FFT and multigrid accelerated integral equation solvers for multi-scale electromagnetic analysis in complex backgrounds

textNovel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure’s geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing ‘fast integral-equation algorithms’ are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems.Electrical and Computer Engineerin

Wave Propagation in Materials for Modern Applications

In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas

Electronic, optical, mechanical and thermoelectric properties of graphene

Graphene, a two-dimensional allotrope of graphite with sp2 bonded carbon atoms, is arranged in honeycomb structure. Its quasi one-dimensional form is graphene nanoribbon (GNR). Graphene related materials have been found to display excellent electronic, chemical, mechanical properties along with uniquely high thermal conductivity, electrical conductivity and high optical transparency. With excellent electrical characteristics such as high carrier transport properties, quantum Hall effect at room temperature and unusual magnetic properties, graphene has applications in optoelectronic devices. Electronically, graphene is a zero bandgap semiconductor making it essential to tailor its structure for obtaining specific band structure. Narrow GNRs are known to open up bandgap and found to exhibit variations for different chiralities i.e., armchair and zigzag. Doping graphene, with p- or n- type elements, is shown to exhibit bandgap in contrast to pristine graphene. In this study, optical properties including dielectric functions, absorption coefficient, transmittance, and reflectance, as a function of wavelength and incident energy, are studied. Refractive index and extinction coefficient of pristine graphene are presented. A key optical property in the infrared region, emissivity, is studied as a function of wavelength for various multilayered configurations having graphene as one of the constituent layers. Application of such a structure is in the fabrication of a Hot Electron Bolometer (a sensor that operates on the basis of temperature-dependent electrical resistance). Graphene is found to have very high elastic modulus and intrinsic strength. Nanoindentation of graphene sheet is simulated to study the force versus displacement curves. Effects of variation of diameter of indenter, speed of indentation and number of layers of graphene on the mechanical properties are presented. Shrinking size of electronic devices has led to an acute need for thermal management. This prompted the study of thermoelectric (TE) effects in graphene based systems. TE devices are finding applications in power generation and solid state refrigeration. This study involves analyzing the electronic, thermal and electrical transport properties of these systems. Electronic thermal conductivity, of graphene based systems (κe), is found to be negligible as compared to its phonon-induced lattice thermal conduction (κp). Variations in κp of graphene and GN Rs are evaluated as a function of their width and length of their edges, chiralities, temperature, and number of layers. The interdependence of transport parameters, i.e., electrical conductivity (σ), thermoelectric power (TEP) or Seebeck coefficient (S), and κ of graphene are discussed. The thermoelectric performance of these materials is determined mainly by a parameter called Figure-of-Merit. Effective methods to optimize the value of Figure-of-Merit are explored. Reducing the thermal conductivity and increasing the power factor of these systems are found to improve the Figure-of-Merit significantly. This involves correlation of structure and transport properties. Effects of doping on σ, κ and Hall coefficient are discussed

Measurement techniques and instruments suitable for life-prediction testing of photovoltaic arrays

Array failure modes, relevant materials property changes, and primary degradation mechanisms are discussed as a prerequisite to identifying suitable measurement techniques and instruments. Candidate techniques and instruments are identified on the basis of extensive reviews of published and unpublished information. These methods are organized in six measurement categories - chemical, electrical, optical, thermal, mechanical, and other physicals. Using specified evaluation criteria, the most promising techniques and instruments for use in life prediction tests of arrays were selected

Characterisation Protocol for Liquid- Phase-Synthesised Graphene

Graphene, a two-dimensional honeycomb sp2 carbon lattice has received enormous attention because of the potential for various applications such as the electrodes of photovoltaic devices and batteries, next-generation flexible electronics and even antibacterial coatings. Interest in the application of graphene is mainly due to its unique physical and chemical properties, flexibility, and tuneability of the properties in graphene-based materials. However, while promising applications of graphene are being discussed, the term ‘graphene’ is often misused, and the difficulties in large-scale production of true two-dimensional graphene have further limited its applications. Methods such as top-down solution-processed exfoliation were developed to overcome the obstacles for large-scale graphene production, but these approaches do not yet produce completely delaminated and homogeneous graphene. To monitor and optimise the graphene production process, the development of a fast, standardised and reliable characterisation protocol for large-scale solution-processed graphene is therefore desirable. Among the many characteristics of graphene flakes, the nano-structural features including the lateral dimension, crystal imperfections and the thicknesses of graphene are the most important factors that affect the various properties of graphene. However, though many of the analytical techniques have continuously been improved, methods to obtain and quantify these graphene nano-structural features are still limited. This is owing to the difficulties of visualising the ultra-thin nano-flakes and the fact that many of the properties of graphene are still unknown to be used to identify the material. In this study, a characterisation protocol was proposed to quantify the fundamental nano- structural features of graphene. In all cases, the nano-structural feature was initially characterised by using the most precise technique based on direct imaging from transmission electron microscopy (TEM), the results were being used as benchmarks for the other fast but less direct methods that based on photon-probe techniques. To integrate and assess different characterisation techniques, quantification and statistical analysis of results have been used. By utilising the method proposed, it was found that the lateral dimension distribution of graphene can be rapidly obtained by Dynamic Light Scattering (DLS), especially for flakes smaller than 1000 nm. The crystalline imperfections within graphene can be obtained and quantified by conventional Raman spectroscopy, in which a simple method based on linear correlation and random sampling was proposed to indicate the source of disorder in graphene samples. The result was compared to the TEM study, and the differences were assigned to the uneven distribution of the defects in graphene flakes. The thickness of graphene was characterised via various techniques. Several empirical equations were derived in order to can be rapidly obtained the thickness of graphene. However, it may not be feasible at this stage to develop a method to accurately determine graphene thickness for large-scale characterisation. It was found that the level of graphitic character could be obtained utilising the variation of Raman 2D (G’) band, which is rather more important, and can be used to improve the graphene synthesis process. In summary, the proposed graphene characterisation protocol offers a practical method to integrate and evaluate different characterisation techniques. Also, the protocol development method can be used as a reference point, which can be applied to other materials for developing material-specific characterisation protocols. Nevertheless, it has been shown that such a graphene characterisation protocol has the ability to quantify and differentiate between inhomogeneous solution-processed graphene samples and can be used for optimising the graphene synthesis processes

Mechanical properties of Metal Based Flexible Transparent Conductive Electrode: From Fracture Mechanics perspective

With increasing interests for transparent conductive electrode for flexible electronic devices, many researchers have developed flexible electrodes from curved devices to wearable and foldable devices. But they are faced with new challenges because these devices not only require high optical transmittance and low sheet resistance value, but also must be able to change its shape to flexible, bendable, and even stretchable form. Studies in the past focused heavily on the process and material development to improve functionality and flexibility without a thorough mechanical investigation and a deep understanding failure mechanisms. Dielectric/Metal/Dielectric (DMD) layer consists of few tens of nanometer thick structure, and despite its outstanding optoelectronic performance, research on the mechanical and electrical relationship has not yet been investigated thoroughly. One of the reasons is that studies on nanoscale mechanics and flexible electronics have been conducted independently by researchers in different fields. Moreover, fracture mechanics confront new challenges at the nanoscale. It is known that the fracture mechanics of nanoscale materials are significantly different from those on the macroscopic scale. As the structural dimensions of materials are scaled down to nanoscale, only an extremely limited number of atoms exist in the vicinity of the crack tip, which challenges the conventional fracture mechanics theory. It brings up fundamental questions about what scale fracture mechanics effectively govern and what the basic principles and theories are in a nanometer scale. Due to experimental difficulties at the nanometer scale, very few attempts have tried to solve this important issue. xv In this study, we investigate the fracture characteristics of multilayer DMD structure and its unique cracking behavior. Abnormal crack propagation and toughening of multilayer DMD structures are analyzed and its underlying mechanism are explained. Various experiments and theoretical analyses are carried out to uncover the details of multilayered hierarchical structures and their underlying crack deflections. We analyze the fracture behavior of thin film structures during bending process and proposed a theoretical framework to identify the underlying principles of robustness for DMD multilayered structures. Bio-inspired ductile brittle combination strategy and experiments on crack deflection behavior of DMD layers are carried out to find the fracture toughness in thin materials. We also investigate fatigue failure for various conductive materials through cyclic experiments. Various bending speed experiments are performed to study the effect of strain rates, and we present that they control mobility of atoms, which changes its mechanical and electrical property. Most notably, we introduce a unique crack deflection propagating phenomenon where a crack can deflect along with the metallic layer and create a step-like fracture. Lastly, we generate multiple neutral plane and insert stretchable layer in the middle to minimize the strain exerted on the electrode during bending and also to achieve better flexibility in DMD samples. We provide a concise and accurate analytical model for this multilayer structure with dissimilar elastic properties and make it conclusive with numerical simulation and experimental results.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149813/1/sangeon_1.pd

Numerical Simulations

This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation