Related papers: The stochastic relativistic advection diffusion eq…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
This work presents the mathematical and computational aspects of a smooth dissipative particle dynamics with dynamic virtual particle allocation method (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains. The…
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction…
Starting with the relativistic Boltzmann equation where the collision term is generalized to include nonlocal effects via gradients of the phase-space distribution function, and using Grad's 14-moment approximation for the distribution…
The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded)…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…
Relativistic fluid dynamics finds application in astrophysics, cosmology and the physics of high-energy heavy-ion collisions. In this thesis, we present our work on the formulation of relativistic dissipative fluid dynamics within the…
Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most…
The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or…
We consider the Random Walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. It is well known (see Roberts et al. (Ann. Appl. Probab. 7…
Focusing on the numerical aspects and accuracy we study a class of bulk viscosity driven expansion scenarios using the relativistic Navier-Stokes and truncated Israel-Stewart form of the equations of relativistic dissipative fluids in 1+1…
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…