Nonlinearity: Problems, Solutions, Applications

Contents......Page 7
Preface......Page 11
Section I. Differential Equations, Numerical Methods, Algorithms and Solutions......Page 13
Computational Methods for Two-Dimensional Neural Fields......Page 15
Abstract......Page 45
Statement of the Problem and Kinetic Equation......Page 46
Analysis of Results......Page 53
References......Page 54
Abstract......Page 57
Introduction: the Brioschi Identity and the 16-Spinor Field Model......Page 58
Interaction with Physical Vector Fields......Page 62
Solitons and the Stochastic Representation of Quantum Mechanics......Page 63
Leptonic Axially-Symmetric Configurations......Page 70
Conclusion......Page 72
References......Page 73
Abstract......Page 75
Introduction......Page 76
Statement of the Problem and Mathematical Model......Page 77
Results and Discussion......Page 82
Conclusion......Page 84
References......Page 85
Abstract......Page 87
Introduction......Page 88
Scalar Inequalities......Page 96
Systems of Inequalities......Page 103
Conclusion......Page 111
References......Page 112
Abstract......Page 115
Introduction......Page 116
Equation of Two Bodies’ Orbital Link Motion with Aero-Gradient Dissipative Factors......Page 117
Limit Cycles in a Cylindrical Phase Space......Page 120
Analysis of the Model and Results of the Computer Simulation......Page 121
Conclusion......Page 124
References......Page 125
Abstract......Page 127
2. Semilinear Elliptic Inequalities......Page 128
3. Quasilinear Elliptic Inequalities......Page 130
4. Systems of Quasilinear Ellipticine Qualities......Page 132
5. Parabolic Inequalities......Page 138
Acknowledgments......Page 141
References......Page 142
Abstract......Page 143
Introduction......Page 144
Sufficient Conditions of Stability for Delay TS Systems......Page 146
Examples......Page 154
Conclusion......Page 160
References......Page 161
Abstract......Page 163
Introduction......Page 164
Fourier matrix integral transforms on the real axis......Page 165
Fourier matrix integral sin - transforms on the real semi-axis......Page 167
Fourier matrix integral cos –transform on the real semi-axis......Page 168
General Fourier matrix integral transforms on the real semi-axis......Page 169
Fourier matrix integral transforms on the composite real axis......Page 170
Vector wave equation on the real axis. Generalization of d'Alembert formula......Page 172
Vector equation of heat and mass transfer on the real axis......Page 174
Vector equation of heat and mass transfer on the two-layer real axis......Page 175
Dirichlet vector problem for the Laplace system of equations......Page 177
Dirichlet vector problem for the Laplace equation on a two-layer half-plane......Page 179
References......Page 180
Abstract......Page 183
Introduction......Page 184
Differential Equations not Containing Explicitly Desired Function......Page 185
Autonomous Differential Equation (not Containing Explicitly Independent Variable)......Page 187
Equations Homogeneous in Relation to......Page 189
Differential Equations, Homogeneous in Relation to Independent Variable......Page 195
Differential Equations Homogeneous with Respect to Two Variables......Page 198
Generalized Homogeneous Differential Equations......Page 200
Application......Page 208
References......Page 210
Section II. Kinetics, Dynamics and Thermochemistry of Micro-, Meso- and Macro-Scale Systems......Page 213
Abstract......Page 215
Spinability of Polymer Solution......Page 216
Hydrodynamics of Electrospinning......Page 217
Initial State of Entangled Semi-Dilute Polymer Solution......Page 219
Stretching of Polymer Topological Network in Initial Stage of Electrospinning......Page 220
Disentanglement of Polymer Topological Network in the Further Stages of Electrospinning......Page 225
Instabilities of Spinning Jet......Page 227
Polymer Solution Solidification and Fiber Formation......Page 232
Post-Relaxation of the Polymer Matrix......Page 234
Conclusion......Page 238
References......Page 239
Abstract......Page 245
Introduction......Page 246
Problem Statement of Structural Identification Nonlinear Systems......Page 248
Approach to Identification of Class Nonlinearities......Page 249
Formation of Set......Page 250
Frameworks ,......Page 251
About Properties . Structural Identifiability of System (3)......Page 253
Estimation of Nonlinearity Class......Page 259
Estimation of Nonlinearity Structure......Page 261
Class......Page 262
Class......Page 264
SFA and Its Application......Page 265
Frameworks in Identification Systems of Linear Dynamic Systems......Page 270
Problem Statement......Page 271
LE. Coefficient of Structural Properties......Page 272
Frameworks for Estimation LE......Page 274
Decision-Making about Type of Roots......Page 275
Procedure of Definition LE......Page 276
Structural Methods in Identification Systems of Nonlinear Static Systems......Page 280
Conclusion......Page 281
References......Page 283
Abstract......Page 287
Introduction......Page 288
Wigner’s Equation......Page 289
Wigner’s Equation Solution......Page 291
Electric Current in Quantum Plasma......Page 293
Longitudinal Current in Quantum Plasma......Page 294
Wave Number Small Values......Page 298
References......Page 299
Abstract......Page 303
Introduction......Page 304
The Governing Equations of the Proposed Model......Page 308
Models of Dynamic Interaction “Wheel - Rail”......Page 313
Numerical Investigation......Page 314
Conclusion......Page 315
References......Page 316
Abstract......Page 319
Introduction......Page 320
Layout Production......Page 321
Conclusion......Page 326
References......Page 327
Abstract......Page 329
Introduction......Page 330
Formulation of the Problem......Page 331
Temperature Fields Outside and Inside the Particle......Page 336
Solution of the Hydrodynamic Problem......Page 338
Determination of the Photophoretic Force and Velocity. Analysis of the Obtained Results......Page 340
Conclusion......Page 344
References......Page 345
Abstract......Page 347
Introduction......Page 348
Coherent Structures and Coherent Turbulence......Page 350
Properties of Single Coherent Structures......Page 352
Properties of the Mixtures (Sums) of Various Coherent Structures......Page 354
Software......Page 358
Hardware......Page 359
Experiment and Simulation......Page 360
Large Altazimuth Telescope (BTA) Dome......Page 362
Boundary Value Problem......Page 363
Experiment and Simulation......Page 364
Boundary Value Problem......Page 365
Simulation......Page 366
Simulation......Page 367
Boundary Value Problem......Page 368
Simulation......Page 369
Parietal Turbulence (The Thermals)......Page 370
Conclusion to Section 2......Page 372
Section 3. Structure of Air Motions on the Optical Paths Inside Specialized Rooms of Astronomical Telescopes. Numerical Simulation......Page 374
Boundary Value Problem......Page 375
Simulation......Page 376
Spectral Analysis......Page 377
Boundary Value Problem......Page 378
Simulation......Page 381
Spectral Analysis......Page 384
Boundary Value Problem......Page 385
Simulation......Page 386
Evolution of Convective Cells......Page 390
Spectral Analysis......Page 391
Conclusion to Section 3......Page 392
Boundary Value Problem......Page 393
Spectral Analysis......Page 394
Spectral Analysis......Page 395
Boundary Value Problem......Page 396
Spectral Analysis......Page 397
Modeling......Page 398
Spectral Analysis......Page 400
Modeling......Page 401
Spectral Analysis......Page 402
Comparison with Experiment......Page 403
Conclusion to Section 4......Page 404
Experiment......Page 405
Simulation......Page 407
Boundary Value Problem......Page 408
The Airflows and the Convective Cells......Page 410
Spectral Analysis......Page 411
Conclusion......Page 412
Acknowledgments......Page 416
References......Page 417
Abstract......Page 425
Introduction......Page 426
Problem Statement......Page 427
Modeling Processes at Boundary......Page 430
References......Page 438
Scalar chiral model......Page 441
Ripple on Graphene Surface......Page 444
Carbon Nano-Tubes......Page 445
Spinor Chiral Model of Graphene......Page 446
Interaction with Magnetic Field Orthogonal to Graphene Plane......Page 450
References......Page 454
Abstract......Page 459
Statement of the Problem......Page 460
Thermophoretic Force and Velocity......Page 461
Analysis of Obtained Results......Page 464
Conclusion......Page 466
References......Page 467
Abstract......Page 469
Introduction......Page 470
Problem Definition......Page 471
Derivation of Formulas Describing Thermophoresis......Page 472
The Findings Analysis......Page 476
References......Page 478
Abstract......Page 481
Introduction......Page 482
Description of Methods for Constructing the Structure-Property Models......Page 483
Some Examples of Applications of Suggested Methods......Page 484
References......Page 490
Abstract......Page 493
Introduction......Page 494
The Rules of Construction of Hk-Models by Structural Formula of Molecules......Page 497
The Relations between Adjacency Matrices of G- and Hk-Models......Page 503
Local Vertex Invariants of Graphs and Hypergraphs and Comparison of Their Capacities to Distinguish Non-Equivalent Vertices in Molecular Graph G......Page 504
Codes of Graphs and Hypergraphs Based on LVI, and Comparison of Their Degeneration Degrees......Page 505
Some Invariants of Graphs and Hypergraphs Defined by Their Adjacency Matrices and Comparison of Their Degeneration Degrees......Page 506
Conclusion......Page 507
References......Page 508
Abstract......Page 511
Introduction......Page 512
Statement of the Problem and Its Solution......Page 513
Conclusion......Page 525
References......Page 528
Abstract......Page 531
Heat Transfer in the System of Spherical Particles......Page 532
The Class Number 1......Page 542
The Class Number 2......Page 543
Interaction of Electromagnetic Radiation with Two Non-Uniform Cylindrical Particles......Page 544
Systems of Uniform Cylinders with Various Values of Complex Dielectric Permittivity of Substance of a Particle......Page 545
Systems of Non-Uniform on Structure Cylinders......Page 547
About Holding of Computational Experiments on Heat Transfer in the Collective of Disperse Particles......Page 550
References......Page 551
Abstract......Page 555
Introduction......Page 556
Mathematical Model......Page 557
Statement of Model Problem......Page 562
Supercomputer Tests......Page 564
Simulation Results......Page 565
References......Page 567
About the Editors......Page 569
Index......Page 573
Blank Page......Page 2