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Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…

The pseudopotential and free energy models are two popular extensions of the lattice Boltzmann method for multiphase flows. Until now, they have been developed apart from each other in the literature. However, important questions about…

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We…

Reaction systems are a computational model inspired by the bio-chemical reactions that happen inside biological cells. They have been and currently are studied for their many nice theoretical properties. They are also a useful modeling tool…

A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…

We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distributions functions of the original system as accurately as possible. We consider standard…

The problem of the insensitivity of the macroscopic behavior of any thermodynamical system to partitioning generates a bias between the reproducibility of its macroscopic behavior viewed as the simplest form of causality and its long-term…

We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…

We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating a probability measure-valued process. In order to establish a bridge between microscopic and macroscopic behaviors,…

A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to…

Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogues, transformations between distinct metastable states in active matter proceed through rare…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

Thermal transport through nanosystems is central to numerous processes in chemistry, material sciences, electrical and mechanical engineering, with classical molecular dynamics as the key simulation tool. Here we focus on thermal junctions…

The lattice Boltzmann method has become a standard technique for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular…

Transition pathways of stochastic dynamical systems are typically approximated by instantons. Here we show, using a dynamical system containing two competing pathways, that at low-to-intermediate temperatures, instantons can fail to capture…

Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…

Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…

Increasing shares of fluctuating renewable energy sources induce higher and higher power flow variability at the transmission level. The question arises as to what extent existing networks can absorb additional fluctuating power injection…

A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…

In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying…