Related papers: Perturbed minimizing movements of families of func…
The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple,…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
In many cases, groundwater flow in an unconfined aquifer can be simplified to a one-dimensional Sturm-Liouville model of the form: \begin{equation*} x''(t)+\lambda x(t)=h(t)+\varepsilon f(x(t)),\hspace{.1in}t\in(0,\pi) \end{equation*}…
We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
Three very different algorithms have been proposed for solution of the Rayleigh-Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow, which serve to complete…
We compute the $\Gamma$-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal…
In this paper we study the motion of a fluid with several dispersed particles whose concentration is very small (smaller than $10^{-3}$), with possible applications to problems coming from geophysics, meteorology, and oceanography. We…
In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
In recent years, asymptotic approximation schemes have been developed to describe the motion of a small compact object through a vacuum background to any order in perturbation theory. The schemes are based on rigorous methods of matched…
A particle moves randomly over the integer points of the real line. Jumps of the particle outside the membrane (a fixed "locally perturbating set") are i.i.d., have zero mean and finite variance, whereas jumps of the particle from the…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
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…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
This paper presents a minimum flow approach applicable to a wide range of doubly nonlinear diffusion problems. We introduce a minimum flow steepest descent algorithm that seeks an optimal traffic flow by minimizing an internal energy…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
This chapter describes how gradient flows and nonlinear power methods in Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how convergence of (discretized) approximations can be verified. We review…