Related papers: Time averages and periodic attractors at high Rayl…
We establish rigorous upper bounds on the time-averaged heat transport for a model of rotating Rayleigh-Benard convection between no-slip boundaries at infinite Prandtl number and with Ekman pumping. The analysis is based on the…
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…
We consider the kinetic transport equation that arise in the Boltzmann-Grad limit of the two-dimensional periodic Lorentz Gas. This equation has been obtained by extending the phase space of positions and velocities through the introduction…
We investigate the existence of periodic solutions for a class of nonlocal continuity equations, which include mean-field equations derived from systems of coupled oscillators. While periodic solutions at the particle level have been…
We consider a family of non-autonomous reaction-diffusion equations with almost periodic, rapidly oscillating principal part and nonlinear interactions. As the frequency of the oscillations tends to infinity, we prove that the solutions of…
Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the…
A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories,…
One of the most remarkable features of known nonstationary solutions to the incompressible Euler equations is the phenomenon known as the Taylor hypothesis, which predicts that coarse scale averages of the velocity carry the fine scale…
We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative…
Upper bounds on time-averaged heat transport are obtained for an eight-mode Galerkin truncation of Rayleigh's 1916 model of natural thermal convection. Bounds for the ODE model---an extension of Lorenz's three-ODE system---are derived by…
We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories.…
For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such…
Bounds for the poloidal and toroidal kinetic energies and the heat transport are computed numerically for rotating convection at infinite Prandtl number with both no slip and stress free boundaries. The constraints invoked in this…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…
The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical…
In many physical situations in which many-body assemblies exist at temperature $T$, a characteristic quantum-mechanical time scale of approximately $\hbar/k_{B}T$ can be identified in both theory and experiment, leading to speculation that…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic…
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic…