Ebook: Mathematical Modeling: Problems, Methods, Applications

This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: • mathematical and computer discrete systems models; • non-linear excitation in condensed media; • complex systems evolution; • mathematical models in economics; • non-equilibrium processes kinematics; • dynamics and structure of the molecular and biomolecular systems; • mathematical transfer models in non-linear systems; • numerical simulation and algorithms; • turbulence and determined chaos; • chemical physics of polymer. This conference was supported by the Russian Ministry of Education, Russian foundation for Basic Research and Federal Program "Integration". This volume contains the following sections: 1. models of non-linear phenomena in physics; 2. numerical methods and computer simulations; 3. mathematical computer models of discrete systems; 4. mathematical models in economics; 5. non-linear models in chemical physics and physical chemistry; 6. mathematical models of transport processes in complex systems. In Sections One and Five a number of fundamental and sufficiently general problems, concerning real physical and physical-chemical systems simulation, is discussed.

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This book contains review articles and original results in problems and methods of mathematical simulation and their applications in various fields. The articles included are based on the reports that were presented at the Fourth International Mathematical Modeling Conference (Moscow, Russia, June 27 - July 1, 2000). The book is intended for specialists, as well as for post-graduates and students in the areas of mathematical modeling, algorithms and computational theory, mathematical physics, discrete mathematics, physics, physical chemistry, transfer theory, and economics.

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This book contains review articles and original results in problems and methods of mathematical simulation and their applications in various fields. The articles included are based on the reports that were presented at the Fourth International Mathematical Modeling Conference (Moscow, Russia, June 27 - July 1, 2000). The book is intended for specialists, as well as for post-graduates and students in the areas of mathematical modeling, algorithms and computational theory, mathematical physics, discrete mathematics, physics, physical chemistry, transfer theory, and economics.
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Spectral Changes of 1/F Noise in Metals at Clusterization of Light Interstitials....Pages 3-16
Analytic Solutions of Boundary Value Problems for Model Kinetic Equations....Pages 17-24
Mathematical Models in Non-Linear Systems Thermodynamics....Pages 25-36
Critical Opalescence: Models—Experiment....Pages 37-50
Front Matter....Pages 51-51
Methane Combustion Simulation on Multiprocessor Computer Systems....Pages 53-59
Computer Simulation of Structural Modifications in the Metal Samples Irradiated by Pulsed Beams....Pages 61-69
Visualisation of Grand Challenge Data on Distributed Systems....Pages 71-78
Simulation of Electron Transport in Semiconductor Microstructures: Field Emission from Nanotip....Pages 79-89
Reliable Computing Experiment in the Study of Generalized Controllability of Linear Functional Differential Systems....Pages 91-98
Heat Transfer in Disperse Systems of Various Structures and Configurations....Pages 99-111
Front Matter....Pages 113-113
Some New Results in the Theory of Intelligent Systems....Pages 115-119
An Automata Approach to Analysis and Synthesis of Audio and Video Patterns....Pages 121-125
Front Matter....Pages 127-127
A Mathematical Model of Controlling the Portfolio of a Commercial Bank....Pages 129-134
Tutoring Process as Object for Situational Control....Pages 135-139
Front Matter....Pages 141-141
Nonlinear Dynamics of Strongly Non-Homogeneous Chains with Symmetric Characteristics....Pages 143-154
Models of Directed Self-Avoiding Walks and Statistics of Rigid Polymer Molecules....Pages 155-166
Postulate of the Arithmetical Mean and Nonbonded Interactions....Pages 167-174
Quantum—Chemical Models of the Structure and the Functions of the Active Centres of the Polynuclear Complexes....Pages 175-179
Front Matter....Pages 181-181
Asymptotics of Transport Equations for Spherical Geometry in L2 with Reflecting Boundary Conditions....Pages 183-195
Traveling Heat Waves in High Temperature Medium....Pages 197-203
Front Matter....Pages 181-181
Smooth Lyapunov Manifolds and Correct Mathematical Simulation of Nonlinear Singular Problems in Mathematical Physics....Pages 205-217
Computational Methods for the Estimation of the Aerosol Size Distributions....Pages 219-230
Two Disperse Particles in the Field of the Electromagnetic Radiation....Pages 231-243
Transport Processes in Aerodisperse Systems: Transitional Growth of Non-Spherical Particles and Mobility of Ions....Pages 245-254
Solution of Some Non-Linear Problems in the Theory of Heating, Vaporization and Burning of Solid Particles and Drops....Pages 255-266
On the Irreducible Tensors Method in the Theory of Diffusive Interaction between Particles....Pages 267-278
Evaporation and Growth of Single Drops and Finite Array of Interacting Drops of Pure Liquids and Hygroscopic Solutions....Pages 279-290
Back Matter....Pages 291-294

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This book contains review articles and original results in problems and methods of mathematical simulation and their applications in various fields. The articles included are based on the reports that were presented at the Fourth International Mathematical Modeling Conference (Moscow, Russia, June 27 - July 1, 2000). The book is intended for specialists, as well as for post-graduates and students in the areas of mathematical modeling, algorithms and computational theory, mathematical physics, discrete mathematics, physics, physical chemistry, transfer theory, and economics.
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Spectral Changes of 1/F Noise in Metals at Clusterization of Light Interstitials....Pages 3-16
Analytic Solutions of Boundary Value Problems for Model Kinetic Equations....Pages 17-24
Mathematical Models in Non-Linear Systems Thermodynamics....Pages 25-36
Critical Opalescence: Models—Experiment....Pages 37-50
Front Matter....Pages 51-51
Methane Combustion Simulation on Multiprocessor Computer Systems....Pages 53-59
Computer Simulation of Structural Modifications in the Metal Samples Irradiated by Pulsed Beams....Pages 61-69
Visualisation of Grand Challenge Data on Distributed Systems....Pages 71-78
Simulation of Electron Transport in Semiconductor Microstructures: Field Emission from Nanotip....Pages 79-89
Reliable Computing Experiment in the Study of Generalized Controllability of Linear Functional Differential Systems....Pages 91-98
Heat Transfer in Disperse Systems of Various Structures and Configurations....Pages 99-111
Front Matter....Pages 113-113
Some New Results in the Theory of Intelligent Systems....Pages 115-119
An Automata Approach to Analysis and Synthesis of Audio and Video Patterns....Pages 121-125
Front Matter....Pages 127-127
A Mathematical Model of Controlling the Portfolio of a Commercial Bank....Pages 129-134
Tutoring Process as Object for Situational Control....Pages 135-139
Front Matter....Pages 141-141
Nonlinear Dynamics of Strongly Non-Homogeneous Chains with Symmetric Characteristics....Pages 143-154
Models of Directed Self-Avoiding Walks and Statistics of Rigid Polymer Molecules....Pages 155-166
Postulate of the Arithmetical Mean and Nonbonded Interactions....Pages 167-174
Quantum—Chemical Models of the Structure and the Functions of the Active Centres of the Polynuclear Complexes....Pages 175-179
Front Matter....Pages 181-181
Asymptotics of Transport Equations for Spherical Geometry in L2 with Reflecting Boundary Conditions....Pages 183-195
Traveling Heat Waves in High Temperature Medium....Pages 197-203
Front Matter....Pages 181-181
Smooth Lyapunov Manifolds and Correct Mathematical Simulation of Nonlinear Singular Problems in Mathematical Physics....Pages 205-217
Computational Methods for the Estimation of the Aerosol Size Distributions....Pages 219-230
Two Disperse Particles in the Field of the Electromagnetic Radiation....Pages 231-243
Transport Processes in Aerodisperse Systems: Transitional Growth of Non-Spherical Particles and Mobility of Ions....Pages 245-254
Solution of Some Non-Linear Problems in the Theory of Heating, Vaporization and Burning of Solid Particles and Drops....Pages 255-266
On the Irreducible Tensors Method in the Theory of Diffusive Interaction between Particles....Pages 267-278
Evaporation and Growth of Single Drops and Finite Array of Interacting Drops of Pure Liquids and Hygroscopic Solutions....Pages 279-290
Back Matter....Pages 291-294
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