Related papers: Fickian Insights Using Probability Theory as Logic
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation…
Design and characterisation of capsules is not an easy task owing to the multiple involved preparation factors and parameters. Here, a novel method to characterise capsule membrane permeability to solute molecules by an inverse approach is…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…
We present the arising of the Fick cross-diffusion system of equations for fluid mixtures from the multi-species Boltzmann in a rigorous manner in Sobolev spaces. To this end, we formally show that, in a diffusive scaling, the…
Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in…
We review some recent results concerning the derivation of the diffusion equation and the validation of Fick's law for the microscopic model given by the random Lorentz Gas. These results are achieved by using a linear kinetic equation as…
We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…
A quasiparticle description of various condensed media is a very popular tool in study of their transport and thermodynamic properties. I present here a microscopic theory for the description of diffusion processes in two-component gas of…
Continuous time Feynman-Kac measures on path spaces are central in applied probability, partial differential equation theory, as well as in quantum physics. This article presents a new duality formula between normalized Feynman-Kac…
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of…
Based on Fick's 2nd law the development of moving particle semi-implicit method for predicting diffusion process is proposed in this study
The word-frequency distribution provides the fundamental building blocks that generate discourse in language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information…