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We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
Molecular communication (MC), one of the emerging techniques in the field of communication, is entering a new phase following several decades of foundational research. Recently, attention has shifted toward MC in liquid media, particularly…
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
Molecular communication (MC) enables cooperation of spatially dispersed molecular robots through the feedback control mediated by diffusing signal molecules. However, conventional analysis frameworks for the MC channels mostly consider the…
A new semi-analytical solution to the advection-dispersion-reaction equation for modelling solute transport in layered porous media is derived using the Laplace transform. Our solution approach involves introducing unknown functions…
Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
Understanding the transport behavior of quantum many-body systems constitutes an important physical endeavor, both experimentally and theoretically. While a reliable classification into normal and anomalous dynamics is known to be…
The relationship between the spatiotemporal distribution of oxygen transport and blood flow dynamics, accounting for the motion and deformation of individual red blood cells (RBCs), is of fundamental importance for understanding…
Microfluidic multipoles (MFMs) have been realized experimentally and hold promise for "open-space" biological and chemical surface processing. Whereas convective flow can readily be predicted using hydraulic-electrical analogies, the design…
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 relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time towards a thermal equilibrium limit, is derived from nonequilibrium-statistical considerations: Adapting an…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the…
Recently, molecular communication (MC) has been studied as a micro-scale communication between cells or molecular robots. In previous works, the MC channels in unbounded environment was analyzed. However, many of the experimentally…
In many biological and small scale technological applications particles may transiently bind to a cylindrical surface. In between two binding events the particles diffuse in the bulk, thus producing an effective translation on the cylinder…