This document discusses arrays of radiating elements and how to shape their radiation patterns. It begins by explaining that arrays can provide more directive characteristics than single elements by combining the fields from multiple elements constructively in desired directions and destructively elsewhere. The key controls for shaping an array's pattern are its geometry, element spacing, excitation amplitudes, excitation phases, and individual element patterns. It then provides examples of calculating the radiation pattern for a two-element array and a uniform linear array with any number of elements. Important concepts covered include the array factor, nulls and maxima, and how to configure arrays for broadside or end-fire maximum radiation.
This document provides solutions to homework problems from a physics course. It solves problems about the reflection and transmission of electromagnetic waves at the interface between two dielectric materials. When the incident angle is below the critical angle, the transmission and reflection coefficients exhibit interference behavior and oscillate as a function of the gap width. When above the critical angle, transmission decreases exponentially with gap width due to total internal reflection. Reflection from a conductor is also derived, showing the reflection coefficient approaches 1 at radio frequencies. Power conservation is demonstrated by relating the transmitted power to the imaginary part of the dielectric constant.
This document discusses different types of antenna arrays, including uniform linear arrays and how their radiation patterns can be shaped. It describes 2-element arrays and calculates their array factors. It also covers N-element uniform linear arrays, including scanning arrays with a progressive phase shift between elements to direct the main beam, broadside arrays with in-phase elements, and end-fire arrays with a phase shift to direct the main beam along the array axis. Non-uniform arrays like binomial and Chebyshev arrays are also introduced. Pattern multiplication is used to calculate approximate radiation patterns from array factors and element patterns.
This document provides an introduction to the KKR (Korringa-Kohn-Rostoker) method, a computational technique for electronic structure calculations. It describes how the KKR method uses the Green's function formalism to solve the Kohn-Sham equations and obtain the electronic density of states without explicitly calculating energy eigenvalues. The document outlines the key steps of the KKR method, including representing the crystal potential as a muffin-tin model, calculating the scattering t-matrix, and obtaining the Green's function by summing multiple scattering processes. It also discusses how the KKR method can be applied to study properties of materials with defects or disorder.
An antenna array is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas are usually connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship.
Cs6402 design and analysis of algorithms may june 2016 answer keyappasami
The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.
Design of Non-Uniform Linear Antenna Arrays Using Dolph- Chebyshev and Binomi...IJERA Editor
This paper explores the analytical methods of synthesizing linear antenna arrays. The synthesis employed is
based on non-uniform methods. In particular, the Dolph-Chebyshev and binomial methods are used, so as to
improve the directivity of the array and to reduce the level of the secondary lobes by adjusting the geometrical
and electric parameters of the array. The radiation patterns, the directivity, and the array factors of the uniform
and the non-uniform methods are presented. It is shown that the Chebyshev arrays have better directivity than
binomial arrays for the same number of elements and separation distance, while binomial arrays have very low
side lobes compared with Chebyshev and uniform excitation arrays. Finally, numerical results of both methods
are analyzed and compared.
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 discusses wire antennas and antenna arrays. It begins by categorizing radiation patterns from an engineering, analytical, and technical perspective. It then covers basic wire antenna structures like dipoles and loops. The document focuses on linear, planar and array types including properties like radiation patterns, array factors, and design considerations for arrays like element spacing, progressive phase shifts and different array geometries. Specific array examples covered include uniform, broadside, endfire, binomial and filled disk arrays.
This document provides solutions to homework problems from a physics course. It solves problems about the reflection and transmission of electromagnetic waves at the interface between two dielectric materials. When the incident angle is below the critical angle, the transmission and reflection coefficients exhibit interference behavior and oscillate as a function of the gap width. When above the critical angle, transmission decreases exponentially with gap width due to total internal reflection. Reflection from a conductor is also derived, showing the reflection coefficient approaches 1 at radio frequencies. Power conservation is demonstrated by relating the transmitted power to the imaginary part of the dielectric constant.
This document discusses different types of antenna arrays, including uniform linear arrays and how their radiation patterns can be shaped. It describes 2-element arrays and calculates their array factors. It also covers N-element uniform linear arrays, including scanning arrays with a progressive phase shift between elements to direct the main beam, broadside arrays with in-phase elements, and end-fire arrays with a phase shift to direct the main beam along the array axis. Non-uniform arrays like binomial and Chebyshev arrays are also introduced. Pattern multiplication is used to calculate approximate radiation patterns from array factors and element patterns.
This document provides an introduction to the KKR (Korringa-Kohn-Rostoker) method, a computational technique for electronic structure calculations. It describes how the KKR method uses the Green's function formalism to solve the Kohn-Sham equations and obtain the electronic density of states without explicitly calculating energy eigenvalues. The document outlines the key steps of the KKR method, including representing the crystal potential as a muffin-tin model, calculating the scattering t-matrix, and obtaining the Green's function by summing multiple scattering processes. It also discusses how the KKR method can be applied to study properties of materials with defects or disorder.
An antenna array is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas are usually connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship.
Cs6402 design and analysis of algorithms may june 2016 answer keyappasami
The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.
Design of Non-Uniform Linear Antenna Arrays Using Dolph- Chebyshev and Binomi...IJERA Editor
This paper explores the analytical methods of synthesizing linear antenna arrays. The synthesis employed is
based on non-uniform methods. In particular, the Dolph-Chebyshev and binomial methods are used, so as to
improve the directivity of the array and to reduce the level of the secondary lobes by adjusting the geometrical
and electric parameters of the array. The radiation patterns, the directivity, and the array factors of the uniform
and the non-uniform methods are presented. It is shown that the Chebyshev arrays have better directivity than
binomial arrays for the same number of elements and separation distance, while binomial arrays have very low
side lobes compared with Chebyshev and uniform excitation arrays. Finally, numerical results of both methods
are analyzed and compared.
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 discusses wire antennas and antenna arrays. It begins by categorizing radiation patterns from an engineering, analytical, and technical perspective. It then covers basic wire antenna structures like dipoles and loops. The document focuses on linear, planar and array types including properties like radiation patterns, array factors, and design considerations for arrays like element spacing, progressive phase shifts and different array geometries. Specific array examples covered include uniform, broadside, endfire, binomial and filled disk arrays.
1) Four positive charges are located at the corners of a square in the xy-plane. A fifth positive charge is located 8cm from the others. The total force on the fifth charge is calculated to be 4.0x10-4 N directed along the z-axis.
2) Two charges of Q1 coulombs are located at z=±1. For a third charge Q2 to produce zero total electric field at (0,1,0), Q2 must lie along the y-axis at y=1±21/4|Q2|/Q1, where the sign depends on the sign of Q2.
3) The total force on a 50nC charge
This document describes using particle swarm optimization (PSO) to detect defective elements in a spaceborne planar antenna array. PSO is an optimization technique that models social behavior to iteratively find the global minimum of a cost function. Here, PSO is used to minimize the difference between measured and expected far-field radiation patterns to determine the location of any defective array elements. The document outlines designing a 2x2 planar array in IE3D software, introducing defects, calculating error patterns, and using PSO to optimize element positions to minimize error and correctly identify defective elements based only on far-field power measurements. The technique is shown to successfully detect randomly defective elements in the array, making it useful for locating failures in space applications where
Schelkunoff Polynomial Method for Antenna SynthesisSwapnil Bangera
The document discusses the Schelkunoff polynomial method for antenna synthesis. It involves designing an antenna array to produce a desired radiation pattern with nulls in specific directions. The method models the array factor as a polynomial and solves for the roots, which correspond to null locations. Array coefficients are then determined to produce the required roots within the visible region of the unit circle based on the element spacing and progressive phase shifts. As an example, a 4 element linear array is designed with nulls at 0, 90, and 180 degrees.
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
The document discusses using relativistic many-body theories like DF, CASCI, CASPT2 and RASCI to calculate parity-time (PT) odd effects in polar molecules like YbF and BaF. It summarizes previous work calculating spectroscopic constants of YbF using various methods and outlines future work to calculate electron electric dipole moment (EDM) and hyperfine constants using the above methods in other molecules.
07 periodic functions and fourier seriesKrishna Gali
This document discusses periodic functions and Fourier series. A periodic function repeats its values over a time period. The Fourier series represents a periodic function as an infinite sum of trigonometric terms (sines and cosines). The coefficients in the Fourier series (an and bn) can be determined by integrating the function multiplied by trigonometric terms over one period. Even functions can be represented by cosine terms alone, while odd functions use sine terms alone. The number of terms needed for an accurate representation depends on the function.
Kittel c. introduction to solid state physics 8 th edition - solution manualamnahnura
1. The document discusses crystallographic planes and directions in a cube, the Miller indices of planes with respect to primitive axes, and the spacing between dots projected onto different planes of a crystal structure.
2. Key concepts from crystallography such as Miller indices, primitive lattice vectors, reciprocal lattice vectors, and the first Brillouin zone are defined. Calculations of interplanar spacing and lattice parameters are shown for simple cubic and face-centered cubic lattices.
3. Binding energies, cohesive energies, and equilibrium properties are calculated and compared for body-centered cubic and face-centered cubic crystal structures. Approximations made in describing crystal binding using Madelung energies and pair potentials are
The document discusses discrete probability concepts including sample spaces, events, axioms of probability, conditional probability, Bayes' theorem, random variables, probability distributions, expectation, and classical probability problems. It provides examples and explanations of key terms. The Monty Hall problem is used to demonstrate defining the sample space, event of interest, assigning probabilities, and computing the probability of winning by sticking or switching doors.
1) The document analyzes the geometry of stacking circles of increasing radius inside an equilateral triangle. It derives that for a large number of circles N, the ratio of the total area of the circles to the area of the triangle is maximized when the angle at the tip of the triangle α is approximately equal to lnN/N.
2) The derivation is generalized to higher dimensions, showing that for stacking spheres inside a cone in d dimensions, the optimal angle is approximately equal to 2lnN/dN.
3) Numerical solutions show that for large N, the radius of the top circle approaches 1 - lnN/N and the ratio of circle area to triangle area approaches π/4.
1) The document analyzes the geometry of stacking circles of increasing radius inside an equilateral triangle. It derives that for a large number of circles N, the ratio of the total area of the circles to the area of the triangle is maximized when the angle at the tip of the triangle α is approximately equal to lnN/N.
2) The derivation is generalized to higher dimensions, showing that for stacking spheres inside a cone in d dimensions, the optimal angle is approximately equal to 2lnN/dN.
3) For large N, the radius of the top circle approaches 1 - lnN/N, α approaches lnN/N, and the ratio of circular to triangular area approaches π/
Electromagnetic Scattering from Objects with Thin Coatings.2016.05.04.02Luke Underwood
This document discusses a numerical method for modeling electromagnetic scattering from objects with thin coatings. It presents a method that properly weights the integration of near-singular behaviors introduced by thin coatings. The weighting is applied to the Fourier coefficients of Dirac delta functions. This allows the modeling of how varying a thin coating's properties alters an object's far-field scattering pattern.
This document provides solutions to theoretical physics problems from the 1st Asian Physics Olympiad held in Karawaci, Indonesia in April 2000. The solutions include:
1) Deriving an expression for the relative angular velocity of Jupiter and Earth and calculating the relative velocity.
2) Calculating the detection limit of a radioactive source using an ionization chamber and determining the necessary voltage pulse amplifier gain.
3) Using Gauss' law to calculate the electric field and potential between the plates of a parallel plate capacitor and deriving an expression for the capacitance per unit length.
POTENCIAS Y RAÍCES DE NÚMEROS COMPLEJOS-LAPTOP-3AN2F8N2.pptxTejedaGarcaAngelBala
The document discusses complex numbers and their properties. It covers representing complex numbers in polar form, exponential form, products and powers of complex numbers, and finding square roots of complex numbers. Some key points include:
1. A complex number z can be written in polar form as z = r(cosθ + i sinθ) where r is the modulus and θ is the argument.
2. Complex numbers can also be written in exponential form as z = reiθ using Euler's formula.
3. The product of two complex numbers z1 and z2 in exponential form is z1z2 = (r1r2)ei(θ1+θ2).
4. Taking powers
The document provides an overview of signals and systems topics to be covered in an EE 207 class, including detailed analysis of sinusoidal signals, phasor representation, frequency domain spectra, and practice problems. It defines a sinusoidal signal using amplitude, frequency, phase, and discusses representing the signal using a phasor or complex exponential. It also describes representing signals as the sum of complex conjugate signals, and plotting single-sided and double-sided frequency spectra. Practice problems cover determining if signals are periodic, calculating energy and power, representing signals using phasors, and sketching signals.
Geometric Applications of the Definite Integrals- Sampayan, Jill Ann.pptxGtScarlet
Definite integrals can be used to find the area of regions defined in polar coordinates. The area element in polar coordinates is dA = (1/2)ρ^2 dθ. To calculate the area, the integral A = ∫[θ1, θ2] ∫[ρ1(θ), ρ2(θ)] (1/2)ρ^2 dρ dθ is set up and evaluated over the specified angular range [θ1, θ2] and radial bounds [ρ1(θ), ρ2(θ)] of the region. An example calculates the area between the curves r = 2 + 4cos(θ) and r = 6 by identifying the angular range, determining the
The document provides an overview of sets and logic. It defines basic set concepts like elements, subsets, unions and intersections. It explains Venn diagrams can be used to represent relationships between sets. Logic is introduced as the study of correct reasoning. Propositions are defined as statements that can be determined as true or false. Logical connectives like conjunction, disjunction and negation are explained through truth tables. Compound statements can be formed using these connectives.
M. Dimitrijević, Noncommutative models of gauge and gravity theoriesSEENET-MTP
- The document describes a talk on noncommutative geometry and gravity theories given at a workshop in Serbia.
- Noncommutative geometry arises in string theory and could help address problems in quantum gravity and the standard model. The talk presents an approach using a star product to represent noncommutative algebras.
- Actions for noncommutative gauge theory and gravity are discussed. For gravity, a deformation of the MacDowell-Mansouri action is proposed based on the Seiberg-Witten map. This leads to modified field equations and corrections to the Einstein-Hilbert and cosmological constant terms.
This document provides an introduction and solutions to problems in Modern Particle Physics. It contains 18 chapters covering topics in particle physics like the Dirac equation, decay rates, scattering processes, and the Standard Model. The preface explains that the guide gives numerical solutions and hints to help understand questions from the first edition of the textbook. Instructors can obtain fully worked solutions from the publisher.
1) Four positive charges are located at the corners of a square in the xy-plane. A fifth positive charge is located 8cm from the others. The total force on the fifth charge is calculated to be 4.0x10-4 N directed along the z-axis.
2) Two charges of Q1 coulombs are located at z=±1. For a third charge Q2 to produce zero total electric field at (0,1,0), Q2 must lie along the y-axis at y=1±21/4|Q2|/Q1, where the sign depends on the sign of Q2.
3) The total force on a 50nC charge
This document describes using particle swarm optimization (PSO) to detect defective elements in a spaceborne planar antenna array. PSO is an optimization technique that models social behavior to iteratively find the global minimum of a cost function. Here, PSO is used to minimize the difference between measured and expected far-field radiation patterns to determine the location of any defective array elements. The document outlines designing a 2x2 planar array in IE3D software, introducing defects, calculating error patterns, and using PSO to optimize element positions to minimize error and correctly identify defective elements based only on far-field power measurements. The technique is shown to successfully detect randomly defective elements in the array, making it useful for locating failures in space applications where
Schelkunoff Polynomial Method for Antenna SynthesisSwapnil Bangera
The document discusses the Schelkunoff polynomial method for antenna synthesis. It involves designing an antenna array to produce a desired radiation pattern with nulls in specific directions. The method models the array factor as a polynomial and solves for the roots, which correspond to null locations. Array coefficients are then determined to produce the required roots within the visible region of the unit circle based on the element spacing and progressive phase shifts. As an example, a 4 element linear array is designed with nulls at 0, 90, and 180 degrees.
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
The document discusses using relativistic many-body theories like DF, CASCI, CASPT2 and RASCI to calculate parity-time (PT) odd effects in polar molecules like YbF and BaF. It summarizes previous work calculating spectroscopic constants of YbF using various methods and outlines future work to calculate electron electric dipole moment (EDM) and hyperfine constants using the above methods in other molecules.
07 periodic functions and fourier seriesKrishna Gali
This document discusses periodic functions and Fourier series. A periodic function repeats its values over a time period. The Fourier series represents a periodic function as an infinite sum of trigonometric terms (sines and cosines). The coefficients in the Fourier series (an and bn) can be determined by integrating the function multiplied by trigonometric terms over one period. Even functions can be represented by cosine terms alone, while odd functions use sine terms alone. The number of terms needed for an accurate representation depends on the function.
Kittel c. introduction to solid state physics 8 th edition - solution manualamnahnura
1. The document discusses crystallographic planes and directions in a cube, the Miller indices of planes with respect to primitive axes, and the spacing between dots projected onto different planes of a crystal structure.
2. Key concepts from crystallography such as Miller indices, primitive lattice vectors, reciprocal lattice vectors, and the first Brillouin zone are defined. Calculations of interplanar spacing and lattice parameters are shown for simple cubic and face-centered cubic lattices.
3. Binding energies, cohesive energies, and equilibrium properties are calculated and compared for body-centered cubic and face-centered cubic crystal structures. Approximations made in describing crystal binding using Madelung energies and pair potentials are
The document discusses discrete probability concepts including sample spaces, events, axioms of probability, conditional probability, Bayes' theorem, random variables, probability distributions, expectation, and classical probability problems. It provides examples and explanations of key terms. The Monty Hall problem is used to demonstrate defining the sample space, event of interest, assigning probabilities, and computing the probability of winning by sticking or switching doors.
1) The document analyzes the geometry of stacking circles of increasing radius inside an equilateral triangle. It derives that for a large number of circles N, the ratio of the total area of the circles to the area of the triangle is maximized when the angle at the tip of the triangle α is approximately equal to lnN/N.
2) The derivation is generalized to higher dimensions, showing that for stacking spheres inside a cone in d dimensions, the optimal angle is approximately equal to 2lnN/dN.
3) Numerical solutions show that for large N, the radius of the top circle approaches 1 - lnN/N and the ratio of circle area to triangle area approaches π/4.
1) The document analyzes the geometry of stacking circles of increasing radius inside an equilateral triangle. It derives that for a large number of circles N, the ratio of the total area of the circles to the area of the triangle is maximized when the angle at the tip of the triangle α is approximately equal to lnN/N.
2) The derivation is generalized to higher dimensions, showing that for stacking spheres inside a cone in d dimensions, the optimal angle is approximately equal to 2lnN/dN.
3) For large N, the radius of the top circle approaches 1 - lnN/N, α approaches lnN/N, and the ratio of circular to triangular area approaches π/
Electromagnetic Scattering from Objects with Thin Coatings.2016.05.04.02Luke Underwood
This document discusses a numerical method for modeling electromagnetic scattering from objects with thin coatings. It presents a method that properly weights the integration of near-singular behaviors introduced by thin coatings. The weighting is applied to the Fourier coefficients of Dirac delta functions. This allows the modeling of how varying a thin coating's properties alters an object's far-field scattering pattern.
This document provides solutions to theoretical physics problems from the 1st Asian Physics Olympiad held in Karawaci, Indonesia in April 2000. The solutions include:
1) Deriving an expression for the relative angular velocity of Jupiter and Earth and calculating the relative velocity.
2) Calculating the detection limit of a radioactive source using an ionization chamber and determining the necessary voltage pulse amplifier gain.
3) Using Gauss' law to calculate the electric field and potential between the plates of a parallel plate capacitor and deriving an expression for the capacitance per unit length.
POTENCIAS Y RAÍCES DE NÚMEROS COMPLEJOS-LAPTOP-3AN2F8N2.pptxTejedaGarcaAngelBala
The document discusses complex numbers and their properties. It covers representing complex numbers in polar form, exponential form, products and powers of complex numbers, and finding square roots of complex numbers. Some key points include:
1. A complex number z can be written in polar form as z = r(cosθ + i sinθ) where r is the modulus and θ is the argument.
2. Complex numbers can also be written in exponential form as z = reiθ using Euler's formula.
3. The product of two complex numbers z1 and z2 in exponential form is z1z2 = (r1r2)ei(θ1+θ2).
4. Taking powers
The document provides an overview of signals and systems topics to be covered in an EE 207 class, including detailed analysis of sinusoidal signals, phasor representation, frequency domain spectra, and practice problems. It defines a sinusoidal signal using amplitude, frequency, phase, and discusses representing the signal using a phasor or complex exponential. It also describes representing signals as the sum of complex conjugate signals, and plotting single-sided and double-sided frequency spectra. Practice problems cover determining if signals are periodic, calculating energy and power, representing signals using phasors, and sketching signals.
Geometric Applications of the Definite Integrals- Sampayan, Jill Ann.pptxGtScarlet
Definite integrals can be used to find the area of regions defined in polar coordinates. The area element in polar coordinates is dA = (1/2)ρ^2 dθ. To calculate the area, the integral A = ∫[θ1, θ2] ∫[ρ1(θ), ρ2(θ)] (1/2)ρ^2 dρ dθ is set up and evaluated over the specified angular range [θ1, θ2] and radial bounds [ρ1(θ), ρ2(θ)] of the region. An example calculates the area between the curves r = 2 + 4cos(θ) and r = 6 by identifying the angular range, determining the
The document provides an overview of sets and logic. It defines basic set concepts like elements, subsets, unions and intersections. It explains Venn diagrams can be used to represent relationships between sets. Logic is introduced as the study of correct reasoning. Propositions are defined as statements that can be determined as true or false. Logical connectives like conjunction, disjunction and negation are explained through truth tables. Compound statements can be formed using these connectives.
M. Dimitrijević, Noncommutative models of gauge and gravity theoriesSEENET-MTP
- The document describes a talk on noncommutative geometry and gravity theories given at a workshop in Serbia.
- Noncommutative geometry arises in string theory and could help address problems in quantum gravity and the standard model. The talk presents an approach using a star product to represent noncommutative algebras.
- Actions for noncommutative gauge theory and gravity are discussed. For gravity, a deformation of the MacDowell-Mansouri action is proposed based on the Seiberg-Witten map. This leads to modified field equations and corrections to the Einstein-Hilbert and cosmological constant terms.
This document provides an introduction and solutions to problems in Modern Particle Physics. It contains 18 chapters covering topics in particle physics like the Dirac equation, decay rates, scattering processes, and the Standard Model. The preface explains that the guide gives numerical solutions and hints to help understand questions from the first edition of the textbook. Instructors can obtain fully worked solutions from the publisher.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
New techniques for characterising damage in rock slopes.pdf
Antenna arrays
1. Arrays
Ranga Rodrigo
August 19, 2010
Lecture notes are fully based on Balanis [?]. Some diagrams and text are directly
from the books.
Contents
1 Two-Element Array 2
2 N-Element Linear Array: Uniform Amplitude and Spacing 6
Usually the radiation pattern of a single element is relatively wide, and each
element provides low values of directivity. In many applications it is necessary
to design antennas with very directive characteristics to meet the demands of
long distance communication. This can only be accomplished by increasing
the electrical size of the antenna. Enlarging the dimensions of single elements
often leads to more directive characteristics. Another way to enlarge the di-
mensions of the antenna, without necessarily increasing the size of the indi-
vidual elements, is to form an assembly of radiating elements in an electrical
and geometrical configuration. This new antenna, formed by multi-elements,
is referred to as an array. To provide very directive patterns, it is necessary that
the fields from the elements of the array interfere constructively (add) in the de-
sired directions and interfere destructively (cancel each other) in the remaining
space.
Shaping the Pattern of the Array
In an array of identical elements, there are usually five controls that can be
used to shape the overall pattern of the antenna. These are:
1. the geometrical configuration of the overall array (linear, circular, rectan-
gular, spherical, etc.)
2. the relative displacement between the elements
1
2. 3. the excitation amplitude of the individual elements
4. the excitation phase of the individual elements
5. the relative pattern of the individual elements
1 Two-Element Array
Let us assume that the antenna under investigation is an array of two infinites-
imal horizontal dipoles positioned along the z-axis. The resultant field, assum-
z
y
P
r2
θ2
r
θ
r1
θ1
d/2
d/2
ing no coupling between the elements, is equal to the sum of the two and in the
y-z plane it is given by
Et = E1 +E2 = âθ jη
kI0l
4π
·
e−j(kr1−β/2)
r1
cosθ1 +
e−j(kr2+β/2)
r2
cosθ2
¸
,
where β is the difference in phase excitation between the elements. Assuming
far-field observations
θ1 = θ = θ2.
2
3. z
y
P
r2
θ
r
θ
r1
θ
d/2
d/2
For phase variations
r1 ' r −
d
2
cosθ,
r2 ' r +
d
2
cosθ.
For amplitude variations
r1 ' r2 ' r.
Simplifying,
Et = âθ jη
kI0le−jkr
4πr
cosθ
h
e+j(kd cosθ+β)/2
+e−j(kd cosθ+β)/2
i
,
= âθ jη
kI0le−jkr
4πr
cosθ2cos
·
1
2
(kd cosθ +β)
¸
.
From this, tt is apparent that the total field of the array is equal to the field of
a single element positioned at the origin multiplied by a factor which is widely
referred to as the array factor. Thus for the two-element array of constant am-
plitude, the array factor is given by
AF = 2cos
·
1
2
(kd cosθ +β)
¸
.
3
4. Normalized,
AFn = cos
·
1
2
(kd cosθ +β)
¸
.
The array factor is a function of the geometry of the array and the excitation
phase. By varying the separation d and/or the phase β between the elements,
the characteristics of the array factor and of the total field of the array can be
controlled.
The far-zone field of a uniform two-element array of identical elements is
equal to the product of the field of a single element, at a selected reference point
(usually the origin), and the array factor of that array.
E(total) = [E(single element at reference point)]×[array factor].
This is valid for arrays with any number of identical elements which do not
necessarily have identical magnitudes, phases, and/or spacings between them.
The array factor, in general, is a function of the number of elements, their
geometrical arrangement, their relative magnitudes, their relative phases, and
their spacings. The array factor will be of simpler form if the elements have
identical amplitudes, phases, and spacings. Since the array factor does not de-
pend on the directional characteristics of the radiating elements themselves,
it can be formulated by replacing the actual elements with isotropic (point)
sources. Once the array factor has been derived using the point-source array,
the total field of the actual array is obtained by the use of the aforementioned
formula.
Example 1. Consider the two-element array of infinitesimal dipoles. Find the
nulls of the total field when d = λ/4 and
1. β = 0.
2. β = +π
2
.
3. β = −π
2 .
Solution:
1. β = 0 The normalized field is given by
Etn = cosθcos
³π
4
cosθ
´
Setting to zero to find the nulls,
Etn = cosθcos
³π
4
cosθ
´¯
¯
¯
θ=θn
= 0
4
5. Thus,
cosθn = 0 ⇒ θn = 90◦
,
and ³π
4
cosθn
´
= 0 ⇒
π
4
cosθn =
π
2
,−
π
2
⇒ θn does not exist.
The only null at θ = 90◦
is due to the pattern of the individual elements.
The array factor does not contribute to any additional nulls, because there
is not enough separation between them to introduce a phase difference
of 180◦
between the elements for any observation angle.
2. β = +π
2
The normalized field is given by
Etn = cosθcos
³π
4
(cosθ +1)
´
Setting to zero to find the nulls,
Etn = cosθcos
³π
4
(cosθ +1)
´¯
¯
¯
θ=θn
= 0
Thus,
cosθn = 0 ⇒ θn = 90◦
,
and
³π
4
(cosθn +1)
´
= 0 ⇒
π
4
(cosθn +1) =
π
2
⇒ θn = 0◦
,
⇒
π
4
(cosθn +1) = −
π
2
⇒ θn does not exist.
The nulls of the array occur at θ = 90◦
and 0◦
. The null at 0◦
is introduced
by the arrangement of the elements (array factor).
3. β = −π
2 The normalized field is given by
Etn = cosθcos
³π
4
(cosθ −1)
´
Setting to zero to find the nulls,
Etn = cosθcos
³π
4
(cosθ −1)
´¯
¯
¯
θ=θn
= 0
Thus,
cosθn = 0 ⇒ θn = 90◦
,
and
³π
4
(cosθn −1)
´
= 0 ⇒
π
4
(cosθn −1) =
π
2
⇒ θn does not exist,
⇒
π
4
(cosθn −1) = −
π
2
⇒ θn = 180◦
.
The nulls of the array occur at θ = 90◦
and 180◦
. The null at 180◦
is intro-
duced by the arrangement of the elements (array factor).
5
6. 2 N-Element Linear Array: Uniform Amplitude and
Spacing
The method followed for the two-element array can be generalized to include
N elements. Let us assume that all the elements have identical amplitudes but
each succeeding element has a β progressive phase lead current excitation rel-
ative to the preceding one (β represents the phase by which the current in each
element leads the current of the preceding element). An array of identical ele-
ments all of identical magnitude and each with a progressive phase is referred
to as a uniform array.
z
y
r1
θ
r2
θ
r3
θ
r4
θ
rN
θ
d
d
d
d cosθ
The array factor can be obtained by considering the elements to be point
sources. If the actual elements are not isotropic sources, the total field can be
formed by multiplying the array factor of the isotropic sources by the field of a
single element.
AF = 1+e+j(kd cosθ+β)
+e+j2(kd cosθ+β)
+···+e+j(N−1)(kd cosθ+β)
.
This can be written as
AF =
N
X
n=1
e j(n−1)ψ
,
where
ψ = kd cosθ +β.
6
7. AF = 1+e+jψ
+e+j2ψ
+···+e+j(N−1)ψ
,
AFe jψ
= e+jψ
+e+j2ψ
+e+j3ψ
+···+e+j Nψ
,
AF(e jψ
−1) = −1+e+j Nψ
.
AF =
·
e j Nψ
−1
e jψ −1
¸
,
= e j[(N−1)/2]ψ
·
e+j(N/2)ψ
−e−j(N/2)ψ
e+j(1/2)ψ −e−j(1/2)ψ
¸
,
= e j[(N−1)/2]ψ
"
sin
¡N
2
ψ
¢
sin
¡1
2ψ
¢
#
If the reference point is the physical center of the array
AF =
"
sin
¡N
2 ψ
¢
sin
¡1
2
ψ
¢
#
.
For small values of ψ,
AF '
"
sin
¡N
2 ψ
¢
1
2
ψ
#
.
As the maximum value is N, when normalized,
AFn =
1
N
"
sin
¡N
2
ψ
¢
sin
¡1
2ψ
¢
#
.
and
AFn '
1
N
"
sin
¡N
2 ψ
¢
N
2
ψ
#
.
Nulls and Maxima
• Nulls:
sin
µ
N
2
ψ
¶
= 0 ⇒
N
2
ψ
¯
¯
¯
¯
θ=90◦
= ±nπ ⇒ θn = cos−1
·
λ
2πd
µ
−β±
2n
N
π
¶¸
,
where
n = 1,2,3,...
n 6= N,2N,3N,....
For n = N,2N,3N,..., correspond to maxima (sin(0)/0 form).
7
8. • Maxima (when denominator becomes zero)
ψ
2
=
1
2
(kd cosθ +β)|θ=θm
= ±mπ = cos−1
·
λ
2πd
¡
−β±2mπ
¢
¸
where
m = 0,1,2,...
The array factor has only one maximum and occurs when m = 0.
θm = cos−1
µ
λβ
2πd
¶
.
Broadside Array: Maximum Normal to the Array
In many applications it is desirable to have the maximum radiation of an
array directed normal to the axis of the array (broadside; θ = 90◦
). To optimize
the design, the maxima of the single element and of the array factor should both
be directed toward θ = 90◦
. The requirements of the array factor by the proper
separation and excitation of the individual radiators.
Maximum of the array factor occurs when
ψ = kd cosθ +β = 0.
Since it is desired to have the maximum directed toward θ = 90◦
, then
ψ = kd cosθ +β|θ=90◦ = β = 0.
Thus to have the maximum of the array factor of a uniform linear array directed
broadside to the axis of the array, it is necessary that all the elements have the
same phase excitation(in addition to the same amplitude excitation).
Ordinary End-Fire Array: Maximum Along the Array
It may be desirable to direct it along the axis of the array (end-fire), at 0◦
,180◦
,
or both.
To direct maximum toward 0◦
ψ = kd cosθ +β|θ=0◦ = kd +β ⇒ β = −kd.
To direct maximum toward 180◦
ψ = kd cosθ +β|θ=180◦ = −kd +β ⇒ β = kd.
Thus end-fire radiation is accomplished when β = −kd (for θ = 0◦
) or β = kd
(for θ = 180◦
). If the element separation is d = λ/2, end-fire radiation exists si-
multaneously in both directions (θ = 0◦
and θ = 180◦
). If the element spacing is
a multiple of a wavelength (d = nλ, n = 1,2,3,...), then in addition to having
end-fire radiation in both directions, there also exist maxima in the broadside
directions. To have only one end-fire maximum and to avoid any grating lobes,
the maximum spacing between the elements should be less than dmax < λ/2.
8