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Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
We present a Multi-Index Quasi-Monte Carlo method for the solution of elliptic partial differential equations with random coefficients. By combining the multi-index sampling idea with randomly shifted rank-1 lattice rules, the algorithm…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the…
A common feature of wall-bounded turbulent particle-laden flows is enhanced particle concentrations in a thin layer near the wall due to a phenomenon known as turbophoresis. Even at relatively low bulk volume fractions, particle-particle…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
Particles confined to a single file, in a narrow quasi-one dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles can begin to pass each other. The…
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem.…
Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response…
Yeh and Hummer's simplified estimation method has often been adopted to obtain diffusion coefficients for solute molecules using molecular dynamic simulation. However, the simplified formula is not necessarily valid when a small basic cell…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
The Kob-Andersen model is a fundamental example of a kinetically constrained lattice gas, that is, an interacting particle system with Kawasaki type dynamics and kinetic constraints. In this model, a particle is allowed to jump when…
Cross-classified data frequently arise in scientific fields such as education, healthcare, and social sciences. A common modeling strategy is to introduce crossed random effects within a regression framework. However, this approach often…
A pseudo ternary diffusion couple technique in a multicomponent system by simplifying the mathematical complications of Onsager formalism is proposed for the estimation of composition dependent values of the interdiffusion coefficients.…
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such…
This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic diffusion equation defined on a domain $D$ such that…