Related papers: An Analytical Model for Molecular Communication ov…
Recent advances in diffusion models have shown remarkable potential in the conditional generation of novel molecules. These models can be guided in two ways: (i) explicitly, through additional features representing the condition, or (ii)…
Nonlinear interference is modeled by a time-varying conditionally Gaussian channel. It is shown that approximating this channel with a time-invariant channel imposes considerable loss in the performance of channel decoding. An adaptive…
This paper proposes an effective phase diffusion method to analyze chemical exchange in nuclear magnetic resonance (NMR). The chemical exchange involves spin jumps around different sites where the spin angular frequencies vary, which leads…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional…
We consider molecular communication, with information conveyed in the time of release of molecules. The main contribution of this paper is the development of a theoretical foundation for such a communication system. Specifically, we develop…
We consider anomalous diffusion for molecular communication with a passive receiver. We first consider the probability density function of molecules' location at a given time in a space of arbitrary dimension. The expected number of…
We present a simulation algorithm that accurately propagates a molecule pair using large time steps without the need to invoke the full exact analytical solutions of the Smoluchowski diffusion equation. Because the proposed method only uses…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in weak external fields. The application of…
Molecular communication between biological entities is a new paradigm in communications. Recently, we studied molecular communication between two nodes formed from synthetic bacteria. Due to high randomness in behavior of bacteria, we used…
Compaction in reactive porous media is modelled as a reaction-diffusion process with a moving boundary. Asymptotic analysis is used to find solutions for the coupled nonlinear compaction equations, and a traveling wave solution is obtained…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…
Active transport such as fluid flow is sought in molecular communication to extend coverage, improve reliability, and mitigate interference. Flow models are often over-simplified, assuming one-dimensional diffusion with constant drift.…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…