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The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and…
This paper is concerned with equilibrium configurations of one-dimensional particle system with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness…
This paper develops expansive gradient dynamics in deep neural network-induced mapping spaces. Specifically, we generate tools and concepts for minimizing a class of energy functionals in an abstract Hilbert space setting covering a wide…
We prove that a certain discrete energy for triangulated surfaces, defined in the spirit of discrete differential geometry, converges to the Willmore energy in the sense of $\Gamma$-convergence. Variants of this discrete energy have been…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…
We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…
Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in brittle fracture via Gamma-convergence. The convergence is given in terms of rescaled displacement fields measuring…
Dynamical system analysis of a universe model which contains matter, radiation, and quintessence with exponential potential, $V \!(\phi)=V_{\!o} \, exp(-\alpha \kappa \phi) \,$, is studied in the light of recent observations and the…
Our work deals with the dynamical system analysis of quintessence dark energy scalar field model with exponential potential. A dynamical system analysis has been applied at the background level. Using suitable transformation of variables,…
The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics e.g. of micro- and nano-positioning instruments and devices and their controlled operation. The associated…
The gradient expansion of the kinetic energy functional, when applied for atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the…
We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling…
The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur due to an external energy supply or dissipation effects.…
There is a growing attention given to utilizing Lagrangian and Hamiltonian mechanics with network training in order to incorporate physics into the network. Most commonly, conservative systems are modeled, in which there are no frictional…
In the context of cell motility modelling and more particularly related to the Filament Based Lamelipodium Model [Manhart et al 2015 & 2017], this work deals with a rigorous mathematical proof of convergence between solutions of two…