Nonlinearity : Problems, Solutions and Applications, Volume 1

The book has two volumes and consists of forty-four chapters, which are divided into five sections: (i) Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; (ii) theoretical and computational studies dedicated to the physics and chemistry of advanced materials, nanostructured systems and fractal systems; (iii) articles dedicated to non-linear processes in complex biological processes, systems and objects; (iv) theoretical and modeling studies of kinetics, dynamics and thermochemistry of micro-, meso- and macro-scale systems; and (v) multidisciplinary research focused on forecasting, control and management problems.

Table of Contents

Section I. Differential Equations, Numerical Methods, Algorithms and Solutions
Chapter 1 Computational Methods for Two-Dimensional Neural Fields
Chapter 2 Mathematical Simulation of the Heat and Mass Transfer in a Plane Channel with Infinite Parallel Walls under the Action of a Temperature Gradient
Chapter 3 The Hopfions in the Skyrme – Faddeev Spinor Model
Chapter 4 Mathematical Simulation of the Mass Transfer in a Long Rectangular Channel under the Action of a Temperature Gradient
Chapter 5 The Nonexistence of Solutions for Some Elliptic Inequalities and Systems with Variable Exponents and Singular Coefficients on the Boundary
Chapter 6 The Analysis of a Motion Model of Orbital Tether Systems Based on Properties of Limit Cycles
Chapter 7 The Nonexistence of Solutions for Some Nonlinear Inequalities with a Transformed Argument in Bounded Domains
Chapter 8 TS Models and Semidefinite Lyapunov Functions in Stability Analysis of Nonlinear Delay Systems
Chapter 9 Matrix Fourier Integral Transforms for Coupled Mathematical Models
Chapter 10 Some Approaches to the Design of Partial Solutions for Nonlinear Equations of Mathematical Physics
Section II. Kinetics, Dynamics and Thermochemistry of Micro-, Mesoand Macro-Scale Systems
Chapter 11 The Evolution of Polymer Systems During Electrospinning: From a Semi-Dilute Polymer Solution to a Non-Equilibrium State
Chapter 12 Structural Methods of Design Identification Systems
Chapter 13 Non-Linear Longitudinal Current in Quantum Plasma Generated by N Transverse Electromagnetic Waves
Chapter 14 Mathematical Modeling of Railway Track Structure under Changing Rigidity Parameters
Chapter 15 An Experimental Study of the Effects of the Wind on a Metal Bridge Crossing with Two Independent Parallel Spans
Chapter 16 The Photophoretic Motion of Moderately Large Spherical Aerosol Particles with Arbitrary Temperature Differences
Chapter 17 The Evolution of Turbulence Structure over Inhomogeneously Heated Surfaces
Chapter 18 The Computer Simulation of Nonlinear Processes in Gas-Metal Microsystems
Chapter 19 Magnetic Excitations in a Chiral Graphene Model
Chapter 20 Thermophoresis of Non-Uniform Moderately Large Spherical Aerosol Particles
Chapter 21 The Thermophoresis of a Cylindrical Aerosol Particle of Non-Uniform Thermal Conductivity
Chapter 22 On Some Methods of Construction of Nonlinear Structure-Property Relationships for Organic Compounds
Chapter 23 Modeling the Structures of Organic Compounds: From Molecular Graphs to Molecular Hypergraphs
Chapter 24 The Mathematical and Physical Modeling of Distribution Operations in Crimp Conical Shells
Chapter 25 Modeling of Heat Transfer in the System of Small Spherical and Cylinrical Particles under the Action of Elecromagnetic Radiation
Chapter 26 HPC Simulation of Gasdynamic Flows on Macroscopic and Molecular Levels