Related papers: Analytical Investigation of Long-time Diffusion Dy…
Channels are fundamental building blocks from biophysics to soft robotics, often used to transport or separate solutes. As solute particles inevitably transverse between streamlines along the channel by molecular diffusion, the effective…
We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose of this work is to identify when solutions decay to…
This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…
We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
Information theory provides powerful tools for understanding communication systems. This analysis can be applied to intercellular signal transduction, which is a means of chemical communication among cells and microbes. We discuss how to…
Molecular communication (MC) is a communication paradigm in which information is conveyed through the controlled release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside…
Intercellular signaling has an important role in organism development, but not all communication occurs using the same mechanism. Here, we analyze the energy efficiency of intercellular signaling by two canonical mechanisms: diffusion of…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard…
Recent Brain-Machine Interfaces have shifted towards miniature devices that are constructed from nanoscale components. While these devices can be implanted into the brain, their functionalities can be limited, and will require communication…
We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one…
Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion…
We present a study of the spatial correlation functions of a one-dimensional reaction-diffusion system in both equilibrium and out of equilibrium. For the numerical simulations we have employed the Gillespie algorithm dividing the system in…
Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
Using extensive Brownian dynamics computer simulations, the long-time self-diffusion coefficient is calculated for Gaussian-core particles as a function of the number density. Both spherical and rod-like particles interacting via Gaussian…
This letter develops a one-dimensional (1D) diffusion-based molecular communication system to analyze channel responses between a single transmitter (TX) and two fully-absorbing receivers (RXs). Incorporating molecular degradation in the…
We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory…
The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this…