This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various...
This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent be...
This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The book, unique in the literature, presents working knowledge, theory, techniques, and typical phenomena in rarefied gases for theoretical development and application. Basic theory is developed in a systematic way and presented in a form easily applied for practical use. In this work, the ghost effect and non-Navier-Stokes effects are demonstrated for typical examples-Benard and Taylor-Couette problems-in the context of a new framework. A new type of ghost...
This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The book, unique ...
This book offers a unified presentation that does not discriminate between atmospheric and space flight. It demonstrates that the two disciplines have evolved from the same set of physical principles and introduces a broad range of critical concepts in an accessible, yet mathematically rigorous presentation.
The book presents many MATLAB and Simulink-based numerical examples and real-world simulations. Replete with illustrations, end-of-chapter exercises, and selected solutions, the work is primarily useful as a textbook for advanced undergraduate and beginning graduate-level students.
This book offers a unified presentation that does not discriminate between atmospheric and space flight. It demonstrates that the two disciplines h...
This volume aims to provide an overview of some recent developments of mathematical kinetic theory focused on its application in modelling complex systems in various ?elds of applied sciences. Mathematical kinetic theory is essentially based on the Boltzmann eq- tion, which describes the evolution, possibly far from equilibrium, of a class of particles modelled as point masses. The equation de?nes the evolution in time and space of the distribution function over the possible microscopic states of the test particle, classically position and velocity. The test particle is subject to pair...
This volume aims to provide an overview of some recent developments of mathematical kinetic theory focused on its application in modelling complex sys...
Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a variety of mathematical problems. These include wave motion models, hydrodynamic models of vehicular traffic flow, convection-diffusion models, reaction-diffusion models, and population dynamics models. The book may be used as a textbook for graduate courses on collocation methods, nonlinear modeling, and nonlinear differential equations....
Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important ...
This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention. The complexity of modeling living matter requires the development of new mathematical methods and ideas. This volume, written by first-rate researchers in the field of mathematical biology, is one of the first steps in that...
This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing ...
In the context of network theory, Complex networks can be de?ned as a collection of nodes connected by edges representing various complex int- actions among the nodes. Almost any large-scale system, be it natural or man-made, can be viewed as a complex network of interacting entities, which is dynamically evolving over time. Naturally occurring networks include - ological, ecological and social networks (e. g., metabolic networks, gene r- ulatory networks, protein interaction networks, signaling networks, epidemic networks, food webs, scienti?c collaboration networks and acquaintance n-...
In the context of network theory, Complex networks can be de?ned as a collection of nodes connected by edges representing various complex int- actions...
One of the main goals of optimal control theory is to provide a theoretical basis for choosing an appropriate controller for whatever system is under consideration by the researcher or engineer. Two popular norms that have proved useful are known as H-2 and H - infinity control. The first has been particularly applicable to problems arising in the aerospace industry. However, most industrial problems are badly modeled and the second norm proved to be more appropriate when the actual conditions of the problem did not conform to the stipulated conditions of the theory. This book takes the...
One of the main goals of optimal control theory is to provide a theoretical basis for choosing an appropriate controller for whatever system is und...
