Rutherford Aris – författare

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer''s Perspective provides an elementary introduction to the craft by one of the century''s most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author''s frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities.- Describes pitfalls as well as principles of mathematical modeling- Presents twenty examples of engineering problems- Features seventeen reprinted papers- Presents personal reflections on some of the great natural philosophers- Emphasizes modeling procedures that precede extensive calculations

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

Ever since the seminal works on traveling waves and morphogenesis by Fisher, by Kolmogorov, Petrovski and Piscunov, and by Turing, scientists from many disciplines have been fascinated by questions concerning the formation of steady or dynamic patterns in reactive media. Contributions to this volume have been made by chemists, chemical engineers, mathematicians (both pure and applied), and physicists. The topics covered range from reports of experimental studies, through descriptions of numerical experiments, to rather abstract theoretical investigations, each exhibiting different aspects of a very diverse field.

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.

Ever since the seminal works on traveling waves and morphogenesis by Fisher, by Kolmogorov, Petrovski and Piscunov, and by Turing, scientists from many disciplines have been fascinated by questions concerning the formation of steady or dynamic patterns in reactive media. Contributions to this volume have been made by chemists, chemical engineers, mathematicians (both pure and applied), and physicists. The topics covered range from reports of experimental studies, through descriptions of numerical experiments, to rather abstract theoretical investigations, each exhibiting different aspects of a very diverse field.

Ever since the seminal works on traveling waves and morphogenesis by Fisher, by Kolmogorov, Petrovski and Piscunov, and by Turing, scientists from many disciplines have been fascinated by questions concerning the formation of steady or dynamic patterns in reactive media. Contributions to this volume have been made by chemists, chemical engineers, mathematicians (both pure and applied), and physicists. The topics covered range from reports of experimental studies, through descriptions of numerical experiments, to rather abstract theoretical investigations, each exhibiting different aspects of a very diverse field.

Elementary Chemical Reactor Analysis focuses on the processes, reactions, methodologies, and approaches involved in chemical reactor analysis, including stoichiometry, adiabatic reactors, external mass transfer, and thermochemistry. The publication first takes a look at stoichiometry and thermochemistry and chemical equilibrium. Topics include heat of formation and reaction, measurement of quantity and its change by reaction, concentration changes with a single reaction, rate of generation of heat by reaction, and equilibrium of simultaneous and heterogeneous reactions. The manuscript then offers information on reaction rates and the progress of reaction in time. Discussions focus on systems of first order reactions, concurrent reactions of low order, general irreversible reaction, variation of reaction rate with extent and temperature, and heterogeneous reaction rate expressions. The book examines the interaction of chemical and physical rate processes, continuous flow stirred tank reactor, and adiabatic reactors. Concerns include multistage adiabatic reactors, adiabatic stirred tank, stability and control of the steady state, mixing in the reactor, effective reaction rate expressions, and external mass transfer. The publication is a dependable reference for readers interested in chemical reactor analysis.

Mathematical Understanding of Chemical Engineering Systems is a collection of articles that covers the mathematical model involved in the practice of chemical engineering. The materials of the book are organized thematically into section. The text first covers the historical development of chemical engineering, and then proceeds to tackling a much more technical and specialized topics in the subsequent sections. The second section talks about the physical separation process, while the third section deals with stirred tank stability and control. Next, the book tackles polymerization and particle problems. Section 6 discusses empty tubular and fixed-bed catalytic reactors, while Section 7 details fluid-bed reactors and coal combustion. In the last two sections, the text presents mathematical and miscellaneous papers. The book will be most useful to researchers and practitioners of chemical engineering. Mathematicians and chemists will also benefit from the text.

Mathematics in Science and Engineering, Volume 3: The Optimal Design of Chemical Reactors: A Study in Dynamic Programming covers some of the significant problems of chemical reactor engineering from a unified point of view. This book discusses the principle of optimality in its general baring on chemical processes. Organized into nine chapters, this volume begins with an overview of the whole range of optimal problems in chemical reactor design. This text then provides the fundamental equations for reactions and reactors. Other chapters consider the objective function needed to define a realistic optimal problem and explain separately the main types of chemical reactors and their associated problems. This book discusses as well the three problems with a stochastic element. The final chapter deals with the optimal operation of existing reactors that may be regarded as partial designs in which only some of the variables can be optimally chosen. This book is a valuable resource for chemical engineers.