N. Bellomo's Books

Modeling Complex Living Systems

A Kinetic Theory and Stochastic Game Approach

By: N. Bellomo

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Modeling Complex Living Systems

A Kinetic Theory and Stochastic Game Approach

By: N. Bellomo

Develops different mathematical methods and tools to model living systems. This book presents material that can be used in such real-world applications as immunology, transportation engineering, and economics. It is of interest to those involved in modeling complex social systems and living matter in general.

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Page Count

229

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645101

ISBN 13

9780817645106

Mathematical Topics in Nonlinear Kinetic Theory II

The Enskog Equation

By: N. Bellomo

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Mathematical Topics in Nonlinear Kinetic Theory II

The Enskog Equation

By: N. Bellomo

This book deals with the relevant mathematical aspects related to the kinetic equations for moderately dense gases with particular attention to the Enskog equation.

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Page Count

228

Publisher

World Scientific

Published Date

ISBN 10

9810204477

ISBN 13

9789810204471

Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models

By: N. Bellomo,Mauro Lo Schiavo

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Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models

By: N. Bellomo,Mauro Lo Schiavo

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.

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Page Count

360

Publisher

World Scientific

Published Date

ISBN 10

9810240783

ISBN 13

9789810240783

Nonlinear Stochastic Evolution Problems in Applied Sciences

By: N. Bellomo,Zdzislaw Brzezniak,L.M. de Socio

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Nonlinear Stochastic Evolution Problems in Applied Sciences

By: N. Bellomo,Zdzislaw Brzezniak,L.M. de Socio

This volume deals with the analysis of nonlinear evolution problems described by partial differential equations having random or stochastic parameters. The emphasis throughout is on the actual determination of solutions, rather than on proving the existence of solutions, although mathematical proofs are given when this is necessary from an applications point of view. The content is divided into six chapters. Chapter 1 gives a general presentation of mathematical models in continuum mechanics and a description of the way in which problems are formulated. Chapter 2 deals with the problem of the evolution of an unconstrained system having random space-dependent initial conditions, but which is governed by a deterministic evolution equation. Chapter 3 deals with the initial-boundary value problem for equations with random initial and boundary conditions as well as with random parameters where the randomness is modelled by stochastic separable processes. Chapter 4 is devoted to the initial-boundary value problem for models with additional noise, which obey Ito-type partial differential equations. Chapter 5 is essential devoted to the qualitative and quantitative analysis of the chaotic behaviour of systems in continuum physics. Chapter 6 provides indications on the solution of ill-posed and inverse problems of stochastic type and suggests guidelines for future research. The volume concludes with an Appendix which gives a brief presentation of the theory of stochastic processes. Examples, applications and case studies are given throughout the book and range from those involving simple stochasticity to stochastic illposed problems. For applied mathematicians, engineers and physicists whose work involves solving stochastic problems.

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228

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401118205

ISBN 13

9789401118200

Mathematical Topics in Nonlinear Kinetic Theory

By: N. Bellomo,A. Palczewski,Giuseppe Toscani

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Mathematical Topics in Nonlinear Kinetic Theory

By: N. Bellomo,A. Palczewski,Giuseppe Toscani

This book has the aim of dealing with the Nonlinear evolution problems related to the spatially dependent Boltzmann and Enskog equations.

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248

Publisher

World Scientific

Published Date

ISBN 10

9971507021

ISBN 13

9789971507022

Towards a Mathematical Theory of Complex Biological Systems

By: Carlo Bianca,Concetta Bianca,N. Bellomo

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Towards a Mathematical Theory of Complex Biological Systems

By: Carlo Bianca,Concetta Bianca,N. Bellomo

This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, celular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

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Page Count

227

Publisher

World Scientific

Published Date

ISBN 10

9814340537

ISBN 13

9789814340533

Nonlinear Stochastic Systems in Physics and Mechanics

By: N. Bellomo,Riccardo Riganti

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Nonlinear Stochastic Systems in Physics and Mechanics

By: N. Bellomo,Riccardo Riganti

This book presents the conceptional line which goes from the observation of physical systems to their modeling and analysis by ordinary differential nonlinear stochastic equations.First, the problems of the mathematical modeling of physical systems are developed. These mathematical models are then classified in terms of ordinary differential stochastic equations from which both qualitative and quantitative results are developed.Each one of the various subjects are methods dealt with ends with an application in mathematical physics or in nonlinear mechanics.

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Page Count

268

Publisher

World Scientific

Published Date

ISBN 10

9971502496

ISBN 13

9789971502492

Generalized Collocation Methods

Solutions to Nonlinear Problems

By: Nicola Bellomo,Bertrand Lods,Roberto Revelli,Luca Ridolfi

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Generalized Collocation Methods

Solutions to Nonlinear Problems

By: Nicola Bellomo,Bertrand Lods,Roberto Revelli,Luca Ridolfi

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. Examples and exercises are included in every chapter.

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Page Count

206

Publisher

Springer Science & Business Media

Published Date

ISBN 10

081764525X

ISBN 13

9780817645250

Mathematical Topics in Nonlinear Kinetic Theory II

By: N. Bellomo,M. Lachowicz,J. Polewczak

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Mathematical Topics in Nonlinear Kinetic Theory II

By: N. Bellomo,M. Lachowicz,J. Polewczak

The first volume in a new series apparently incorporates material contained in the first edition (1988). Describes the current methods for analyzing the mathematical aspects of the initial and initial- boundary value problem, in the context of developments of mathematical analysis techniques and of the modelling of dense fluids in the framework of kinetic theory. No subject index. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

224

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9810204485

ISBN 13

9789810204488

A Survey of Models for Tumor-immune System Dynamics

By: John A. Adam,N. Bellomo

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A Survey of Models for Tumor-immune System Dynamics

By: John A. Adam,N. Bellomo

This unique book is a collection of seven interdisciplinary surveys on modeling tumor dynamics and interactions between tumors and immune system. The goal is to provide an accessible, comprehensive report on the field and to help define a framework for future interdisciplinary research activity. Modeling and simulation of general behaviors of immune systems are also discussed. Each survey carefully covers a specialized field and provides a detailed description of the present state-of-the-art in research. The reader will be able to obtain essential information on the methodological approach used and on the models that are categorized and used. The book is an excellent resource and survey for applied mathematicians, mathematical biologists and biologists interested in modeling methods in immunology and related sciences.

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Page Count

344

Publisher

Birkhauser

Published Date

ISBN 10

3764339012

ISBN 13

9783764339012

Book's by N. Bellomo

Modeling Complex Living Systems

Modeling Complex Living Systems

Mathematical Topics in Nonlinear Kinetic Theory II

Mathematical Topics in Nonlinear Kinetic Theory II

Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models

Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models

Nonlinear Stochastic Evolution Problems in Applied Sciences

Nonlinear Stochastic Evolution Problems in Applied Sciences

Mathematical Topics in Nonlinear Kinetic Theory

Mathematical Topics in Nonlinear Kinetic Theory

Towards a Mathematical Theory of Complex Biological Systems

Towards a Mathematical Theory of Complex Biological Systems

Nonlinear Stochastic Systems in Physics and Mechanics

Nonlinear Stochastic Systems in Physics and Mechanics

Generalized Collocation Methods

Generalized Collocation Methods

Mathematical Topics in Nonlinear Kinetic Theory II

Mathematical Topics in Nonlinear Kinetic Theory II

A Survey of Models for Tumor-immune System Dynamics

A Survey of Models for Tumor-immune System Dynamics

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