A constructive approach to steady nonlinear kinetic equations

A New Analytical Approach to Flight Equations

The six-degree equations of flight in their classic form do not provide a proper physical perception due to a number of interferences. Nor do they render visible the important role of attack angles. In this study, attempts have been made to develop a complete set of 3D acceleration equations from the equations of normal and tangential acceleration αN=vωv, αt=v ̇. For this purpose, a coordinate s...

A New Analytical Approach to Flight Equations

The six-degree equations of flight in their classic form do not provide a proper physical perception due to a number of interferences. Nor do they render visible the important role of attack angles. In this study, attempts have been made to develop a complete set of 3D acceleration equations from the equations of normal and tangential acceleration αN=vωv, αt=v ̇. For this purpose, a coordinate s...

Nonlinear stochastic equations with calculable steady states.

We consider generalizations of the Kardar-Parisi-Zhang equation that accommodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and nonperturbative properties. In particular, we derive generalized fluctuation-dissipation conditions on the form of the (nonlinear) equations for the realization of a Gaussian probability density of the fields in the ...

Nonlinear Markov processes and kinetic equations

On the Master-Equation Approach to Kinetic Theory: Linear and Nonlinear Fokker-Planck Equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one nonlinear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac’s propagation-of-chaos limit. The linear Fokker-Planck equations are well known, but here they are derived as a limit N ! 1 of a simple linear diffusion equation on 3N-C-dimensiona...