Related papers: A kinetic chemotaxis model with internal states an…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
In this paper we examine boundary effects in a fractional chemotactic equation derived from a kinetic transport model describing cell movement in response to chemical gradients (chemotaxis). Specifically, we analyze reflecting boundary…
The Kramers problem for quantum fermi-gases with specular - diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers problem the new generalised method of a source of the decision of the boundary problems…
A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base…
We derive transport equations for fermions and bosons in spatially or temporally varying backgrounds with special symmetries, by use of the Schwinger-Keldysh formalism. In a noninteracting theory the coherence information is shown to be…
The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on the 2-dimensional torus exchanging energy among Fourier modes in a \emph{chaotic-like} way. We say…
We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that…
We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding…
We develop the constrained adiabatic trajectory method (CATM) which allows one to solve the time-dependent Schr\"odinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet…
This paper consists in two parts. First we set up a general scheme of local traps in an homogeneous deterministic quantum system. The current of particles caught by the trap is linked to the dynamical behaviour of the trap states. In this…
We study the long-range, long-time behavior of the reactive-telegraph equation and a related reactive-kinetic model. The two problems are equivalent in one spatial dimension. We point out that the reactive-telegraph equation, meant to model…
We propose and investigate general kinetic models %of Boltzmann type with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many…
Chemical kinetics plays an important role in governing the thermal evolution in reactive flows problems. The possible interactions between chemical species increase drastically with the number of species considered in the system. Various…
The temporal dynamics of the quantum Zakharov equations (QZEs) in one spatial dimension, which describes the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is revisited by considering their…
Results are presented for the quench dynamics of a clean and interacting electron system, where the quench involves varying the strength of the attractive interaction along arbitrary quench trajectories. The initial state before the quench…
The article presents new model of equilibrium in open chemical systems suggesting a linear dependence of the reaction shift from equilibrium in presence of the external thermodynamic force. Basic equation of this model contains traditional…
We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle…
The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…
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…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines…