Exact solutions of time-dependent oscillations in multipolar spherical vortices

A class of exact multipolar vortices

A class of exact solutions to the steady Euler equations representing finite area patches of nonuniform vorticity is presented. It is demonstrated that the solutions constitute a special class of steady multipolar vortical structures and have many qualitative similarities with the multipolar equilibria observed in two-dimensional flows at high Reynolds numbers. The results provide insights into...

Exact Solutions to Time-Dependent MDPs

We describe an extension of the Markov decision process model in which a continuous time dimension is incllMcd in the stat(', space. This allows tbr the representation and exact solution of a wide range of prohleins in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Multipolar vortices and algebraic curves

This paper demonstrates that analytical solutions to the steady two-dimensional Euler equations possessing all the qualitative properties of multipolar vortices observed experimentally and numerically can be constructed using the theory of algebraic curves and quadrature domains. The solutions consist of a finite set of line vortices superposed on finite-area patches of uniform vorticity. By wa...

Exact solutions for the flow of a generalized second grade due to a Longitudinal quadratic time-dependent shear stress

Exact solutions of the mKdV equation with time-dependent coefficients

In this paper, we study the time variable coefficient modified Korteweg-de Vries (mKdV) equation from group-theoretic point of view. We obtain Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary variable coefficients. Finally, the solitary ...