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We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the…

Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…

In this paper we provide bound estimates for the two fastest wave speeds emerging from the solution of the Riemann problem for three well-known hyperbolic systems, namely the Euler equations of gas dynamics, the shallow water equations and…

We establish Fourier extension estimates for compact subsets of the hyperbolic hyperboloid in three dimensions via polynomial partitioning.

In this paper we prove semiclassical resolvent estimates for operators with normally hyperbolic trapping which are lossless relative to non-trapping estimates but take place in weaker function spaces. In particular, we obtain non-trapping…

Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=\partial H(x,t)/…

We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…

This paper introduces a new pseudodifferential preconditioner for the Helmholtz equation in variable media with absorption. The pseudodifferential operator is associated with the multiplicative inverse to the symbol of the Helmholtz…

Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…

We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial…

We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting contains the purely nonlocal, as well as the purely local…

In this brief note we present a very simple strategy to investigate dynamical determinants for uniformly hyperbolic systems. The construction builds on the recent introduction of suitable functional spaces which allow to transform simple…

We aim at constructing an analog of the Weyl calculus in an infinite dimensional setting, in which the usual configuration and phase spaces are ultimately replaced by infinite dimensional measure spaces, the so-called abstract Wiener…

We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex…

The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…

Periodic orbit expressions for the density of states lead to spurious results when directly used to calculate quantities of thermodynamic interest. This is because the trace formula is usually valid only for large energies while the…

In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one…

We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…

We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…

We present a new reciprocal space analytical method to cutoff the long range interactions in supercell calculations for systems that are infinite and periodic in 1 or 2 dimensions, extending previous works for finite systems. The proposed…