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"Addresses external biofluiddynamics concerning animal locomotion through surrounding fluid media - and internal biofluiddynamics concerning heat and mass transport by fluid flow systems within an animal."

"Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models. Haberman develops the method of characteristics to analyze the nonlinear partial differential equations that describe traffic flow. Fan-shaped characteristics describe the traffic situation that occurs when a traffic light turns green and shock waves describe the effects of a red light or traffic accident. Although it was written over 20 years ago, this book is still relevant. It is intended as an introduction to applied mathematics, but can be used for undergraduate courses in mathematical modeling or nonlinear dynamical systems or to supplement courses in ordinary or partial differential equations."

"The papers were elicited primarily from Mathematics for Industry: Challenges and Frontiers, a conference sponsored by SIAM in October, 2003. This conference was different from other SIAM conferences in that it was a forum for scientific experts from industry and government to meet with members of the mathematical community to discuss the visions they had for their industries and the obstacles they saw to reaching those goals.A distinctive feature of this work is its organization. The three sections: Industrial Problems; Mathematical Responses to Industrial Problems; and The Process of Mathematical Modeling, Practice, and Education offer a process view, always initiated by a practical problem, leading to the need for responsive mathematics both at the research and educational levels. All topics are tightly integrated with contemporary computing technology. Mathematical topics include splines, modeling, computational fluid dynamics, statistical model verification, and mathematics for design and simulation."

"The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples."

"Traditional mathematics often plays a vital role in the solution of industrial problems. This volume describes industrial problems presented at a graduate-level modeling workshop designed to improve the graduate students' vision about the type of mathematics and science they should pursue whether they aspire to academic or nonacademic postgraduate careers. The problems represent a broad spectrum of mathematical topics and applications including statistics, signal processing, fluid dynamics, ODE, and PDE, optimization, and numerical analysis. This volume can be used as a reference for mathematical modeling, signal processing, PDE, and applied control courses. Industry representatives presented the following topics for graduate students to investigate during the ten-day workshop: Curvature Modeling in THUNDER Actuators; Maximizing Deflection While Minimizing Power Consumption in a Piezoelectric Actuator Design; Mathematical Modeling of High Power Amplifier (HPA) and HPA Linearization Through a Predistorter; Time Dependent Consolidation of Fine Powders; High Precision, High Accuracy Control of Fluid Microdispenser Under Variable Load; and Mass Transport and Surface Reaction of Immunoassay."

"This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes."

"The relatively recent increase in computational power available for mathematical modeling and simulation raises the possibility that modern numerical methods can play a significant role in the analysis of complex particulate flows. This introductory monograph focuses on basic models and physically based computational solution strategies for the direct and rapid simulation of flowing particulate media. Its emphasis is primarily on fluidized dry particulate flows in which there is no significant interstitial fluid, although fully coupled fluid-particle systems are discussed as well. An introduction to basic computational methods for ascertaining optical responses of particulate systems also is included.The successful analysis of a wide range of applications requires the simulation of flowing particulate media that simultaneously involves near-field interaction and contact between particles in a thermally sensitive environment. These systems naturally occur in astrophysics and geophysics; powder processing pharmaceutical industries; bio-, micro- and nanotechnologies; and applications arising from the study of spray processes involving aerosols, sputtering, and epitaxy."

"The human cardiovascular and respiratory control systems represent an important focal point for developing physiological control theory because of the complexity of the control mechanisms involved, the interaction between cardiovascular and respiratory function, and the importance of this interaction in many clinical situations. This volume brings together the range of control processes involved in the effective regulation of these systems and develops modeling themes, strategies, and key clinical applications using contemporary mathematical and control methodologies. The reader will gain an appreciation of how analytical techniques and ideas from optimal control theory, systems theory, and numerical analysis can be utilized to better understand the regulation processes in human cardiovascular and respiratory systems.Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships. Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted."

"Mathematical modeling he ability to apply mathematical concepts and techniques to real-life systems as expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts.Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to extensively worked-out case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics."

"Mathematical methods based on the theory of stochastic processes have long been used effectively in telephone traffic modeling. Today's modern network traffic, which is distinctly different from traditional voice traffic, generates challenging mathematical and statistical problems. Stochastic Modeling in Broadband Communications Systems provides a concise overview of stochastic models and mathematical techniques for solving these problems and enhances readers' overall understanding of communication systems. The book also presents an excellent introduction, particularly for students and professionals in probability and applied mathematics, to a huge area of interesting problems and models arising from modern developments in broadband channel transmission systems. The author's clear presentation is based on sound mathematical reasoning, and he has taken special care to make the material easily accessible to readers unable to devote hours of time on rigorous mathematical detail and generality. Topics include models ranging over different time scales of calls, bursts, and cells; different protocol layers for transport, control, and applications; mechanisms for queuing, collisions, delay, and loss; and the effects of buffering, retransmission, multiplexing, and traffic control. Comprehensive exercises are provided at the end of each chapter."