Related papers: On diffusion in narrow random channels
Within the domain of molecular communications, researchers mimic the techniques in nature to come up with alternative communication methods for collaborating nanomachines. This work investigates the channel transfer function for molecular…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated, that the process of liquid spreading in this type of porous materials at low saturation can be…
A contour dynamics model for electrical discharges is obtained and analyzed. The model is deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion.…
Motion prediction is a challenging problem in autonomous driving as it demands the system to comprehend stochastic dynamics and the multi-modal nature of real-world agent interactions. Diffusion models have recently risen to prominence, and…
In this paper we study an asymptotic expansion for the distribution of a random motion of a particle driven by a Markov process in diffusion approximation. We show that the singularly perturbed equation of a Markovian random motion can be…
We consider random walks on quasi one dimensional lattices, as introduced in \cite{FS}. This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general…
Anomalously slow passive diffusion, $\langle \delta x^2(t)\rangle\simeq t^{\alpha}$, with $0<\alpha<1$, of larger tracers such as messenger RNA and endogenous submicron granules in the cytoplasm of living biological cells has been…
A hopping model for molecular motors is presented consisting of a state with asymmetric hopping rates with period 2 and a state with uniform hopping rates. State changes lead to a stationary unidirectional current of a particle. The current…
We propose a general variance reduction strategy for diffusion processes. Our approach does not require the knowledge of the measure that is sampled, which may indeed be unknown as for nonequilibrium dynamics in statistical physics. We show…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
In this paper, a diffusion-based molecular communication channel between two nano-machines is considered. The effect of the amount of memory on performance is characterized, and a simple memory-limited decoder is proposed and its…
We present a study of sound wave propagation in a time dependent random medium and an application to imaging. The medium is modeled by small temporal and spatial random fluctuations in the wave speed and density, and it moves due to an…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
In this paper, we shall establish the spreading speed and existence of traveling waves for a non-cooperative system arising from epidermal wound healing and characterize the spreading speed as the slowest speed of a family of non-constant…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, molecular dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks, confined to long, narrow,…
In this letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
Intracellular components explore the cytoplasm via active motor-driven transport in conjunction with passive diffusion. We model the motion of organelles in narrow tubular cells using analytical techniques and numerical simulations to study…