Mathematical Models in Natural Science and Engineering

✍ Scribed by Juri I. Neimark (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 560
• Series: Foundations of Engineering Mechanics
• Edition: 1
• Category: Library

✦ Synopsis

This book helps the reader become familiar with various mathematical models for mechanical, electrical, physical, atronomical, chemical, biological, ecological, cybernetical and other systems and processes. The models examined are evolutionary models, i.e. the models of time-varying processes known as dynamic systems, such as fluid flow, biological processes, oscillations in mechanical and electromagnetic systems, and social systems. The book shows readers how to identify appropriate situations for modelling, how to address difficulties in creating models, and how to learn what mathematics teaches us about the modelling of dynamical phenomena in our surrounding world.It is interesting for a wide spectrum of readers, students of natural science and engineering, and also for researchers in these fields.

✦ Table of Contents

Front Matter....Pages I-XII
Introduction....Pages 1-3
Dynamical systems....Pages 5-28
Fluid outflow from a vessel....Pages 29-45
Equilibrium and auto-oscillations of fluid level in the vessel with simultaneous inflow and outflow....Pages 47-52
Transitive processes, equilibrium states and auto-oscillations....Pages 53-56
Dynamics of the water surface level in a reservoired hydropower station....Pages 57-63
Energetic model of the heart....Pages 65-68
Soiling a water reservoir with a bay and the Caspian Sea puzzles....Pages 69-82
Exponential processes....Pages 83-95
Dynamics in coexistence of populations....Pages 97-110
Flow biological reactor....Pages 111-115
Mathematical model for the immune response of a living organism to an infectious invasion....Pages 117-125
Mathematical model for the community “Producers — Products — Managers”....Pages 127-139
Linear oscillators....Pages 141-157
Electromechanical analogies. Lagrange-Maxwell equations....Pages 159-172
Galileo-Huygens clock....Pages 173-187
Generator of electric oscillations....Pages 189-196
Soft and hard regimes of exciting auto-oscillations....Pages 197-203
Stochastic oscillator (the “contrary clock”)....Pages 205-216
Instability and auto-oscillations caused by friction....Pages 217-228
Forced oscillations of a linear oscillator....Pages 229-242
Parametric excitation and stabilization....Pages 243-251
Normal oscillations and beatings....Pages 253-259
Stabilizing an inverted pendulum....Pages 261-273
Controlled pendulum and a two-legged pacing....Pages 275-286
Dynamical models for games, teaching and rational behaviour....Pages 287-307
Perceptron and pattern recognition....Pages 309-318
Kepler laws and the two-body problem solved by Newton....Pages 319-335
Distributed dynamical models in mechanics and physics....Pages 337-348
Fundamental solution of the thermal conductivity equation....Pages 349-361
Running waves and the dispersion equation....Pages 363-374
Faraday–Maxwell theory of electromagnetism and the Maxwell–Hertz electromagnetic waves....Pages 375-379
Wave reflection and refraction....Pages 381-385
Standing waves and oscillations of a bounded string....Pages 387-394
Microparticles....Pages 395-422
Space and time....Pages 423-440
Speeding up relativistic microparticles in a cyclotron....Pages 441-446
Mathematics as a language and as an operating system and models....Pages 447-453
Geometrical, physical, analogous, mathematical and imitative types of modelling....Pages 455-466
General scheme of mathematical modelling....Pages 467-470
Models of vibratory tongue driving....Pages 471-477
Fundamental mathematical model of the contemporary science and the theory of oscillations....Pages 479-500
Mathematical model as a fruitful idea of research. The D-partition....Pages 501-510
Idealization, mathematical correctness and reality....Pages 511-529
Dynamical interpretation of the least-square method and global search optimization with use of an adaptive model....Pages 531-537
Theoretical game model of the human society....Pages 539-561
Back Matter....Pages 563-572

✦ Subjects

Theoretical and Applied Mechanics;Computational Intelligence;Mathematical Methods in Physics;Numerical and Computational Physics;Visualization