Mathematical Models in Natural Science and Engineering

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