Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500 stock index within this framework by direct analysis and by simulation. We f...

Many real time processes have complex, uncertain and nonlinear dynamics. Boilers are nonlinear, time varying, multi-input multi-output (MIMO) systems, whose states generally vary with operating conditions. The major problem in controlling that system is that its drum water pressure and steam flow dynamics include an integrator that results a critically stable behavior. Conventional controller p...

The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

Reduced-order models of the nonlinear Complex Ginzburg-Landau (CGL) equation are computed using a nonlinear generalization of balanced truncation. The method involves Galerkin projection of the nonlinear dynamics onto modes determined by balanced truncation of a linearized system, and is compared to a standard method using projection onto Proper Orthogonal Decomposition (POD) modes computed fro...

An epitaxial thin film can undergo surface instability and break up into discrete islands. The stress field and the interface interaction have profound effects on the dynamics of surface evolution. In this work, we develop a nonlinear evolution equation with a second-order approximation for the stress field and a nonlinear wetting potential for the interface. The equation is solved numerically ...

The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

We investigate the Nonlinear Schrödinger Equation with a timedependent nonlinear coefficient. By means of Painlevé analysis we establish the integrability of a particular case, when the nonlinear coefficient decays with t. The corresponding soliton solution is shown to be of the self-similar kind. We discuss implications of the result to the dynamics of attractive Bose-Einstein condensates unde...

In this paper, we investigate the boundary layer behavior of solutions to the one dimensional Broadwet1 modet of the nonlinear Boltzrnann equation for small mean free path. We consider the analogue of Maxwell’s diffusive and the reflexive boundary conditions. I t is found that even for such a simple model, there are boundary layers due to purely kinetic effects which cannot be detected by the c...

the olefins polymerization process in a slurry reactor is discussed. the reaction rate dynamics was analyzed and the contributions of feed flow, gas-liquid mass transfer, polymerization reaction, and catalyst deactivation were estimated. the propylene solubility in a solvent mixture “heptane” was calculated using soave-redlich-kwong equation of state. these data were then approximated by henry-...