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We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
This paper proposes a charge-conserving, variational, spatio-temporal discretization for the drift-kinetic Vlasov-Maxwell system, utilizing finite-elements for the electromagnetic fields and the particle-in-cell approach for the Vlasov…
Basing on a new approach to the fundamental conception of the momentum of a variable-mass point, the paper deals with the hyperreactive model of motion. The equations of motion are different in this model from the known…
This paper deals with the analysis of the asymptotic limit toward the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory. After having chosen an appropriate…
Two moment-matching methods for model reduction of linear switched systems (LSSs) are presented. The methods are similar to the Krylov subspace methods used for moment matching for linear systems. The more general one of the two methods, is…
Linear models for the radiative transfer equation have been well developed, while nonlinear models are seldom investigated even for slab geometry due to some essential difficulties. We have proposed a moment model in MPN for slab geometry…
The second moment method has always been an effective tool to lower bound the satisfiability threshold of many random constraint satisfaction problems. However, the calculation is usually hard to carry out and as a result, only some loose…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
We derive a nonlinear moment model for radiative transfer equation in 3D space, using the method to derive the nonlinear moment model for the radiative transfer equation in slab geometry. The resulted 3D HMPN model enjoys a list of…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell's equations under the Lorenz gauge. Our recent work introduced the concept of…
A novel method aimed at a kinetic moments closure for a magnetized plasma with arbitrary collisionality is proposed. The intended first application is to a tokamak edge and scrape-off-layer plasma. The velocity distribution function for…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
A new one-dimensional fluid model for ions in weakly-ionized plasma is proposed. The model differs from the existing ones in two aspects. First, a more accurate approximation of the collision terms in the fluid equations is suggested. For…
We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction…