Tube model for the elasticity of entangled nematic rubbers

Dense rubbery networks are highly entangled polymer systems, with significant topological restrictions for the mobility of neighbouring chains and crosslinks preventing the reptation constraint release. In a mean-field approach, entanglements are treated within the famous reptation approach, since they effectively confine each individual chain in a tube-like geometry. We apply these classical ideas to calculate the effective rubber-elastic free energy of anisotropic networks, nematic liquid crystal elastomers, and present the first theory of entanglements for such a material. Received 25 June 2001     

Activated drift motion of a classical particle with a dynamical pinning effect

A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of “ageing” effects. The depth of each trap increases with the time elapsed since the particle has fallen into it. The consequences of this dynamical pinning are studied, and velocity-force characteristics are numerically obtained. A special attention is paid to the situation where the particle is pulled with a spring to ensure a finite average velocity. In the low velocity regime, the presence of a broad distribution of trapping times leads to suppression of linear response, replaced by a threshold or by sublinear dynamics. A regime of strong fluctuations is obtained when the particle is driven at intermediate velocities. Received: 12 December 1997 / Accepted: 25 February 1998     

On the 1/D expansion for directed polymers

We present a variational approach for directed polymers in D transversal dimensions which is used to compute the correction to the mean field theory predictions with broken replica symmetry. The trial function is taken to be a symmetrized version of the mean-field solution, which is known to be exact for . We compute the free energy corresponding to that function and show that the finite-D corrections behave like D ^-4/3 . It means that the expansion in powers of 1/D should be used with great care here. We hope that the techniques developed in this note will be useful also in the study of spin glasses. Receveid 19 May 1998     

A model for the enzyme activity in systems with large composition fluctuations. An application to the unusual kinetics of phospholipase A2

A non-equilibrium thermodynamics based model is proposed in order to describe the role of large concentration fluctuations of enzymes, reactants and products in modulating the macroscopic time evolution of chemical kinetics. The encounter probabilities between reactants and enzyme depend on their local concentration. Fluctuations modify the bimolecular encounter probability. Since, in turn, the amplitude of fluctuations depends itself on the instantaneous composition of the reacting mixture, the time-varying chemical composition acts as a positive feedback mechanism for the reactive fluid mixture near the critical temperature for phase separation. The model is applied to rationalize the unusual features of phospholipase kinetics, an enzyme which catalyzes the hydrolisis of membrane forming phospholipids, yielding products which are still soluble in the lipid matrix. A typical feature of the enzyme reaction is the long induction time prior to a ”burst” of activity. This effect is well reproduced by the theory, together with the dependence of the induction time on the exogeneous addition of products or other liposoluble substances, the effects of enzyme and substrate concentration, and the temperature dependence of the enzyme activation. All these properties emerge as a consequence of the coupling between enconter probability and time-varying bilayer heterogeneity. A good qualitative agreement between theoretical results and the available experimental results has been generally found. Received: 25 June 1996 / Revised: 17 April 1997 / Accepted: 26 November 1997     

Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances

In the Nagel-Schreckenberg model of vehicular traffic on single-lane highways vehicles are modelled as particles which hop forward from one site to another on a one dimensional lattice and the inter-particle interactions mimic the manner in which the real vehicles influence each other's motion. In this model the number of empty lattice sites in front of a particle is taken to be a measure of the corresponding distance-headway (DH). The time-headway (TH) is defined as the time interval between the departures (or arrivals) of two successive particles recorded by a detector placed at a fixed position on the model highway. We investigate the effects of spatial inhomogeneities of the highway (static hindrances) on the DH and TH distributions in the steady-state of this model. Received: 2 March 1988 / Revised: 13 April 1998 / Accepted: 17 April 1998     

Low q-moment multifractal analysis of Gold price, Dow Jones Industrial Average and BGL-USD exchange rate

An estimate of the low q-moment values of the assumed multifractal spectrum of Gold price, Dow Jones Industrial Average (DJIA) and Bulgarian Lev - USA Dollar (BGL-USD) exchange rate over a 6 1/2 year time span has been made. The findings can be compared to the analysis made on 23 foreign currency exchange rates by Vandewalle and Ausloos but there is a clear indication of some differences. Comparison to fractional Brownian motion is made. The analysis shows that these three financial data are not likely fractal but rather multifractal indeed. Received 17 October 1998 and Received in final form 2 November 1998     

A simulation study of an asymmetric exclusion model with open and periodic boundaries for parallel dynamics

The effect of jumping rate probability on the phase diagram of an asymmetric exclusion model is studied by numerical simulations. Density, current and velocity of particles are calculated for parallel dynamics. In the open boundaries case for one species of particles (particles 1), a passage from first to second order transition occurs by decreasing the jumping rate. In the periodic boundaries case, by introducing another species of particle (particle 2) which plays the role of obstacle for particles 1, the average velocity of particles 1 increases with increasing the jumping rate for small density. While the average velocity of particle 2 decreases for small and intermediate densities. Received: 21 October 1997     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

Frequency-sensitive stochastic resonance in periodically forced and globally coupled systems

A model of globally coupled bistable systems consisting of two kinds of sites, subject to periodic driving and spatially uncorrelated stochastic force, is investigated. The extended system models the competing process of activators and suppressers. Analytical computations for linear response of the system to the external periodic forcing is carried out. Noise-induced Hopf bifurcation is revealed, and stochastic resonance, sensitively depending on the frequency of the external forcing, is predicted under the Hopf bifurcation condition. Numerical simulations agree with the analytical predictions satisfactorily. Received: 5 September 1997 / Revised: 13 May 1998 / Accepted: 18 May 1998     

Quenching problem of globally coupled bistable stochastic systems with finite size

The transient process of globally coupled bistable systems from an unstable state to metastable state (i.e, quenching process) is studied analytically for small noise intensity. The influences of noise intensity and system size on the system evolution are investigated. The problem of a large number of coupled Langevin equations is reduced to a simple problem of a one-dimensional ordinary differential equation, subject to a white noise with intensity explicitly given. The analytical results are fully confirmed by direct numerical computations. Received: 3 July 1997 / Revised: 4 December 1997 / Accepted: 15 January 1998     

Kinetics of reversible surface crystallization and melting in poly(ethylene oxide): Effect of crystal thickness observed in the dynamic heat capacity

Poly(ethylene oxide) (PEO) in the semi-crystalline state shows a reversible surface crystallization and melting; a temperature decrease leads to a certain crystal thickening, a temperature increase reversely to an expansion of the amorphous intercrystallite layers. Dynamic calorimetry provides a means to investigate the kinetics of the process. The structural rearrangement in the region of the crystalline-amorphous interface can only be accomplished if the chains can slide through the crystallites. One therefore expects the associated time to change with the crystallite thickness. Variations of the crystal thickness of PEO can be achieved by choosing different crystallization temperatures. We studied the effect of the crystal thickness employing temperature-modulated differential scanning calorimetry and heat wave spectroscopy, and by carrying out small-angle X-ray scattering experiments for the structural characterization. The effect of the crystal thickness is clearly observed. Results indicate that the sliding diffusion through the crystallites takes place by helical jumps of whole stems. Data yield the activation energy per unit length of the stems. Received 20 April 2001 and Received in final form 13 August 2001     

Canonically invariant formulation of Langevin and Fokker-Planck equations

We present a canonically invariant form for the generalized Langevin and Fokker-Planck equations. We discuss the role of constants of motion and the construction of conservative stochastic processes. Received : 24 July 1997 / Revised : 30 October 1997 / Accepted : 26 January 1998     

Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model

A Bus Route Model (BRM) can be defined on a one-dimensional lattice, where buses are represented by “particles” that are driven forward from one site to the next with each site representing a bus stop. We replace the random sequential updating rules in an earlier BRM by parallel updating rules. In order to elucidate the connection between the BRM with parallel updating (BRMPU) and the Nagel-Schreckenberg (NaSch) model, we propose two alternative extensions of the NaSch model with space-/time-dependent hopping rates. Approximating the BRMPU as a generalization of the NaSch model, we calculate analytically the steady-state distribution of the time headways (TH) which are defined as the time intervals between the departures (or arrivals) of two successive particles (i.e., buses) recorded by a detector placed at a fixed site (i.e., bus stop) on the model route. We compare these TH distributions with the corresponding results of our computer simulations of the BRMPU, as well as with the data from the simulation of the two extended NaSch models. We also investigate interesting kinetic properties exhibited by the BRMPU during its time evolution from random initial states towards its steady-states. Received 16 December 1999     

Influence of polydispersity on the phase behavior of statistical multiblock copolymers with Schultz-Zimm block molecular weight distributions

In this paper we investigate in a systematic way the influence of polydispersity in the block lengths on the phase behavior of AB-multiblock copolymer melts. As model system we take a polydisperse multiblock copolymer for which both the A-blocks and the B-blocks satisfy a Schultz-Zimm distribution. In the limit of low polydispersity the expressions for the vertex functions are clarified by using simple physical arguments. For various values of the polydispersity the phase diagram is presented, which shows that the region of stability of the bcc phase increases considerably with increasing polydispersity. The strong dependence of the periodicity of the microstructure on the polydispersity and on the interaction strength is presented. Received 2 July 1998     

Stochastic diagrams for critical point spectra

A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an N-dimensional phase-space. These serve as a useful paradigm for describing critical point phase transitions in numerous equilibrium and non-equilibrium systems, ranging from chemistry, physics and biology, to engineering, sociology and economics. The technique consists in developing the stochastic variable as a power series in time, and using this to compute the short time expansion for the correlation functions. This is then extrapolated to large times, and Fourier transformed to obtain the spectrum. Stochastic diagrams are developed to facilitate computation of the coefficients of the relevant power series expansion. Two different types of long-time extrapolation technique, involving either simple exponentials or logarithmic rational approximations, are evaluated for third-order diagrams. The analytical results thus obtained are compared with numerical simulations, together with exact results available in special cases. The agreement is found to be excellent up to and including the neighborhood of the critical point. Exponential extrapolation works especially well even above the critical point at large N values, where the dynamics is one of phase-diffusion in the presence of a spontaneously broken symmetry. This method also enables the calculation of the steady state spectra of polynomial functions of the stochastic variables. In these cases, the final correlations can be non-bistable even above threshold. Here logarithmic rational extrapolation has the greater accuracy of the two extrapolation methods. Stochastic diagrams are also applicable to more general problems involving spatial variation, in addition to temporal variation. Received: 12 January 1998     

Orbital effect of a magnetic field on two-leg Hubbard ladder

By setting up the relevant recursion relations and by doing exact and approximate calculations, we show that there is no critical dimension in a self-avoiding random walk on a simplex fractal. Received: 6 April 1998 / Revised: 4 August 1998 / Accepted: 26 August 1998     

The sharp peak-flat trough pattern and critical speculation

We find empirically a characteristic sharp peak-flat trough pattern in a large set of commodity prices. We argue that the sharp peak structure reflects an endogenous inter-market organization, and that peaks may be seen as local “singularities” resulting from imitation and herding. These findings impose a novel stringent constraint on the construction of models. Received: 2 February 1998 / Revised and accepted: 22 February 1998     

Wealth distributions in asset exchange models

A model for the evolution of the wealth distribution in an economically interacting population is introduced, in which a specified amount of assets are exchanged between two individuals when they interact. The resulting wealth distributions are determined for a variety of exchange rules. For “random” exchange, either individual is equally likely to gain in a trade, while “greedy” exchange, the richer individual gains. When the amount of asset traded is fixed, random exchange leads to a Gaussian wealth distribution, while greedy exchange gives a Fermi-like scaled wealth distribution in the long-time limit. Multiplicative processes are also investigated, where the amount of asset exchanged is a finite fraction of the wealth of one of the traders. For random multiplicative exchange, a steady state occurs, while in greedy multiplicative exchange a continuously evolving power law wealth distribution arises. Received: 13 August 1997 / Revised: 31 December 1997 / Accepted: 26 January 1998     

Mean magnetic field and noise cross-correlation in magnetohydrodynamic turbulence: results from a one-dimensional model

We show that a recently proposed [J. Fleischer, P.H. Diamond, Phys. Rev. E 58, R2709 (1998)] one-dimensional Burgers-like model for magnetohydrodynamics (MHD) is in effect identical to existing models for drifting lines and sedimenting lattices. We use the model to demonstrate, contrary to claims in the literature, that the energy spectrum of MHD turbulence should be independent of mean magnetic field and that cross-correlations between the noise sources for the velocity and magnetic fields cannot change the structure of the equations under renormalisation. We comment on the scaling and the multiscaling properties of the stochastically forced version of the model. Received 29 October 1998 and Received in final form 8 December 1998     

Visualizing the log-periodic pattern before crashes

We present a method for visualizing the pattern which we believe to be a precursor signature of financial crashes (or ruptures). The log-periodicity of the pattern is investigated through the envelope function technique. Three periods of the Dow Jones Industrial Average (DJIA) are investigated: 1982-1987, 1992-1997 and 1993-1998. The presence of a rupture in the end of 1998 is outlined from data taken before the end of August 1998. Received 15 October 1998 and Received in final form 19 November 1998