Related papers: Brakke's inequality for the thresholding scheme

The kinetic energy of barotropic flow coupled to an infnitely massive rotating sphere by an unresolved complex torque mechanism is approximated by a discrete spin-lattice model of fluid vorticity on a rotating sphere, analogous to a…

We make a consistent derivation, from the governing equations, of the pressure transfer function in the small-amplitude Stokes wave regime and the hydrostatic approximation in the small-amplitude solitary water wave regime, in the presence…

We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix…

This is a contribution to the program of dynamical approach to mean curvature flow initiated by Colding and Minicozzi. In this paper, we prove two main theorems. The first one is local in nature and the second one is global. In this first…

We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the…

We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into…

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this…

We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly…

Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…

We study a stochastically perturbed mean curvature flow for graphs in $\mathbb{R}^3$ over the two-dimensional unit-cube subject to periodic boundary conditions. In particular, we establish the existence of a weak martingale solution. The…

In this paper, we first present a Gearhardt-Pr\"uss type theorem with a sharp bound for m-accretive operators. Then we give two applications: (1) give a simple proof of the result proved by Constantin et al. on relaxation enhancement…

We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. Our model of the blood flow network consists of a bifurcating tree, into which we introduce particles (emboli) that halt flow on…

There is evidence that taking the time average of the work performed by a thermally isolated system effectively "transforms" the adiabatic process into an isothermal one. This approach allows inherent quantities of adiabatic processes to be…

This paper establishes the convergence of a time-steeping scheme for time fractional diffusion problems with nonsmooth data. We first analyze the regularity of the model problem with nonsmooth data, and then prove that the time-steeping…

We prove a quantitative convergence result of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow. The proof uses gradient flow calibrations and the relative entropy method, which has been used in the recent…

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…

We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of…

We develop further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors. The theory leads to optimal estimates in the form of concentration comparison inequalities for both elliptic…

The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity…