Related papers: Variational formulas and cocycle solutions for dir…
We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to…
In this paper, we study univariate and planar random motions with variable propagation speeds. We first consider motions with space-varying velocity, which can be reduced to constant-velocity motions by means of suitable nonlinear…
In this paper we consider a two-dimensional model of a copolymer consisting of a random concatenation of hydrophilic and hydrophobic monomers, immersed in a micro-emulsion of random droplets of oil and water. The copolymer interacts with…
Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations…
We study directed last-passage percolation on the planar square lattice whose weights have general distributions, or equivalently, queues in series with general service distributions. Each row of the last passage model has its own randomly…
Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse…
We study the behavior of the elastic polymer, a model of a directed polymer in a continuous Gaussian random environment that is independent in time and correlated in space, as the dimension of the environment is taken to infinity. We give…
We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…
Understanding the complex viscoelastic properties of polymeric liquids remains a challenge in materials science and soft matter physics. Here, we present a simple and computationally efficient criterion for the topological constraints in…
Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. The free boundary in the present context is defined with regard to a…
Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
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…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…
Bead spring models for polymers in solution are nonlinear if either the finite extensibility of the polymer, excluded volume effects or hydrodynamic interactions between polymer segments are taken into account. For such models we use a…