We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along traject ...
Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to impro ...
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an impor ...
Novel generalized Cartesian product rules for the computation of weakly singular integrals, arising in the mixed potential integral equation formulations are presented in this paper. The key feature of the proposed integration schemes lies in the incorpora ...
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We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...