Related papers: Coarse-graining a restricted solid-on-solid model

Granular systems confined in a shallow box and driven by vertical vibration provide a simple geometry to study fluidized granular media. Grains gain kinetic energy vertically through collisions with the walls and redistribute it…

Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…

Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity…

The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic…

We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…

In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the non-negativity of the solution, conserves the mass and, as the discretization parameters tend to zero,…

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…

Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of…

We present an algebraic method for constructing a highly effective coarse grid correction to accelerate domain decomposition. The coarse problem is constructed from the original matrix and a small set of input vectors that span a low-degree…

We introduce a general framework for deriving effective dynamics from arbitrary time-dependent generators, based on a systematic operator cumulant expansion. Unlike traditional approaches, which typically assume periodic or adiabatic…

Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into…

The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…

Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the…

We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…

We give a proof of the strong existence and the regularity of stochastic differential equations driven by a Brownian motion and a measurable, Markovian drift without no regularity hypothesis except that the Girsanov exponential associated…

Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…

Bottom-up coarse-grained molecular dynamics models are parameterized using complex effective Hamiltonians. These models are typically optimized to approximate high dimensional data from atomistic simulations. In contrast, human validation…

To develop, calibrate and/or validate continuum models from experimental or numerical data, micro-macro transition methods are required. These methods are used to obtain the continuum fields (such as density, momentum, stress) from the…