Related papers: Dynamic Transition and Pattern Formation for Chemo…
Transition of molecular hydrogen to atomic ionized state with increase of temperature and pressure poses still unresolved problems for experimental methods and theory. Here we analyze the dynamics of this transition and show its…
A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between…
Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the…
We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional traps across the thermal crossover from an amorphous solid- to liquid-like behaviors. While static correlations, that…
We investigate the numerical discretization of a two-stream kinetic system with an internal state, such system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level.…
We develop and analyze numerical methods for a stochastic Keller-Segel system perturbed by Stratonovich noise, which models chemotactic behavior under randomly fluctuating environmental conditions. The proposed fully discrete scheme couples…
Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation, and vascular tumors provide a focus on optimization strategies. Experiments can characterize…
In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows only for…
In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for…
We use molecular-dynamics computer simulations to study the translational and reorientational dynamics of a glass-forming liquid of dumbbells. For sufficiently elongated molecules the standard strong steric hindrance scenario for the…
Fluctuations in thermal many-particle systems reflect fundamental dynamical processes in both equilibrium and nonequilibrium (NEQ) physics. In NEQ systems \cite{ritort} fluctuations are important in a variety of contexts ranging from…
We study the critical phenomena of the dynamical transition from a metastable state to a stable state in the model of first-order phase transition via two different triggering mechanisms. Three universal stages during the fully nonlinear…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…
We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbour two-dimensional lattice system with spin variables taking values in -1,0,+1. We consider large but finite volume, small fixed magnetic field…
The paper investigates influence of the Le Chatelier response on the chemical system behavior under stress, the shape of its domains of states in terms of static and dynamic bifurcation diagrams, and the system proneness to evolution. The…
Interest in the dynamical arrest leading to a fluid --> solid transition in thermal and athermal systems has led to questions about the nature of these transitions. These jamming transitions may be dependent on the influence of extended…
Soft modulated phases have been shown to undergo complex morphological transitions, in which layer remodeling induced by mean and Gaussian curvatures plays a major role. This is the case in smectic films under thermal treatment, where focal…
The Keller-Segel partial differential equation is a two-dimensional model for chemotaxis. When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity $\chi$ of bacteria to the…