. ͑44͒
For all known materials, nϳO(1). So if vgӶc, we must
have
vgӍ
c
͑dn/d͒
. ͑45͒
For vgϭ0.45 m/s, as observed in the experiment by Hau’s
group,1
one must have
͑dn/d͒Ӎ6.7ϫ108
. ͑46͒
From the given permittivity, we have
nϩi
c␣
2
Ӎ1ϩ
1
2
d͑Ϫ2͒
R
2
/4Ϫ͑Ϫ2͒2
Ϫi␥͑Ϫ2͒
. ͑47͒
Considering that is very close to 2 , we have
nϩi
c␣
2
Ӎ1ϩ
2d͑Ϫ2͒
R
2
ϫͫ1ϩ
4͑Ϫ2͒2
R
2 ϩ
i4␥͑Ϫ2͒
R
2 ϩ¯ͬ,
͑48͒
which gives
͑dn/d͒Ӎ
2
ប⑀0
na͉p20͉2
R
2 . ͑49͒
We have used dϭna͉p20͉2
/ប⑀0 . With the numerical values
of the quantities given, we then obtain naӍ2ϫ1020
mϪ3
, a
density quite difficult to achieve experimentally.
Note that the absorption coefficient ␣ is zero at the reso-
nance frequency. This is the essence of the electromagneti-
cally induced transparency, a condition that must be met in
order to have a significant light transmission at the resonance
frequency. Otherwise, the drastically slowed group velocity
of light observed by Hau’s group would not have been pos-
sible.
a͒
Electronic mail: pang@nevada.edu
1
L. V. Hau, presentation at the American Association for the Advancement
of Science, February 2000, Washington, DC.
2
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, ‘‘Light speed
reduction to 17 meters per second in an ultracold atomic gas,’’ Nature
͑London͒ 397, 594–598 ͑1999͒.
3
For a recent review, see R. Y. Chiao and A. M. Steinberg, Tunneling
Times and Superluminality, Progress in Optics Vol. 37, edited by E. Wolf
͑Elsevier, Amsterdam, 1997͒, pp. 347–405.
4
A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, ‘‘Electromagnetically
introduced transparency: Propagation dynamics,’’ Phys. Rev. Lett. 74,
2447–2450 ͑1995͒.
5
S. E. Harris, ‘‘Electromagnetically induced transparency,’’ Phys. Today
50 ͑7͒, 36–42 ͑1997͒.
6
M. O. Scully and M. S. Zubairy, Quantum Optics ͑Cambridge U.P., Cam-
bridge, 1997͒, Secs. 7.2 and 7.3.
7
D. J. Jackson, Classical Electrodynamics ͑Wiley, New York, 1999͒, 3rd
ed., Secs. 7.5 and 7.8.
606 606Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
8. law11
͑since tϭsinϪ1
͓(ni /nt)sin i͔ can be in either the first
or second quadrant͒, but they seemed physically implausible
and the topic was largely dropped.
Present interest in negative group velocity is based on
anomalous dispersion in a gain medium, where the sign of
the phase velocity is the same for incident and transmitted
waves, and energy flows inside the gain medium in the op-
posite direction to the incident energy flow in vacuum.
The propagation of electromagnetic waves at frequencies
near those of spectral lines of a medium was first extensively
discussed by Sommerfeld and Brillouin,12
with emphasis on
the distinction between signal velocity and group velocity
when the latter exceeds c. The solution presented here is
based on the work of Garrett and McCumber,13
as extended
by Chiao et al.14,15
A discussion of negative group velocity
in electronic circuits has been given by Mitchell and Chiao.16
A. Negative group velocity
In a medium of index of refraction n(), the dispersion
relation can be written
kϭ
n
c
, ͑2͒
where k is the wave number. The group velocity is then
given by
vgϭReͫd
dk ͬϭ
1
Re͓dk/d͔
ϭ
c
Re͓d͑n͒/d͔
ϭ
c
nϩ Re͓dn/d͔
.
͑3͒
We see from Eq. ͑3͒ that if the index of refraction de-
creases rapidly enough with frequency, the group velocity
can be negative. It is well known that the index of refraction
decreases rapidly with frequency near an absorption line,
where ‘‘anomalous’’ wave propagation effects can occur.12
However, the absorption makes it difficult to study these
effects. The insight of Garrett and McCumber13
and of Chiao
et al.14,15,17–19
is that demonstrations of negative group ve-
locity are possible in media with inverted populations, so
that gain rather than absorption occurs at the frequencies of
interest. This was dramatically realized in the experiment of
Wang et al.4
by use of a closely spaced pair of gain lines, as
perhaps first suggested by Steinberg and Chiao.17
We use a classical oscillator model for the index of refrac-
tion. The index n is the square root of the dielectric constant
⑀, which is in turn related to the atomic polarizability ␣ ac-
cording to
Dϭ⑀EϭEϩ4PϭE͑1ϩ4N␣͒ ͑4͒
͑in Gaussian units͒, where D is the electric displacement, E is
the electric field, and P is the polarization density. Then, the
index of refraction of a dilute gas is
nϭͱ⑀Ϸ1ϩ2N␣. ͑5͒
The polarizability ␣ is obtained from the electric dipole
moment pϭexϭ␣E induced by electric field E. In the case
of a single spectral line of frequency j , we say that an
electron is bound to the ͑fixed͒ nucleus by a spring of con-
stant Kϭmj
2
, and that the motion is subject to the damping
force Ϫm␥jx˙, where the dot indicates differentiation with
respect to time. The equation of motion in the presence of an
electromagnetic wave of frequency is
x¨ϩ␥jx˙ϩj
2
xϭ
eE
m
ϭ
eE0
m
eit
. ͑6͒
Hence,
xϭ
eE
m
1
j
2
Ϫ2
Ϫi␥j
ϭ
eE
m
j
2
Ϫ2
ϩi␥j
͑j
2
Ϫ2
͒2
ϩ␥j
2
2 , ͑7͒
and the polarizability is
␣ϭ
e2
m
j
2
Ϫ2
ϩi␥j
͑j
2
Ϫ2
͒2
ϩ␥j
2
2 . ͑8͒
In the present problem we have two spectral lines, 1,2
ϭ0Ϯ⌬/2, both of oscillator strength Ϫ1 to indicate that the
populations of both lines are inverted, with damping con-
stants ␥1ϭ␥2ϭ␥. In this case, the polarizability is given by
␣ϭϪ
e2
m
͑0Ϫ⌬/2͒2
Ϫ2
ϩi␥
͑͑0Ϫ⌬/2͒2
Ϫ2
͒2
ϩ␥2
2
Ϫ
e2
m
͑0ϩ⌬/2͒2
Ϫ2
ϩi␥
͑͑0ϩ⌬/2͒2
Ϫ2
͒2
ϩ␥2
2
ϷϪ
e2
m
0
2
Ϫ⌬0Ϫ2
ϩi␥
͑0
2
Ϫ⌬0Ϫ2
͒2
ϩ␥2
2
Ϫ
e2
m
0
2
ϩ2⌬0Ϫ2
ϩi␥
͑0
2
ϩ⌬0Ϫ2
͒2
ϩ␥2
2 , ͑9͒
where the approximation is obtained by the neglect of terms
in ⌬2
compared to those in ⌬0 .
For a probe beam at frequency , the index of refraction
͑5͒ has the form
n͑͒Ϸ1Ϫ
p
2
2 ͫ 0
2
Ϫ⌬0Ϫ2
ϩi␥
͑0
2
Ϫ⌬0Ϫ2
͒2
ϩ␥2
2
ϩ
0
2
ϩ⌬0Ϫ2
ϩi␥
͑0
2
ϩ⌬0Ϫ2
͒2
ϩ␥2
2ͬ, ͑10͒
where p is the plasma frequency given by Eq. ͑1͒. This is
illustrated in Fig. 1.
The index at the central frequency 0 is
Fig. 1. The real and imaginary parts of the index of refraction in a medium
with two spectral lines that have been pumped to inverted populations. The
lines are separated by angular frequency ⌬ and have widths ␥ϭ0.4⌬.
608 608Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
9. n͑0͒Ϸ1Ϫi
p
2
␥
͑⌬2
ϩ␥2
͒0
Ϸ1Ϫi
p
2
⌬2
␥
0
, ͑11͒
where the second approximation holds when ␥Ӷ⌬. The
electric field of a continuous probe wave then propagates
according to
E͑z,t͒ϭei͑kzϪ0t͒
ϭei͑n͑0͒z/cϪt͒
Ϸez/͓⌬2c/␥͑2/p͔͒
ei0͑z/cϪt͒
. ͑12͒
From this we see that at frequency 0 the phase velocity is c,
and the medium has an amplitude gain length ⌬2
c/␥p
2
.
To obtain the group velocity ͑3͒ at frequency 0 , we need
the derivative
d͑n͒
d
ͯ0
Ϸ1Ϫ
2p
2
͑⌬2
Ϫ␥2
͒
͑⌬2
ϩ␥2
͒2 , ͑13͒
where we have neglected terms in ⌬ and ␥ compared to 0 .
From Eq. ͑3͒, we see that the group velocity can be negative
if
⌬2
p
2Ϫ
␥2
p
2 у
1
2 ͩ⌬2
p
2 ϩ
␥2
p
2 ͪ2
. ͑14͒
The boundary of the allowed region ͑14͒ in (⌬2
,␥2
) space is
a parabola whose axis is along the line ␥2
ϭϪ⌬2
, as shown
in Fig. 2. For the physical region ␥2
у0, the boundary is
given by
␥2
p
2 ϭͱ1ϩ4
⌬2
p
2Ϫ1Ϫ
⌬2
p
2 . ͑15͒
Thus, to have a negative group velocity, we must have
⌬р&p , ͑16͒
which limit is achieved when ␥ϭ0; the maximum value of ␥
is 0.5p when ⌬ϭ0.866p .
Near the boundary of the negative group velocity region,
͉vg͉ exceeds c, which alerts us to concerns of superluminal
behavior. However, as will be seen in the following sections,
the effect of a negative group velocity is more dramatic when
͉vg͉ is small rather than large.
The region of recent experimental interest is ␥Ӷ⌬Ӷp ,
for which Eqs. ͑3͒ and ͑13͒ predict that
vgϷϪ
c
2
⌬2
p
2 . ͑17͒
A value of vgϷϪc/310 as in the experiment of Wang cor-
responds to ⌬/pϷ1/12. In this case, the gain length
⌬2
c/␥p
2
was approximately 40 cm.
For later use we record the second derivative,
d2
͑n͒
d2 ͯ0
Ϸ8i
p
2
␥͑3⌬2
Ϫ␥2
͒
͑⌬2
ϩ␥2
͒3 Ϸ24i
p
2
⌬2
␥
⌬2 , ͑18͒
where the second approximation holds if ␥Ӷ⌬.
B. Propagation of a monochromatic plane wave
To illustrate the optical properties of a medium with nega-
tive group velocity, we consider the propagation of an elec-
tromagnetic wave through it. The medium extends from z
ϭ0 to a, and is surrounded by vacuum. Because the index of
refraction ͑10͒ is near unity in the frequency range of inter-
est, we ignore reflections at the boundaries of the medium.
A monochromatic plane wave of frequency and incident
from zϽ0 propagates with phase velocity c in vacuum. Its
electric field can be written
E͑z,t͒ϭE0eiz/c
eϪit
͑zϽ0͒. ͑19͒
Inside the medium this wave propagates with phase velocity
c/n() according to
E͑z,t͒ϭE0einz/c
eϪit
͑0ϽzϽa͒, ͑20͒
where the amplitude is unchanged since we neglect the small
reflection at the boundary zϭ0. When the wave emerges into
vacuum at zϭa, the phase velocity is again c, but it has
accumulated a phase lag of (/c)(nϪ1)a, and so appears as
E͑z,t͒ϭE0eia͑nϪ1͒/c
eiz/c
eϪit
ϭE0eian/c
eϪi͑tϪ͑zϪa͒/c͒
͑aϽz͒. ͑21͒
It is noteworthy that a monochromatic wave for zϾa has the
same form as that inside the medium if we make the
frequency-independent substitutions
z→a, t→tϪ
zϪa
c
. ͑22͒
Since an arbitrary waveform can be expressed in terms of
monochromatic plane waves via Fourier analysis, we can use
these substitutions to convert any wave in the region 0Ͻz
Ͻa to its continuation in the region aϽz.
A general relation can be deduced in the case where the
second and higher derivatives of n() are very small. We
can then write
n͑͒Ϸ0n͑0͒ϩ
c
vg
͑Ϫ0͒, ͑23͒
where vg is the group velocity for a pulse with central fre-
quency 0 . Using this in Eq. ͑20͒, we have
E͑z,t͒ϷE0ei0z͑n͑0͒/cϪ1/vg͒
eiz/vgeϪit
͑0ϽzϽa͒.
͑24͒
In this approximation, the Fourier component E(z) at fre-
quency of a wave inside the gain medium is related to that
of the incident wave by replacing the frequency dependence
Fig. 2. The allowed region ͑14͒ in (⌬2
,␥2
) space such that the group ve-
locity is negative.
609 609Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
10. eiz/c
by eiz/vg, i.e., by replacing z/c by z/vg , and multi-
plying by the frequency-independent phase factor
ei0z(n(0)/cϪ1/vg)
. Then, using transformation ͑22͒, the wave
that emerges into vacuum beyond the medium is
E͑z,t͒ϷE0ei0a͑n͑0͒/cϪ1/vg͒
ϫei͑z/cϪa͑1/cϪ1/vg͒͒
eϪit
͑aϽz͒. ͑25͒
The wave beyond the medium is related to the incident wave
by multiplying by a frequency-independent phase, and by
replacing z/c by z/cϪa(1/cϪ1/vg) in the frequency-
dependent part of the phase.
The effect of the medium on the wave as described by
Eqs. ͑24͒ and ͑25͒ has been called ‘‘rephasing.’’ 4
C. Fourier analysis and ‘‘rephasing’’
The transformations between the monochromatic incident
wave ͑19͒ and its continuation in and beyond the medium,
͑24͒ and ͑25͒, imply that an incident wave
E͑z,t͒ϭf͑z/cϪt͒ϭ ͵Ϫϱ
ϱ
E͑z͒eϪit
d ͑zϽ0͒, ͑26͒
whose Fourier components are given by
E͑z͒ϭ
1
2
͵Ϫϱ
ϱ
E͑z,t͒eit
dt, ͑27͒
propagates as
E͑z,t͒Ϸ
Ά
f͑z/cϪt͒ ͑zϽ0͒
ei0z͑n͑0͒/cϪ1/vg͒
f͑z/vgϪt͒ ͑0ϽzϽa͒
ei0a͑n͑0͒/cϪ1/vg͒
f͑z/cϪtϪa͑1/cϪ1/vg͒͒
͑aϽz͒.
͑28͒
An interpretation of Eq. ͑28͒ in terms of ‘‘rephasing’’ is as
follows. Fourier analysis tells us that the maximum ampli-
tude of a pulse made of waves of many frequencies, each of
the form E(z,t)ϭE0()ei()
ϭE0()ei(k()zϪtϩ0())
with E0у0, is determined by adding the amplitudes E0().
This maximum is achieved only if there exist points ͑z,t͒
such that all phases ͑͒ have the same value.
For example, we consider a pulse in the region zϽ0
whose maximum occurs when the phases of all component
frequencies vanish, as shown at the left of Fig. 3. Referring
to Eq. ͑19͒, we see that the peak occurs when zϭct. As
usual, we say that the group velocity of this wave is c in
vacuum.
Inside the medium, Eq. ͑24͒ describes the phases of the
components, which all have a common frequency-
independent phase 0z(n(0)/cϪ1/vg) at a given z, as well
as a frequency-dependent part (z/vgϪt). The peak of the
pulse occurs when all the frequency-dependent phases van-
ish; the overall frequency-independent phase does not affect
the pulse size. Thus, the peak of the pulse propagates within
the medium according to zϭvgt. The velocity of the peak is
vg , the group velocity of the medium, which can be nega-
tive.
The ‘‘rephasing’’ ͑24͒ within the medium changes the
wavelengths of the component waves. Typically the wave-
length increases, and by greater amounts at longer wave-
lengths. A longer time is required before the phases of the
waves all become the same at some point z inside the me-
dium, so in a normal medium the velocity of the peak ap-
pears to be slowed down. But in a negative group velocity
medium, wavelengths short compared to 0 are lengthened,
long waves are shortened, and the velocity of the peak ap-
pears to be reversed.
By a similar argument, Eq. ͑25͒ tells us that in the vacuum
region beyond the medium the peak of the pulse propagates
according to zϭctϩa(1/cϪ1/vg). The group velocity is
again c, but the ‘‘rephasing’’ within the medium results in a
shift of the position of the peak by the amount a(1/c
Ϫ1/vg). In a normal medium where 0Ͻvgрc the shift is
negative; the pulse appears to have been delayed during its
passage through the medium. But after a negative group ve-
locity medium, the pulse appears to have advanced!
This advance is possible because, in the Fourier view,
each component wave extends over all space, even if the
pulse appears to be restricted. The unusual ‘‘rephasing’’ in a
negative group velocity medium shifts the phases of the fre-
quency components of the wave train in the region ahead of
the nominal peak such that the phases all coincide, and a
peak is observed, at times earlier than expected at points
beyond the medium.
As shown in Fig. 3 and further illustrated in the examples
in the following, the ‘‘rephasing’’ can result in the simulta-
neous appearance of peaks in all three regions.
Fig. 3. A snapshot of three Fourier components of a pulse in the vicinity of a negative group velocity medium. The component at the central wavelength 0
is unaltered by the medium, but the wavelength of a longer wavelength component is shortened, and that of a shorter wavelength component is lengthened.
Then, even when the incident pulse has not yet reached the medium, there can be a point inside the medium at which all components have the same phase,
and a peak appears. Simultaneously, there can be a point in the vacuum region beyond the medium at which the Fourier components are again all in phase,
and a third peak appears. The peaks in the vacuum regions move with group velocity vgϭc, but the peak inside the medium moves with a negative group
velocity, shown as vgϭϪc/2. The phase velocity vp is c in vacuum, and close to c in the medium.
610 610Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
11. D. Propagation of a sharp wave front
To assess the effect of a medium with negative group ve-
locity on the propagation of a signal, we first consider a
waveform with a sharp front, as recommended by Sommer-
feld and Brillouin.12
As an extreme but convenient example, we take the inci-
dent pulse to be a Dirac delta function, E(z,t)ϭE0␦(z/c
Ϫt). Inserting this in Eq. ͑28͒, which is based on the linear
approximation ͑23͒, we find
E͑z,t͒Ϸ
Ά
E0␦͑z/cϪt͒ ͑zϽ0͒
E0ei0z͑n͑0͒/cϪ1/vg͒
␦͑z/vgϪt͒ ͑0ϽzϽa͒
E0ei0a͑n͑0͒/cϪ1/vg͒
␦͑z/cϪtϪa͑1/cϪ1/vg͒͒
͑aϽz͒.
͑29͒
According to Eq. ͑29͒, the delta-function pulse emerges
from the medium at zϭa at time tϭa/vg . If the group ve-
locity is negative, the pulse emerges from the medium before
it enters at tϭ0!
A sample history of ͑Gaussian͒ pulse propagation is illus-
trated in Fig. 4. Inside the negative group velocity medium,
an ͑anti͒pulse propagates backwards in space from zϭa at
time tϭa/vgϽ0 to zϭ0 at time tϭ0, at which point it ap-
pears to annihilate the incident pulse.
This behavior is analogous to barrier penetration by a rela-
tivistic electron20
in which an electron can emerge from the
far side of the barrier earlier than it hits the near side, if the
electron emission at the far side is accompanied by positron
emission, and the positron propagates within the barrier so as
to annihilate the incident electron at the near side. In the
Wheeler–Feynman view, this process involves only a single
electron which propagates backwards in time when inside
the barrier. In this spirit, we might say that pulses propagate
backwards in time ͑but forward in space͒ inside a negative
group velocity medium.
The Fourier components of the delta function are indepen-
dent of frequency, so the advanced appearance of the sharp
wave front as described by Eq. ͑29͒ can occur only for a gain
medium such that the index of refraction varies linearly at all
frequencies. If such a medium existed with negative slope
dn/d, then Eq. ͑29͒ would constitute superluminal signal
propagation.
However, from Fig. 1 we see that a linear approximation
to the index of refraction is reasonable in the negative group
velocity medium only for ͉Ϫ0͉Շ⌬/2. The sharpest wave
front that can be supported within this bandwidth has char-
acteristic rise time Ϸ1/⌬.
For the experiment of Wang et al. where ⌬/2Ϸ106
Hz,
an analysis based on Eq. ͑23͒ would be valid only for pulses
with տ0.1 s. Wang et al. used a pulse with Ϸ1 s,
close to the minimum value for which Eq. ͑23͒ is a reason-
able approximation.
Since a negative group velocity can only be experienced
over a limited bandwidth, very sharp wave fronts must be
excluded from the discussion of signal propagation. How-
ever, it is well known12
that great care must be taken when
discussing the signal velocity if the waveform is not sharp.
E. Propagation of a Gaussian pulse
We now consider a Gaussian pulse of temporal length
centered on frequency 0 ͑the carrier frequency͒, for which
the incident waveform is
Fig. 4. Ten ‘‘snapshots’’ of a Gaussian pulse as it traverses a negative group
velocity region (0ϽzϽ50), according to Eq. ͑31͒. The group velocity in the
gain medium is vgϭϪc/2, and c has been set to 1.
611 611Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
12. E͑z,t͒ϭE0eϪ͑z/cϪt͒2/22
ei0z/c
eϪi0t
͑zϽ0͒. ͑30͒
Inserting this in Eq. ͑28͒ we find
E͑z,t͒ϭ
Ά
E0eϪ͑z/cϪt͒2/22
ei0͑z/cϪt͒
͑zϽ0͒
E0eϪ͑z/vgϪt͒2/22
ei0͑n͑0͒z/cϪt͒
͑0ϽzϽa͒
E0ei0a͑n͑0͒Ϫ1͒/c
eϪ͑z/cϪa͑1/cϪ1/vg͒Ϫt͒2/22
ϫei0͑z/cϪt͒
͑aϽz͒.
͑31͒
The factor ei0a(n(0)Ϫ1)/c
in Eq. ͑31͒ for aϽz becomes
ep
2
␥a/⌬2c
using Eq. ͑11͒, and represents a small gain due to
traversing the negative group velocity medium. In the experi-
ment of Wang et al., this factor was only 1.16.
We have already noted in the previous section that the
linear approximation to n() is only good over a fre-
quency interval about 0 of order ⌬, and so Eq. ͑31͒ for the
pulse after the gain medium applies only for pulse widths
տ
1
⌬
. ͑32͒
Further constraints on the validity of Eq. ͑31͒ can be ob-
tained using the expansion of n() to second order. For
this, we repeat the derivation of Eq. ͑31͒ in slightly more
detail. The incident Gaussian pulse ͑30͒ has the Fourier de-
composition ͑27͒,
E͑z͒ϭ
ͱ2
E0eϪ2
͑Ϫ0͒2/2
eiz/c
͑zϽ0͒. ͑33͒
We again extrapolate the Fourier component at frequency
into the region zϾ0 using Eq. ͑20͒, which yields
E͑z͒ϭ
ͱ2
E0eϪ2
͑Ϫ0͒2/2
einz/c
͑0ϽzϽa͒. ͑34͒
We now approximate the factor n() by its Taylor ex-
pansion through second order:
n͑͒Ϸ0n͑0͒ϩ
c
vg
͑Ϫ0͒
ϩ
1
2
d2
͑n͒
d2 ͯ0
͑Ϫ0͒2
. ͑35͒
With this, we find from Eqs. ͑26͒ and ͑34͒ that
E͑z,t͒ϭ
E0
A
eϪ͑z/vgϪt͒2/2A22
ei0n͑0͒z/c
eϪi0t
͑0ϽzϽa͒. ͑36͒
where
A2
͑z͒ϭ1Ϫi
z
c2
d2
͑n͒
d2 ͯ0
. ͑37͒
The waveform for zϾa is obtained from that for 0ϽzϽa by
the substitutions ͑22͒ with the result
E͑z,t͒ϭ
E0
A
ei0a͑n͑0͒Ϫ1͒/c
eϪ͑z/cϪa͑1/cϪ1/vg͒Ϫt͒2/2A22
ϫei0z/c
eϪi0t
͑aϽz͒, ͑38͒
where A is evaluated at zϭa here. As expected, the forms
͑36͒ and ͑38͒ revert to those of Eq. ͑31͒ when
d2
(n(0))/d2
ϭ0.
So long as the factor A(a) is not greatly different from
unity, the pulse emerges from the medium essentially undis-
torted, which requires
a
c
Ӷ
1
24
⌬2
p
2
⌬
␥
⌬, ͑39͒
using Eqs. ͑18͒ and ͑37͒. In the experiment of Wang et al.,
this condition is that a/cӶ1/120, which was well satisfied
with aϭ6 cm and cϭ300 m.
As in the case of the delta function, the centroid of a
Gaussian pulse emerges from a negative group velocity me-
dium at time
tϭ
a
vg
Ͻ0, ͑40͒
which is earlier than the time tϭ0 when the centroid enters
the medium. In the experiment of Wang et al., the time ad-
vance of the pulse was a/͉vg͉Ϸ300a/cϷ6ϫ10Ϫ8
s
Ϸ0.06.
If one attempts to observe the negative group velocity
pulse inside the medium, the incident wave would be per-
turbed and the backwards-moving pulse would not be de-
tected. Rather, one must deduce the effect of the negative
group velocity medium by observation of the pulse that
emerges into the region zϾa beyond that medium, where the
significance of the time advance ͑40͒ is the main issue.
The time advance caused by a negative group velocity
medium is larger when ͉vg͉ is smaller. It is possible that
͉vg͉Ͼc, but this gives a smaller time advance than when the
negative group velocity is such that ͉vg͉Ͻc. Hence, there is
no special concern as to the meaning of negative group ve-
locity when ͉vg͉Ͼc.
The maximum possible time advance tmax by this tech-
nique can be estimated from Eqs. ͑17͒, ͑39͒, and ͑40͒ as
tmax
Ϸ
1
12
⌬
␥
⌬Ϸ1. ͑41͒
The pulse can advance by at most a few rise times due to
passage through the negative group velocity medium.
While this aspect of the pulse propagation appears to be
superluminal, it does not imply superluminal signal propaga-
tion.
In accounting for signal propagation time, the time needed
to generate the signal must be included as well. A pulse with
a finite frequency bandwidth ⌬ takes at least time Ϸ1/⌬ to
be generated, and so is delayed by a time of order of its rise
time compared to the case of an idealized sharp wave front.
Thus, the advance of a pulse front in a negative group veloc-
ity medium by Շ can at most compensate for the original
delay in generating that pulse. The signal velocity, as defined
by the path length between the source and detector divided
by the overall time from onset of signal generation to signal
detection, remains bounded by c.
As has been emphasized by Garrett and McCumber13
and
by Chiao,18,19
the time advance of a pulse emerging from a
gain medium is possible because the forward tail of a smooth
pulse gives advance warning of the later arrival of the peak.
The leading edge of the pulse can be amplified by the gain
medium, which gives the appearance of superluminal pulse
612 612Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
13. velocities. However, the medium is merely using information
stored in the early part of the pulse during its ͑lengthy͒ time
of generation to bring the apparent velocity of the pulse
closer to c.
The effect of the negative group velocity medium can be
dramatized in a calculation based on Eq. ͑31͒ in which the
pulse width is narrower than the gain region ͓in violation of
condition ͑39͔͒, as shown in Fig. 4. Here, the gain region is
0ϽzϽ50, the group velocity is taken to be Ϫc/2, and c is
defined to be unity. The behavior illustrated in Fig. 4 is per-
haps less surprising when the pulse amplitude is plotted on a
logarithmic scale, as in Fig. 5. Although the overall gain of
the system is near unity, the leading edge of the pulse is
amplified by about 70 orders of magnitude in this example
͓the implausibility of which underscores that condition ͑39͒
cannot be evaded͔, while the trailing edge of the pulse is
attenuated by the same amount. The gain medium has tem-
porarily loaned some of its energy to the pulse permitting the
leading edge of the pulse to appear to advance faster than the
speed of light.
Our discussion of the pulse has been based on a classical
analysis of interference, but, as remarked by Dirac,21
classi-
cal optical interference describes the behavior of the wave
functions of individual photons, not of interference between
photons. Therefore, we expect that the behavior discussed
above will soon be demonstrated for a ‘‘pulse’’ consisting of
a single photon with a Gaussian wave packet.
ACKNOWLEDGMENTS
The author thanks Lijun Wang for discussions of his ex-
periment, and Alex Granik for references to the early history
of negative group velocity and for the analysis contained in
Eqs. ͑14͒–͑16͒.
a͒
Electronic mail: mcdonald@puphed.princeton.edu
1
L. V. Hau et al., ‘‘Light speed reduction to 17 metres per second in an
ultracold atomic gas,’’ Nature ͑London͒ 397, 594–598 ͑1999͒.
2
K. T. McDonald, ‘‘Slow light,’’ Am. J. Phys. 68, 293–294 ͑2000͒. A
figure to be compared with Fig. 1 of the present paper has been added in
the version at http://arxiv.org/abs/physics/0007097
3
This is in contrast to the ‘‘⌳’’ configuration of the three-level atomic
system required for slow light ͑Ref. 2͒ where the pump laser does not
produce an inverted population, in which case an adequate classical de-
scription is simply to reverse the sign of the damping constant for the
pumped oscillator.
4
L. J. Wang, A. Kuzmich, and A. Dogariu, ‘‘Gain-assisted superluminal
light propagation,’’ Nature ͑London͒ 406, 277–279 ͑2000͒. Their website,
http://www.neci.nj.nec.com/homepages/lwan/gas.htm, contains additional
material, including an animation much like Fig. 4 of the present paper.
5
W. R. Hamilton, ‘‘Researches respecting vibration, connected with the
theory of light,’’ Proc. R. Ir. Acad. 1, 267,341 ͑1839͒.
6
J. S. Russell, ‘‘Report on waves,’’ Br. Assoc. Reports ͑1844͒, pp. 311–
390. This report features the first recorded observations of solitary waves
͑p. 321͒ and of group velocity ͑p. 369͒.
7
G. G. Stokes, Problem 11 of the Smith’s Prize examination papers ͑2
February 1876͒, in Mathematical and Physical Papers ͑Johnson Reprint
Co., New York, 1966͒, Vol. 5, p. 362.
8
T. H. Havelock, The Propagation of Disturbances in Dispersive Media
͑Cambridge U.P., Cambridge, 1914͒.
9
H. Lamb, ‘‘On Group-Velocity,’’ Proc. London Math. Soc. 1, 473–479
͑1904͒.
10
See p. 551 of M. Laue, ‘‘Die Fortpflanzung der Strahlung in Dispergier-
enden und Absorbierenden Medien,’’ Ann. Phys. ͑Leipzig͒ 18, 523–566
͑1905͒.
11
L. Mandelstam, Lectures on Optics, Relativity and Quantum Mechanics
͑Nauka, Moscow, 1972͒; in Russian.
12
L. Brillouin, Wave Propagation and Group Velocity ͑Academic, New
York, 1960͒. That the group velocity can be negative is mentioned on p.
122.
13
C. G. B. Garrett and D. E. McCumber, ‘‘Propagation of a Gaussian Light
Pulse through an Anomalous Dispersion Medium,’’ Phys. Rev. A 1, 305–
313 ͑1970͒.
14
R. Y. Chiao, ‘‘Superluminal ͑but causal͒ propagation of wave packets in
transparent media with inverted atomic populations,’’ Phys. Rev. A 48,
R34–R37 ͑1993͒.
Fig. 5. The same as Fig. 4, but with the electric field plotted on a logarith-
mic scale from 1 to 10Ϫ65
.
613 613Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
15. The force depends on the orientation of the dipole ͑repre-
sented by M͒ in the local field ͑represented by H͒ and on the
gradient of the local field in the vicinity of the dipole. There
is no force, only a torque, acting on a dipole in a uniform
field. The derivation of the last equality in Eq. ͑1͒ reasonably
assumes that “ÃHϭ0 and that the magnetic flux density B
is linearly related to the magnetic field strength and to the
magnetization as follows:
BϭHϭ0͑HϩM͒ ͑2͒
with the permeability of the film. Using Eq. ͑2͒ to repre-
sent the body force in terms of the magnetic flux density in
the second equality of Eq. ͑1͒ gives
fϭ
1
ͩ1Ϫ
0
ͪB“Bϭ
1
2 ͩ1Ϫ
0
ͪ“B2
. ͑3͒
Consequently, the negative square of the magnetic flux den-
sity within the film corresponds to a ‘‘potential field’’ to
which the film responds.
Consider the film to be of constant thickness and spread
uniformly over the surface of the water when in the presence
of the external magnetic field. In the absence of magnetic
charge and surface current density, consideration of the Max-
well equations leads to the following boundary conditions
for the magnetic field strength and magnetic flux density:
͑BϪB0͒"nϭ0, ͑HϪH0͒Ãnϭ0, ͑4͒
where the terms with a subscript refer to the air ͑or vacuum͒
side of the film boundary and the terms without a subscript to
the ferrofluid. The vector n is a unit normal to the film sur-
face. Note that these are the same boundary conditions and
field relationships used to find the field inside an ellipsoid
subjected to a uniform external field. For the film problem,
we take the normal to the film, the zˆ direction, to be parallel
to the magnet axis and assume azimuthal symmetry. The unit
vector ˆ designates the radial direction with respect to the
Fig. 3. Ellipsoidal ‘‘clump’’ or cone of ferrofluid.
Fig. 1. Experimental setup for viewing the dynamics of a ferrofluid film.
Fig. 2. Ferrofluid film before the magnet was introduced ͑a͒, after 1 min ͑b͒, after 3
1
4 min ͑c͒, and after 21 min ͑d͒. Note that any dark spots that appear the
same in all frames are due to imperfections in the optical train.
615 615Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
16. magnet axis. Using the relationships given in Eqs. ͑2͒ and
͑4͒, the magnetic flux density and magnetic field strength just
inside the film are represented in terms of the magnetic flux
density just outside the film as
BϭB0zzˆϩ
0
B0ˆ,
͑5͒
Hϭ
1
B0zzˆϩ
1
0
B0ˆ.
Since the film is thin, we assume these boundary results to
represent the field within the film.
Next we approximate the external field at the surface of
the film by a dipole field with moment m directed parallel
to zˆ,
B0ϭ
0
4r3 ͑3͑m"rˆ͒rˆϪm͒
ϭ
0m
4 ͫ 3z
͑2
ϩz2
͒5/2 ˆ ϩ
2z2
Ϫ2
͑2
ϩz2
͒5/2 zˆ ͬ, ͑6͒
where z measures the distance from the film to the dipole
source ͑cylindrical magnet͒, is the radial position in the
film, rϭͱ2
ϩz2
is the position vector magnitude in spheri-
cal coordinates, and the vectors with a caret are unit vectors.
This magnetic flux density, when plugged into the right-hand
side of Eq. ͑5͒, gives an estimate of the magnetic flux density
inside the film. Directly beneath the dipole the magnetic flux
density is normal to the film and has the same magnitude on
both sides of the film surface. As increases from zero,
however, there is a component of the magnetic flux density
which is parallel to the surface and larger inside the film than
outside for /0Ͼ1. While the magnitude of the external
magnetic flux density decreases monotonically with increas-
ing for this dipole field, the magnetic flux density inside
the film will increase for sufficiently large permeability ratio,
/0 , before decreasing to zero. The increasing magnetic
flux density results in a force ͓see Eq. ͑3͔͒ that pushes the
film outward radially to collect in a ring where the flux den-
sity reaches a maximum. Note that we neglected contribu-
tions from the film to the external magnetic field on the
assumption that this field is small for a very thin film. While
an exact solution to this problem is beyond the scope of a
typical undergraduate course in electromagnetism, we
checked our results using the method of images to find the
magnetic flux density produced by a dipole near a thin plane
of material with permeability . In the limit that the thick-
ness goes to zero, the fields inside and outside the film be-
come identical to those approximated here. There is one ca-
veat. The body force must be calculated using the second
equality in Eq. ͑1͒. The first equality involves a derivative
with respect to z, which must be performed before the film
thickness is taken to zero.
Figure 4 shows the reduced potential, estimated for our
ferrofluid film using the dipole field given in Eq. ͑6͒, as a
function of for zϭ1, and different values of the permeabil-
ity ratio /0 . The functional form of this reduced potential
is
⌽ϭϪ
B2
͑0m/4͒2
ϭϪͩ4
ϩ͑Ϫ4ϩ9͑/0͒2
͒2
z2
ϩ4z4
͑2
ϩz2
͒5 ͪ. ͑7͒
For permeability ratios greater than ͱ8/3Ϸ1.63 a potential
minimum obtains at finite radius. The minimum position min
obeys the following linear relationship with respect to z:
min /zϭͱϪ6͑/0͒2
ϩ3ϩͱ36͑/0͒4
Ϫ33͑/0͒2
ϩ1.
͑8͒
This ratio ranges between zero and one half as the perme-
ability ratio increases from 1.63 to infinity. Since the initial
magnetic susceptibility of our ferrofluid is ϭ1.9, the per-
meability ratio is 2.9, and Eq. ͑8͒ predicts min /zϭ0.43. Ap-
proximating the magnet by a dipole placed at the lower end
of the magnet, the end closest to the ferrofluid, gives min /z
ϳ1.0 cm/3.3 cmϳ0.30 or placing the dipole at the physical
center of the magnet gives min /zϳ1.0 cm/5.8 cmϳ0.17.
Considering that the magnet is an extended source rather
than a point dipole, the agreement is quite good.
The response of a ferrofluid film to a nonuniform external
field is complex, but a fairly straightforward undergraduate
boundary value calculation explains puzzling observations.
The large susceptibility of the magnetic fluid and fluid sur-
face orientation beneath a magnet determines the net force
on the ferrofluid, giving attraction for the cones and repul-
sion for the film.
a͒
Author to whom correspondence should be addressed; electronic mail:
bjack@okstate.edu
b͒
This communication originated as an honors thesis project of A.N., who is
presently a graduate student in physics at Colorado State University.
1
R. E. Rosensweig, Ferrohydrodynamics ͑Cambridge U.P., Cambridge,
1985͒, p. 110 ff.
2
R. E. Rosensweig, ‘‘Magnetic Fluids,’’ Sci. Am. 247 ͑4͒, 136–145 ͑1982͒.
3
B. M. Berkovsky, V. F. Medvedev, and M. S. Krakov, Magnetic Fluids
Engineering Applications ͑Oxford U.P., Oxford, 1993͒, Chap. 6.
4
Ferrofluidics Corporation, 40 Simon Street, Nashua, NH 03060-3075.
5
Ferrofluidics: Catalog No. EMG 905, Lot No. F8193A.
6
V. I. Arkhipenko, Yu. D. Barkov, and V. G. Bashtovoi, ‘‘Study of a
magnetized fluid drop shape in a homogeneous magnetic field,’’ Magn.
Gidrodin. ͑3͒, 131–134 ͑1978͒.
7
G. Arfken, Mathematical Methods for Physicists ͑Academic, New York,
1970͒, p. 603; S. D. Poisson, ‘‘Seconde me´moire sur la the´orie du mag-
ne´tisme,’’ Mem. Acad. R. Sci. Inst. France 5, 488–533 ͑1821–1822͒.
8
A. T. Skjeltorp, ‘‘One- and two-dimensional crystallization of magnetic
holes,’’ Phys. Rev. Lett. 51 ͑25͒, 2306–2309 ͑1983͒.
Fig. 4. Reduced potential for an element of ferrofluid film for zϭ1 as a
function of the distance from the magnet axis and shown for different
values of the permeability ratio /0ϭ1, 2, 2.9, and 5 from top to bottom.
616 616Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems
18. r2
ϭR2
ez2
, ͑16͒
which has a minimum radius R, and a critical radius rcrit
ϭRͱ4
eϭ1.28R.
Our final example is the surface
rϭϪ
k
zͱ1Ϫz2
͑Ϫ1ϽzϽ0͒, ͑17͒
which has a minimum radius of Rϭ2k, approaches the sur-
face rϭϪk/z at large r ͑small z͒, and has a critical radius of
rcritϭ6k/ͱ5ϭ1.34R.
These examples arise in a 2ϩ1 geometry with curved
space but flat time. As such, they are not fully analogous to
black holes in 3ϩ1 geometry with both curved space and
curved time. Still, they provide a glimpse as to how a particle
in curved space–time can undergo considerably more com-
plex motion than in flat space–time.
ACKNOWLEDGMENTS
The author wishes to thank Ori Ganor and Vipul Periwal
for discussions of this problem.
a͒
Electronic mail: mcdonald@puphed.princeton.edu
1
The Vortx͑tm͒ Miniature Wishing Well, Divnick International, Inc., 321 S.
Alexander Road, Miamisburg, OH 45342, http://www.divnick.com/
AWESTRUCK SCIENTISTS
The second feature of science is that it shows that the world is simple. Even many scientists do
not appreciate that they are hewers of simplicity from complexity. They are often more deluded
than those they aim to tell. Scientists are often overawed by the complexity of detecting simplicity.
They look at the latest fundamental particle experiment, see that it involves a thousand kilograms
of apparatus and a discernible percentage of a gross national product, and become thunderstruck.
They see the complexity of the apparatus and the intensity of the effort needed to construct and
operate it, and confuse that with the simplicity that the experiment, if successful, will expose.
Some scientists are so awestruck that they even turn to religion! Others keep a cool head, and
marvel not at an implied design but at the richness of simplicity.
P. W. Atkins, ‘‘The Limitless Power of Science,’’ in Nature’s Imagination—The Frontiers of Scientific Vision, edited by
John Cornwell ͑Oxford University Press, New York, 1995͒.
618 618Am. J. Phys., Vol. 69, No. 5, May 2001 New Problems