Related papers: Multidimensional decay in van der Corput lemma

The aim of this paper is to apply direct methods to the study of integrals that appear naturally in Statistical Mechanics and Euclidean Field Theory. We provide weighted estimates leading to the exponential decay of the two-point…

We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…

We call a function "constructible" if it has a globally subanalytic domain and can be expressed as a sum of products of globally subanalytic functions and logarithms of positively-valued globally subanalytic functions. Our main theorem…

We study the energy decay rate of the Kelvin-Voigt damped wave equation with piecewise smooth damping on the multi-dimensional domain. Under suitable geometric assumptions on the support of the damping, we obtain the optimal polynomial…

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…

In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6]. A key purpose of this work is to determine when such…

The author's modified Coulomb damping model has been generalized to accommodate internal friction that derives from several dissipation mechanisms acting simultaneously. Because of its fundamental nonlinear nature, internal friction damping…

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…

We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different…

Many discrete models of biological networks rely exclusively on Boolean variables and many tools and theorems are available for analysis of strictly Boolean models. However, multilevel variables are often required to account for threshold…

Hamiltonian dynamics describing conservative systems naturally preserves the standard notion of phase-space volume, a result known as the Liouville's theorem which is central to the formulation of classical statistical mechanics. In this…

The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…

We quantize the ModMax oscillator, which is the dimensional reduction of the Modified Maxwell theory to one spacetime dimension. We show that the propagator of the ModMax oscillator satisfies a differential equation related to the Laplace…

We give the p-adic and F_q((t)) analogue of the real van der Corput Lemma, where the real condition of sufficient smoothness for the phase is replaced by the condition that the phase is a convergent power series. This van der Corput style…

Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In particular, under mild assumptions on the…

In structural dynamics, energy dissipative mechanisms with non-viscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary…

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase.…