Nonequilibrium stationary states of harmonic chains with bulk noises

We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.

Nonequilibrium stationary states of a particle in a gravitational field driven by a vibrating surface

Stationary velocity distribution functions are determined for a particle in a gravitational field driven by a vibrating surface in the limit of small dissipation. It is found that the form of the distribution function is sensitive to the mechanism of energy dissipation, inelastic collisions or viscous drag, and also to the form of the amplitude function of the vibrating surface. The velocity distributions obtained analytically are found to be in excellent agreement with the results of computer simulations in the limit of low dissipation. [S0031-9007(99)08898-5].

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Stationary states of fermions in a sign potential with a mixed vector-scalar coupling

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Wannier-function approach to electron states in superlattices under an electric field

Electron quasi-stationary states in a periodic semiconductor superlattice are calculated, as linear combinations of Wannier-Kohn functions, for different values of an electric field applied along the heterostructure. A comparison with an alternative approach, which is based on the localization of quasi-stationary states, is performed. (C) 2004 Elsevier Ltd. All rights reserved.

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

A density functional theory study on CO2 capture and activation by graphene-like boron nitride with boron vacancy

First principle calculations for a hexagonal (graphene-like) boron nitride (g-BN) monolayer sheet in the presence of a boron-atom vacancy show promising properties for capture and activation of carbon dioxide. CO2 is found to decompose to produce an oxygen molecule via an intermediate chemisorption state on the defect g-BN sheet. The three stationary states and two transition states in the reaction pathway are confirmed by minimum energy pathway search and frequency analysis. The values computed for the two energy barriers involved in this catalytic reaction after enthalpy correction indicate that the catalytic reaction should proceed readily at room temperature.

Modelling electronegative complex plasma systems

The control of the generation and assembly of the electronegative plasma-grown particles is discussed. Due to the large number of elementary processes of particle creation and loss, electronegative complex plasmas should be treated as open systems where the stationary states are sustained by various particle creation and loss processes in the plasma bulk, on the walls, and on the dust grain surfaces. To be physically self-consistent, ionization, diffusion, electron attachment, recombination, dust charge variation, and dissipation due to electron and ion elastic collisions with neutrals and fine particles, as well as charging collisions with the dust, must be accounted for.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Ito calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N -> infinity and t -> infinity(t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Evolution of the interfacial tension between polydisperse "immiscible" polymers in the absence and in the presence of a compatibilizer

The interfacial tension sigma between two polyisobutylenes (PIB) of dissimilar polydispersity and two polydisperse samples of poly(dimethylsiloxane) (PDMS) was measured as a function of time by means of a pendent drop apparatus at different temperatures ranging from 30 to 110 degreesC. In addition to three of the four possible binary blends, the time evolution of sigma was also determined for one ternary system, where the PIB phase contained 0.03 wt % of a diblock copolymer poly(isobutylene-b-dimethylsiloxane). The pronounced decrease of sigma with advancing time, observed in all cases, is attributed to the migration of the interfacially active lower molecular weight components of the homopolymers and of the compatibilizer into the interphase. Several days are normally required until a becomes constant. These time independent values are not considered as equilibrium data, but accredited to stationary states. A kinetic model is established for sigma(t), which enables a detailed investigation of the rates of transport of the different migrating species of average molar mass of M.

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.