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Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or…
We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized…
Absorbing boundary condition approach to nuclear breakup reactions is investigated. A key ingredient of the method is an absorbing potential outside the physical area, which simulates the outgoing boundary condition for scattered waves.…
We present a novel immersed boundary method that implements acoustic perturbation theory to model an acoustically levitated droplet. Instead of resolving sound waves numerically, our hybrid method solves acoustic scattering…
Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. This…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
Acting in cluttered environments requires predicting and avoiding collisions while still achieving precise control. Conventional optimization-based controllers can enforce physical constraints, but they struggle to produce feasible…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
We describe an immersed boundary method in which the fluid-structure coupling is achieved in an Eulerian framework. The method is an improved extension of the immersed boundary method originally developed by Kajishima et al. [1], which…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
We analyse the self-diffusiophoresis of a spherical particle animated by a nonuniform chemical reaction at its boundary. We consider two models of solute absorption, one with a specified distribution of interfacial solute flux, and one…