1) The document discusses travelling wave solutions for pulse propagation in negative index materials (NIMs) in the presence of an external source.
2) It obtains fractional-type solutions containing trigonometric and hyperbolic functions by using a fractional transform to map the governing equation to an elliptic equation.
3) Specific solutions include periodic solutions and bright/dark solitary wave solutions, with the intensity profiles of the bright solitary wave shown.
Investigation of Steady-State Carrier Distribution in CNT Porins in Neuronal ...Kyle Poe
In this work, the carrier distribution of a carbon nanotube inserted into the spinal ganglion neuronal membrane is examined. After primary characterization based on previous work, the nanotube is approximated as a one-dimensional system, and the Poisson and Schrödinger equations are solved using an iterative finite-difference scheme. It was found that carriers aggregate near the center of the tube, with a negative carrier density of ⟨ρn⟩ = 7.89 × 10^13 cm−3 and positive carrier density of ⟨ρp⟩ = 3.85 × 10^13 cm−3. In future work, the erratic behavior of convergence will be investigated.
This document provides an introduction to quantum Monte Carlo methods. It discusses using Monte Carlo integration to evaluate multi-dimensional integrals that arise in quantum mechanical problems. Variational Monte Carlo is introduced as using a trial wavefunction to sample configuration space and estimate observables, like the energy. The Metropolis algorithm is described as a way to generate Markov chains that sample a given probability distribution. This allows using Monte Carlo methods to solve the electronic structure problem by approximating many-body wavefunctions and integrals over configuration space.
This document reviews research on the convergence of perturbation series in quantum field theory. It discusses Dyson's argument that perturbation series in quantum electrodynamics (QED) have zero radius of convergence due to vacuum instability when the coupling constant is negative. Large-order estimates show that perturbation series coefficients grow factorially fast in quantum mechanics and field theories. Finally, it describes the method of Borel summation, which may allow extracting the exact physical quantity from a divergent perturbation series through a unique mapping.
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
The document studies small excitonic complexes in a disk-shaped quantum dot using the Bethe-Goldstone equation. It examines systems with up to 12 electron-hole pairs. For symmetric configurations where the number of electrons equals the number of holes, it finds:
1) The triexciton and four-exciton system show weak binding or possible unbinding in the weak confinement regime.
2) Higher complexes beyond four pairs exhibit binding in the weak confinement regime.
3) The Bethe-Goldstone approach provides better energies than the BCS variational method in the weak confinement regime.
This document summarizes the uses of the Christoffel-Darboux (CD) kernel in the spectral theory of orthogonal polynomials. The CD kernel is defined in terms of orthogonal polynomials and can be interpreted as the integral kernel of a projection operator. It has applications in analyzing the zeros of orthogonal polynomials, Gaussian quadrature, variational principles, and characterizing the absolutely continuous, singular continuous, and pure point spectra of measures. Recent work has expanded its uses in studying universality in the bulk of the spectrum and properties of orthogonal polynomials.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
1) This chapter discusses electromagnetic wave propagation based on Maxwell's equations. It will derive wave motion in free space, lossless dielectrics, lossy dielectrics, and good conductors.
2) A wave is a function of both space and time that transports energy or information from one point to another. Electromagnetic waves include radio waves, light, and more.
3) Key wave characteristics include amplitude, wavelength, frequency, period, phase, and velocity. The velocity is the frequency multiplied by the wavelength based on a fixed relationship between them.
Investigation of Steady-State Carrier Distribution in CNT Porins in Neuronal ...Kyle Poe
In this work, the carrier distribution of a carbon nanotube inserted into the spinal ganglion neuronal membrane is examined. After primary characterization based on previous work, the nanotube is approximated as a one-dimensional system, and the Poisson and Schrödinger equations are solved using an iterative finite-difference scheme. It was found that carriers aggregate near the center of the tube, with a negative carrier density of ⟨ρn⟩ = 7.89 × 10^13 cm−3 and positive carrier density of ⟨ρp⟩ = 3.85 × 10^13 cm−3. In future work, the erratic behavior of convergence will be investigated.
This document provides an introduction to quantum Monte Carlo methods. It discusses using Monte Carlo integration to evaluate multi-dimensional integrals that arise in quantum mechanical problems. Variational Monte Carlo is introduced as using a trial wavefunction to sample configuration space and estimate observables, like the energy. The Metropolis algorithm is described as a way to generate Markov chains that sample a given probability distribution. This allows using Monte Carlo methods to solve the electronic structure problem by approximating many-body wavefunctions and integrals over configuration space.
This document reviews research on the convergence of perturbation series in quantum field theory. It discusses Dyson's argument that perturbation series in quantum electrodynamics (QED) have zero radius of convergence due to vacuum instability when the coupling constant is negative. Large-order estimates show that perturbation series coefficients grow factorially fast in quantum mechanics and field theories. Finally, it describes the method of Borel summation, which may allow extracting the exact physical quantity from a divergent perturbation series through a unique mapping.
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
The document studies small excitonic complexes in a disk-shaped quantum dot using the Bethe-Goldstone equation. It examines systems with up to 12 electron-hole pairs. For symmetric configurations where the number of electrons equals the number of holes, it finds:
1) The triexciton and four-exciton system show weak binding or possible unbinding in the weak confinement regime.
2) Higher complexes beyond four pairs exhibit binding in the weak confinement regime.
3) The Bethe-Goldstone approach provides better energies than the BCS variational method in the weak confinement regime.
This document summarizes the uses of the Christoffel-Darboux (CD) kernel in the spectral theory of orthogonal polynomials. The CD kernel is defined in terms of orthogonal polynomials and can be interpreted as the integral kernel of a projection operator. It has applications in analyzing the zeros of orthogonal polynomials, Gaussian quadrature, variational principles, and characterizing the absolutely continuous, singular continuous, and pure point spectra of measures. Recent work has expanded its uses in studying universality in the bulk of the spectrum and properties of orthogonal polynomials.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
1) This chapter discusses electromagnetic wave propagation based on Maxwell's equations. It will derive wave motion in free space, lossless dielectrics, lossy dielectrics, and good conductors.
2) A wave is a function of both space and time that transports energy or information from one point to another. Electromagnetic waves include radio waves, light, and more.
3) Key wave characteristics include amplitude, wavelength, frequency, period, phase, and velocity. The velocity is the frequency multiplied by the wavelength based on a fixed relationship between them.
This document discusses atomic structure, beginning with the hydrogen atom and one-electron atoms. It then discusses the Hamiltonian and solutions of the Schrodinger equation for these systems. It introduces quantum numbers and describes the orbitals and energy levels. For polyelectronic atoms, it discusses separating the Schrodinger equation and introduces Hartree-Fock self-consistent field approximations. It describes Slater determinants which satisfy the Pauli exclusion principle for many-electron wavefunctions.
This document contains problems related to simple harmonic motion, forced vibrations, and the origin of refractive index. Problem 7.1 asks the reader to plot the displacement of a string at various points over time given an equation describing the wave. Problem 7.2 asks the reader to analyze the time variation of displacement in loops of a standing wave given another equation. Problem 7.3 asks the reader to show that a mass dropped in a tunnel through the earth would execute simple harmonic motion and calculate the time period. The remaining problems involve calculating various properties related to simple harmonic motion, polarization, dielectric constants, plasma frequencies, and refractive indices.
1. This chapter discusses electrostatic fields, beginning with Coulomb's law and electric field intensity.
2. Coulomb's law describes the force between two point charges, and electric field intensity is defined as the force per unit charge.
3. Examples show how to calculate the electric force and field given point charge configurations using Coulomb's law and the superposition principle.
(1) Biot-Savart's law states that the magnetic field intensity produced at a point P by a differential current element is proportional to the product of the current and the sine of the angle between the element and the line joining P to the element, and inversely proportional to the square of the distance between P and the element.
(2) The magnetic field intensity due to different current distributions such as line, surface, and volume currents can be determined using Biot-Savart's law.
(3) Example problems demonstrate applying Biot-Savart's law to calculate the magnetic field intensity at a point due to straight and semi-infinite current filaments.
Generalization of Tensor Factorization and ApplicationsKohei Hayashi
This document presents two tensor factorization methods: Exponential Family Tensor Factorization (ETF) and Full-Rank Tensor Completion (FTC). ETF generalizes Tucker decomposition by allowing for different noise distributions in the tensor and handles mixed discrete and continuous values. FTC completes missing tensor values without reducing dimensionality by kernelizing Tucker decomposition. The document outlines these methods and their motivations, discusses Tucker decomposition, and provides an example applying ETF to anomaly detection in time series sensor data.
Resolving the dissociation catastrophe in fluctuating-charge modelsJiahao Chen
The document discusses issues that arise when using fluctuating charge models to describe chemical systems. It summarizes the concept of fluctuating charges based on electronegativity equalization. However, this leads to an unphysical "dissociation catastrophe" where charges do not decay to zero at infinite separation. The document proposes fixing this by introducing distance-dependent electronegativity or charge transfer variables between atoms to attenuate long-range charge transfer. It also discusses the topological relationship between charge transfer variables and atomic charges to convert between representations.
Spectroscopic ellipsometry is a technique for investigating the optical properties and electrodynamics of materials. It has several advantages over other optical techniques:
1) It provides an exact numerical inversion with no need for Kramers-Kronig transformations, allowing consistency checks.
2) Measurements are non-invasive and highly reproducible as they do not require reference samples.
3) It is very sensitive to thin film properties due to its ability to measure at oblique angles of incidence.
Ellipsometry has been used to study phenomena like superconductivity in cuprates and pnictides by measuring changes in spectral weight, and collective charge ordering in oxide superlattices.
Okay, let's break this down step-by-step:
* River flows southeast at 10 km/hr
* Let's define southeast as 45° from the east
* So the river's velocity is 10 cos(45°)ax + 10 sin(45°)ay = 7.07ax + 7.07ay
* Boat moves in the direction of the river at vB
* Man walks on deck at 2 km/hr perpendicular to the boat
* So the man's velocity is 2ay
* To find the total velocity, we add the velocities:
Total velocity = River velocity + Boat velocity + Man's velocity
= 7.07ax + 7.07ay + vB + 2
This document summarizes research on quantum chaos, including the principle of uniform semiclassical condensation of Wigner functions, spectral statistics in mixed systems, and dynamical localization of chaotic eigenstates. It discusses how in the semiclassical limit, Wigner functions condense uniformly on classical invariant components. For mixed systems, the spectrum can be seen as a superposition of regular and chaotic level sequences. Localization effects can be observed if the Heisenberg time is shorter than the classical diffusion time. The document presents an analytical formula called BRB that describes the transition between Poisson and random matrix statistics. An example is given of applying this to analyze the level spacing distribution for a billiard system.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
This document provides an outline for a lecture on complex dynamics in Hamiltonian systems. Some key points:
1) Simple periodic orbits called nonlinear normal modes exist and can destabilize, leading to weak or strong chaos depending on their properties.
2) Dynamical indicators like Lyapunov exponents and the Generalized Alignment Index (GALI) can identify regions of order and chaos. The Lyapunov spectrum indicates when orbits explore the same chaotic region.
3) GALI rapidly detects chaos as deviation vectors become aligned, and identifies quasiperiodic motion by vectors remaining independent. It distinguishes weak and strong chaos based on exponential decay rates.
1) The document summarizes research on the ground state of strongly coupled quark matter with a finite isospin chemical potential.
2) A Ginzburg-Landau theory approach is used to qualitatively analyze the phase transition near the critical point in a model-independent way.
3) It is found that at zero isospin chemical potential, the chiral condensation transition becomes first-order at high densities due to the formation of spatial inhomogeneities. At finite isospin chemical potential, charged pion condensation can occur in addition to chiral condensation.
This document is the front cover of a physics exam from the University of Cambridge International Examinations. It provides instructions for a multiple choice exam with 40 questions on physics. The exam covers topics such as mechanics, materials, waves, electricity, quantum and nuclear physics, thermodynamics, and astronomy. Candidates are instructed to choose the correct answer for each question and record their choice on an answer sheet provided. They are given 1 hour to complete the exam.
This document summarizes key concepts from Sobolev spaces and their applications in mechanics problems. It introduces Sobolev spaces Wm,p(Ω) whose norms involve integrals of function and derivative values. These spaces allow generalized notions of derivatives. Sobolev's imbedding theorem establishes continuity properties of mappings between Sobolev and other function spaces. These properties are important for analyzing mechanical models that involve elements in Sobolev spaces.
This document summarizes Chapter 2 of a textbook on functional analysis in mechanics. It introduces Sobolev spaces, which are function spaces used to model mechanical problems. Sobolev spaces allow for generalized notions of derivatives of functions. The chapter discusses imbedding theorems for Sobolev spaces, which describe how functions in one Sobolev space can be mapped continuously or compactly to other function spaces. It provides examples of imbedding properties for specific Sobolev spaces over different domains.
The Effective Fragment Molecular Orbital Methodcsteinmann
The document describes the Effective Fragment Molecular Orbital (EFMO) method, which combines the Fragment Molecular Orbital (FMO) method with the Effective Fragment Potential (EFP) method. EFMO treats large systems by dividing them into fragments and using quantum mechanics (QM) to calculate the gas phase energies of each fragment and effective fragment potentials (EFP) to describe many-body interactions between fragments. This allows EFMO to achieve a balance between the accuracy of QM methods and the efficiency of forcefield methods for treating large molecular systems.
(1) The document discusses electric fields in material spaces and summarizes some key properties of conductors and dielectrics.
(2) Conductors have an abundance of free electrons that allow conduction current to flow according to Ohm's law, while dielectrics have few free electrons.
(3) A perfect conductor cannot contain an electric field within it due to the migration and accumulation of free charges on its surface when an external field is applied.
1) The document discusses instanton effects in M-theory that describe tunneling across potential barriers and can have important quantum gravitational effects. It focuses on explicit exact solutions of M-theory compactified on S7.
2) The author constructs instanton solutions for a conformally coupled scalar field with a quartic interaction in an AdS4 background. The solutions have a vanishing stress-energy tensor and describe the decay of the unstable AdS4 vacuum via tunneling.
3) Holographically, the instantons correspond to an instability of the dual CFT effective potential for large values of the deformation parameter α, driving the theory from marginal to total instability. The tunneling probability depends exponentially on α.
Gloria Marchant has over 15 years of experience in the San Jose Unified School District as a teacher and administrator. She has served as an RSP teacher and case manager, developing individual education plans and coordinating services for students. Marchant has also been the department chair and a union representative. In these roles, she attends meetings, disseminates information, and represents staff interests. Additionally, she has experience teaching a variety of subjects as a long term substitute and for the extended school year program.
This document discusses atomic structure, beginning with the hydrogen atom and one-electron atoms. It then discusses the Hamiltonian and solutions of the Schrodinger equation for these systems. It introduces quantum numbers and describes the orbitals and energy levels. For polyelectronic atoms, it discusses separating the Schrodinger equation and introduces Hartree-Fock self-consistent field approximations. It describes Slater determinants which satisfy the Pauli exclusion principle for many-electron wavefunctions.
This document contains problems related to simple harmonic motion, forced vibrations, and the origin of refractive index. Problem 7.1 asks the reader to plot the displacement of a string at various points over time given an equation describing the wave. Problem 7.2 asks the reader to analyze the time variation of displacement in loops of a standing wave given another equation. Problem 7.3 asks the reader to show that a mass dropped in a tunnel through the earth would execute simple harmonic motion and calculate the time period. The remaining problems involve calculating various properties related to simple harmonic motion, polarization, dielectric constants, plasma frequencies, and refractive indices.
1. This chapter discusses electrostatic fields, beginning with Coulomb's law and electric field intensity.
2. Coulomb's law describes the force between two point charges, and electric field intensity is defined as the force per unit charge.
3. Examples show how to calculate the electric force and field given point charge configurations using Coulomb's law and the superposition principle.
(1) Biot-Savart's law states that the magnetic field intensity produced at a point P by a differential current element is proportional to the product of the current and the sine of the angle between the element and the line joining P to the element, and inversely proportional to the square of the distance between P and the element.
(2) The magnetic field intensity due to different current distributions such as line, surface, and volume currents can be determined using Biot-Savart's law.
(3) Example problems demonstrate applying Biot-Savart's law to calculate the magnetic field intensity at a point due to straight and semi-infinite current filaments.
Generalization of Tensor Factorization and ApplicationsKohei Hayashi
This document presents two tensor factorization methods: Exponential Family Tensor Factorization (ETF) and Full-Rank Tensor Completion (FTC). ETF generalizes Tucker decomposition by allowing for different noise distributions in the tensor and handles mixed discrete and continuous values. FTC completes missing tensor values without reducing dimensionality by kernelizing Tucker decomposition. The document outlines these methods and their motivations, discusses Tucker decomposition, and provides an example applying ETF to anomaly detection in time series sensor data.
Resolving the dissociation catastrophe in fluctuating-charge modelsJiahao Chen
The document discusses issues that arise when using fluctuating charge models to describe chemical systems. It summarizes the concept of fluctuating charges based on electronegativity equalization. However, this leads to an unphysical "dissociation catastrophe" where charges do not decay to zero at infinite separation. The document proposes fixing this by introducing distance-dependent electronegativity or charge transfer variables between atoms to attenuate long-range charge transfer. It also discusses the topological relationship between charge transfer variables and atomic charges to convert between representations.
Spectroscopic ellipsometry is a technique for investigating the optical properties and electrodynamics of materials. It has several advantages over other optical techniques:
1) It provides an exact numerical inversion with no need for Kramers-Kronig transformations, allowing consistency checks.
2) Measurements are non-invasive and highly reproducible as they do not require reference samples.
3) It is very sensitive to thin film properties due to its ability to measure at oblique angles of incidence.
Ellipsometry has been used to study phenomena like superconductivity in cuprates and pnictides by measuring changes in spectral weight, and collective charge ordering in oxide superlattices.
Okay, let's break this down step-by-step:
* River flows southeast at 10 km/hr
* Let's define southeast as 45° from the east
* So the river's velocity is 10 cos(45°)ax + 10 sin(45°)ay = 7.07ax + 7.07ay
* Boat moves in the direction of the river at vB
* Man walks on deck at 2 km/hr perpendicular to the boat
* So the man's velocity is 2ay
* To find the total velocity, we add the velocities:
Total velocity = River velocity + Boat velocity + Man's velocity
= 7.07ax + 7.07ay + vB + 2
This document summarizes research on quantum chaos, including the principle of uniform semiclassical condensation of Wigner functions, spectral statistics in mixed systems, and dynamical localization of chaotic eigenstates. It discusses how in the semiclassical limit, Wigner functions condense uniformly on classical invariant components. For mixed systems, the spectrum can be seen as a superposition of regular and chaotic level sequences. Localization effects can be observed if the Heisenberg time is shorter than the classical diffusion time. The document presents an analytical formula called BRB that describes the transition between Poisson and random matrix statistics. An example is given of applying this to analyze the level spacing distribution for a billiard system.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
This document provides an outline for a lecture on complex dynamics in Hamiltonian systems. Some key points:
1) Simple periodic orbits called nonlinear normal modes exist and can destabilize, leading to weak or strong chaos depending on their properties.
2) Dynamical indicators like Lyapunov exponents and the Generalized Alignment Index (GALI) can identify regions of order and chaos. The Lyapunov spectrum indicates when orbits explore the same chaotic region.
3) GALI rapidly detects chaos as deviation vectors become aligned, and identifies quasiperiodic motion by vectors remaining independent. It distinguishes weak and strong chaos based on exponential decay rates.
1) The document summarizes research on the ground state of strongly coupled quark matter with a finite isospin chemical potential.
2) A Ginzburg-Landau theory approach is used to qualitatively analyze the phase transition near the critical point in a model-independent way.
3) It is found that at zero isospin chemical potential, the chiral condensation transition becomes first-order at high densities due to the formation of spatial inhomogeneities. At finite isospin chemical potential, charged pion condensation can occur in addition to chiral condensation.
This document is the front cover of a physics exam from the University of Cambridge International Examinations. It provides instructions for a multiple choice exam with 40 questions on physics. The exam covers topics such as mechanics, materials, waves, electricity, quantum and nuclear physics, thermodynamics, and astronomy. Candidates are instructed to choose the correct answer for each question and record their choice on an answer sheet provided. They are given 1 hour to complete the exam.
This document summarizes key concepts from Sobolev spaces and their applications in mechanics problems. It introduces Sobolev spaces Wm,p(Ω) whose norms involve integrals of function and derivative values. These spaces allow generalized notions of derivatives. Sobolev's imbedding theorem establishes continuity properties of mappings between Sobolev and other function spaces. These properties are important for analyzing mechanical models that involve elements in Sobolev spaces.
This document summarizes Chapter 2 of a textbook on functional analysis in mechanics. It introduces Sobolev spaces, which are function spaces used to model mechanical problems. Sobolev spaces allow for generalized notions of derivatives of functions. The chapter discusses imbedding theorems for Sobolev spaces, which describe how functions in one Sobolev space can be mapped continuously or compactly to other function spaces. It provides examples of imbedding properties for specific Sobolev spaces over different domains.
The Effective Fragment Molecular Orbital Methodcsteinmann
The document describes the Effective Fragment Molecular Orbital (EFMO) method, which combines the Fragment Molecular Orbital (FMO) method with the Effective Fragment Potential (EFP) method. EFMO treats large systems by dividing them into fragments and using quantum mechanics (QM) to calculate the gas phase energies of each fragment and effective fragment potentials (EFP) to describe many-body interactions between fragments. This allows EFMO to achieve a balance between the accuracy of QM methods and the efficiency of forcefield methods for treating large molecular systems.
(1) The document discusses electric fields in material spaces and summarizes some key properties of conductors and dielectrics.
(2) Conductors have an abundance of free electrons that allow conduction current to flow according to Ohm's law, while dielectrics have few free electrons.
(3) A perfect conductor cannot contain an electric field within it due to the migration and accumulation of free charges on its surface when an external field is applied.
1) The document discusses instanton effects in M-theory that describe tunneling across potential barriers and can have important quantum gravitational effects. It focuses on explicit exact solutions of M-theory compactified on S7.
2) The author constructs instanton solutions for a conformally coupled scalar field with a quartic interaction in an AdS4 background. The solutions have a vanishing stress-energy tensor and describe the decay of the unstable AdS4 vacuum via tunneling.
3) Holographically, the instantons correspond to an instability of the dual CFT effective potential for large values of the deformation parameter α, driving the theory from marginal to total instability. The tunneling probability depends exponentially on α.
Gloria Marchant has over 15 years of experience in the San Jose Unified School District as a teacher and administrator. She has served as an RSP teacher and case manager, developing individual education plans and coordinating services for students. Marchant has also been the department chair and a union representative. In these roles, she attends meetings, disseminates information, and represents staff interests. Additionally, she has experience teaching a variety of subjects as a long term substitute and for the extended school year program.
D. Jaime García Almagro solicita la homologación de su título de "Licenciado en Ciencias Jurídicas" expedido por la Universidad Libre de Caracas en 1992 al título español de "Licenciado en Derecho". Adjunta documentación que acredita su título y estudios, y solicita que las notificaciones se envíen a su domicilio en Ejea de los Caballeros por correo ordinario.
El documento habla sobre conceptos básicos de las máquinas simples, incluyendo la velocidad, palancas, ruedas, planos inclinados y poleas. Explica que las máquinas simples sirven para multiplicar fuerzas o cambiar su dirección y que siguen el principio de conservación de la energía, además de dar ejemplos de cómo se usan y como una pequeña fracción de energía se disipa en forma de calor.
Este decreto autoriza a la Junta de Andalucía a realizar emisiones de deuda pública y concertar otras operaciones de endeudamiento hasta un importe máximo de 1.276.311.410,97 euros. Los fondos se destinarán a completar la financiación prevista en el Programa Anual de Endeudamiento acordado con el Estado para 2012. Se establecen las características de las operaciones de endeudamiento y se autoriza a la Dirección General de Tesorería y Deuda Pública a determinar los detalles de las emisiones.
El documento clasifica las energías en renovables e inagotables como la energía mareomotriz, hidráulica, eólica y solar, las cuales se obtienen de fuentes naturales; no renovables como el petróleo, carbón y gas que se agotan con el uso; y analiza su impacto ambiental, señalando que energías como la solar, eólica y mareomotriz no son contaminantes a diferencia de fuentes como el petróleo y la energía nuclear.
El documento describe los diferentes prototipos textuales, incluyendo narrativo, descriptivo, de exposición, diálogo y argumentativo. Explica brevemente las características y los tipos de texto donde se emplean cada uno. El resumen concluye que conocer los diferentes prototipos textuales es importante para crear textos cohesivos e interesantes para diferentes propósitos.
The story is about an emperor who is tricked into believing that he is wearing a magnificent new suit of clothes that is invisible to those who are unfit for their positions, stupid, or incompetent. In reality, he is wearing nothing at all. On the day of a procession, a child cries out that the emperor has nothing on, causing all of the emperor's subjects to see that he is, in fact, naked.
Están funcionando los juicios orales en MéxicoLiliJrzLemini
El documento analiza la implementación de los juicios orales en México tras la reforma de 2008. Aunque diez estados ya trabajan en aplicar la reforma, México enfrenta desafíos como bajos niveles educativos, alta corrupción y falta de cultura de legalidad que podrían poner en riesgo el éxito de los nuevos juicios orales. No obstante, muchos mexicanos siguen luchando por consolidar un sistema de justicia penal más justo.
La estudiante Jhorleudys Sánchez García está cursando el primer semestre de Contaduría Pública en la Universidad Minuto de Dios. Su número de identificación es 455821 y su correo electrónico es Jsanchezga5@uniminuto.edu.co.
This document discusses energy detection of unknown signals in fading environments. It proposes modeling the received signal power distribution under combined slow and fast fading. This allows deriving the distribution of the detector's decision variable in closed form. Specifically:
1) It models the received signal as the sum of the signal and noise, scaled by a complex channel amplitude representing fast and slow fading.
2) It derives an expression for the sufficient statistic at the detector's output and simplifies it under assumptions of high sample numbers and independent samples.
3) It expresses the distribution of the decision variable as an integral of the distribution for a fixed SNR, averaged over the SNR distribution due to fading.
4) It provides the specific
Widom and Larsen ULM Neutron Catalyzed LENRs on Metallic Hydride Surfaces-EPJ...Lewis Larsen
This document discusses ultra low momentum neutron catalyzed nuclear reactions on metallic hydride surfaces. Weak interaction catalysis initially occurs when neutrons (along with neutrinos) are produced from protons that capture "heavy" electrons. Surface electron masses are shifted upwards by localized condensed matter electromagnetic fields. Condensed matter quantum electrodynamic processes may also shift the densities of final states, allowing an appreciable production of extremely low momentum neutrons, which are thereby efficiently absorbed by nearby nuclei. No Coulomb barriers exist for the weak interaction neutron production or other resulting catalytic processes.
Talk given at the Twelfth Workshop on Non-Perurbative Quantum Chromodynamics ...Marco Frasca
This document summarizes the key steps in deriving an effective Nambu–Jona-Lasinio (NJL) model from QCD in the infrared limit. It shows that QCD can be written as a Gaussian theory for gluon fields, with a trivial infrared fixed point. This leads to a Yukawa interaction between quarks and an effective scalar field, along with a nonlocal four-quark interaction. Truncating to the lowest scalar excitation reproduces the NJL model, with couplings determined from the gluon propagator.
The document discusses the effective mass approximation in quantum mechanics. It begins by defining the effective mass as inversely proportional to the curvature of energy bands. Having a effective mass allows electrons in crystals to be treated similarly to classical particles, with the crystal forces and quantum properties accounted for in the mass. The effective mass can be a tensor and depends on the crystal direction. It then discusses measuring the effective mass using cyclotron resonance and how it varies by crystallographic direction. In general, the effective mass incorporates the quantum mechanical behavior of electrons in crystals to allow a classical particle treatment.
Apartes de la Conferencia de la SJG del 14 y 21 de Enero de 2012Nonlinear ele...SOCIEDAD JULIO GARAVITO
This document summarizes a research article about nonlinear electrodynamics and its effects on the polarization of the cosmic microwave background radiation. It introduces nonlinear electrodynamics models as alternatives to Maxwell's electrodynamics. The document then discusses how nonlinear electrodynamics is minimally coupled to gravity and derives the relevant equations of motion. It focuses on analyzing the Pagels-Tomboulis nonlinear electrodynamics Lagrangian and computing the polarization angle of photons propagating in an expanding universe with planar symmetry. Constraints on the nonlinear electrodynamics parameter are obtained using data on cosmic magnetic field strengths and the rotation of CMB polarization spectra measured by experiments.
Alexei Starobinsky - Inflation: the present statusSEENET-MTP
This document summarizes a presentation on inflation and the present status of inflationary cosmology. It discusses the key epochs in the early universe, including inflation, and how inflation solved issues with prior models. Observational evidence for inflation is presented, including measurements of the primordial power spectrum and constraints on the tensor-to-scalar ratio. Simple single-field inflation models are shown to match observations. The document also discusses the generation of primordial perturbations from quantum fluctuations during inflation and how this provides the seeds for structure formation.
1) The document explains Johann Balmer's empirical formula for the emission spectrum of hydrogen and how it relates the energies of emitted photons to integer values.
2) It then discusses early quantum models like the "electron in a box" model which showed energy must be quantized.
3) Finally, it describes Erwin Schrödinger's wave equation theory of quantum mechanics which successfully explained the quantization of energy levels in hydrogen and allowed prediction of atomic emission spectra.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
This document summarizes a talk on the variation of fundamental constants over time. It discusses several methods for measuring potential variations, including analyses of the cosmic microwave background, quasar absorption spectra, radioactive decay rates from the natural nuclear reactor at Oklo, and comparisons of atomic clock rates. Measurements from big bang nucleosynthesis and quasar data suggest the fine structure constant may have been smaller in the early universe, varying on the order of 10^-15 per year. However, results are not conclusive and depend on theoretical models. Ongoing work using improved atomic clocks aims to more precisely measure any drift of fundamental constants like the fine structure constant and quark-mass ratios over time.
The document discusses the structure of atoms and the development of atomic models. It summarizes:
1) The subatomic particles that make up atoms - electrons, protons, and neutrons - along with their relative charges and masses.
2) Early experiments that led to the discovery of electrons and the Thomson and Rutherford atomic models.
3) Quantum numbers like atomic number and mass number that are used to describe atoms.
4) Developments in quantum theory that resulted in Bohr's model of the hydrogen atom and explanation of atomic spectra through quantized energy levels.
The document summarizes the key results of a research paper on representation rings of cyclic groups over algebraically closed fields. It calculates the Jordan form of the tensor product of invertible Jordan block matrices whose pth power is the identity, for both characteristic zero and positive characteristic p fields.
It shows that for tensor products of Jordan blocks of size less than or equal to p, over a field of characteristic p, the Jordan form is a direct sum of indecomposable representations of the cyclic group of order p. Explicit formulas for various tensor product cases are provided, such as J2 ⊗ Jn and Jm ⊗ Jp for p ≥ m. Applications to arithmetic geometry, K-theory, cryptography and
1) The document derives the Bogoliubov-de Gennes (BdG) equation to solve for the eigenstates and eigenenergies of a superconductor with a single static magnetic impurity.
2) Using the BdG equation and Nambu spinor formalism, analytic expressions are obtained for the subgap Shiba states induced by the magnetic impurity. The Shiba state energies are given by E0 = ∆(1 - α2)/(1 + α2), where α is the dimensionless impurity strength.
3) The BdG spinor eigenstates for the Shiba states are derived. They consist of spin-up electrons and spin-down holes for one state, and spin
This document presents two variations on the periscope theorem in geometry optics. It summarizes:
1) For a "spherical periscope" system of two mirrors that reflects rays emanating from a point back to that point, the vector field relating the incoming and outgoing ray directions is projectively gradient.
2) For a "reversed periscope" system reflecting upward rays downward, the local diffeomorphism relating the ray directions and the function describing the second mirror can be expressed in terms of the function for the first mirror.
3) In both cases, the document provides theorems characterizing the relationships between the mirror surfaces and ray mappings in terms of gradients and differential equations.
The document discusses the structure of atoms, including:
1) Solving the Schrodinger equation for hydrogen-like atoms to determine allowed energies and wavefunctions.
2) The quantization of energy levels, orbital angular momentum, and other properties for hydrogen-like atoms.
3) How the concepts for hydrogen-like atoms can be applied to describe multi-electron atoms and molecules using approximations like the orbital model.
This document discusses quantum theory and the electronic structure of atoms. It begins by introducing properties of waves and electromagnetic radiation. It then covers early discoveries and models in atomic structure, including Planck's quantization of energy, Einstein's explanation of the photoelectric effect using photons, Bohr's model of electron orbits, de Broglie's proposal that electrons exhibit wave-particle duality, and Schrodinger's wave equation describing electron probability distributions. The document concludes by discussing how the Schrodinger equation is used to determine electron configurations and orbital diagrams for atoms.
Rutherford's model of the atom proposed that:
1. Most alpha particles passed through the atom undeflected, indicating most of the atom is empty space.
2. Some alpha particles were deflected, indicating a small, positively charged nucleus at the center of the atom.
3. Very few alpha particles were reflected backwards, showing the nucleus occupies an extremely small volume compared to the atom.
This model explained experimental observations of alpha particle scattering and established the basics of atomic structure, including the small, dense nucleus at the center of the atom.
1. Bohr's model of the atom describes electrons orbiting the nucleus in fixed, quantized energy levels.
2. Light is emitted when an electron moves from a higher to lower energy level, with frequency determined by Planck's equation.
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
1. Travelling wave solutions in negative index materials in the
presence of external source
Vivek Kumar Sharma∗ , Amit Goyal∗ , C. N. Kumar∗ and J. Goswamy†
∗
Department of Physics, Panjab University, Chandigarh 160 014, India
†
UIET, Panjab University, Chandigarh 160 014, India
Abstract. Negative index materials (NIMs) are artificially materials which have attracted lot of interest due to their
remarkable properties. In this work, we discuss some of the properties of NIMs and obtained travelling wave solutions for
pulse propagation in NIMs in the presence of external source. The reported solutions are necessarily of the fractional-type
containing trigonometric and hyperbolic functions.
Keywords: Optical solitons, Optical materials
PACS: 42.65.Tg, 42.70-a
INTRODUCTION NIMs, the group and phase velocities always points in
opposite direction.
Negative index materials (NIMs) are designed to have
exotic and unique properties that cannot be obtained with
naturally occurring materials and thus offer entirely new
prospects for manipulating light [1]. In 1967, Veselago
[2] first considered the case of a medium that had permit-
tivity ε < 0 and permeability µ < 0 at a given frequency
and concluded that the medium should then be consid-
ered to have a negative refractive index. In the last few FIGURE 1. Right handed and left handed material
years, theoretical proposals by Pendry et al. [3] for struc-
Let us consider the refraction of a ray at the interface
tured photonic media in certain frequency ranges were
of LHM and RHM. Then as per Snell’s Law, after refrac-
developed experimentally and this has brought Vese-
tion the ray of light turn towards negative side of nor-
lago’s result into the limelight. This field has become
mal in NIMs as shown in Fig. 2. Due to peculiar nature
a hot topic of scientific research and debate over the
Doppler effect will also be reversed in NIMs.
past one decade. In this context study of nonlinear pulse
propagation is new and exciting field of research. M.
Scalora et al. [4] was the first who derived generalized
nonlinear Schrödinger equation (GNLSE) for pulse prop-
agation in NIMs. Various research groups have studied
GNLSE in different contexts and obtained solitary wave
solutions[5, 6]. In this paper we considered GNLSE with
a source term and obtained solitary wave and periodic
solutions. FIGURE 2. Negative refraction and reversed Doppler effect
in NIMs.
PROPERTIES OF NIMS
FRACTIONAL TRANSFORM
It is clear from the Maxwell’s equations that if µ and SOLUTIONS FOR NIMS
ε are simultaneously negative then ⃗ H and ⃗ form
E, ⃗ k
the left handed system as shown in Fig. 1. Hence the The wave propagation in NIMs in the presence of ex-
material is also known as left handed material (LHM). ternal source can be modeled by following equation
The phase velocity of a wave is given by v = ω , hence,
k
(GNLSE)
if k is negative then v should also be negative. We know ∂ ϕ P ∂ 2ϕ ∂ 3ϕ ∂ (|ϕ |2 ϕ )
Poynting vector, ⃗ = 2 (E × H), is always positive, hence
P 1 ⃗ ⃗ i − −iQ 3 + γ |ϕ |2 ϕ +iΛ = β ei(ψ (ξ )−kz) ,
∂z 2 ∂t 2 ∂t ∂t
group velocity will always be positive. Therefore, in (1)
2. where ϕ is complex envelop of the field and P, Q, γ , Λ, β Dark/bright solitary wave solution
represent group velocity dispersion, third order disper-
sion, cubic nonlinearity, self-steepening and external We found general localized solution for the case when
source coefficients respectively. This equation without the Jacobian elliptic modulus m = 1. The set of Eqs.
source has already been studied by Tsitsas et al. [5] and (5) to (8) can be solved consistently for the unknown
obtained solitary wave solutions. parameters A, B, D and for a particular value of c1 . The
In order to find exact travelling wave solutions, we generic profile of the solution reads
have chosen the following ansatz
A + B sech2 ξ
i[ψ (ξ )−kz] α (ξ ) = . (10)
ϕ (z,t) = α (ξ ) e , (2) 1 + D sech2 ξ
where ξ = (t − uz) is the travelling coordinate. Substi- Since the analytical form of solution is known, a simple
tuting Eq. (2) in Eq. (1), and separating real and imagi- maxima-minima analysis can be done to distinguish pa-
nary part we obtain two coupled equations in α and ψ . rameter regimes supporting dark and bright soliton solu-
Choosing ψ ′ (ξ ) = m, the imaginary part can be solved tions. In this case, when AD < B one gets a bright soliton,
to obtain whereas if AD > B then a dark soliton exists. Typical in-
α ′′ = aα + bα 3 + c1 , (3) tensity profile for bright solitary wave solution is shown
2
Λ
where a = − P+u−3Qm , b = Q and c1 is integration con- in Fig. 3b.
Q a b
stant. Using these relations, the real part can be solved
consistently to obtain the various travelling wave param-
( ) 3 2.0
eters as m = 4Λ γ + PΛ , k = aP + Qm3 − um − 3aQm +
1
Intensity
Intensity
2
2Q 2 1.5
2β 1
Pm2
2 and c1 = For β = 0, c1 goes to zero and Eq.
6Qm−P . 0
1.0
1.0 10
1.0
0.5 Z
(3) have bright or dark soliton solutions [5, 6]. 0
0.5 Z 5
0
t t 5
Eq. (3) can be solved for travelling wave solutions by 5 0.0 100.0
using a fractional transformation [7]
FIGURE 3. Typical intensity profiles for (a) periodic and (b)
A + By2 (ξ ) solitary wave solutions.
α (ξ ) = , (4)
1 + Dy2 (ξ )
which maps the solutions of Eq.(1) to the elliptic equa-
tion y′′ ± py ± qy3 = 0, provided AD ̸= B. For explicit- CONCLUSION
ness, we consider the case where y = cn(ξ , m) with m
as modulus parameter. Then upon substitution of Eq. (2) We have obtained periodic and solitary wave solutions
into Eq. (1) and equating the coefficients of equal powers for pulse propagation in NIMs with external source. The
of cn(ξ , m) will yield the following consistency condi- reported solutions are necessarily of the fractional-type.
tions: Negative refractive index provided a new mechanism for
−aA − 2(AD − B)(1 − m) − bA3 − c1 = 0, (5) nonlinear optics in NIMs and resulting in a new class
−2aAD − aB + 6(AD − B)D(1 − m) − 4(AD − B)(2m − 1) of solutions that cannot exist in positive-index materials.
− 3bA2 B − 3c1 D = 0, (6) Because NIMs are artificial materials and we might have
−aAD 2 − 2aBD + 4(AD − B)D(2m − 1) + 6(AD − B)m
the flexibility of controlling these pulses at our will.
− 3bAB2 − 3c1 D2 = 0, (7)
−aBD 2 − 2(AD − B)Dm − bB3 − c D3
1 = 0. (8)
For different values of m, we can obtain different types ACKNOWLEDGMENTS
of travelling wave solutions.
A.G. would like to thank CSIR, New Delhi, for financial
support through S.R.F. during the course of this work.
Periodic solution
REFERENCES
For m = 0 and A = 0, Eq. (3) admits the non-singular
periodic solution of the following type 1. V. M. Shalaev, Nat. Photon. 1, 41 (2007).
( ) 2. V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1967).
2c1 cos2 ξ
α (ξ ) = , (9) 3. J. B. Pendry et al., Phys. Rev. Lett. 76, 4773 (1996).
a 1 − 2 cos2 ξ
3
4. M. Scalora et al., Phys. Rev. Lett. 95, 013902 (2005).
5. N. L. Tsitsas et al., Phys. Rev. Lett. E 79, 037601 (2009).
where a = 4 and c1 2 = (−128/27b). Typical intensity 6. A. K. Sarma Eur. Phy. J. D 62, 421 (2011).
profile for periodic solution is shown in Fig. 3a. 7. V. M. Vyas et al., J. Phys. A 39, 9151 (2006).