Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

Generalized Sznajd model for opinion propagation

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule-a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabaacutesi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

Coexistence of interacting opinions in a generalized Sznajd model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

Thermodynamic origin of cooperativity in actomyosin interactions: The coupling of short-range interactions with actin bending stiffness in an Ising-like model

We present Monte Carlo simulations for a molecular motor system found in virtually all eukaryotic cells, the acto-myosin motor system, composed of a group of organic macromolecules. Cell motors were mapped to an Ising-like model, where the interaction field is transmitted through a tropomyosin polymer chain. The presence of Ca(2+) induces tropomyosin to block or unblock binding sites of the myosin motor leading to its activation or deactivation. We used the Metropolis algorithm to find the transient and the equilibrium states of the acto-myosin system composed of solvent, actin, tropomyosin, troponin, Ca(2+), and myosin-S1 at a given temperature, including the spatial configuration of tropomyosin on the actin filament surface. Our model describes the short- and long-range cooperativity during actin-myosin binding which emerges from the bending stiffness of the tropomyosin complex. We found all transition rates between the states only using the interaction energy of the constituents. The agreement between our model and experimental data also supports the recent theory of flexible tropomyosin.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Charged hadron multiplicity fluctuations in Au+Au and Cu+Cu collisions from root S(NN) = 22.5 to 200 GeV

A comprehensive survey of event-by-event fluctuations of charged hadron multiplicity in relativistic heavy ions is presented. The survey covers Au+Au collisions at s(NN)=62.4 and 200 GeV, and Cu+Cu collisions at s(NN)=22.5,62.4, and 200 GeV. Fluctuations are measured as a function of collision centrality, transverse momentum range, and charge sign. After correcting for nondynamical fluctuations due to fluctuations in the collision geometry within a centrality bin, the remaining dynamical fluctuations expressed as the variance normalized by the mean tend to decrease with increasing centrality. The dynamical fluctuations are consistent with or below the expectation from a superposition of participant nucleon-nucleon collisions based upon p+p data, indicating that this dataset does not exhibit evidence of critical behavior in terms of the compressibility of the system. A comparison of the data with a model where hadrons are independently emitted from a number of hadron clusters suggests that the mean number of hadrons per cluster is small in heavy ion collisions.

Frustration and anomalous behavior in the Bell-Lavis model of liquid water

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core,models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

Electronic properties of liquid ammonia: A sequential molecular dynamics/quantum mechanics approach

The electronic properties of liquid ammonia are investigated by a sequential molecular dynamics/quantum mechanics approach. Quantum mechanics calculations for the liquid phase are based on a reparametrized hybrid exchange-correlation functional that reproduces the electronic properties of ammonia clusters [(NH(3))(n); n=1-5]. For these small clusters, electron binding energies based on Green's function or electron propagator theory, coupled cluster with single, double, and perturbative triple excitations, and density functional theory (DFT) are compared. Reparametrized DFT results for the dipole moment, electron binding energies, and electronic density of states of liquid ammonia are reported. The calculated average dipole moment of liquid ammonia (2.05 +/- 0.09 D) corresponds to an increase of 27% compared to the gas phase value and it is 0.23 D above a prediction based on a polarizable model of liquid ammonia [Deng , J. Chem. Phys. 100, 7590 (1994)]. Our estimate for the ionization potential of liquid ammonia is 9.74 +/- 0.73 eV, which is approximately 1.0 eV below the gas phase value for the isolated molecule. The theoretical vertical electron affinity of liquid ammonia is predicted as 0.16 +/- 0.22 eV, in good agreement with the experimental result for the location of the bottom of the conduction band (-V(0)=0.2 eV). Vertical ionization potentials and electron affinities correlate with the total dipole moment of ammonia aggregates. (c) 2008 American Institute of Physics.

Numerical study of a model for nonequilibrium wetting

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

Slavnov-Taylor identities for the 2+1 dimensional noncommutative CPN-1 model

In the context of the 1/N expansion, the validity of the Slavnov-Taylor identity relating three- and two-point functions for the 2 + 1-dimensional noncommutative CP(N-1) model is investigated, up to subleading 1/N order, in the Landau gauge.

Coleman-Weinberg mechanism in a three-dimensional supersymmetric Chern-Simons-matter model

Using the superfield formalism, we study the dynamical breaking of gauge symmetry and super-conformal invariance in the N = 1 three-dimensional supersymmetric Chern-Simons model, coupled to a complex scalar superfield with a quartic self-coupling. This is an analogue of the conformally invariant Coleman-Weinberg model in four spacetime dimensions. We show that a mass for the gauge and matter superfields are dynamically generated after two-loop corrections to the effective superpotential. We also discuss the N = 2 extension of our work, showing that the Coleman-Weinberg mechanism in such model is not feasible, because it is incompatible with perturbation theory.

Field theory model for dark matter and dark energy in interaction

We propose a field theory model for dark energy and dark matter in interaction. Comparing the classical solutions of the field equations with the observations of the CMB shift parameter, baryonic acoustic oscillations, lookback time, and the Gold supernovae sample, we observe a possible interaction between dark sectors with energy decay from dark energy into dark matter. The observed interaction provides an alleviation to the coincidence problem.