H.T. Banks – författare

Electromagnetic theory offers fascination and challenge from both a physical and a mathematical perspective. This monograph contains the newest results on the use of electromagnetic probes to interrogate dielectric material structures for material properties and geometry. This volume systematically exploits interface phenomena, the electrodynamics of material responses, and time dependent interrogating signals in an integrated manner. The authors begin with basic electromagnetics, such as Maxwell's equations, and present modeling, theory, and computational results.The book's strengths include a clear discussion of materials properties from the electromagnetic point of view, a careful formulation of the imaging problems addressed, rigorous treatment of mathematical issues, and useful illustration of computational methods and results. While confined to internal vision in one-dimensional settings, this volume will stimulate further developments in internal vision to include two- and three-dimensional interior assessments. It is an excellent and robust source of applied mathematics and engineering research challenges for the future.Imaging technology stands to benefit much from this research on low energy electromagnetic radiation. The use of electromagnetic pulses interacting with specially placed reflective surfaces, whether solid or acoustic, is a new dimension that will substantively impact medical imaging, subsoil investigation, and structure evaluation.

Globalization and the possibility of bioterrorist acts have highlighted the pressing need for the development of theoretical and practical mathematical frameworks that may be useful in our systemic efforts to anticipate, prevent, and respond to acts of destabilization.This book collects the detailed contributions of selected groups of experts from the fields of biostatistics, control theory, epidemiology, and mathematical biology who have engaged in the development of frameworks, models, and mathematical methods needed to address some of the pressing challenges posed by acts of terror. The ten chapters of this volume touch on a large range of issues in the subfields of biosurveillance, agroterrorism, bioterror response logistics, deliberate release of biological agents, impact assessment, and the spread of fanatic behaviours.

Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional analysis can be the basis of modern partial differential equation (PDE) and delay differential equation (DDE) techniques.Recent Examples of Functional Analysis in Biology, Electromagnetics, Materials, and MechanicsThrough numerous application examples, the book illustrates the role that functional analysis—a classical subject—continues to play in the rigorous formulation of modern applied areas. The text covers common examples, such as thermal diffusion, transport in tissue, and beam vibration, as well as less traditional ones, including HIV models, uncertainty in noncooperative games, structured population models, electromagnetics in materials, delay systems, and PDEs in control and inverse problems. For some applications, computational aspects are discussed since many problems necessitate a numerical approach.

Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model.Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them. Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.

Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional analysis can be the basis of modern partial differential equation (PDE) and delay differential equation (DDE) techniques.Recent Examples of Functional Analysis in Biology, Electromagnetics, Materials, and MechanicsThrough numerous application examples, the book illustrates the role that functional analysis—a classical subject—continues to play in the rigorous formulation of modern applied areas. The text covers common examples, such as thermal diffusion, transport in tissue, and beam vibration, as well as less traditional ones, including HIV models, uncertainty in noncooperative games, structured population models, electromagnetics in materials, delay systems, and PDEs in control and inverse problems. For some applications, computational aspects are discussed since many problems necessitate a numerical approach.

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob­ lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen­ tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en­ deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago.

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob­ lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen­ tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en­ deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago.

These notes are based on (i) a series of lectures that I gave at the 14th Biennial Seminar of the Canadian Mathematical Congress held at the University of Western Ontario August 12-24, 1973 and (li) some of my lectures in a modeling course that I have cotaught in the Division of Bio-Medical Sciences at Brown during the past several years. An earlier version of these notes appeared in the Center for Dynamical Systems Lectures Notes series (CDS LN 73-1, November 1973). I have in this revised and extended version of those earlier notes incorporated a number of changes based both on classroom experience and on my research efforts with several colleagues during the intervening period. The narrow viewpoint of the present notes (use of optimization and control theory in biomedical problems) reflects more the scope of the CMC lectures given in August, 1973 than the scope of my own interests. Indeed, my real interests have included the modeling process itself as well as the contributions made by investiga­ tors who employ the techniques and ideas of control theory, systems analysis, dif­ ferential equations, and stochastic processes. Some of these contributions have quite naturally involved application of optimal control theory. But in my opinion many of the interesting efforts being made in modeling in the biomedical sciences encompass much more than the use of control theory.