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We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles…
High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
Shocks in astrophysical fluids can generate suprathermal particles by first order (or diffusive) Fermi acceleration. In the test particle regime there is a simple relation between the spectrum of the accelerated particles and the jump…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form…
We describe a new computational method for the numerically stable particle-based simulation of open-boundary flows, including volume conserving chemical reactions. The novel method is validated for the case of heterogeneous catalysis…
Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection…
We consider a controlled second order differential equation which is partially observed with an additional fractional noise. we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of…
Generative flow and diffusion models provide the continuous, multimodal action distributions needed for high-precision robotic policies. However, their reliance on iterative sampling introduces severe inference latency, degrading control…
A three-level explicit time-split MacCormack scheme is proposed for solving the two-dimensional nonlinear reaction-diffusion equations. The computational cost is reduced thank to the splitting and the explicit MacCormack scheme. Under the…
We present a fully adaptive multiresolution scheme for spatially two-dimensional, possibly degenerate reaction-diffusion systems, focusing on combustion models and models of pattern formation and chemotaxis in mathematical biology.…
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure can not be computed exactly. Instead, we insert a well-chosen state…
This paper establishes the convergence of a time-steeping scheme for time fractional diffusion problems with nonsmooth data. We first analyze the regularity of the model problem with nonsmooth data, and then prove that the time-steeping…
We consider suspensions of rigid bodies in a two-dimensional viscous fluid. Even with high-fidelity numerical methods, unphysical contact between particles occurs because of spatial and temporal discretization errors. We apply the method of…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…