Statistical Methods -- Uniform and Correlated Mass Density Fields -- The Power Spectrum and the Classification of Stationary Stochastic Fields -- Fractals -- Multifractals and Mass Distributions -- Applications to Cosmology -- Fluctuations in Standard Cosmological Models: A Real Space View -- Discrete Representation of Fluctuations in Cosmological Models -- Galaxy Surveys: An Introduction to Th…
Statistical Description of Large Systems. Postulates of Statistical Physics -- The Different Statistical Ensembles. General Methods in Statistical Physics -- Thermodynamics and Statistical Physics in Equilibrium -- The Ideal Gas -- Indistinguishability, the Pauli Principle (Quantum Mechanics) -- General Properties of the Quantum Statistics -- Free Fermions Properties -- Elements of Bands Theory…
Basic Information on Capital Markets -- Random Walks in Finance and Physics -- The Black-Scholes Theory of Option Prices -- Scaling in Financial Data and in Physics -- Turbulence and Foreign Exchange Markets -- Derivative Pricing Beyond Black—Scholes -- Microscopic Market Models -- Theory of Stock Exchange Crashes -- Risk Management -- Economic and Regulatory Capital for Financial Institution…
KdV-Class Solitons -- Generalized KdV Equations. NLS and DNLS Equations -- Classic Two- and Three-Dimensional KP Models and Their Applications -- Generalized Two- and Three-Dimensional Models and Their Applications -- Appendices.This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced …
Basic quantities and definitions -- The Boltzmann equation and its properties -- The Chapman-Enskog method -- Moment equations -- Grad’s moment method -- Regularization of Grad equations -- Order of magnitude approach -- Macroscopic transport equations for rarefied gas flows -- Stability and dispersion -- Shock structures -- Boundary value problems.The well known transport laws of Navier-Stok…
Differential equations -- Time invariant systems -- Time varying systems -- Differential inclusions -- Additional properties of strict Liapunov functions -- Monotonicity and generalized derivatives.This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem…
Bifurcation, Chaos and Control -- Chaotic Clocks: A Paradigm for the Evolution of Noise in Machines -- Explorations into the Nonlinear Dynamics of a Single DOF System Coupled to a Wideband Auto-Parametric Vibration Absorber -- Adaptive Partial Observers with Application to Time-Varying Chaotic Systems -- Nonlinear Dynamics of a Heavy Material Particle along a Circle Which Rotates and Optimal Co…
Introduction -- Neural network Wiener models -- Neural network Hammerstein models -- Polynomial Wiener models -- Polynomial Hammerstein models -- Applications.This monograph systematically presents the existing identification methods of nonlinear systems using the block-oriented approach It surveys various known approaches to the identification of Wiener and Hammerstein systems which are applic…
Percolation Theory -- Porous Media Primer for Physicists -- Specific Examples of Critical Path Analysis -- Basic Constitutive Relations for Unsaturated Media -- Pressure Saturation Curves and the Critical Volume Fraction of Percolation -- Applications of the Correlation Length -- Applications of the Cluster Statistics -- Effects of Multi-Scale Heterogeneity.The present monograph presents, for t…
Fundamentals -- Strongly Nonlinear Fokker-Planck Equations -- Free Energy Fokker-Planck Equations -- Free Energy Fokker-Planck Equations with Boltzmann Statistics -- Entropy Fokker-Planck Equations -- General Nonlinear Fokker-Planck Equations -- Epilogue.Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stat…