Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Mathematical+Modeling+of+Cooling+High-Temperature+Cylindrical+Workpieces

AbstractThe paper presents the results of modeling the process of cooling a cylindrical metal workpiece made of structural steel by a flowing cooling medium. The authors give a mathematical description of their solution for the problem of convective heat exchange that occurs when a longitudinal water flow is used for cooling. The control volume approach has been used for solving the systems of equations. The parameters of the flow field are calculated by the SIMPLE algorithm. The mathematical model factors in the presence of vapor being generated at the boundary between the high-temperature workpiece and the cooling water flow. It uses the effective vapor volume fraction calculated according to the heat-balance equation. The calculation results obtained by using the proposed model are compared to calculations by a mathematical model that uses criterial equations for determining the boundary conditions on the surface of a high-temperature cylindrical work piece in contact with the water flow. The authors discuss cases of cooling metal workpieces with different initial heating temperatures. The results of the numerical calculations of the heat exchange parameters are analyzed with regard to the time of the cooling process as well as in regard to whether the vapor presence on the cylinder surface is or is not taken into account

Noise Enhanced Signaling in STDP Driven Spiking-Neuron Network

Population spike signaling is widely observed both in intact brain and neuronal cultures. Experimental evidence suggests that a locally applied electrical stimulus can shape the network architecture and thus the neuronal response. However, there is no clue on how this process can be controlled. Here we study a realistic model of a culture of cortical-like neurons with spike timing dependent plasticity. We show that a stimulus applied at a corner of the culture can rebuild synaptic couplings. Then the network eventually switches from a turbulent-like asynchronous spiking to an ordered population spike signaling mode. The structural analysis shows that the stimulus potentiates centrifugal couplings, which promotes spiking waves traveling outwards the stimulus location. This phenomenon can be catalyzed by noise of an intermediate strength. We predict that matured cultures with high connectivity are more susceptible to reconfiguration and generation of a population spike response than young cultures with low connectivity. We also report on an intermittent synchronization causing switches between two quasi-stable states: generation of time-locked population spikes and turbulent spiking. In the turbulent mode the stimulus excites patches of spiking activity randomly traveling in the network. Such a regime can be implemented through a large scale looping of couplings backwards to the stimulus location. We anticipate that the robust mechanisms of shaping the network architecture discussed here can also be effective in more complex preparations and studies of the relationship between network structure and function

Phosphorus removal from high-phosphorus hot metal in the converter

[No abstract available