Related papers: A kinetic chemotaxis model with internal states an…
This paper investigates a class of chemotaxis systems modeling lethal interactions in a smooth, bounded domain $\Omega \subset \mathbb{R}^n$ with homogeneous Neumann boundary conditions. We examine two distinct cases: (i) a fully parabolic…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their…
Modeling of turbulent combustion system requires modeling the underlying chemistry and the turbulent flow. Solving both systems simultaneously is computationally prohibitive. Instead, given the difference in scales at which the two…
We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…
We introduce a modeling framework for an urban tram network based on a hyperbolic partial differential equation describing the transport of passengers along the network, coupled with a family of stochastic processes representing passenger…
An exact Quantum Kinetic Monte Carlo method is proposed to calculate electron transport for 1D Fermi Hubbard model. The method is directly formulated in real time and can be applied to extract time dependent dynamics of general interacting…
A thermo-mechanical model describing hydrogen storage by use of metal hydrides has been recently proposed in a paper by Bonetti, Fr\'emond and Lexcellent. It describes the formation of hydrides using the phase transition approach. By virtue…
We study the movement of the living organism in a band form towards the presence of chemical substrates based on a system of partial differential evolution equations. We incorporate Einstein's method of Brownian motion to deduce the…
We present a novel approach to kinetic theory modeling enabling the simulation of a generic, real gas presented by its corresponding equation of state. The model is based on mass, momentum and energy conservation, and unlike the lattice…
Using the formalism of the classical nucleation theory, we derive a novel kinetic equation for the size and composition distribution of an ensemble of aqueous organic aerosols, evolving via nucleation and concomitant chemical aging. This…
We consider two dimensional Keller-Segel equations coupled with the Navier-Stokes equations modelled by Tuval et al.[32]. Assuming that the chemotactic sensitivity and oxygen consumption rate are nondecreasing and differentiable, we prove…
We introduce stochastic models of chemotaxis generalizing the deterministic Keller-Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean's…
This paper aims to determine the initial conditions for quasi-linear hyperbolic equations that include nonlocal elements. We suggest a method where we approximate the solution of the hyperbolic equation by truncating its Fourier series in…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schroedinger equation. We explicitly renounce on any other…
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller-Segel equation and a…
We introduce new lower bounds for the fractional Fisher information. Equipped with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove the global existence of solutions in certain dissipation regimes.
This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at…
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are…