arXiv subjects

Qianhan Liu

Publications and source records attributed to Qianhan Liu.

3 recordsLinked to original sources

arXiv2026

Mean Field Limits for Stochastic, Underdamped Reactive Langevin Dynamics Models

We rigorously derive the effective large-population, mean-field dynamics of particle-based reactive Langevin dynamics (PBRLD) models. These models extend particle-based stochastic reaction-diffusion (PBSRD) descriptions by incorporating velocities, inertial effects, and underdamped motion. In Isaacson, Liu, Spiliopoulos, and Yao, SIAP 2026, PBRLD models were formulated and shown to recover Doi volume reactivity PBSRD model in the overdamped limit. In this work we prove convergence of the associated measure-valued stochastic processes, representing species concentration fields on position-velocity phase space, to a deterministic mean-field limit. The limiting equations form a novel system of nonlocal kinetic reaction-diffusion partial integro-differential equations, coupling hypoelliptic transport with reaction terms that retain the spatial and velocity structure of the underlying particle interactions.

math.PR↗

arXiv2025

A Macroscopically Consistent Reactive Langevin Dynamics Model

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such models may be inappropriate, necessitating the use of more microscopic Langevin Dynamics models for spatial transport. In this work we develop a novel particle-based Reactive Langevin Dynamics (RLD) model, with a focus on deriving reactive interaction kernels that are consistent with the physical constraint of detailed balance of reactive fluxes at equilibrium. We demonstrate that, to leading order, the overdamped limit of the resulting RLD model corresponds to the volume reactivity PBSRD model, of which the well-known Doi model is a particular instance. Our work provides a step towards systematically deriving PBSRD models from more microscopic reaction models, and suggests possible constraints on the latter to ensure consistency between the two physical scales.

physics.bio-ph↗

arXiv2024

Mean field limits of particle-based stochastic reaction-drift-diffusion models

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 of the particles are formulated as measure-valued stochastic processes (MVSPs), which describe the evolution of the singular, stochastic concentration fields of each chemical species. The mean field large population limit of such models is derived and proven, giving coarse-grained deterministic partial integro-differential equations (PIDEs) for the limiting deterministic concentration fields' dynamics. We generalize previous studies on the mean field limit of models involving only diffusive motion, with care to formulating the MVSP representation to ensure detailed balance of reversible reactions in the presence of potentials. Our work illustrates the more general set of PIDEs that arise in the mean field limit, demonstrating that the limiting macroscopic reactive interaction terms for reversible reactions obtain additional nonlinear concentration-dependent coefficients compared to the purely diffusive case. Numerical studies are presented which illustrate that two-body repulsive potential interactions can have a significant impact on the reaction dynamics, and also demonstrate the empirical numerical convergence of solutions to the PBSRDD model to the derived mean field PIDEs as the population size increases.

math.PR↗