Evolutionary $2\times 2$ games are studied with players located on a square lattice. During the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability dependent on the difference of their summed payoffs between the final and initial states assuming quenched strategies in their neighborhood. In the case of the anticoordination game this system behaves like an antiferromagnetic kinetic Ising model. Within a wide region of social dilemmas this dynamical rule supports the formation of similar spatial arrangement of the cooperators and defectors ensuring the optimum total payoff if the temptation to choose defection exceeds a threshold value dependent on the sucker’s payoff. The comparison of the results with those achieved for pairwise imitation and myopic strategy updates has indicated the relevant advantage of pairwise collective strategy update in the maintenance of cooperation.

In this paper, we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of nonequilibrium hard-disk fluids and discuss general implications of our model.

We have experimentally studied the interparticle force between two particles accompanied by hyperbolic hedgehog defects in a nematic liquid crystal. The force $F$ was measured with dual-beam optical tweezers at various temperatures and in cells with various thicknesses. In a thick cell, the dependence of $F$ on the interparticle distance $R$ obtained at different temperatures can be scaled to a universal curve of $F\propto R^{-4}$ for $R>3a$, where $a$ is the radius of a particle. The effective elastic constant evaluated from $F$ is found to be in good agreement with splay constant of the nematic liquid crystal. In a thin cell, the magnitude of $F$ decreases and the dependence of $F$ on $R$ becomes short-ranged as the thickness of a cell, $L$, decreases. The reduced force curves, $F{L}^4$ against $R/L$, at different $L$ are found to be scaled to a single theoretical curve which has been proposed recently.

Both the right and left eigenfunctions and eigenvalues of the linearized homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to the hydrodynamic modes are calculated. Also, some nonhydrodynamic modes are identified. It is shown that below a critical value of the parameter characterizing the inelasticity, one of the kinetic modes decays slower than one of the hydrodynamic ones. As a consequence, a closed hydrodynamic description does not exist in that regime. Some implications of this behavior on the formally computed Navier-Stokes transport coefficients are discussed.

We investigate the influence of field ramp rate on the kinetics of magnetic dipole-dipole induced chainlike structure formation in a nonaqueous nanoparticle dispersion using light scattering studies. With increase in magnetic field, at a constant ramp rate, the transmitted light intensity diminishes and the transmitted light spot is transformed to a diffused ring due to scattering from the self-assembled linear aggregates. The decay rate of transmitted intensity increases up to an optimum ramp rate, above which the trend becomes reverse. At an optimum ramp rate, the minimum time for initial aggregation coincides with the exposure time where the intensity decay is fastest. The variation of transmitted intensity at different ramp rate is explained on the basis of initial aggregation time that depends on Brownian motion, dipolar magnetic attraction and multibody hydrodynamic interactions. The slope of the transmitted light intensity after the removal of magnetic field depends on the time required for dissociation of ordered linear structures. Disappearance of the ring pattern and the reappearance of original light spot, upon removal of the magnetic field, confirm the perfect reversibility of the linear aggregates. The observed concentration dependant decay rates are in good agreement with aggregation theory.

We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analyzed within the linear noise approximation. The endemic fixed point is unstable to internal demographic noise, and leads to sustained oscillations. This is ensured when the eigenvalues $\left(\lambda \right)$ of the linearized drift matrix are complex, which in turn, is possible only if detailed balance is violated. In the oscillatory state, the phases decorrelate asymptotically, distinguishing such oscillations from those produced by external periodic forcing. These so-called quasicycles are of sufficient strength to be detected reliably only when the ratio $\left|\text{Im}\left(\lambda \right)/\text{Re}\left(\lambda \right)\right|$ is of order unity. The coherence or regularity of these oscillations show a maximum as a function of population size, an effect known variously as stochastic coherence or coherence resonance. We find that stochastic coherence can be simply understood as resulting from a nonmonotonic variation of $\left|\text{Im}\left(\lambda \right)/\text{Re}\left(\lambda \right)\right|$ with population size. Thus, within the linear noise approximation, stochastic coherence can be predicted from a purely deterministic analysis. The non-normality of the linearized drift matrix, associated with the violation of detailed balance, leads to enhanced fluctuations in the population amplitudes.

Protein folding dynamics is one of major issues constantly investigated in the study of protein functions. The molecular dynamic (MD) simulation with the replica exchange method (REM) is a common theoretical approach considered. Yet a trade-off in applying the REM is that the dynamics toward the native configuration in the simulations seems lost. In this work, we show that given REM-MD simulation results, protein folding dynamics can be directly derived from laws of inference. The applicability of the resulting approach, the entropic folding dynamics, is illustrated by investigating a well-studied Trp-cage peptide. Our results are qualitatively comparable with those from other studies. The current studies suggest that the incorporation of laws of inference and physics brings in a comprehensive perspective on exploring the protein folding dynamics.

Using a nonlocal electrostatic approach that incorporates the short-range structure of the contacting media, we evaluated the electrostatic contribution to the energy of the complex formation of two model proteins. In this study, we have demonstrated that the existence of an ordered interfacial water layer at the protein-solvent interface reduces the charging energy of the proteins in the aqueous solvent, and consequently increases the electrostatic contribution to the protein binding (change in free energy upon the complex formation of two proteins). This is in contrast with the finding of the continuum electrostatic model, which suggests that electrostatic interactions are not strong enough to compensate for the unfavorable desolvation effects.

The response to a knockout of a node is a characteristic feature of a networked dynamical system. Knockout resilience in the dynamics of the remaining nodes is a sign of robustness. Here we study the effect of knockouts for binary state sequences and their implementations in terms of Boolean threshold networks. Besides random sequences with biologically plausible constraints, we analyze the cell cycle sequence of the species Saccharomyces cerevisiae and the Boolean networks implementing it. Comparing with an appropriate null model we do not find evidence that the yeast wildtype network is optimized for high knockout resilience. Our notion of knockout resilience weakly correlates with the size of the basin of attraction, which has also been considered a measure of robustness.

The onset of transient instability driven by a coupling of thermal and magnetic effects in an initially quiescent ferrofluid layer is investigated using the energy method. Following the work of Kim et al. [Phys. Lett. A 372, 4709 (2008)], an energy stability criterion is derived for the underlying dynamical system by taking into account the different boundary conditions and the Prandtl number effects. The critical onset time of the instability is determined as a function of the Rayleigh number, the Prandtl number, and the thermomagnetic parameter. For larger times, our analysis predicts that the energy stability theory and the linear theory yield essentially the same results irrespective of whether the fluid under consideration is a magnetically polarizable or a nonmagnetic fluid and subcritical instabilities are not possible. For the global nonlinear stability boundary in the impulsively heated ferrofluid layer, the minimum critical onset time is found to occur when the values of the Rayleigh number and the thermomagnetic parameter are same.

The population annealing algorithm introduced by Hukushima and Iba is described. Population annealing combines simulated annealing and Boltzmann weighted differential reproduction within a population of replicas to sample equilibrium states. Population annealing gives direct access to the free energy. It is shown that unbiased measurements of observables can be obtained by weighted averages over many runs with weight factors related to the free-energy estimate from the run. Population annealing is well suited to parallelization and may be a useful alternative to parallel tempering for systems with rough free-energy landscapes such as spin glasses. The method is demonstrated for spin glasses.

By means of $N$-body simulations, we consider self-gravitating open systems enclosed in a spherical container with semipermeable reflecting walls, in order to investigate the thermodynamics of the evaporation process in self-gravitating $N$-body systems (such as the escape of stars from globular clusters). To simulate the evaporation process, when the energy of a particle exceeds a certain threshold value, the particle passes through the semipermeable reflecting wall freely. We show that the thermodynamic properties of the evaporation process, such as the dependence of the temperature on energy, agree well with those of stellar polytropes, if the system is in an approximate virial equilibrium state. However, in a lower-energy region or for a rapid evaporation process, the thermodynamic properties deviate from those for the stellar polytrope. Nevertheless, we found that a negative specific heat occurs even in the lower-energy region or for a rapid evaporation process.

Spatially nonlocal transport describes the evolution of solute concentration due to mass transfer over long ranges. Such long-range mass transfer, present in many flow situations, changes the character of mixing and consequent chemical reactions. We study mixing in terms of the scalar dissipation and reaction rates for mixing-limited equilibrium reactions, using the space-fractional advection-dispersion equation (fADE) to model long range mass transfer. The scalar dissipation and global reaction rates decay as power-laws at late time. As opposed to the Fickian (local) transport model, local reaction rates are not zero where the concentration has zero gradient. As $\alpha$, the fractional derivative exponent, decreases from two in the fADE, the reaction rate grows larger at the position of zero gradient, due to long-range transfer of reactants from distances larger than Fick’s law allows. The reaction rates are also greater far from the reactant source for non-Fickian transport; however, the globally integrated reaction rate decreases with smaller $\alpha$. This behavior may provide a method to investigate spatial nonlocality as a proper model of upscaling: the reaction products would be found in places precluded by Fickian dispersion, and overall reaction rates are suppressed.

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

We studied the curvature-driven roughening of a disk domain pattern with a variable interface window. The relaxation of interface is driven by negative “surface tension.” When a domain boundary propagates radially at a constant rate, we found that evolution of interface roughness follows scaling dynamic behavior. The local growth exponents are substantially different from the global exponents. Curvature-driven roughening belongs to a new class of anomalous roughening dynamics. However, a different “surface tension” leads to different global exponents. This is different from that of interface evolution with a fixed-size window, which has universal exponent. The variable growth window leads to a class of anomalous roughening dynamics.

Strategy evaluation schemes are a crucial factor in any agent-based market model, as they determine the agents’ strategy preferences and consequently their behavioral pattern. This study investigates how the strategy evaluation schemes adopted by agents affect their performance in conjunction with the market circumstances. We observe the performance of three strategy evaluation schemes, the history-dependent wealth game, the trend-opposing minority game, and the trend-following majority game, in a stock market where the price is exogenously determined. The price is either directly adopted from the real stock market indices or generated with a Markov chain of order $\le 2$. Each scheme’s success is quantified by average wealth accumulated by the traders equipped with the scheme. The wealth game, as it learns from the history, shows relatively good performance unless the market is highly unpredictable. The majority game is successful in a trendy market dominated by long periods of sustained price increase or decrease. On the other hand, the minority game is suitable for a market with persistent zigzag price patterns. We also discuss the consequence of implementing finite memory in the scoring processes of strategies. Our findings suggest under which market circumstances each evaluation scheme is appropriate for modeling the behavior of real market traders.

In this paper we determine the velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number $w$ given by the ratio of the number of meridian wraps to that of longitudinal wraps. We find that for $w<1$ vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for $w>1$ knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by writhe contributions. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid ${}^4\text{H}\text{e}$.

Water flow through model porous media was studied in the presence of surface relaxation, internal magnetic field inhomogeneities and exchange with stagnant water pools with different relaxation behavior, demonstrating how the apparent flow parameters average velocity, volume flow and flow conducting area in these situations depend on the observation time. To investigate the water exchange process a two component biological model system consisting of water flowing through a biofilm reactor (column packed with methanogenic granular sludge beads) was used, before and after a heat treatment to introduce exchange. We show that correction of the stagnant fluid signal amplitude for relaxation at increasing observation time using the observed relaxation times reveals exchange between the two fractions in the system. Further it is demonstrated how this exchange can be quantified.

A strongly coupled dusty plasma containing strongly correlated negatively charged dust grains and weakly correlated (Maxwellian) electrons and ions has been considered. The effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains) and effective dust temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure) on the dust-acoustic (DA) solitary and shock waves propagating in such a strongly coupled dusty plasma are taken into account. The DA solitary and shock waves are found to exist with negative potential only. It has been shown that the strong correlation among the charged dust grains is a source of dissipation and is responsible for the formation of the DA shock waves. It has also been shown that the effects of polarization force and effective dust-temperature significantly modify the basic features (e.g., amplitude, width, and speed) of the DA solitary and shock waves. It has been suggested that a laboratory experiment be performed to test the theory presented in this work.

We follow the nonequilibrium Green’s function formalism to study time-dependent thermal transport in a linear chain system consisting of two semi-infinite leads connected together by a coupling that is harmonically modulated in time. The modulation is driven by an external agent that can absorb and emit energy. We determine the energy current flowing out of the leads exactly by solving numerically the Dyson equation for the contour-ordered Green’s function. The amplitude of the modulated coupling is of the same order as the interparticle coupling within each lead. When the leads have the same temperature, our numerical results show that modulating the coupling between the leads may direct energy to either flow into the leads simultaneously or flow out of the leads simultaneously, depending on the values of the driving frequency and temperature. A special combination of values of the driving frequency and temperature exists wherein no net energy flows into or out of the leads, even for long times. When one of the leads is warmer than the other, net energy flows out of the warmer lead. For the cooler lead, however, the direction of the energy current flow depends on the values of the driving frequency and temperature. In addition, we find transient effects to become more pronounced for higher values of the driving frequency.