In this work, the Ligand-Receptor model and the way it affects the message exchange process in a biological nanonetwork are under scrutiny. To this aim, a set of efficient simulation schemes for the effects of the number of receptors and the residence ...

In this paper, a new multi-hop relay algorithm based on three attractants is proposed for the traditional multi-hop relay model. When the nano-machine encounters different attractants, the algorithm allows the nano-machine to choose the direction with a ...

This work proposes a new switching scheme between different chemotactic substances, as a way to affect bacterial movement and to enhance message delivery in biological nanonetworks. By switching between different chemotactic substances release plans, ...

This paper analyzes a finite element scheme for the Keller–Segel chemotaxis model of two-competing-species. A regularized problem of the truncated system has been presented. Then, we obtain some a priori estimates of the regularized solutions by obtaining ...

We derive a thermodynamically consistent model for liquid-solid phase change in sea ice by incorporating a phase sensitive scalar to a classical framework of liquid-solid phase change. The entropy of the scalar is taken relative to the liquid molar ...

A three-component reaction-diffusion system is considered which originates from an extension of the classical May--Nowak model for viral infections to situations in which spatially heterogeneous dynamics need to be accounted for. In accordance with recent ...

We investigate the numerical discretization of a two-stream kinetic system with an internal state; such a system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level. It adds a ...

The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes equations through transport and buoyancy. It is shown that when posed with no-flux/no-flux/Dirichlet boundary conditions in smoothly bounded planar domains and along ...

Biological nanonetworks have unique properties that can be exploited so as to develop relative communication paradigms. The aim of this work is to examine the use of the chemotaxis phenomenon to speed up the delivery of a message by directing bacteria ...

In this paper, we consider the fast numerical solution of an optimal control formulation of the Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the solution of huge-scale saddle point systems to guarantee accurate ...

This work focuses on an extension to the May--Nowak model for virus dynamics, additionally accounting for diffusion in all components and chemotactically directed motion of healthy cells in response to density gradients in the population of infected cells. ...

In this paper we develop a unified approach to study the eventual smoothness and exponential stabilization of global weak solutions of two different chemotaxis systems. One is a Keller--Segel system with consumption of chemo-attractants recently studied ...

In this work, we study a model consisting of a Cahn--Hilliard-type equation for the concentration of tumor cells coupled to a reaction-diffusion-type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip the system with a ...

The existence of generalized global supersolutions with a control upon the total mass is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as a ...

The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Leźvy distribution. This article clarifies the form of biologically relevant model equations. We derive ...

We consider the chemotaxis-fluid system given by $n_{t}+u\cdot\!\nabla n=\Delta n^m-\nabla\!\cdot(n\nabla c)$, $c_{t}+u\cdot\!\nabla c=\Delta c-c+n$, $u_{t}+(u\cdot\nabla)u=\Delta u+\nabla P+n\nabla\phi$, and $\nabla\cdot u=0$, for $x\in\Omega$ and $t>0$, ...

We study the qualitative behavior of solutions to the Cauchy problem of a coupled system in $(p,q)$ of parabolic conservation laws in one space dimension posed on $\mathbb{R}$. This system arises from a Keller--Segel type repulsive model for chemotaxis ...

The purpose of this note is to analyze a two-fluid model which can be understood as a generalization of Keller--Segel type of models for cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a ...

We consider a mathematical model motivated by the studies of coral broadcast spawning in spatial dimensions two and three. We establish the local and global well-posedness of regular solutions for the model. We also prove that the total mass of the egg (...

The article concerns the growth of biofilms made by chemotactical bacteria within a saturated porous media. The increase of a biomass on the surface of the solid matrix changes the porosity and impedes the flow through the pores. By formal periodic ...