A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

Kauffman networks with threshold functions

We investigate Threshold Random Boolean Networks with K = 2 inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks should be critical but it turns out that they show a rich variety of behaviors, including periodic and chaotic oscillations. The analytical results are supported by computer simulations.     

Nonlinear excitations and electric transport in dissipative Morse-Toda lattices

We investigate the onset and maintenance of nonlinear soliton-like excitations in chains of atoms with Morse interactions at rather high densities, where the exponential repulsion dominates. First we discuss the atomic interactions and approximate the Morse potential by an effective Toda potential with adapted density-dependent parameters. Then we study several mechanisms to generate and stabilize the soliton-like excitations: (i) External forcing: we shake the masses periodically, mimicking a piezoelectric-like excitation, and delay subsequent damping by thermal excitation; (ii) heating, quenching and active friction: we heat up the system to a relatively high temperature Gaussian distribution, then quench to a low temperature, and subsequently stabilize by active friction. Finally, we assume that the atoms in the chain are ionized with free electrons able to move along the lattice. We show that the nonlinear soliton-like excitations running on the chain interact with the electrons. They influence their motion in the presence of an external field creating dynamic bound states (“solectrons”, etc.). We show that these bound states can move very fast and create extra current. The soliton-induced contribution to the current is constant, field-independent for a significant range of values when approaching the zero-field value.     

Landau expansion for a metamagnetic model

We performed a detailed Landau expansion of the free energy for a metamagnetic model considering terms up to twelfth order. We obtained explicit expressions for the coefficients as a function of the temperature and the ratio between ferro- and antiferromagnetic interactions. We showed that a naive analysis based on the signs of these coefficients cannot always give us sufficient guarantee about the correctness of the phase diagram of the model. In these cases it is necessary to resort to the full expression of the free energy in order to characterize the nature of the phase transition. Received 28 November 2001     

Reaction-diffusion system with self-organized critical behavior

We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general mechanism to generate self-organized criticality in conserving systems. Extensive simulations in d = 2 and 3 reveal critical exponents compatible with the universality class of the stochastic Manna sandpile model. Received 16 November 2000     

Self-organized branching process for a one-dimensional rice-pile model

A self-organized branching process is introduced to describe one-dimensional rice-pile model with stochastic topplings. Although the branching processes are generally expected to describe well high-dimensional systems, our modification highlights some of the peculiarities present in one dimension. We find analytically that the crossover behavior from the trivial one-dimensional BTW behaviour to self-organized criticality is characterised by a power-law distribution of avalanches. The finite-size effects, which are crucial to the crossover, are calculated. Received 21 June 2001 and Received in final form 14 November 2001     

Dilational rheology of monolayers of a miscible polymer blend: From good- to poor-solvent conditions

The viscoelastic moduli (elasticity and dilational viscosity) of monolayers of PVAc + P4HS has been studied over a broad frequency range (0.1 mHz-200 kHz) using a combination of relaxation and capillary-waves techniques. The analysis of the surface pressure, the elasticity and the viscosity on the semidilute regime show that the air-water interface is a good solvent for the monolayers of PVAc-rich blends, and a poor (near-Θ) solvent for the monolayers of P4HS-rich blends. The solvent quality changes continuously over a broad concentration range. The results of viscoelastic moduli show that there is a broad relaxation process in the low-frequency range ( ω < 1 Hz). While for PVAc-rich monolayers this relaxation process follows the reptation-like behavior described by Noskov, for P4HS-rich monolayers the model does not describe the amplitudes of the different relaxation modes. For PVAc-rich monolayers two processes are clearly distinguished at higher frequencies: one centered at around 500 Hz and another one at around 40 kHz. However, for P4HS-rich monolayers only one broad relaxation mode is found below 1 kHz. The crossover from one type of behavior to the other one takes place in a very narrow blend-composition range, and is not clearly related to the crossover from good- to poor-solvent condition. Received 7 June 2002 and Received in final form 5 November 2002 RID="a" ID="a"Current address: Complex Fluids Lab., Cranbury Res. Ctr., Rhodia Inc., Cranbury, NJ 08512-7500, USA. RID="b" ID="b"e-mail: rgrubio@quim.ucm.es     

A simple model of DNA denaturation and mutually avoiding walks statistics

Recently Garel, Monthus and Orland [Europhys. Lett. 55, 132 (2001)] considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition. Received 8 July 2002 / Received in final form 25 July 2002 Published online 17 September 2002     

Chaotic temperature dependence in a model of spin glasses

We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies of these states. We find that this model exhibits strong, weak or no temperature chaos depending on the value of an exponent. This allows us to write a general criterion for temperature chaos in disordered systems, predicting the presence of temperature chaos in the Sherrington-Kirkpatrick and Edwards-Anderson spin glass models, albeit when the number of spins is large enough. The absence of chaos for smaller systems may justify why it is difficult to observe chaos with current simulations. We also illustrate our findings by studying temperature chaos in the naıve mean field equations for the Edwards-Anderson spin glass. Received 27 March 2002 Published online 19 July 2002     

Effects of random biquadratic couplings in a spin-1 spin-glass model

A spin-1 model, appropriated to study the competition between bilinear (J _ij S _i S _j ) and biquadratic (K _ij S _i ² S _j ²) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins. Received 18 May 1999 and Received in final form 20 October 1999     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Deviations from perfect memory in spin glass temperature cycling experiments

We study the deviations from perfect memory in negative temperature cycle spin glass experiments. It is known that the a.c. susceptibility after the temperature is raised back to its initial value is superimposed to the reference isothermal curve for large enough temperature jumps ΔT (perfect memory). For smaller ΔT, the deviation from this perfect memory has a striking non monotonous behavior: the `memory anomaly' is negative for small ΔT's, becomes positive for intermediate ΔT's, before vanishing for still larger ΔT's. We show that this interesting behavior can be reproduced by simple Random Energy trap models. We discuss an alternative interpretation in terms of droplets and temperature chaos. Received 23 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sasaki@ipno.in2p3.fr     

Simple Landau model of the smectic- A-isotropic phase transition

A simple Landau-type free energy function is presented to describe the smectic-A-isotropic phase transition. Varying the coupling between orientational and positional order parameters, a smectic-A-isotropic or a nematic-isotropic phase transition occurs. Within this model the smectic-A-isotropic phase transition is found to be always more strongly first order than the nematic-isotropic phase transition. The theoretical results are found to be in good agreement with all published experimental results. Received 27 June 2000     

Randomness and a step-like distribution of pile heights in avalanche models

This paper considers a one-parameter family of sand-piles. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean pile height is used to describe the crossover. The height densities corresponding to the models with relaxation of both types approach one another as the parameter increases. Relaxation is supposed to deal with the local losses of grains by a fixed amount. In that case the densities show a step-like behaviour in contrast to the peaked shape found in the models with the local loss of grains down to a fixed level [S. Lübeck, Phys. Rev. E 62, 6149 (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes between the two cases for admissible parameter values.     

Cellular oscillator with a small number of particles

To illustrate complex spatio-temporal effects which are possible in cellular reactions with a small number of particles, we present Monte Carlo simulations of the formation of oscillatory spark-like patterns in a model completely stochastic Ca⁺² oscillator. Our analysis shows that in order to observe such patterns the minimum average number of Ca⁺² ions in the cytosol may be as low as about 50. Received 21 April 2002 / Received in final form 19 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: zhdanov@catalysis.nsk.su     

Paradoxical magnetic cooling in a structural transition model

In contrast to the experimentally widely used isentropic demagnetization process for cooling to ultra-low temperatures we examine a particular classical model system that does not cool, but rather heats up with isentropic demagnetization. This system consists of several magnetite particles in a colloidal suspension, and shows the uncommon behavior of disordering structurally while ordering magnetically in an increasing magnetic field. For a six-particle system, we report an uncommon structural transition from a ring to a chain as a function of magnetic field and temperature. Received 5 September 2000     

Solute effects on the helix-coil transition

We discuss the effects of the solvent composition on the helix-coil transition of a polypeptide chain. We use a simple model to demonstrate that improving the hydrogen-bonding ability of the solvent can make the transition less cooperative, without affecting the transition temperature. This effect is very different from other solvent effects which primarily influence the melting transition rather than the cooperativity. Received 10 December 2001 and Received in final form 22 March 2002     

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     

Persistence distributions in a conserved lattice gas with absorbing states

Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents are determined in two and higher dimensions. The local persistence exponent obeys a scaling relation involving the order parameter exponent of the absorbing phase transition. Furthermore we observe that the global persistence exponent exceeds its local counterpart in all dimensions in contrast to the known persistence behavior in reversible phase transitions. Received 27 August 2001 and Received in final form 15 November 2001