Discrete-continuum Coupling Method to Simulate Highly Dynamic Multi-scale Problems

Complex behavior models (plasticity, cracks, visco elascticity) face some theoretical difficulties for the determination of the behavior law at the continuous scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a meso scale in order to simulate directly a set of discrete properties that are responsible of the macroscopic behavior. The discrete element model has been developed for granular material. The proposed set shows how this method is capable to solve the problem of complex behavior that are linked to discrete meso scale effects. The first book solves the local problem, the second one presents a coupling approach to link the structural effects to the local ones, this third book presents the software workbench that includes all the theoretical developments.

Complex behavior models (plasticity, cracks, visco elascticity) face some theoretical difficulties for the determination of the behavior law at the continuous scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a meso scale in order to simulate directly a set of discrete properties that are responsible of the macroscopic behavior. The discrete element model has been developed for granular material. The proposed set shows how this method is capable to solve the problem of complex behavior that are linked to discrete meso scale effects.

Discrete Signals and Inverse Problems examines fundamental concepts necessary to engineers and scientists working with discrete signal processing and inverse problem solving, and places emphasis on the clear understanding of algorithms within the context of application needs. Based on the original ‘Introduction to Discrete Signals and Inverse Problems in Civil Engineering’, this expanded and enriched version: combines discrete signal processing and inverse problem solving in one book covers the most versatile tools that are needed to process engineering and scientific data presents step-by-step ‘implementation procedures’ for the most relevant algorithms provides instructive figures, solved examples and insightful exercises Discrete Signals and Inverse Problems is essential reading for experimental researchers and practicing engineers in civil, mechanical and electrical engineering, non-destructive testing and instrumentation. This book is also an excellent reference for advanced undergraduate students and graduate students in engineering and science.

Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particles Provides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulation Highlights the numerical tricks and pitfalls that are usually only realized after years of experience, with relevant simple experiments as applications Presents a logical approach starting withthe mechanical and physical bases,followed by a description of the techniques and finally their applications Written by a key author presenting ideas on how to model the dynamics of angular particles using polygons and polyhedral Accompanying website includes MATLAB-Programs providing the simulation code for two-dimensional polygons Recommended for researchers and graduate students who deal with particle models in areas such as fluid dynamics, multi-body engineering, finite-element methods, the geosciences, and multi-scale physics.

This volume examines important experimental techniques needed to characterise inorganic materials in order to elucidate their properties for practical application. Addressing methods that examine the structures and properties of materials over length scales ranging from local atomic order to long-range order on the meso- and macro-scopic scales, Multi Length-Scale Characterisation contains five detailed chapters: Measurement of Bulk Magnetic Properties Thermal Methods Atomic Force Microscopy Gas Sorption in the Analysis of Nanoporous Solids Dynamic Light Scattering Ideal as a complementary reference work to other volumes in the series (Local Structural Characterisation and Structure from Diffraction Methods) or as an examination of the specific characterisation techniques in their own right, Multi Length-Scale Characterisation is a valuable addition to the Inorganic Materials Series.

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: • Brings together the perspectives of researchers in areas of inverse problems and data assimilation. • Assesses the current state-of-the-art and identify needs and opportunities for future research. • Focuses on the computational methods used to analyze and simulate inverse problems. • Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Electromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing. In this book, the Method of Moments (MoM) is applied to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Since the problem is considered to be 2D, the integral equations (IEs) are scalar and only the TE (transverse electric) and TM (transverse magnetic) polarizations are addressed (no cross-polarizations occur). In Chapter 1, the MoM is applied to convert the IEs into a linear system, while Chapter 2 compares the MoM with the exact solution of the field scattered by a cylinder in free space, and with the Physical Optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM, of the coherent and incoherent intensities scattered by a random rough surface and an object below a random rough surface. The final chapter presents the same results as in Chapter 3, but for an object above a random rough surface. In these last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks. Contents 1. Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces. 2. Validation of the Method of Moments for a Single Scatterer. 3. Scattering from Two Illuminated Scatterers. 4. Scattering from Two Scatterers Where Only One is Illuminated. Appendix. Matlab Codes. About the Authors Christophe Bourlier works at the IETR (Institut d’Electronique et de T?l?communications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) as well as being a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conference papers. Nicolas Pinel is currently working as a Research Engineer at the IETR laboratory at Polytech Nantes and is about to join Alyotech Technologies in Rennes, France. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers. Gildas Kubick? is in charge of the “Expertise in electroMagnetism and Computation” (EMC) laboratory at the DGA (Direction G?n?rale de l’Armement), French Ministry of Defense, where he works in the field of radar signatures and electromagnetic stealth. His research interests include electromagnetic scattering and radar cross-section modeling.

A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

A much-needed introduction to the field of discrete-valued time series, with a focus on count-data time series Time series analysis is an essential tool in a wide array of fields, including business, economics, computer science, epidemiology, finance, manufacturing and meteorology, to name just a few. Despite growing interest in discrete-valued time series—especially those arising from counting specific objects or events at specified times—most books on time series give short shrift to that increasingly important subject area. This book seeks to rectify that state of affairs by providing a much needed introduction to discrete-valued time series, with particular focus on count-data time series. The main focus of this book is on modeling. Throughout numerous examples are provided illustrating models currently used in discrete-valued time series applications. Statistical process control, including various control charts (such as cumulative sum control charts), and performance evaluation are treated at length. Classic approaches like ARMA models and the Box-Jenkins program are also featured with the basics of these approaches summarized in an Appendix. In addition, data examples, with all relevant R code, are available on a companion website. Provides a balanced presentation of theory and practice, exploring both categorical and integer-valued series Covers common models for time series of counts as well as for categorical time series, and works out their most important stochastic properties Addresses statistical approaches for analyzing discrete-valued time series and illustrates their implementation with numerous data examples Covers classical approaches such as ARMA models, Box-Jenkins program and how to generate functions Includes dataset examples with all necessary R code provided on a companion website An Introduction to Discrete-Valued Time Series is a valuable working resource for researchers and practitioners in a broad range of fields, including statistics, data science, machine learning, and engineering. It will also be of interest to postgraduate students in statistics, mathematics and economics.

Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.