Based on learning theory, we adopt a stochastic learning updating rule to investigate the evolution of cooperation in the Prisoner’s Dilemma game on Newman-Watts small-world networks with different payoff aspiration levels. Interestingly, simulation results show that the mechanism of intermediate aspiration promoting cooperation resembles a resonancelike behavior, and there exists a ping-pong vibration of cooperation for large payoff aspiration. To explain the nontrivial dependence of the cooperation level on the aspiration level, we investigate the fractions of links, provide analytical results of the cooperation level, and find that the simulation results are in close agreement with analytical ones. Our work may be helpful in understanding the cooperative behavior induced by the aspiration level in society.

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Lévy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdös-Renyi and the scale free models.

A maximum entropy theorem is developed and tested for granular contact forces. Although it is idealized, describing two-dimensional packings of round, rigid, frictionless, cohesionless disks with coordination number $Z=4$, it appears to describe a central part of the physics present in the more general cases. The theorem does not make the strong claims of Edwards’ hypothesis, nor does it rely upon Edwards’ hypothesis at any point. Instead, it begins solely from the physical assumption that closed loops of grains are unable to impose strong force correlations around the loop. This statement is shown to be a generalization of Boltzmann’s assumption of molecular chaos (his stosszahlansatz), allowing for the extra symmetries of granular stress propagation compared to the more limited symmetries of momentum propagation in a thermodynamic system. The theorem that follows from this is similar to Boltzmann’s $H$ theorem and is presented as an alternative to Edwards’ hypothesis for explaining some granular phenomena. It identifies a very interesting feature of granular packings: if the generalized stosszahlansatz is correct, then the bulk of homogeneous granular packings must satisfy a maximum entropy condition simply by virtue of being stable, without any exploration of phase space required. This leads to an independent derivation of the contact force statistics, and these predictions have been compared to numerical simulation data in the isotropic case. The good agreement implies that the generalized stosszahlansatz is indeed accurate at least for the isotropic state of the idealized case studied here, and that it is the reductionist explanation for contact force statistics in this case.

Thermodiffusion in a lyotropic mixture of water and potassium laurate is investigated by means of an optical technique ($Z$ scan) distinguishing the index variations due to the temperature gradient and the mass gradients. A phenomenological framework allowing for coupled diffusion is developed in order to analyze thermodiffusion in multicomponent systems. An observable parameter relating to the mass gradients is found to exhibit a sharp change around the critical micellar concentration, and thus may be used to detect it. The change in the slope is due to the markedly different values of the Soret coefficients of the surfactant and the micelles. The difference in the Soret coefficients is due to the fact that the micellization process reduces the energy of interaction of the ball of amphiphilic molecules with the solvent.

We introduce a measure of complexity, an energy, for any conformation of filaments. It is the occlusion, the portion hidden when viewed from an arbitrary exterior point. By inverting we get the exposure, a first approximation of the accessibility of the filaments. Assuming the filament is a source, we get the self-irradiation, which leads to both an interpretation as the temperature and a visualization technique: ray tracing as a virtual laboratory. There is a wide variety of applications, from enzyme action on and radiation damage of biopolymers, to the geometry of light bulb filaments. Energy minimization provides automatic detangling, resulting in symmetric and pleasing conformations.

This paper studies the mutation-selection balance in three simplified replication models. The first model considers a population of organisms replicating via the production of asexual spores. The second model considers a sexually replicating population that produces identical gametes. The third model considers a sexually replicating population that produces distinct sperm and egg gametes. All models assume diploid organisms whose genomes consist of two chromosomes, each of which is taken to be functional if equal to some master sequence, and defective otherwise. In the asexual population, the asexual diploid spores develop directly into adult organisms. In the sexual populations, the haploid gametes enter a haploid pool, where they may fuse with other haploids. The resulting immature diploid organisms then proceed to develop into mature organisms. Based on an analysis of all three models, we find that, as organism size increases, a sexually replicating population can only outcompete an asexually replicating population if the adult organisms produce distinct sperm and egg gametes. A sexual replication strategy that is based on the production of large numbers of sperm cells to fertilize a small number of eggs is found to be necessary in order to maintain a sufficiently low cost for sex for the strategy to be selected for over a purely asexual strategy. We discuss the usefulness of this model in understanding the evolution and maintenance of sexual replication as the preferred replication strategy in complex, multicellular organisms.

Ventricular tachycardia is a type of cardiac arrhythmia that can be associated with a wave circulating around in a loop. Because this rhythm is potentially fatal, its termination is highly desirable. Theoretical approaches have suggested that discontinuity in the phase resetting response to electrical stimuli is indicative of the ability for such termination. We investigate the usefulness of such theoretical predictions when the stimulus site is located at some distance away from the reentrant loop, as would typically be the case during antitachycardia pacing in the heart. We show that there exists a critical tail length below which termination of reentry occurs over a range of stimulus timing values as predicted theoretically by a discontinuous window in the phase resetting curve. Above this critical length, however, a paradoxical situation exists: termination of reentry appears impossible, yet there is a point discontinuity in the phase resetting curve. These findings offer insight into termination using a single stimulus in a loop-and-tail model, an important step toward understanding the mechanism of antitachycardia pacing.

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

We report the hydrodynamic instabilities found in a simple exothermic neutralization reaction. Although the heavier aqueous NaOH solution was put below the lighter layer of aqueous HCl solution, fingering at the interface in a Hele-Shaw cell was observed. The reaction front, which propagates downward, becomes buoyantly unstable in the gravity field. The mixing zone length and wave number depend on the reactant concentrations. The mixing zone length increases and the wave number decreases when the reactant concentrations decrease.

An evolutionary battle-of-the-sexes game is proposed to model the opinion formation on networks. The individuals of a network are partitioned into different classes according to their unaltered opinion preferences, and their factual opinions are considered as the evolutionary strategies, which are updated with the birth-death or death-birth rules to imitate the process of opinion formation. The individuals finally reach a consensus in the dominate opinion or fall into (quasi)stationary fractions of coexisting mixed opinions, presenting a phase transition at the critical modularity of the multiclass individuals’ partitions on networks. The stability analysis on the coexistence of mixed strategies among multiclass individuals is given, and the analytical predictions agree well with the numerical simulations, indicating that the individuals of a community (or modular) structured network are prone to form coexisting opinions, and the coexistence of mixed evolutionary strategies implies the modularity of networks.

The motion of heavy particles in isotropic turbulence is investigated using direct numerical simulation. The statistics related to the velocity and acceleration of heavy particles for a wide range of Stokes numbers, defined as the ratio of the particle response time to the Kolmogorov time scale of turbulence $\left(\text{St}={\tau }_p/{\tau }_{\eta }\right)$, are investigated. A particular emphasis is placed on the statistics of the fluid experienced by heavy particles, which provide essential information on the dispersion of these particles. The integral time scale of the velocity correlation of fluid seen by the particles $T_f$, which determines the diffusivity of heavy particles, displays a complex behavior different from the Lagrangian integral time scale of fluid $T_L$. A plausible physical explanation for the behavior of the time scale is provided.

It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrödinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

Acoustical vortices (AV) are the acoustical equivalent of optical vortices (OV) that are a key feature in the discipline of singular optics. For linear waves, OV and AV possess the same properties. But as nonlinearities are different in optics and acoustics, the nonlinear behavior of these structures has to be different. In this paper, a numerical investigation of the three-dimensional (3D) nonlinear propagation of acoustical vortices through homogeneous or heterogeneous media is reported. First, an original numerical method is described and compared to existing ones. Then, it is used to study the dynamics of AV in a nonlinear regime. The nonlinear properties of acoustical vortices in a homogeneous medium are investigated. It is shown that shock waves can be produced during propagation, leading to an interesting spatiotemporal wave field with an azimuthal shock. The dynamics of the topological charge, intrinsic property of AV or OV, is studied in the nonlinear regime through different focusing lenses. Inversion of the topological charge is observed if the AV propagates through a 1D focusing medium (cylindrical lens), while the charge remains constant if the medium is 2D (spherical lens). These last results already observed in linear optics are generalized here to the nonlinear behavior through the investigation of harmonics which show the same behavior as the fundamental with respect to inversion.

Although the second displacement moments for Lévy flights are not defined in their usual sense, a few years ago it was shown that nonextensive statistical mechanics can be used to define them for symmetric flights. Here it is shown that the displacement moments for long-jump asymmetric Lévy flights can also be regularized by calculating the averages in the form prescribed by nonextensive statistical mechanics. The dependence of the generalized diffusion coefficient on the asymmetry strength is investigated. It is also shown that no extremum $q$-entropy principle can be associated with the asymmetric Lévy attractors.

The over-passing probability across an inverted parabolic potential barrier is investigated according to the classical and quantal generalized Langevin equations. It is shown that, in the classical case, the asymptotic value of the over-passing probability is determined by a single dominant root of the “characteristic function,” and it is given by a simple expression. The expression for the over-passing probability is quite general, and details of dissipation mechanism and memory effects enter into the expression only through the dominant root of the characteristic equation.

An expression for the near-contact pair correlation function of $D$-dimensional weakly polydisperse hard spheres is presented, which arises from elementary free-volume arguments. Its derivative at contact agrees very well with our simulations for $D=2$. For jammed states, the expression predicts that the number of exact contacts is equal to 2D, in agreement with established simulations. When the particles are wetted, they interact by the formation and rupture of liquid capillary bridges. Since formation and rupture events of capillary bonds are well separated in configuration space, the interaction is hysteretic with a characteristic energy loss $E_{\mathrm{cb}}$. The pair correlation is strongly affected by this capillary interaction depending on the liquid-bond status of neighboring particles. A theory is derived for the nonequilibrium probability currents of the capillary interaction which determines the pair correlation function near contact. This finally yields an analytic expression for the equation of state, $P=P(N∕V,T)$, of wet granular matter for $D=2$, valid in the complete density range from gas to jamming. Driven wet granular matter exhibits a van der Waals–like unstable branch at granular temperatures $T<T_{\mathrm{c}}$ corresponding to a first order segregation transition of clusters. For the realistic rupture length of the liquid bridge, $s_{\mathrm{crit}}=0.07d$, the critical point is located at $T_{\mathrm{c}}=0.274E_{\mathrm{cb}}$. While the critical temperature weakly depends on the rupture length, the critical density ${\varphi }_{\mathrm{c}}$ is shown to scale with $s_{\mathrm{crit}}$ according to $s_{\mathrm{crit}}=4d(\sqrt{{\varphi }_{\mathrm{J}}∕{\varphi }_{\mathrm{c}}}-1)$. The segregation transition is closely related to the precipitation of granular droplets reported for the free cooling of one-dimensional wet granular matter [A. Fingerle and S. Herminghaus, Phys. Rev. Lett. 97, 078001 (2006)], and extends the effect to higher dimensional systems. Since the limiting case of sticky bonds, $E_{\mathrm{cb}}⪢T$, is of relevance for aggregation in general, simulations have been performed which show very good agreement with the theoretically predicted coordination $K$ of capillary bonds as a function of the bond length $s_{\mathrm{crit}}$. This result implies that particles that stick at the surface, $s_{\mathrm{crit}}=0$, form isostatic clusters. An extension of the theory in which the bridge coordination number $K$ plays the role of a self-consistent mean-field is proposed.

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet number (Pe) ranging from 0.08 to 12. Hydrodynamic backflow causes a reduction of the average sedimentation velocity relative to the Stokes velocity. We find that this effect is independent of Pe number. Velocity fluctuations show the expected effects of thermal fluctuations at short correlation times. At longer times, nonequilibrium hydrodynamic fluctuations are visible, and their character appears to be independent of the thermal fluctuations. The hydrodynamic fluctuations dominate the diffusive behavior even for modest Pe number, while conversely the short-time fluctuations are dominated by thermal effects for surprisingly large Pe numbers. Inspired by recent experiments, we also study finite sedimentation in a horizontal planar slit. In our simulations distinct lateral patterns emerge, in agreement with observations in the experiments.

We explore correlation and fluctuation effects in an overall neutral system consisting of a single homogeneously charged planar surface with both the counterions and coions distributed on both sides of the surface. Using a field-theoretic formulation, we compute the one-loop correction to the electrostatic potential, to the ion densities, to the surface tension, and to the surface free energy. From the asymptotic behavior of the electrostatic potential, we obtain an exact expression for the effective surface charge density, which can become negative, indicating charge inversion. Furthermore, we find that the ion distributions can be substantially different from the mean-field ion densities. In particular, the counterion density, at high couplings, develops a minimum at some intermediate distances, larger than the Gouy-Chapman length, away from the charged surface, whereas the coion density develops a maximum, whose values can be greater than the counterion density. Therefore, the coions develop a second layer. Moreover, the one-loop correction always lowers the electrostatic contributions to the surface tension and at high couplings, the surface tension may become negative.

Molecular dynamics simulations of uniaxial Gay-Berne ellipsoids as prolate liquid crystal molecules confined between two flat, structureless walls have been carried out in order to investigate anisotropy in their dynamic properties. Several physical quantities are profiled as a function of distance from a wall. The walls stimulate ellipsoids into different behaviors from those of the bulk system. The profiles of self-diffusion coefficients, which are distinguished in each direction of a director-based coordinate system, show that the ellipsoids are more diffusive parallel to the walls and less diffusive perpendicular to the walls with decreasing distance from the walls. According to the self-rotation coefficient and rotational viscosity profiles, ellipsoids are easy to rotate parallel to the walls and hard to rotate in the plane perpendicular to the walls. The analyses of velocity autocorrelation functions, angular velocity autocorrelation functions, director angular velocity autocorrelation functions, and their spectra are useful for the investigation of anisotropy near the walls. We conclude that the flat, structureless wall not only prevents ellipsoids from diffusing and rotating in the plane perpendicular to the walls, but also stimulates them to diffuse and rotate in the plane parallel to the walls.

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a one-dimensional Ising model, which describes the internal base-pair states, coupled to a discrete wormlike chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of poly(dA)-poly(dT) and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square radius as a function of temperature leads to a coherent explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulas, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square radius, all as a function of temperature and DNA length.