Noise-induced transitions for random versions of Verhulst model

According to the Verhulst model the rate of increase/decrease of a biological population with size x(t) at time t is equal to the sum of $\rho x\left(t\right)$ and $-x{(t)}^2$, where $\rho \in \mathbb{R}$ is a constant. The constant ρ is positive and negative for favorable and hostile environments, respectively. The limitation of resources is quantified by the term $-x{(t)}^2$. We examine random versions of the Verhulst model obtained by replacing ρ with $(\rho +\mathrm{white}\mathrm{noise})$. Gaussian (GWN) and Poisson (PWN) white noise processes are considered. The state X(t) of the random Verhulst model satisfies stochastic differential equations driven by Gaussian and Poisson white noises. Our objective is to identify noise-induced transitions, that is, noise levels at which the stationary density of X(t) exhibits qualitative changes. It is shown that noise levels causing transitions under Poisson white noise approach those under Gaussian white noise as the frequency of Poisson jumps increases indefinitely while their size approaches zero.     

Noise-induced coherence in an excitable system with frequency-dependent feedback

The influence of the properties of an excitable system on the characteristics of the coherence resonance effect have been studied by experimental and numerical methods. The transition from monostable to bistable regime is accompanied by the appearance of a false maximum in the regularity parameter of the power spectrum plotted as a function of the noise intensity. An increase in the dimensionality of the system activates a mechanism whereby the noise reveals oscillatory dynamics, also resulting in the appearance of an additional maximum in the regularity parameter.     

Particle size distribution in a coagulating dusty plasma

A modified version of the classical coagulation theory in the diffusion approximation is used to study some anomalies in the behavior of the particle size distribution function. It is established that unlike a normal aerosol, in a dusty plasma the dispersion of the distribution and the average particle size may decrease with time. Pis’ma Zh. Tekh. Fiz. 25, 89–95 (August 12, 1999)     

Computational model of nonequilibrium phase transitions in a Si-Ge system

A computational model of a Si-Ge system melting and solidification induced by pulsed-laser irradiation is presented in the paper. Phase transitions in the system are modeled using the theory of transition states so that undercooling or overheating of the interface and kinetic phase diagrams are taken into account. The computational solution of the mathematical model is performed using the Galerkin finite element method in a one-dimensional approximation and the moving boundary problem is solved by a front-fixing technique. In a practical application of the model, the melting and solidification of both Si-Ge alloys of various composition and thin Ge layers on the Si bulk induced by ArF excimer laser are simulated. The results of numerical simulations are compared with the available experimental data.     

Gelation versus liquid crystal phase transitions in suspensions of plate-like particles

Gelation is a common effect in aqueous suspensions of charged colloidal clay platelets at concentrations as low as 1 wt%. However, in systems of charged gibbsite [Al(OH)3] platelets, gelation can be delayed to concentrations as high as 50 wt% depending on the ionic strength. We investigated the phase behaviour of this system approaching the state of gelation in the delicate region between attractive and repulsive states that originate from competition between Coulomb repulsion and van der Waals attraction. As a function of the ionic strength, isotropic-nematic, nematic-columnar and isotropic-columnar phase separations were observed. Moreover, compression by gravitational forces allowed us to observe phase separation that is arrested by gelation in the homogeneous suspensions.     

Stochastic transitions in a bistable reaction system on the membrane

Transitions between steady states of a multi-stable stochastic system in the perfectly mixed chemical reactor are possible only because of stochastic switching. In realistic cellular conditions, where diffusion is limited, transitions between steady states can also follow from the propagation of travelling waves. Here, we study the interplay between the two modes of transition for a prototype bistable system of kinase–phosphatase interactions on the plasma membrane. Within microscopic kinetic Monte Carlo simulations on the hexagonal lattice, we observed that for finite diffusion the behaviour of the spatially extended system differs qualitatively from the behaviour of the same system in the well-mixed regime. Even when a small isolated subcompartment remains mostly inactive, the chemical travelling wave may propagate, leading to the activation of a larger compartment. The activating wave can be induced after a small subdomain is activated as a result of a stochastic fluctuation. Such a spontaneous onset of activity is radically more probable in subdomains characterized by slower diffusion. Our results show that a local immobilization of substrates can lead to the global activation of membrane proteins by the mechanism that involves stochastic fluctuations followed by the propagation of a semi-deterministic travelling wave.     

Distinctive features of phase transitions in the formation of nanosized aerosol particles

The influence of a foreign gas on the formation of nanosized particles is investigated theoretically. The influence of heating the particles on the concentration of admixture molecules that are trapped in the process of condensation growth of the particles is considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 264–270, March–April, 2008.     

Noise-induced binary synchronization in nonlinear systems

The phenomenon of noise-induced binary synchronization has been discovered in two independent dynamical systems generating aperiodic binary signals under the action of a common noise source. The presence of a synchronous regime was confirmed by the calculation of Lyapunov exponents for the two systems. The mechanism of development of the noise-induced binary synchronization regime has been found. A relation of the observed regime to binary generalized synchronization is established.

     

Noise-induced parametric oscillations in nonlinear oscillator

The onset of stochastic oscillations in a nonlinear oscillator with a noise-modulated frequency is considered. It is demonstrated that these oscillations are characterized by the existence of an attractor (i.e., are independent of the initial conditions), but do not exhibit the phenomenon of synchronization typical of self-oscillatory systems.     

Kinetics of string-gel formation in a system of dipolar colloidal particles

The formation of string-gels of dipolar colloidal particles is investigated using molecular dynamics simulations. The characteristic gelation time consistently increases as the temperature of the system increases; it also increases as the density of the system increases. This latter result suggests that the gel formation is not a simple nucleation process. In particular, the energy barriers separating the embryonic nuclei from the final phase appear to be lower for the low-density system, suggesting an important entropic contribution.     

Nonequilibrium phase transitions and S-shaped current-voltage characteristics in a model semiconductor-metal system

A model of nonequilibrium phase transition in a semiconductor-metal system was considered using a finite-element method. It is shown that, beginning with a certain fraction of the metal component in the heterophase system, the S-shaped current-voltage characteristics exhibit a change: the system features a hysteresis but possesses no singular points.     

Micro instabilities in a system of particles in silos during filling process

The process of filling a silo with particles is simulated by placing them one-by-one at random locations. A planar problem is considered and the particles are represented by disks. After each disk is placed on the system of disks already in a silo, the distribution of normal and shear stresses is recalculated, and if any shear stress exceeds the predetermined limit, then a slide takes place. It is found that a few particles can be involved in a slide simultaneously representing a micro-avalanche. This physical instability in the system is reflected in the numerical instability associated with sudden topological changes. A Recursive Inverse Matrix Algorithm (RIMA) is implemented to handle such changes. It allows efficient addition/removal of contact interfaces between the particles by updating the inverse matrix of the system rather then generating and solving a system of equations after each topological change. The extent of instabilities is determined numerically using RIMA update algorithm iteratively. As a result of irreversible events taking place during the filling operation, the final stress distribution in a filled silo is loading history-dependent. A numerical example of filling a silo with 500 particles is given as an illustration. Received: 30 May 1998     

About the influence of phase transitions on the angular distribution of particles emerging from a cylindrical channel

The influence of evaporation-condensation processes on the walls of a cylindrical channel on the spatial distribution of a molecular beam emerging from it is investigated. The case is considered when a phase transition is realized on a portion of the channel surface.Academic Scientific Complex A. V. Lykov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No.3, pp. 326–332, September, 1992.     

Surface binding affinity measurements from order transitions of lipid membrane-coated colloidal particles

Lipid bilayers can be assembled onto the surface of colloidal silica particles to form a continuous and fluid supported membrane coating. In this configuration, the collective behavior of the colloidal dispersion is governed by interactions between particles and exhibits a sensitive dependency on chemical features of the membrane surface. Protein binding to membrane surface receptors can trigger macroscopic changes in the colloidal order, which provides a label-free readout of such binding events. Here, the relationship between order in the colloidal dispersion and the surface concentration of bound protein is characterized quantitatively in terms of the radial pair distribution function. Using parallel fluorescence measurements for comparison, we construct a scalar measure of the distribution function that exhibits linear proportionality with surface protein binding. This is used to determine binding affinity based only on observations of the colloidal distribution.     

Calculation of the flow of a polydispersed system of particles

We discuss a model which can be used to compute the velocities and temperatures of solid and liquid particles in the presence of collisions and coagulation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 6, pp. 930–936, December, 1987.     

Noise-induced transition between stationary states of a van der Pol oscillator

It is shown that the white-noise-induced transition between the limiting cycle and state of rest of a van der Pol oscillator has a threshold. The threshold value is directly proportional to the product of the characteristic energy of self-oscillations and the friction coefficient. It is shown that not only self-oscillations, but also external noise, disappear in the state of rest.     

Estimation of contiguity for a monodispersed system of spherical particles

A new stereological method for the estimation of the contiguity (the degree of contact) for the monodispersed system of spherical particles is reported. Since this method is applicable to point-like contacts, the contiguity of ceramic particles can be evaluated in a metal matrix composite in which the contact is assumed to be point. The contiguity is derived from the geometrical calculation of centre-to-centre distance between particles, evaluation of contact, and consideration of the geometrical probability that two particles in contact are cut simultaneously by a test plane. The contiguity can be expressed by either the number of contacts per unit volume or the number of contacts per particle. Applying this method to a model material (Shirasu-balloon/aluminium alloy composite), the interrelations between the change in the contiguity and some physical properties of the material can be accurately explained.     

Shear-induced melting and reentrant positional ordering in a system of spherical particles

Computer simulations of dense systems of soft spheres subjected to a shear flow show not only the phenomena of shear-induced melting—transition from a crytalline to an amorphous state—but, at high shear rates, a second nonequilibrium phase transition to a new positionally ordered state. The particles form strings parallel to the stream lines; the strings, in turn, are arranged in a hexagonal pattern. Simulation data on the rheological properties, non-Newtonian viscosity, shear dilatancy, and stress growth and values for the shear moduli are presented; some theoretical ideas for the explanation of these phenomena are discussed.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.