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Author: Luisa Arlotti
Publisher: World Scientific
ISBN: 9789812385604
Category : Mathematics
Languages : en
Pages : 224
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Book Description
This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.
Author: Luisa Arlotti
Publisher: World Scientific
ISBN: 9789812385604
Category : Mathematics
Languages : en
Pages : 224
Get Book Here
Book Description
This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.
Author: Nicola Bellomo
Publisher: Springer Science & Business Media
ISBN: 1461205131
Category : Mathematics
Languages : en
Pages : 429
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Book Description
Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis. Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations. An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications. This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process. Topics and Features: * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinetic traffic-flow models * Models of granular media * Large communication networks * Thorough discussion of numerical simulations of Boltzmann equation This new book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers, and postgraduates will find the book a modern and authoritative guide to the topic.
Author: Alberto d'Onofrio
Publisher: Springer
ISBN: 1493904582
Category : Mathematics
Languages : en
Pages : 336
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Book Description
With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways. Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways. Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.
Author: Nicola Bellomo
Publisher: World Scientific
ISBN: 9814494259
Category : Mathematics
Languages : en
Pages : 355
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Book Description
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 book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.
Author: Mario Primicerio
Publisher: World Scientific
ISBN: 9814480126
Category : Mathematics
Languages : en
Pages : 609
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Book Description
Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in Italy in particular, are becoming increasingly aware of this new trend and are engaged in bridging the gap between highly specialized mathematical research and the emerging demand for innovation from industry. In this respect, the contributions in this volume provide both R&D workers in industry with a general view of existing skills, and academics with state-of-the-art applications of mathematics to real-world problems, which may also be incorporated in advanced courses.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Author: Serge Autexier
Publisher: Springer
ISBN: 3642141285
Category : Mathematics
Languages : en
Pages : 485
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Book Description
This book constitutes the joint refereed proceedings of the 10th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2010, the 17th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2010, and the 9th International Conference on Mathematical Knowledge Management, MKM 2010. All submissions passed through a rigorous review process. From the 25 papers submitted to AISC 2010, 9 were selected for presentation at the conference and inclusion in the proceedings volume. A total of 14 papers were submitted to Calculemus, of which 7 were accepted. MKM 2010 received 27 submissions, of which 16 were accepted for presentation and publication. The events focused on the use of AI techniques within symbolic computation and the application of symbolic computation to AI problem solving; the combination of computer algebra systems and automated deduction systems; and mathematical knowledge management, respectively.
Author: Pierluigi Colli
Publisher: World Scientific
ISBN: 9812566503
Category : Mathematics
Languages : en
Pages : 321
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Book Description
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity.The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area.This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.
Author: Fabio Ancona
Publisher: World Scientific
ISBN: 9812776079
Category : Mathematics
Languages : en
Pages : 377
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Book Description
The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.
Author: Berardino D'acunto
Publisher: World Scientific Publishing Company
ISBN: 9813106417
Category : Mathematics
Languages : en
Pages : 300
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Book Description
This book provides a good introduction to modern computational methods for Partial Differential Equations in Mechanics. Finite-difference methods for parabolic, hyperbolic as well as elliptic partial differential equations are discussed.A gradual and inductive approach to the numerical concepts has been used, such that the presentation of the theory is easily accessible to upper-level undergraduate and graduate students. Special attention has been given to the applications, with many examples and exercises provided along with solutions. For each type of equation, physical models are carefully derived and presented in full details.Windows programs developed in C++ language have been included in the accompanying CD-ROM. These programs can be easily modified to solve different problems, and the reader is encouraged to take full advantage of the innovative features of this powerful development tool.
Author: Pierre Del Moral
Publisher: Springer Science & Business Media
ISBN: 1468493930
Category : Mathematics
Languages : en
Pages : 567
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Book Description
This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.
