Related papers: Average balance equations, scale dependence, and e…
Many biological systems and artificial structures are ramified, and present a high geometric complexity. In this work, we propose a space-averaged model of branched systems for conservation laws. From a one-dimensional description of the…
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
Current theories of heteropolymers are inherently macrpscopic, but are applied to folding proteins which are only mesoscopic. In these theories, one computes the averaged free energy over sequences, always assuming that it is self-averaging…
We prove the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multi-point correlation functions in a simple particle model characterized by slow non-equilibrium…
We study the appearance of large-scale dynamical heterogeneities in a simplified model of a driven, dissipative granular system. Simulations of steady-state gravity-driven flows of inelastically colliding hard disks show the formation of…
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
We study the behavior of the energy fluctuations in the stationary state of a uniformly heated granular gas. The equation for the one-time two-particle correlation function is derived and the hydrodynamic eigenvalues are identified.…
We consider the averaging process on the discrete $d$-dimensional torus. On this graph, the process is known to converge to equilibrium on diffusive timescales, not exhibiting cutoff. In this work, we refine this picture in two ways.…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
We analyze the main features of granular shear flow through experimental measurements in a Couette geometry and a comparison to a locally Newtonian, continuum model of granular flow. The model is based on earlier hydrodynamic models,…
We present theoretical calculations of the ensemble-averaged (a.k.a. effective or coherent) wavefield propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that…
Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive…
In this paper, we study Brinkman's equations with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by an SDE. The particle dynamics can be…
One essential question in material sciences is how to bridge the gap between the microscopic picture and a macroscopic description. The former involves contact forces and deformations, whereas the latter concerns tensorial quantities like…
A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
We present a general and model-independent method to obtain an effective Markovian quantum kinetic equation for the expectation value of a slowly evolving scalar field in an adiabatically evolving background from first principles of…
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…