Thomas Erneux's Books

Laser Dynamics

By: Thomas Erneux,Pierre Glorieux

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Bridging the gap between laser physics and applied mathematics, this book offers a new perspective on laser dynamics. Combining fresh treatments of classic problems with up-to-date research, asymptotic techniques appropriate for nonlinear dynamical systems are shown to offer a powerful alternative to numerical simulations. The combined analytical and experimental description of dynamical instabilities provides a clear derivation of physical formulae and an evaluation of their significance. Starting with the observation of different time scales of an operating laser, the book develops approximation techniques to systematically explore their effects. Laser dynamical regimes are introduced at different levels of complexity, from standard turn-on experiments to stiff, chaotic, spontaneous or driven pulsations. Particular attention is given to quantitative comparisons between experiments and theory. The book broadens the range of analytical tools available to laser physicists and provides applied mathematicians with problems of practical interest, making it invaluable for graduate students and researchers.

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Page Count

379

Publisher

Cambridge University Press

Published Date

ISBN 10

1139486977

ISBN 13

9781139486972

Applied Delay Differential Equations

By: Thomas Erneux

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Applied Delay Differential Equations

By: Thomas Erneux

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.

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204

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387743723

ISBN 13

9780387743721

A Course in Mathematical Biology

Quantitative Modeling with Mathematical and Computational Methods

By: Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch

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A Course in Mathematical Biology

Quantitative Modeling with Mathematical and Computational Methods

By: Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch

This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.

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Page Count

307

Publisher

SIAM

Published Date

ISBN 10

0898718252

ISBN 13

9780898718256

Numerical Simulation in Fluid Dynamics

A Practical Introduction

By: Michael Griebel,Thomas Dornsheifer,Tilman Neunhoeffer

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Numerical Simulation in Fluid Dynamics

A Practical Introduction

By: Michael Griebel,Thomas Dornsheifer,Tilman Neunhoeffer

In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as an expository example, the individual steps of scientific computing are presented: the derivation of the mathematical model; the discretization of the model equations; the development of algorithms; parallelization; and visualization of the computed data. In addition to the treatment of the basic equations for modeling laminar, transient flow of viscous, incompressible fluids - the Navier-Stokes equations - the authors look at the simulation of free surface flows; energy and chemical transport; and turbulence. Readers are enabled to write their own flow simulation program from scratch. The variety of applications is shown in several simulation results, including 92 black-and-white and 18 color illustrations. After reading this book, readers should be able to understand more enhanced algorithms of computational fluid dynamics and apply their new knowledge to other scientific fields.

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Page Count

222

Publisher

SIAM

Published Date

ISBN 10

0898713986

ISBN 13

9780898713985

Methods of Mathematical Modelling

Continuous Systems and Differential Equations

By: Thomas Witelski,Mark Bowen

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Methods of Mathematical Modelling

Continuous Systems and Differential Equations

By: Thomas Witelski,Mark Bowen

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

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Page Count

309

Publisher

Springer

Published Date

ISBN 10

3319230425

ISBN 13

9783319230429

Applied Delay Differential Equations

By: Thomas Erneux

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Applied Delay Differential Equations

By: Thomas Erneux

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Page Count

204

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387743723

ISBN 13

9780387743721

Book's by Thomas Erneux

Laser Dynamics

Laser Dynamics

Applied Delay Differential Equations

Applied Delay Differential Equations

A Course in Mathematical Biology

A Course in Mathematical Biology

Numerical Simulation in Fluid Dynamics

Numerical Simulation in Fluid Dynamics

Methods of Mathematical Modelling

Methods of Mathematical Modelling

Applied Delay Differential Equations

Applied Delay Differential Equations

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