This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.

Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the...

Advances in metrology depend on improvements in scientific and technical knowledge and in instrumentation quality, as well as better use of advanced mathematical tools and development of new ones. In this volume, scientists from both the mathematical and the metrological fields exchange their experiences. Industrial sectors, such as instrumentation and software, are likely to benefit from this exchange, since metrology has a high impact on the overall quality of industrial products, and applied mathematics is becoming more and more important in industrial processes.

This book is of interest...

This book constitutes a comprehensive survey of the balance equations for mass, momentum and energy for the interfaces in pure fluids and mixtures. Constitutive laws are presented for many situations in engineering science, and examples are provided, including surface viscosity effects, variable surface tension and vapor recoil. In addition, some extensions of existing theory are given: stretch effect in premixed flames, relaxation zones downstream two-phase shock waves, and effective surface tension for high gradient zones.

This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.

The book presents the new analytical treatment which can serve as the basis of a combined, analytical --...

In August/September 1999, a group of 68 physicists from 48 laboratories in 17 countries met in Erice, Italy, to participate in the 37th Course of the International School of Subnuclear Physics. This volume constitutes the proceedings of that meeting. It focuses on the basic unity of fundamental physics at both the theoretical and the experimental level.

This volume contains 12 papers dealing with the approximation of first- and second-order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume should attract readers involved in the numerical approximation of differential...

The third conference (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field - more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit.

This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and...

This book contains the papers presented at the conference on "Mathematical Models and Methods for Smart Materials, " held in Italy in 2001. The papers are divided into four parts: "Methods in Materials Science" deals mainly with mathematical techniques fo the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems. "Modelling of Smart Materials" is devoted to...

- An application-oriented introduction to computational numerical methods for PDE
- Complete with numerous exercise sets and solutions
- Includes Windows programs in C++ language