This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.

Mathematical Modelling of Gas-Phase Complex Reaction Systems: Pyrolysis and Combustion, Volume 45, gives an overview of the different steps involved in the development and application of detailed kinetic mechanisms, mainly relating to pyrolysis and combustion processes. The book is divided into two parts that cover the chemistry and kinetic models and then the numerical and statistical methods. It offers a comprehensive coverage of the theory and tools needed, along with the steps necessary for practical and industrial applications.

This reference conveys a basic understanding of chemical reactor design methodologies that incorporate both control and hazard analysis. It demonstrates how to select the best reactor for any particular chemical reaction, and how to estimate its size to determine the best operating conditions.

For rather a long time numerical results in chemical kinetics could only be obtained for very simple chemical reactions, most of which were of minor practi ca 1 importance. The avail abil ity of fast computers has provi ded new opportunities for developments in chemical kinetics. Chemical systems of practical interest are usually very complicated. They consi st of a great number of different el ementary chemi cal reacti ons, mostly with rate constants differi ng by many orders of magni tude, frequently with surface reacti on steps and often wi th transport processes. The deri vati on of a 'true' chemical mechani sm can be extremely cumbersome. Mostly this work is done by setting up 'reaction models' which are im proved step by step in comparison with precise experimental data. At this early stage mathematics is involved, which may al ready be rather complicated. Mathematical methods such as pertubation theory, graph theory, sensitivity analysis or numerical integration are necessary for the derivation and application of optimal chemical reaction models. Most theoretical work aimed at improving the mathematical methods was done on chemical reactions which mostly were of little practical im portance. Chemi cal engi neers, who evi dently k now well how important the chemical model s and their dynamics are for reactor desi gn, have al so to be convinced not only on the theoretical work but also on its practical applic abil ity.

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Advanced Data Analysis and Modeling in Chemical Engineering provides the mathematical foundations of different areas of chemical engineering and describes typical applications. The book presents the key areas of chemical engineering, their mathematical foundations, and corresponding modeling techniques. Modern industrial production is based on solid scientific methods, many of which are part of chemical engineering. To produce new substances or materials, engineers must devise special reactors and procedures, while also observing stringent safety requirements and striving to optimize the efficiency jointly in economic and ecological terms. In chemical engineering, mathematical methods are considered to be driving forces of many innovations in material design and process development. - Presents the main mathematical problems and models of chemical engineering and provides the reader with contemporary methods and tools to solve them - Summarizes in a clear and straightforward way, the contemporary trends in the interaction between mathematics and chemical engineering vital to chemical engineers in their daily work - Includes classical analytical methods, computational methods, and methods of symbolic computation - Covers the latest cutting edge computational methods, like symbolic computational methods

This practical reference explores computer modeling of enzyme reations--techniques that help chemists, biochemists and pharmaceutical researchers understand drug and enzyme action.

This book provides an authoritative introduction to the rapidly growing field of chemical reaction network theory. In particular, the book presents deep and surprising theorems that relate the graphical and algebraic structure of a reaction network to qualitative properties of the intricate system of nonlinear differential equations that the network induces. Over the course of three main parts, Feinberg provides a gradual transition from a tutorial on the basics of reaction network theory, to a survey of some of its principal theorems, and, finally, to a discussion of the theory’s more technical aspects. Written with great clarity, this book will be of value to mathematicians and to mathematically-inclined biologists, chemists, physicists, and engineers who want to contribute to chemical reaction network theory or make use of its powerful results.