6 papers
A Convergent Reaction-Drift-Diffusion Master Equation with Interaction Potentials
Max Heldman, Samuel A. Isaacson
We extend the convergent reaction-diffusion master equation (CRDME) framework on unstructured grids to include two-body interaction potentials between particles. Such interactions…
A monotone finite element method for reaction-drift-diffusion equations with discontinuous reaction coefficients
Max Heldman
We prove an abstract convergence result for a family of dual-mesh based quadrature rules on tensor products of simplical meshes. In the context of the multilinear tensor-product fi…
Mean field limits of particle-based stochastic reaction-drift-diffusion models
Max Heldman, Samuel A. Isaacson, Qianhan Liu +1
We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics…
Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker-Planck-Boltzmann Model
Johann Rudi, Max Heldman, Emil M. Constantinescu +2
In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker-Planck operator for small-angle Coulomb collisions, a radiation damping operat…
Importance Sampling for the Empirical Measure of Weakly Interacting Diffusions
Zachary Bezemek, Max Heldman
We construct an importance sampling method for computing statistics related to rare events for weakly interacting diffusions. Standard Monte Carlo methods behave exponentially poor…
Fluctuation analysis for particle-based stochastic reaction-diffusion models
Max Heldman, Samuel Isaacson, Jingwei Ma +1
Recent works have derived and proven the large-population mean-field limit for several classes of particle-based stochastic reaction-diffusion (PBSRD) models. These limits correspo…