Bøger i Mathematical Modeling serien

This volume contains the proceedings of the US-Australia workshop on Control and Chaos held in Honolulu, Hawaii from 29 June to 1 July, 1995. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Industry, Science and Technology (Australia) under the US-Australia agreement. Control and Chaos-it brings back memories of the endless reruns of "Get Smart" where the good guys worked for Control and the bad guys were associated with Chaos. In keeping with current events, Control and Chaos are no longer adversaries but are now working together. In fact, bringing together workers in the two areas was the focus of the workshop. The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. This involves finding and using orbits in nonlinear systems which can take a system from one region of state space to other regions where we wish to stabilize the system. Control is used to generate useful chaotic trajectories where they do not exist, and to identify and take advantage of useful ones where they do exist. A controller must be able to nudge a system into a proper chaotic orbit and know when to come off that orbit. Also, it must be able to identify regions of state space where feedback control will be effective.

This volume contains the proceedings of the U.S. Australia workshop on Complex Interconnected Biological Systems held in Albany, Western Australia January 1-5, 1989. The workshop was jointly sponsored by the Department of Industry, Trade and Commerce (Australia), and the Na- tional Science Foundation (USA) under the US-Australia agreement. Biological systems are typically hard to study mathematically. This is particularly so in the case of systems with strong interconnections, such as ecosystems or networks of neurons. In the past few years there have been substantial improvements in the mathematical tools available for study- ing complexity. Theoretical advances include substantially improved un- derstanding of the features of nonlinear systems that lead to important behaviour patterns such as chaos. Practical advances include improved modelling techniques, and deeper understanding of complexity indicators such as fractal dimension. Game theory is now playing an increasingly important role in under- standing and describing evolutionary processes in interconnected systems. The strategies of individuals which affect each other's fitness may be incor- porated into models as parameters. Strategies which have the property of evolutionary stabilty result from particular parameter values which may be the main feature of living determined using game theoretic methods. Since systems is that they evolve, it seems appropriate that any model used to describe such systems should have this feature as well. Evolutionary game theory should lead the way in the development of such methods.

Beginning in 1983, the Swedish Council for Planning and Coordination of Research has organized an annual workshop devoted to some aspect of the behavior and modeling of complex systems. These workshops have been held at the Abisko Research Station of the Swedish Academy of Sciences, a remote location far above the Arctic Circle in northern Sweden. During the period of the midnight sun, from May 4-8, 1987 this exotic venue served as the gathering place for a small group of scientists, scholars, and other connoisseurs of the unknown to ponder the problem of how to model "e;living systems,"e; a term singling out those systems whose principal components are living agents. The 1987 Abisko Workshop focused primarily upon the general system-theoretic concepts of process, function, and form. In particular, a main theme of the Workshop was to examine how these concepts are actually realized in biological, economic, and linguistic situations. As the Workshop unfolded, it became increasingly evident that the central concern of the participants was directed to the matter of how those quintessential aspects of living systems-metabolism, self-repair, and replication-might be brought into contact with the long-established modeling paradigms employed in physics, chemistry, and engineering.

Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "e;behave"e; realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985).

This volume offers mathematical models for describing load and material properties in solving problems in structural engineering. Examples are provided, demonstrating how the models are implemented and the limitation of the models are clearly stated.

Many environmental problems contain incomplete data in the initial or boundary conditions. How do we solve problems for which some of the initial and/or boundary conditions are unknown? Using a technique, the sentinel method, this book answers these questions and others as they pertain to inverse problems in environmental pollution.

The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort.

This book deals with the asymptotic methods of analysis of linear elasticity problems for solids with cracks and inclusions. It is designed for applied scientists and students who wish to use the asymptotic analysis of elasticity problems in nonregular boundary as a tool for the strength evaluation.

Offers an understanding of how mathematics is developed for and applies to solving scientific and engineering problems. This book stresses the construction of mathematical descriptions of scientific and engineering situations rather than memorization of proofs and formulas.

Designing Innovations in Industrial Logistics Modelling describes practical methods for approaching the task of designing industrial logistics systems.-- Offers models and methods for designing and optimizing industrial logistics systems-- Surveys the development, methodology, and application of logistics models-- Discusses resource optimization and project planning-- Presents successful applications recently employed in advanced industrial companies-- Describes procedures for developing and evaluating new tools and designs