Related papers: Weighted Energy-Dissipation principle for gradient…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in…
Even though electrowetting-on-dielectric (EWOD) is a useful strategy in a wide array of biological and engineering processes with numerous droplet-manipulation applications, there is still a lack of complete theoretical interpretation on…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
In this work, we quantify the time scales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the…
We examine the energy distribution in a three-dimensional model granular system contained in an open cylinder under the influence of gravity. Energy is supplied to the system by a vibrating base. We introduce spatially resolved, partial…
We study the problem of body-force driven shear flows in a plane channel of width l with free-slip boundaries. A mini-max variational problem for upper bounds on the bulk time averaged energy dissipation rate epsilon is derived from the…
A new resolvent-based method is developed to predict the space-time properties of the flow field. To overcome the deterioration of the prediction accuracy with the increasing distance between the measurements and predictions in the…
This paper deals with the dynamics - driven by the gradient flow of negative fractional seminorms - of empirical measures towards equi-spaced ground states. Specifically, we consider periodic empirical measures $\mu$ on the real line that…
We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…
In this paper the variation principles from theoretical physics is considered that would describe the process of routing in computer networks. The total traffic which is currently served on all hops of the route has been chosen as the…
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
We propose a new semi-discretization scheme to approximate nonlinear Fokker-Planck equations, by exploiting the gradient flow structures with respect to the 2-Wasserstein metric. We discretize the underlying state by a finite graph and…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the…
We consider the governing equations for the motion of the inviscid fluids in two moving domains and an evolving surface from an energetic point of view. We employ our energetic variational approaches to derive inviscid multiphase flow…
We introduce a continuum framework for the energetics of particle-size segregation in bidisperse granular flows. Building on continuum segregation equations and a recent segregation flux model, the proposed framework offers general…