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Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
The method of moments is widely used for the reduction of kinetic equations into fluid models. It consists in extracting the moments of the kinetic equation with respect to a velocity variable, but the resulting system is a priori…
We study the Renyi entropy in the finite temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground state entropy has characteristic features such as a logarithmic divergence with block size and $2\kF$…
A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during…
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating…
Quantum angular moment transport schemes are an important avenue toward describing neutrino flavor mixing phenomena in dense astrophysical environments such as supernovae and merging neutron stars. Successful implementation will require new…
We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…
Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…
We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At mean-field level this approach is consistent with the…
In this paper, we extend the reinterpreted discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal,…
The tube model is a central concept in polymer physics, and allows to reduce the complex many-filament problem of an entangled polymer solution to a single filament description. We investigate the probability distribution function of…
We introduce and study a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term for closed immersed planar curves. We first classify all closed stationary solutions, showing that they are precisely circles…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
We present a one-equation subgrid scale model that evolves the turbulence energy corresponding to unresolved velocity fluctuations in large eddy simulations. The model is derived in the context of the Germano consistent decomposition of the…
We study perturbation theory and uniform ergodicity for discrete-time Markov chains on general state spaces in terms of the uniform moments of the first hitting times on some set. The methods we adopt are different from previous ones. For…