Bøger i Modeling and Simulation in Sci serien

In the modern theory of boundary value problems the following ap­ proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob­ the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob­ lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].

This book is for a general scientific and engineering audience as a guide to current ideas, methods, and models for stochastic modeling of microstructures.It is a reference for professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.

This interdisciplinary collection of surveys highlights the central role played by the mathematical modeling of mechanical properties having an effect on the biology, chemistry, and physics of living matter. One of the main goals of the book is to present-in a single, self-contained resource-topics that are widely scattered across the literature in a variety of journals having mutually nonintersecting communities of readers, such as applied mathematicians, engineers, biologists, and physicians.Readers coming from diverse backgrounds are provided with basic modeling ideas and tools to address important problems in the medical and health sciences. Presented are appropriate models as well as their implementation through numerical and computer simulations, which may lead to potential technological innovations useful in medicine. Models are tested in realistic experiments, results are extracted analytically or numerically, and the success of the developed models is determined by comparing theoretical predictions and actual experimental findings.Written in a user-friendly style that avoids cumbersome mathematical techniques and notation, each chapter examines theoretical and practical issues associated with a specific biomedical applicationSpecific topics covered include:* mechanical properties of biological materials-macroscopic and microscopic perspectives* biochemical and biomechanical aspects of blood flow* formation and growth of intracranial aneurysms* modeling of natural tissue substitutes, including cardiovascular and biodegradable stents* regulation of hemostatic system function* mechanical properties of tumors, bones, and cell membranesModeling of Biological Materials may be used in interdisciplinary, introductory courses covering various biomechanical topics for graduate students in applied mathematics, engineering, and biomedicine. The surveysfeatured in the book will also be a lasting and valuable reference for a wide community of researchers, practitioners, and advanced students in the above-mentioned fields.

Modern aerospace vehicles, such as the space shuttle, other launch vehicles, and long-range ballistic missiles, do not discriminate between atmospheric and space flight. Most texts on flight dynamics, however, make this artificial distinction and therefore do not simultaneously cover aircraft and spacecraft. Bridging this gap in the literature, Atmospheric and Space Flight Dynamics is a unified presentation, demonstrating that the two disciplines have actually evolved from the same set of physical principles.Key features:* Introduction to a broad range of modern topics in an accessible, yet mathematically rigorous presentation* Many numerical examples and simulations utilizing MATLAB® and Simulink® fully integrated throughout the work* Simulations presented-usually not found in books on the same topic-are both realistic and instructive* Examples allow readers to easily build their own simulations for aircraft, missiles, launch vehicles, reentry vehicles, and spacecraft* Software is used as an instructional, hands-on tool, moving away from the "cookbook" approach found in other works* Supplementary material and MATLAB/Simulink code available* Numerous illustrations and end-of-chapter exercises* Separate solutions manual available to instructors upon requestPrimarily useful as a textbook for advanced undergraduate and beginning graduate-level students, the work is also an excellent reference or self-study guide for researchers and practitioners in aerospace engineering, aviation, mechanical engineering, dynamics, astrodynamics, aeronautics, and astronautics.

Combining two important and growing areas of applied mathematics-control theory and modeling-this textbook introduces and builds on methods for simulating and tackling problems in a variety of applied sciences. Control theory has moved from primarily being used in engineering to an important theoretical component for optimal strategies in other sciences, such as therapies in medicine or policy in economics. Applied to mathematical models, control theory has the power to change the way we view biological and financial systems, taking us a step closer to solving concrete problems that arise out of these systems.Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems, stressing concepts and minimizing technicalities. An elementary presentation of advanced concepts from the mathematical theory of optimal control is provided, giving readers the tools to solve significant and realistic problems. Proofs are also given whenever they may serve as a guide to the introduction of new concepts. This approach not only fosters an understanding of how control theory can open up modeling in areas such as the life sciences, medicine, and economics, but also guides readers from applications to new, independent research.Key features include:* An introduction to the main tools of MATLAB®, as well as programs that move from relatively simple ODE applications to more complex PDE models;* Numerous applications to a wide range of subjects, including HIV and insulin treatments, population dynamics, and stock management;* Exploration of cutting-edge topics in later chapters, such as optimal harvesting and optimal control of diffusive models, designed to stimulate further research and theses projects;* Exercises in each chapter, allowing students a chance to work with MATLAB and achieve a better grasp of the applications;* Minimal prerequisites: undergraduate-level calculus;*Appendices with basic concepts and results from functional analysis and ordinary differential equations, including Runge-Kutta methods;* Supplementary MATLAB files are available at the publisher's website: http://www.birkhauser-science.com/978-0-8176-8097-8/.As a guided tour to methods in optimal control and related computational methods for ODE and PDE models, An Introduction to Optimal Control Problems in Life Sciences and Economics serves as an excellent textbook for graduate and advanced undergraduate courses in mathematics, physics, engineering, computer science, biology, biotechnology, and economics. The work is also a useful reference for researchers and practitioners working with optimal control theory in these areas.