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Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers

Introduction to Statistical Methods in Modern Genetics (Hardcover): M.C. Yang Introduction to Statistical Methods in Modern Genetics (Hardcover)
M.C. Yang
R3,629 Discovery Miles 36 290 Ships in 12 - 17 working days

Although the basic statistical theory behind modern genetics is not very difficult, most statistical genetics papers are not easy to read for beginners in the field, and formulae quickly become very tedious to fit a particular area of application.
Introduction to Statistical Methods in Modern Genetics distinguishes between the necessary and unnecessary complexity in a presentation designed for graduate-level statistics students. The author keeps derivations simple, but does so without losing the mathematical details. He also provides the required background in modern genetics for those looking forward to entering this arena. Along with some of the statistical tools important in genetics applications, students will learn:
How a gene is found
How scientists have separated the genetic and environmental aspects of a person's intelligence
How genetics are used in agriculture to improve crops and domestic animals
What a DNA fingerprint is and why there are controversies about it
Although the author assumes students have a foundation in basic statistics, an appendix provides the necessary background beyond the elementary, including multinomial distributions, inference on frequency tables, and discriminant analysis. With clear explanations, a multitude of figures, and exercise sets in each chapter, this text forms an outstanding entr?e into the rapidly expanding world of genetic data analysis.

Modeling Reality with Mathematics (Hardcover, 1st ed. 2022): Alfio Quarteroni Modeling Reality with Mathematics (Hardcover, 1st ed. 2022)
Alfio Quarteroni; Translated by Simon G. Chiossi
R479 Discovery Miles 4 790 Ships in 12 - 17 working days

Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.

Mathematics for Mechanical Engineers (Hardcover): William F. Ames, George Cain, W.Glenn Steele, Hugh W. Coleman, Richard L.... Mathematics for Mechanical Engineers (Hardcover)
William F. Ames, George Cain, W.Glenn Steele, Hugh W. Coleman, Richard L. Kautz, …
R3,189 Discovery Miles 31 890 Ships in 12 - 17 working days

Mathematics for Mechanical Engineers gives mechanical engineers convenient access to the essential problem solving tools that they use each day. It covers applications employed in many different facets of mechanical engineering, from basic through advanced, to ensure that you will easily find answers you need in this handy guide.
For the engineer venturing out of familiar territory, the chapters cover fundamentals like physical constants, derivatives, integrals, Fourier transforms, Bessel functions, and Legendre functions. For the experts, it includes thorough sections on the more advanced topics of partial differential equations, approximation methods, and numerical methods, often used in applications. The guide reviews statistics for analyzing engineering data and making inferences, so professionals can extract useful information even with the presence of randomness and uncertainty. The convenient Mathematics for Mechanical Engineers is an indispensable summary of mathematics processes needed by engineers.

Applied Mathematical Modeling - A Multidisciplinary Approach (Hardcover): Douglas R. Shier, K. T. Wallenius Applied Mathematical Modeling - A Multidisciplinary Approach (Hardcover)
Douglas R. Shier, K. T. Wallenius
R5,418 Discovery Miles 54 180 Ships in 12 - 17 working days

The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines.
The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects.
In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter. Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea.
Applied Mathematical Modeling serves as a handbook of in-depth case studies that span the mathematical sciences, building upon a modest mathematical background. Readers in other applied disciplines will benefit from seeing how selected mathematical modeling philosophies and techniques can be brought to bear on problems in their disciplines. The models address actual situations studied in chemistry, physics, demography, economics, civil engineering, environmental engineering, industrial engineering, telecommunications, and other areas.

Microcomputer Algorithms - Action from Algebra (Hardcover): John Killingbeck Microcomputer Algorithms - Action from Algebra (Hardcover)
John Killingbeck
R3,472 Discovery Miles 34 720 Ships in 12 - 17 working days

Although the computing facilities available to scientists are becoming more powerful, the problems they are addressing are increasingly complex. The mathematical methods for simplifying the computing procedures are therefore as important as ever. Microcomputer Algorithms: Action from Algebra stresses the mathematical basis behind the use of many algorithms of computational mathematics, providing detailed descriptions on how to generate algorithms for a large number of different uses. Covering a wide range of mathematical and physical applications, the book contains the theory of 25 algorithms. The mathematical theory for each algorithm is described in detail prior to discussing the algorithm in full, with complete program listings. The book presents the algorithms in modular form, allowing for easy interpretation, for the adaptation to readers' specific requirements without difficulty, and for use with various microcomputers. Blending mathematics and programming in one volume, this book will be of broad interest to all scientists and engineers, particularly those physicists using microcomputers for scientific problem handling. Students handling numerical data for research projects will also find the book useful.

Functional Analysis in Applied Mathematics and Engineering (Hardcover): Michael Pedersen Functional Analysis in Applied Mathematics and Engineering (Hardcover)
Michael Pedersen
R5,102 Discovery Miles 51 020 Ships in 12 - 17 working days

Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.

This text/reference discusses:
o rudimentary topology
o Banach's fixed point theorem with applications
o L^p-spaces
o density theorems for testfunctions
o infinite dimensional spaces
o bounded linear operators
o Fourier series
o open mapping and closed graph theorems
o compact and differential operators
o Hilbert-Schmidt operators
o Volterra equations
o Sobolev spaces
o control theory and variational analysis
o Hilbert Uniqueness Method
o boundary element methods

Functional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.

Fractional Calculus with Applications for Nuclear Reactor Dynamics (Paperback): Santanu Saha Ray Fractional Calculus with Applications for Nuclear Reactor Dynamics (Paperback)
Santanu Saha Ray
R2,587 Discovery Miles 25 870 Ships in 12 - 17 working days

Introduces Novel Applications for Solving Neutron Transport Equations While deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous ways. Since fractional calculus represents a reactor more closely than classical integer order calculus, Fractional Calculus with Applications for Nuclear Reactor Dynamics focuses on the application of fractional calculus to describe the physical behavior of nuclear reactors. It applies fractional calculus to incorporate the mathematical methods used to analyze the diffusion theory model of neutron transport and explains the role of neutron transport in reactor theory. The author discusses fractional calculus and the numerical solution for fractional neutron point kinetic equation (FNPKE), introduces the technique for efficient and accurate numerical computation for FNPKE with different values of reactivity, and analyzes the fractional neutron point kinetic (FNPK) model for the dynamic behavior of neutron motion. The book begins with an overview of nuclear reactors, explains how nuclear energy is extracted from reactors, and explores the behavior of neutron density using reactivity functions. It also demonstrates the applicability of the Haar wavelet method and introduces the neutron diffusion concept to aid readers in understanding the complex behavior of average neutron motion. This text: Applies the effective analytical and numerical methods to obtain the solution for the NDE Determines the numerical solution for one-group delayed neutron FNPKE by the explicit finite difference method Provides the numerical solution for classical as well as fractional neutron point kinetic equations Proposes the Haar wavelet operational method (HWOM) to obtain the numerical approximate solution of the neutron point kinetic equation, and more Fractional Calculus with Applications for Nuclear Reactor Dynamics thoroughly and systematically presents the concepts of fractional calculus and emphasizes the relevance of its application to the nuclear reactor.

The Intermediate Finite Element Method - Fluid Flow And Heat Transfer Applications (Hardcover, Reissue): Juan C. Heinrich,... The Intermediate Finite Element Method - Fluid Flow And Heat Transfer Applications (Hardcover, Reissue)
Juan C. Heinrich, Darrell W. Pepper
R6,669 R5,247 Discovery Miles 52 470 Save R1,422 (21%) Ships in 12 - 17 working days

This book is a follow-up to the introductory text written by the same authors. The primary emphasis on this book is linear and nonlinear partial differential equations with particular concentration on the equations of viscous fluid motion. Each chapter describes a particular application of the finite element method and illustrates the concepts through example problems. A comprehensive appendix lists computer codes for 2-D fluid flow and two 3-D transient codes.

Mathematical Methods for Physics and Engineering (Hardcover): Mattias Blennow Mathematical Methods for Physics and Engineering (Hardcover)
Mattias Blennow
R7,461 Discovery Miles 74 610 Ships in 12 - 17 working days

Suitable for advanced undergraduate and graduate students, this new textbook contains an introduction to the mathematical concepts used in physics and engineering. The entire book is unique in that it draws upon applications from physics, rather than mathematical examples, to ensure students are fully equipped with the tools they need. This approach prepares the reader for advanced topics, such as quantum mechanics and general relativity, while offering examples, problems, and insights into classical physics. The book is also distinctive in the coverage it devotes to modelling, and to oft-neglected topics such as Green's functions.

Dual-Number Methods in Kinematics, Statics and Dynamics (Hardcover): Ian Fischer Dual-Number Methods in Kinematics, Statics and Dynamics (Hardcover)
Ian Fischer
R6,118 Discovery Miles 61 180 Ships in 12 - 17 working days

This well-organized book uses 3x3 coordinate-transformation matrices and 3-element vectors with dual-number elements to analyze the mechanics of mechanism, robots, and other mechanical systems.
Dual-Number Methods in Kinematics, Statics and Dynamics serves as a text for a course using dual-number methods as well as a manual for the reader to develop his or her abilities for the design of machinery or evaluation of mechanical systems. In addition to the explanatory text and derivations, the author includes numerous examples and exercises to enable the reader to gain insight and perfect skills.

Dynamical Systems - Stability, Symbolic Dynamics, and Chaos (Hardcover, 2nd edition): Clark Robinson Dynamical Systems - Stability, Symbolic Dynamics, and Chaos (Hardcover, 2nd edition)
Clark Robinson
R5,573 Discovery Miles 55 730 Ships in 12 - 17 working days

Several distinctive aspects make Dynamical Systems unique, including:
o treating the subject from a mathematical perspective with the proofs of most of the results included
o providing a careful review of background materials
o introducing ideas through examples and at a level accessible to a beginning graduate student
o focusing on multidimensional systems of real variables

The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.

Classical Electrodynamics (Hardcover): Julian Schwinger, Lester L. Deraad Jr., Kimball Milton, Wu-Yang Tsai Classical Electrodynamics (Hardcover)
Julian Schwinger, Lester L. Deraad Jr., Kimball Milton, Wu-Yang Tsai
R3,365 Discovery Miles 33 650 Ships in 12 - 17 working days

Classical Electrodynamics captures Schwinger's inimitable lecturing style, in which everything flows inexorably from what has gone before. Novel elements of the approach include the immediate inference of Maxwell's equations from Coulomb's law and (Galilean) relativity, the use of action and stationary principles, the central role of Green's functions both in statics and dynamics, and, throughout, the integration of mathematics and physics. Thus, physical problems in electrostatics are used to develop the properties of Bessel functions and spherical harmonics. The latter portion of the book is devoted to radiation, with rather complete treatments of synchrotron radiation and diffraction, and the formulation of the mode decomposition for waveguides and scattering. Consequently, the book provides the student with a thorough grounding in electrodynamics in particular, and in classical field theory in general, subjects with enormous practical applications, and which are essential prerequisites for the study of quantum field theory.An essential resource for both physicists and their students, the book includes a ?Reader's Guide,? which describes the major themes in each chapter, suggests a possible path through the book, and identifies topics for inclusion in, and exclusion from, a given course, depending on the instructor's preference. Carefully constructed problems complement the material of the text, and introduce new topics. The book should be of great value to all physicists, from first-year graduate students to senior researchers, and to all those interested in electrodynamics, field theory, and mathematical physics.The text for the graduate classical electrodynamics course was left unfinished upon Julian Schwinger's death in 1994, but was completed by his coauthors, who have brilliantly recreated the excitement of Schwinger's novel approach.

Computational Diffusion MRI - International MICCAI Workshop, Lima, Peru, October 2020 (Hardcover, 1st ed. 2021): Noemi Gyori,... Computational Diffusion MRI - International MICCAI Workshop, Lima, Peru, October 2020 (Hardcover, 1st ed. 2021)
Noemi Gyori, Jana Hutter, Vishwesh Nath, Marco Palombo, Marco Pizzolato, …
R4,466 Discovery Miles 44 660 Ships in 12 - 17 working days

This book gathers papers presented at the Workshop on Computational Diffusion MRI, CDMRI 2020, held under the auspices of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), which took place virtually on October 8th, 2020, having originally been planned to take place in Lima, Peru.This book presents the latest developments in the highly active and rapidly growing field of diffusion MRI. While offering new perspectives on the most recent research challenges in the field, the selected articles also provide a valuable starting point for anyone interested in learning computational techniques for diffusion MRI. The book includes rigorous mathematical derivations, a large number of rich, full-colour visualizations, and clinically relevant results. As such, it is of interest to researchers and practitioners in the fields of computer science, MRI physics, and applied mathematics. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice.

Test Your Higher Chemistry Calculations 3rd Edition (Paperback, 3rd Revised edition): John Anderson Test Your Higher Chemistry Calculations 3rd Edition (Paperback, 3rd Revised edition)
John Anderson
R425 Discovery Miles 4 250 Ships in 12 - 17 working days

Exam Board: SQA Level: Higher Subject: Chemistry First Teaching: September 2014 First Exam: Summer 2015 Ideal practice material for one of the most challenging areas for Higher Chemistry candidates. This edition of Test Your Higher Chemistry Calculations provides: > Extensive overview of all types of questions likely to be tested > Exploration of the theory behind each topic in each chapter > Worked examples and problems

Mathematics for Scientific and Technical Students (Paperback, 2nd New edition): H. Davies, H.G. Davies, G.A. Hicks Mathematics for Scientific and Technical Students (Paperback, 2nd New edition)
H. Davies, H.G. Davies, G.A. Hicks
R2,424 Discovery Miles 24 240 Ships in 12 - 17 working days

This book covers all the basic mathematical concepts and techniques required in the study of scientific and technical courses at GNVQ/A level and technician level. It is ideal as a bridging text for degree courses and introduces students to more advanced mathematics encountered in higher education.

Health, Safety, and Environmental Data Analysis - A Business Approach (Hardcover): Anthony J. Joseph Health, Safety, and Environmental Data Analysis - A Business Approach (Hardcover)
Anthony J. Joseph
R3,882 Discovery Miles 38 820 Ships in 10 - 15 working days

Professionals in environmental health and safety (EHS) management use statistics every day in making decisions. This book was created to provide the quantitative tools and techniques necessary to make important EHS assessments. Readers need not be statistically or mathematically inclined to make the most of this book-mathematical derivations are kept to a minimum and subjects are approached in a simple and factual manner, complemented with plenty of real-world examples.
Chapters 1-3 cover knowledge of basic statistical concepts such as presentation of data, measurements of location and dispersion, and elementary probability and distributions. Data gathering and analysis topics including sampling methods, sampling theory, testing, and interference as well as skills for critically evaluating published numerical material is presented in Chapters 4-6. Chapters 7-11 discuss information generation topics-regression and correlation analysis, time series, linear programming, network and Gnatt charting, and decision analysis-tools that can be used to convert data into meaningful information. Chapter 12 features six examples of projects made successful through statistical approaches being applied. Readers can use these approaches to solve their own unique problems.
Whether you are a EHS professional, manager, or student, Health, Safety, and Environmental Data Analysis: A Business Approach will help you communicate statistical data effectively.

Reaction Diffusion Systems (Paperback): Gabriela Caristi Reaction Diffusion Systems (Paperback)
Gabriela Caristi
R7,158 Discovery Miles 71 580 Ships in 12 - 17 working days

"Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."

An Introduction to Linear and Nonlinear Scattering Theory (Hardcover): G.F. Roach An Introduction to Linear and Nonlinear Scattering Theory (Hardcover)
G.F. Roach
R5,084 Discovery Miles 50 840 Ships in 12 - 17 working days

This monograph has two main purposes, first to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable, self-contained introduction to linear and nonlinear scattering theory for those who might wish to begin working in the area. Secondly, to indicate how these various aspects might be applied to problems in mathematical physics and the applied sciences. Of particular interest will be the influence of boundary conditions.

The Finite Element Method for Boundary Value Problems - Mathematics and Computations (Hardcover): Karan S. Surana, J.N. Reddy The Finite Element Method for Boundary Value Problems - Mathematics and Computations (Hardcover)
Karan S. Surana, J.N. Reddy
R4,868 Discovery Miles 48 680 Ships in 12 - 17 working days

Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.

A Course in Mathematical Methods for Physicists (Hardcover): Russell L. Herman A Course in Mathematical Methods for Physicists (Hardcover)
Russell L. Herman
R5,611 Discovery Miles 56 110 Ships in 12 - 17 working days

Based on the author's junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions

Mathematical Modeling and Numerical Techniques in Drying Technology (Hardcover): Ian Turner, Arun S. Mujumdar Mathematical Modeling and Numerical Techniques in Drying Technology (Hardcover)
Ian Turner, Arun S. Mujumdar
R10,435 Discovery Miles 104 350 Ships in 12 - 17 working days

Offers information necessary for the development of mathematical models and numerical techniques to solve specific drying problems. The book addresses difficult issues involved with the drying equations of numerical analysis, including mesh generation, discretinization strategies, the nonlinear equation set and the linearized algebraic system, convergance criteria, time step control, experimental validation, optimum methods of visualization results, and more.

Statistics of Quality (Hardcover): Subir Ghosh, William R. Schucany, William B. Smith Statistics of Quality (Hardcover)
Subir Ghosh, William R. Schucany, William B. Smith
R4,390 Discovery Miles 43 900 Ships in 12 - 17 working days

Explains the role of statistics in improving the quality of collecting and analyzing information for a wide variety of applications. The book examines the function of statisticians in quality improvement. It discusses statistical process control, quality statistical tables, and quality and warranty; quality standards in medicine and public health; Taguchi robust designs and survival models; and more.

A First Course on Wavelets (Hardcover, New): Eugenio Hernandez, Guido Weiss A First Course on Wavelets (Hardcover, New)
Eugenio Hernandez, Guido Weiss
R5,425 Discovery Miles 54 250 Ships in 12 - 17 working days

Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis, compactly supported wavelets, and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented. Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.

Geometry and Physics (Paperback): H. Pedersen Geometry and Physics (Paperback)
H. Pedersen
R10,432 Discovery Miles 104 320 Ships in 12 - 17 working days

This important reference - based on the proceedings of the Special Session on Geometry and Physics held over a six-month period at the University of Aarhus, Denmark, and on articles from the summer school held at Odense University, Denmark - offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts, Geometry and Physics presents the Seiberg-Witten invariants that facilitate the solution of open problems in Donaldson's theory...describes applications of the Seiberg-Witten invariants...analyzes moduli spaces of semi-stable bundles over Riemann surfaces...addresses operator algebras and topology...demonstrates the planar topological aspects of subfactors...examines symplectic geometry and Einstein metrics...discusses novel ways of computing curvature and holonomy for the determinant line bundle...elucidates the new topic of finite type invariants of three-manifolds and relations with nonperturbative quantum invariants...delineates recent work on a purely topological approach to physics-inspired invariants...and much more. Generously illustrated and containing over 800 key bibliographic citations, Geometry and Physics is an indispensable resource for geometers, topologists, mathematical and theoretical physicists, and graduate-level students in these disciplines.

Surveying a Dynamical System - A Study of the Gray-Scott Reaction in a Two-Phase Reactor (Hardcover): Khalid Alhumaizi,... Surveying a Dynamical System - A Study of the Gray-Scott Reaction in a Two-Phase Reactor (Hardcover)
Khalid Alhumaizi, Rutherford Aris
R601 Discovery Miles 6 010 Ships in 10 - 15 working days

When a dynamical system has a large number of parameters it is not possible to get a completely comprehensive picture of all the types of behavior that it may display and one must be content with surveying the system along various corridors of lower dimension. Using an example with three differential equations and six parameters it is shown how the available methods of singularity theory, bifurcation analysis, normal forms, etc. can be used to build up a picture of varied and interesting behavior. The model is a generalization of the Gray-Scott reaction scheme in a single stirred vessel to a two-phase reactor consisting of a reaction chamber and a reservoir communicating with each other through a semi-permeable membrane. Two forms exist according as to whether A is fed to the reactor and B to the reservoir or vice-versa, and show interesting differences of behavior. Both models undergo Hopf bifurcations, pitchfork transitions, have homoclinic orbits, take the period doubling route to chaos and one gets there by intermittency. Besides being of interest to mathematicians as an ecological study of a differentiable system, it is hoped that, though idealized, the fact that it corresponds closely to a real type of reactor will make it attractive to control engineers and others as a testing ground for their various methods and devices. This book will be of particular interest to students and researchers in mathematics and engineering , particularly those working in bifurcation or chaos theory.

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