Related papers: Perturbed, Entropy-Based Closure for Radiative Tra…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to the presence of holes in the interval, which terminate…
One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class…
A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…
The largest existing simulations of cosmic reionization model radiative transfer with moment methods that require a closure relation. The two most commonly used closure relations are M1 and OTVET; both close the moment hierarchy at the…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
In this work we present two new closures for the spherical harmonics (PN) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard…
High order methods based on diagonal-norm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEs. These methods can also be interpreted as nodal…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
In the research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the…
We implement a high-order numerical scheme for the entropy-based moment closure, the so-called M$_N$ model, for linear kinetic equations in slab geometry. A discontinuous Galerkin (DG) scheme in space along with a strong-stability…
We present a methodology to determine the best turbulence closure for an eddy-permitting ocean model through measurement of the error-landscape of the closure's subgrid spectral transfers and flux. We apply this method to 6 different…
A closed expression is derived for the probability distribution of the transfer matrix of a particle moving in a one-dimensional system with delta-correlated, weak disorder. The change in the distribution as a function of wire length is…
We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\kappa}_v$ which takes the value $j\in \{0,1,2,3\}$ with probability…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on…