Double Grid Finite Difference Frequency Domain Dg Fdfd Method For Scattering From Chiral Objects

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Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects

Erdogan Alkan,Veysel Demir,Atef Elsherbeni,Ercument Arvas
Double Grid Finite Difference Frequency Domain DG FDFD Method for Scattering from Chiral Objects Book PDF

Author : Erdogan Alkan,Veysel Demir,Atef Elsherbeni,Ercument Arvas
Publisher : Springer Nature
Page : 119 pages
File Size : 45,8 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031017155

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Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects by Erdogan Alkan,Veysel Demir,Atef Elsherbeni,Ercument Arvas Pdf

This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Bianisotropic Medium / Scattering FromThree Dimensional Chiral Structures / ImprovingTime and Memory Efficiencies of FDFD Methods / Conclusions / Appendix A: Notations / Appendix B: Near to Far FieldTransformation

Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects

Erdogan Alkan,Veysel Demir,Atef Z. Elsherbeni,Ercument Arvas
Double Grid Finite Difference Frequency Domain DG FDFD Method for Scattering from Chiral Objects Book PDF

Author : Erdogan Alkan,Veysel Demir,Atef Z. Elsherbeni,Ercument Arvas
Publisher : Morgan & Claypool Publishers
Page : 131 pages
File Size : 53,9 Mb
Release : 2013-01-01
Category : Technology & Engineering
ISBN : 9781627051460

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Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects by Erdogan Alkan,Veysel Demir,Atef Z. Elsherbeni,Ercument Arvas Pdf

This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Bianisotropic Medium / Scattering FromThree Dimensional Chiral Structures / ImprovingTime and Memory Efficiencies of FDFD Methods / Conclusions / Appendix A: Notations / Appendix B: Near to Far FieldTransformation

Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects

Andrew Peterson,Erdoğan Alkan,Mesut Gokten,Xuan Hui Wu,Ahmed Kishk,Atef Elsherbeni,Malcolm Bibby,Veysel Demir,Ercument Arvas
Double Grid Finite Difference Frequency Domain DG FDFD Method for Scattering from Chiral Objects Book PDF

Author : Andrew Peterson,Erdoğan Alkan,Mesut Gokten,Xuan Hui Wu,Ahmed Kishk,Atef Elsherbeni,Malcolm Bibby,Veysel Demir,Ercument Arvas
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 2010
Category : Electrical engineering
ISBN : 8303101714

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Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects by Andrew Peterson,Erdoğan Alkan,Mesut Gokten,Xuan Hui Wu,Ahmed Kishk,Atef Elsherbeni,Malcolm Bibby,Veysel Demir,Ercument Arvas Pdf

This lecture provides a tutorial introduction to the Nyström and locally-corrected Nyström methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution. Classical and generalized Gaussian quadrature rules are reviewed. The traditional Nyström method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nyström method is developed and applied to both the electric field and magnetic field equations. In the presence of target edges, where current or charge density singularities occur, the method must be extended through the use of appropriate singular basis functions and special quadrature rules. This extension is also described. Table of Contents: Introduction / Classical Quadrature Rules / The Classical Nyström Method / The Locally-Corrected Nyström Method / Generalized Gaussian Quadrature / LCN Treatment of Edge Singularities.

Analysis and Design of Transmitarray Antennas

Ahmed H. Abdelrahman,Fan Yang,Atef Z. Elsherbeni,Payam Nayeri
Analysis and Design of Transmitarray Antennas Book PDF

Author : Ahmed H. Abdelrahman,Fan Yang,Atef Z. Elsherbeni,Payam Nayeri
Publisher : Springer Nature
Page : 151 pages
File Size : 54,7 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031015410

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Analysis and Design of Transmitarray Antennas by Ahmed H. Abdelrahman,Fan Yang,Atef Z. Elsherbeni,Payam Nayeri Pdf

In recent years, transmitarray antennas have attracted growing interest with many antenna researchers. Transmitarrays combines both optical and antenna array theory, leading to a low profile design with high gain, high radiation efficiency, and versatile radiation performance for many wireless communication systems. In this book, comprehensive analysis, new methodologies, and novel designs of transmitarray antennas are presented. Detailed analysis for the design of planar space-fed array antennas is presented. The basics of aperture field distribution and the analysis of the array elements are described. The radiation performances (directivity and gain) are discussed using array theory approach, and the impacts of element phase errors are demonstrated. The performance of transmitarray design using multilayer frequency selective surfaces (M-FSS) approach is carefully studied, and the transmission phase limit which are generally independent from the selection of a specific element shape is revealed. The maximum transmission phase range is determined based on the number of layers, substrate permittivity, and the separations between layers. In order to reduce the transmitarray design complexity and cost, three different methods have been investigated. As a result, one design is performed using quad-layer cross-slot elements with no dielectric material and another using triple-layer spiral dipole elements. Both designs were fabricated and tested at X-Band for deep space communications. Furthermore, the radiation pattern characteristics were studied under different feed polarization conditions and oblique angles of incident field from the feed. New design methodologies are proposed to improve the bandwidth of transmitarray antennas through the control of the transmission phase range of the elements. These design techniques are validated through the fabrication and testing of two quad-layer transmitarray antennas at Ku-band. A single-feed quad-beam transmitarray antenna with 50 degrees elevation separation between the beams is investigated, designed, fabricated, and tested at Ku-band. In summary, various challenges in the analysis and design of transmitarray antennas are addressed in this book. New methodologies to improve the bandwidth of transmitarray antennas have been demonstrated. Several prototypes have been fabricated and tested, demonstrating the desirable features and potential new applications of transmitarray antennas.

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

George Fikioris,Ioannis Tastsoglou,Odysseas Bakas
Selected Asymptotic Methods with Applications to Electromagnetics and Antennas Book PDF

Author : George Fikioris,Ioannis Tastsoglou,Odysseas Bakas
Publisher : Springer Nature
Page : 187 pages
File Size : 41,8 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031017162

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Selected Asymptotic Methods with Applications to Electromagnetics and Antennas by George Fikioris,Ioannis Tastsoglou,Odysseas Bakas Pdf

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

Accurate Computation of Mathieu Functions

Andrew Peterson,Malcolm Bibby
Accurate Computation of Mathieu Functions Book PDF

Author : Andrew Peterson,Malcolm Bibby
Publisher : Springer Nature
Page : 123 pages
File Size : 50,7 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031017179

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Accurate Computation of Mathieu Functions by Andrew Peterson,Malcolm Bibby Pdf

This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

Analysis and Design of Transmitarray Antennas

Ahmed H. Abdelrahman,Fan Yang,Atef Z. Elsherbeni,Payam Nayeri
Analysis and Design of Transmitarray Antennas Book PDF

Author : Ahmed H. Abdelrahman,Fan Yang,Atef Z. Elsherbeni,Payam Nayeri
Publisher : Morgan & Claypool Publishers
Page : 177 pages
File Size : 54,7 Mb
Release : 2017-01-18
Category : Technology & Engineering
ISBN : 9781627057066

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Analysis and Design of Transmitarray Antennas by Ahmed H. Abdelrahman,Fan Yang,Atef Z. Elsherbeni,Payam Nayeri Pdf

In recent years, transmitarray antennas have attracted growing interest with many antenna researchers. Transmitarrays combines both optical and antenna array theory, leading to a low profile design with high gain, high radiation efficiency, and versatile radiation performance for many wireless communication systems. In this book, comprehensive analysis, new methodologies, and novel designs of transmitarray antennas are presented. Detailed analysis for the design of planar space-fed array antennas is presented. The basics of aperture field distribution and the analysis of the array elements are described. The radiation performances (directivity and gain) are discussed using array theory approach, and the impacts of element phase errors are demonstrated. The performance of transmitarray design using multilayer frequency selective surfaces (M-FSS) approach is carefully studied, and the transmission phase limit which are generally independent from the selection of a specific element shape is revealed. The maximum transmission phase range is determined based on the number of layers, substrate permittivity, and the separations between layers. In order to reduce the transmitarray design complexity and cost, three different methods have been investigated. As a result, one design is performed using quad-layer cross-slot elements with no dielectric material and another using triple-layer spiral dipole elements. Both designs were fabricated and tested at X-Band for deep space communications. Furthermore, the radiation pattern characteristics were studied under different feed polarization conditions and oblique angles of incident field from the feed. New design methodologies are proposed to improve the bandwidth of transmitarray antennas through the control of the transmission phase range of the elements. These design techniques are validated through the fabrication and testing of two quad-layer transmitarray antennas at Ku-band. A single-feed quad-beam transmitarray antenna with 50 degrees elevation separation between the beams is investigated, designed, fabricated, and tested at Ku-band. In summary, various challenges in the analysis and design of transmitarray antennas are addressed in this book. New methodologies to improve the bandwidth of transmitarray antennas have been demonstrated. Several prototypes have been fabricated and tested, demonstrating the desirable features and potential new applications of transmitarray antennas.

Electromagnetic Scattering using the Iterative Multi-Region Technique

Mohamed H. Al Sharkawy,Veysel Demir
Electromagnetic Scattering using the Iterative Multi Region Technique Book PDF

Author : Mohamed H. Al Sharkawy,Veysel Demir
Publisher : Springer
Page : 99 pages
File Size : 45,7 Mb
Release : 2007-12-31
Category : Technology & Engineering
ISBN : 3031005740

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Electromagnetic Scattering using the Iterative Multi-Region Technique by Mohamed H. Al Sharkawy,Veysel Demir Pdf

In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique. Different enhancement procedures are investigated and introduced toward the construction of this technique. These procedures are the following: 1) a hybrid technique combining the IMR technique and a method of moment technique is found to be efficient in producing accurate results with a remarkable computer memory saving; 2) the IMR technique is implemented on a parallel platform that led to a tremendous computational time saving; 3) together, the multigrid technique and the incomplete lower and upper preconditioner are used with the IMR technique to speed up the convergence rate of the final solution, which reduces the total computational time. Thus, the proposed iterative technique, in conjunction with the enhancement procedures, introduces a novel approach to solving large open-boundary electromagnetic problems including unconnected objects in an efficient and robust way. Contents: Basics of the FDFD Method / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 3D Case / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 2D Case / The IMR Algorithm Using a Hybrid FDFD and Method of Moments Technique / Parallelization of the Iterative Multiregion Technique / Combined Multigrid Technique and IMR Algorithm / Concluding Remarks / Appendices

The Finite Element Method in Electromagnetics

Jian-Ming Jin
The Finite Element Method in Electromagnetics Book PDF

Author : Jian-Ming Jin
Publisher : John Wiley & Sons
Page : 800 pages
File Size : 48,6 Mb
Release : 2015-02-18
Category : Science
ISBN : 9781118842027

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The Finite Element Method in Electromagnetics by Jian-Ming Jin Pdf

A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

Electromagnetic Scattering using the Iterative Multi-Region Technique

Mohamed H. Al Sharkawy,Veysel Demir
Electromagnetic Scattering using the Iterative Multi Region Technique Book PDF

Author : Mohamed H. Al Sharkawy,Veysel Demir
Publisher : Springer Nature
Page : 99 pages
File Size : 41,9 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031017025

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Electromagnetic Scattering using the Iterative Multi-Region Technique by Mohamed H. Al Sharkawy,Veysel Demir Pdf

In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique. Different enhancement procedures are investigated and introduced toward the construction of this technique. These procedures are the following: 1) a hybrid technique combining the IMR technique and a method of moment technique is found to be efficient in producing accurate results with a remarkable computer memory saving; 2) the IMR technique is implemented on a parallel platform that led to a tremendous computational time saving; 3) together, the multigrid technique and the incomplete lower and upper preconditioner are used with the IMR technique to speed up the convergence rate of the final solution, which reduces the total computational time. Thus, the proposed iterative technique, in conjunction with the enhancement procedures, introduces a novel approach to solving large open-boundary electromagnetic problems including unconnected objects in an efficient and robust way. Contents: Basics of the FDFD Method / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 3D Case / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 2D Case / The IMR Algorithm Using a Hybrid FDFD and Method of Moments Technique / Parallelization of the Iterative Multiregion Technique / Combined Multigrid Technique and IMR Algorithm / Concluding Remarks / Appendices

Handbook of Terahertz Technologies

Ho-Jin Song,Tadao Nagatsuma
Handbook of Terahertz Technologies Book PDF

Author : Ho-Jin Song,Tadao Nagatsuma
Publisher : CRC Press
Page : 612 pages
File Size : 52,5 Mb
Release : 2015-04-15
Category : Science
ISBN : 9789814613095

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Handbook of Terahertz Technologies by Ho-Jin Song,Tadao Nagatsuma Pdf

Terahertz waves, which lie in the frequency range of 0.1–10 THz, have long been investigated in a few limited fields, such as astronomy, because of a lack of devices for their generation and detection. Several technical breakthroughs made over the last couple of decades now allow us to radiate and detect terahertz waves more easily, which has triggered the search for new uses of terahertz waves in many fields, such as bioscience, security, and information and communications technology. The book covers some of the technical breakthroughs in terms of device technologies. It discusses not only the theoretical details and typical features of the technology described, but also some issues and challenges related to it. In addition, it is shown what can actually be done with the terahertz-wave technologies by introducing several successful demonstrations, such as wireless communications, industrial uses, remote sensing, chemical analysis, and 2D/3D imaging.

Liquid Crystal on Silicon Devices

Andrés Márquez,Ángel Lizana
Liquid Crystal on Silicon Devices Book PDF

Author : Andrés Márquez,Ángel Lizana
Publisher : MDPI
Page : 172 pages
File Size : 54,5 Mb
Release : 2019-11-19
Category : Science
ISBN : 9783039218288

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Liquid Crystal on Silicon Devices by Andrés Márquez,Ángel Lizana Pdf

Liquid Crystal on Silicon (LCoS) has become one of the most widespread technologies for spatial light modulation in optics and photonics applications. These reflective microdisplays are composed of a high-performance silicon complementary metal oxide semiconductor (CMOS) backplane, which controls the light-modulating properties of the liquid crystal layer. State-of-the-art LCoS microdisplays may exhibit a very small pixel pitch (below 4 μm), a very large number of pixels (resolutions larger than 4K), and high fill factors (larger than 90%). They modulate illumination sources covering the UV, visible, and far IR. LCoS are used not only as displays but also as polarization, amplitude, and phase-only spatial light modulators, where they achieve full phase modulation. Due to their excellent modulating properties and high degree of flexibility, they are found in all sorts of spatial light modulation applications, such as in LCOS-based display systems for augmented and virtual reality, true holographic displays, digital holography, diffractive optical elements, superresolution optical systems, beam-steering devices, holographic optical traps, and quantum optical computing. In order to fulfil the requirements in this extensive range of applications, specific models and characterization techniques are proposed. These devices may exhibit a number of degradation effects such as interpixel cross-talk and fringing field, and time flicker, which may also depend on the analog or digital backplane of the corresponding LCoS device. The use of appropriate characterization and compensation techniques is then necessary.

The First Outstanding 50 Years of “Università Politecnica delle Marche”

Sauro Longhi,Andrea Monteriù,Alessandro Freddi,Giulia Bettin,Silvio Cardinali,Maria Serena Chiucchi,Marco Gallegati
The First Outstanding 50 Years of Universit Politecnica delle Marche Book PDF

Author : Sauro Longhi,Andrea Monteriù,Alessandro Freddi,Giulia Bettin,Silvio Cardinali,Maria Serena Chiucchi,Marco Gallegati
Publisher : Springer Nature
Page : 212 pages
File Size : 43,7 Mb
Release : 2020-01-03
Category : Science
ISBN : 9783030338794

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The First Outstanding 50 Years of “Università Politecnica delle Marche” by Sauro Longhi,Andrea Monteriù,Alessandro Freddi,Giulia Bettin,Silvio Cardinali,Maria Serena Chiucchi,Marco Gallegati Pdf

The book describes significant multidisciplinary research findings at the Università Politecnica delle Marche and the expected future advances. It addresses some of the most dramatic challenges posed by today’s fast-growing, global society and the changes it has caused, while also discussing solutions to improve the wellbeing of human beings. The book covers the main research achievements made in the social sciences and humanities, and includes chapters that focus on understanding mechanisms that are relevant to all aspects of economic and social interactions among individuals. In line with Giorgio Fuà’s contribution, the interdisciplinary research being pursued at the Faculty of Economics of Università Politecnica delle Marche is aimed at interpreting the process of economic development in all of its facets, both at the national and local level, with a particular focus on profit and non-profit organizations. Various disciplines are covered, from economics to sociology, history, statistics, mathematics, law, accounting, finance and management.

The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations

Atef Z. Elsherbeni,Veysel Demir
The Finite Difference Time Domain Method for Electromagnetics with MATLAB Simulations Book PDF

Author : Atef Z. Elsherbeni,Veysel Demir
Publisher : IET
Page : 559 pages
File Size : 55,6 Mb
Release : 2015-11-25
Category : Science
ISBN : 9781613531754

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The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations by Atef Z. Elsherbeni,Veysel Demir Pdf

This is one of the best books on computational electromagnetics both for graduate students focusing on electromagnetics problems and for practicing engineering professionals in industry and government. It is designed as an advanced textbook and self-study guide to the FDTD method of solving EM problems and simulations. This latest edition has been expanded to include 5 entirely new chapters on advanced topics in the mainstream of FDTD practice. In addition to advanced techniques it also includes applications and examples, and some 'tricks and traps' of using MATLAB to achieve them. Compared to the previous version the second edition is more complete and is a good reference for someone who is performing FDTD research. This book is part of the ACES Series on Computational Electromagnetics and Engineering. Supplementary material can be found at the IET's ebook page Supplementary materials for professors are available upon request via email to [email protected].

Optical Tweezers

Arne Gennerich
Optical Tweezers Book PDF

Author : Arne Gennerich
Publisher : Humana
Page : 0 pages
File Size : 50,5 Mb
Release : 2016-11-15
Category : Science
ISBN : 1493964194

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Optical Tweezers by Arne Gennerich Pdf

The aim of this volume is to provide a comprehensive overview of optical tweezers setups, both in practical and theoretical terms, to help biophysicists, biochemists, and cell biologists to build and calibrate their own instruments and to perform force measurements on mechanoenzymes both in isolation in vitro and in living cells. Chapters have been divided in three parts focusing on theory and practical design of optical tweezers, detailed protocols for performing force measurements on single DNA- and microtubule/actin-associated mechanoenzymes in isolation, and describing recent advances that have opened up quantitative force measurements in living cells. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and cutting-edge, Optical Tweezers: Methods and Protocols aims help to further expand the accessibility and use of optical traps by scientists of diverse disciplines.