Related papers: A Lagrangian perspective on nonautonomous advectio…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…
Energetic particle redistribution in the presence of multiple Alfv\'en eigenmodes is analyzed in [PPCF 58, 014019 (2016)] for the ITER 15MA baseline scenario: non-linear hybrid simulations (within their well known limits) point out that…
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…
We compute the Hamiltonian and Lagrangian associated to the large deviations of the trajectory of the empirical distribution for independent Markov processes, and of the empirical measure for translation invariant interacting Markov…
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field…
This work is devoted to radiative transfer equations with long-range interactions. Such equations arise in the modeling of high frequency wave propagation in random media with long-range dependence. In the regime we consider, the singular…
This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…
We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations…
A semi-Lagrangian Characteristic Mapping method for the solution of the tracer transport equations on the sphere is presented. The method solves for the solution operator of the equations by approximating the inverse of the diffeomorphism…
We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We…
We study the asymptotics of solutions of logistic type equations with fractional Laplacian as time goes to infinity and as the exponent in nonlinear part goes to infinity. We prove strong convergence of solutions in the energy space and…
One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are…
We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it…
We consider time-dependent convection-diffusion problems with high P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in thin three-dimensional graph-like networks consisting of cylinders that are interconnected by small domains…
We develop the theory of discrete time Lagrangian mechanics on Lie groups, originated in the work of Veselov and Moser, and the theory of Lagrangian reduction in the discrete time setting. The results thus obtained are applied to the…
This paper explores the asymptotic properties of non-autonomous Lagrangian systems, assuming that the associated Tonelli Lagrangian converges to a time-periodic function. Specifically, given a continuous initial condition, we provide a…
We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…
We establish a dimension-free, uniform-in-time reverse transportation inequality for Langevin dynamics with non-convex potentials. This inequality controls the R\'enyi divergence of arbitrary order between the process distributions starting…