We present calculations for the relaxation rates of phonons in one-dimensional chains in which atoms interact with a class of pairwise potentials which are anharmonic with odd powers. The calculations are based on a self-consistent procedure for second order processes and lead to integral equations for the wave-vector-dependent on-shell relaxation rate ${\Gamma }_q$ for phonons. For the cubic anharmonicity, one finds that for small $q$, ${\Gamma }_q\propto q^{3∕2}$. The self-consistent procedure is extended to potentials with higher odd powers and one finds that the leading order behavior is still ${\Gamma }_q\propto q^{3∕2}+O\left(q^2\right)$. With the assumption that the transport relaxation rate has the same wave-vector dependence, this result implies that the thermal conductivity, $\kappa$ diverges with the chain size, N, as $\kappa \propto N^{1∕3}$ for this class of potentials. Thus, our calculations provide a microscopic basis for one class of universal behavior.

In soft condensed materials consisting of molecules with form anisotropy, the translation and rotation interact with each other. Not only the shear and rotational viscosities but also the coupling viscosity are necessary to theoretically describe the molecular motion under coupling between the different degrees of freedom. In this paper, we report on the determination of all three viscosities with our experimental techniques. We obtained the absolute values for $p\text{−}n$-hexyl-cyanobiphenyl (6CB) in the isotropic phase. The experimental techniques used are the optical-beating spectroscopy of depolarized light scattering and the measurement of birefringence induced by capillary waves. The coupling strength is given in the form $2{\mu }^2/\eta \nu$ for the former and $\mu /\nu$ for the latter; from this we determined the absolute values of $\eta$, $\nu$, and $\mu$. The coupling viscosity was found to be responsible for the critical behavior of the coupling effect reported previously.

An adapted version of the annealing algorithm to identify primitive paths of a melt of ring polymers is presented. This algorithm ensures that the primitive path length becomes zero for nonconcatenated rings, and that no entanglements are observed. The bond-fluctuation model was used to simulate ring-linear blends with $N=150$ and 300 monomers. The primitive path length and the average number of entanglements of the linear component were found to be independent of the blend composition. In contrast, the primitive path length and the average number of entanglements on a ring molecule increased approximately linearly with the fraction of linear chains, and for large $N$, they approached values comparable with linear chains. Threading of ring molecules by linear chains, and ring-ring interactions were observed only in the presence of linear chains. It is conjectured that for large $N$, these latter interactions facilitate the formation of a percolating entangled network, thereby resulting in a disproportionate retardation of the dynamical processes.

Recent research by Xing et al. [Phys. Rev. Lett. 98, 075502 (2007)] has provided an expression for the Helmholtz free energy related to phonon fluctuations in polymer networks. We extend this result by constructing the corresponding nonlinear constitutive equation, usable for entirely general, volume conserving deformation fields. Constitutive equations for the sliplink model and the tube model are derived and the three models are examined by comparison with each other and with data from Xu and Mark [Rubber Chem. Technol. 63, 276 (1990)] and Wang and Mark [J. Polym. Sci., Part B: Polym. Phys. 30, 801 (1992)]. Elastic moduli are derived for the three models and compared with the moduli determined from the chemical stoichiometry. We conclude that the sliplink model and the phonon fluctuation model are relatively consistent with each other and with the data. The tube model seems consistent neither with the other models nor with the data.

The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determine the social diversity of players engaging in the prisoner’s dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game payoffs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrinsic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative strategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that cooperation deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.

A physical scenario accounting for the existence of size-limited submicrometric domains in cell membranes is proposed. It is based on the numerical investigation of the counterpart, in lipidic membranes where proteins are diffusing, of the recently discovered cluster phases in colloidal suspensions. I demonstrate that the interactions between proteins, namely, short-range attraction and longer-range repulsion, make possible the existence of stable small clusters. The consequences are explored in terms of membrane organization and diffusion properties. The connection with lipid rafts is discussed, and the apparent protein diffusion coefficient as a function of their concentration is analyzed.

Small network distance and homogeneous degree distribution have been found to be critical to efficient network synchronization. In this paper, we investigate the synchronizability of clustered networks with regular subnetworks and report a counterintuitive phenomenon: As the density of intracluster links is increased, the network exhibits strong and weak synchronizability in an alternating manner. A theory based on analyzing the eigenvalues and eigenvectors of the coupling matrix is provided to explain this phenomenon. The relevance of the network model to tissue organization for intercellular communication in biological systems is discussed. An implication is that, in order to achieve synchronization, local coupling density in the network needs to be tuned properly.

Community structure is an important property of complex networks. The automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a modularity function $\left(Q\right)$. However, the problem of modularity optimization is NP-hard and the existing approaches often suffer from a prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing $Q$ will have a resolution limit; i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm QCUT, which combines spectral graph partitioning and local search to optimize $Q$. Using both synthetic and real networks, we show that QCUT can find higher modularities and is more scalable than the existing algorithms. Furthermore, using QCUT as an essential component, we propose a recursive algorithm HQCUT to solve the resolution limit problem. We show that HQCUT can successfully detect communities at a much finer scale or with a higher accuracy than the existing algorithms. We also discuss two possible reasons that can cause the resolution limit problem and provide a method to distinguish them. Finally, we apply QCUT and HQCUT to study a protein-protein interaction network and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetected.

We incorporate an attractive interaction in a two-dimensional optimal velocity model and investigate the stability of homogeneous flow in the linear approximation. There exists a different type of instability in this model. We show the phase diagram and the behavior of the flow in each phase by numerical simulations. A new phase due to the new instability appears at low density, and the instability can be a candidate of the group formation mechanism of organisms.

The response of a ferrofluid droplet to a radial magnetic field is investigated, when the droplet is confined in a Hele-Shaw cell. We study how the stability properties of the interface and the shape of the emerging patterns react to the action of the magnetic field. At early linear stages, it is found that the radial field is destabilizing and determines the growth of fingering structures at the interface. In the weakly nonlinear regime, we have verified that the magnetic field favors the formation of peaked patterned structures that tend to become sharper and sharper as the magnitude of the magnetic effects is increased. A more detailed account of the pattern morphology is provided by the determination of nontrivial exact stationary solutions for the problem with finite surface tension. These solutions are obtained analytically and reveal the development of interesting polygon-shaped and starfishlike patterns. For sufficiently large applied fields or magnetic susceptibilities, pinch-off phenomena are detected, tending to occur near the fingertips. We have found that the morphological features obtained from the exact solutions are consistent with our linear and weakly nonlinear predictions. By contrasting the exact solutions for ferrofluids under radial field with those obtained for rotating Hele-Shaw flows with ordinary nonmagnetic fluids, we deduce that they coincide in the limit of very small susceptibilities.

Cyclotron resonant wave-particle interactions are studied in the context of Hamiltonian theory with utilization of Lie transform techniques. The canonical perturbation method for single particle motion is used for providing results for the collective particle behavior under interaction with wave fields of either localized or periodic profiles. Analytical expressions for the calculation of phase-averaged quantities of physical interest as well as the diffusion equation are derived. In the lowest order of perturbation, the method reformulates in a rigorous and unifying context the derivation of well-known results, namely Madey’s theorem and quasilinear diffusion equation. Proceeding to higher order the method provides results consisting of fourth-order accurate analytical expressions for the calculation of phase-averaged quantities as well as the derivation of a fourth-order accurate diffusion equation, with higher-order derivatives, which is the extension of the well-known Fokker-Planck equation beyond the quasilinear approximation. Higher-order terms are related to the effect of nonlinear resonant coupling between different spectral components of the waves, on the evolution of the particle distribution function.

We develop a discretized theory of thermal Casimir interactions to numerically calculate the interactions between fluctuating dielectrics. From a constrained partition function we derive a surface free energy, while handling divergences that depend on system size and discretization. We derive analytic results for parallel plate geometry in order to check the convergence of the numerical methods. We use the method to calculate vertical and lateral Casimir forces for a set of grooves.

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical properties of random networks is very important. In this Brief Report we present an algorithm which is able to construct arbitrarily degree-degree correlated networks with adjustable degree-dependent clustering. We verify the algorithm by using empirical networks as input and describe additionally a simple way to fix a degree-dependent clustering function if degree-degree correlations are given.

For the Bernoulli matching model of the sequence alignment problem we apply the Bethe Ansatz technique via an exact mapping to the five-vertex model on a square lattice. Considering the terracelike representation of the sequence alignment problem, we reproduce by the Bethe Ansatz the results for the averaged length of the longest common subsequence in the Bernoulli approximation. In addition, we compute the average number of nucleation centers of the terraces.

The response of a weakly damped bistable oscillator to an external periodic force is considered theoretically. In the approximation of weak signals we can write a linearized equation for the signal and the corresponding nonlinear equation for the noise. These equations contain two unknown parameters: An effective stiffness and an additional damping factor. In the case of the weakly damped bistable oscillator, considered here, the two-dimensional Fokker-Planck equation corresponding to the equation for the noise can be solved approximately by changing to a slow variable (“energy”) and applying a method of successive approximation. This approach allows us to find the unknown parameters and to calculate the amplitude ratio of the output and input signals, i.e., the gain factor.

The flow behavior of a viscoelastic organogel is investigated using ultrasonic velocimetry combined with rheometry. Our gel presents a decreasing flow curve, i.e., the measured stress decreases as a function of the applied shear rate. Strikingly, we note that the local flow curve calculated from the velocity profiles also exhibits a decreasing part. We attribute this regime to the presence of a fracturing process and three-dimensional motions in the bulk of the sample.

The von Kármán–Howarth equations are derived for three-dimensional Hall magnetohydrodynamics in the case of a homogeneous and isotropic turbulence. From these equations, we derive exact scaling laws for the third-order correlation tensors. We show how these relations are compatible with previous heuristic and numerical results. These multiscale laws provide a relevant tool to investigate the nonlinear nature of the high-frequency magnetic field fluctuations in the solar wind or, more generally, in any plasma where the Hall effect is important.

Anomalous scaling in the statistics of an active scalar is studied in a shell model of homogeneous turbulent convection. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent convection and attribute the origin of the anomalous scaling to variations of the entropy transfer rate. We verify the consequences and thus the validity of our hypothesis by showing that the conditional statistics of the active scalar and the velocity at fixed values of entropy transfer rate are not anomalous but have simple scaling with exponents given by dimensional considerations, and that the intermittency corrections are given by the scaling exponents of the moments of the entropy transfer rate.

A relativistic effect that occurs in a magnetized plasma irradiated by a circularly polarized wave is identified and analyzed: the usual plasma frequency associated with longitudinal oscillations splits into two new frequencies. We set up a Hamiltonian description of the plasma dynamic in order to identify this effect that results from the coupling between the plasma oscillation and the transverse circular motion driven by both the magnetic and wave fields. Within the small oscillations approximation, we compute for right- and left-handed polarization the two characteristics frequencies of the electron oscillations as functions of the field and wave parameters. We also describe the electron trajectories in the wave, magnetic, and restoring plasma fields. This new class of oscillations is rotational and therefore radiate suggesting a method for the diagnostics of strong static magnetic field in laser-plasma experiments.

Two different laser energy absorption mechanisms at the front side of a laser-irradiated foil have been found to occur, such that two distinct relativistic electron beams with different properties are produced. One beam arises from the ponderomotively driven electrons propagating in the laser propagation direction, and the other is the result of electrons driven by resonance absorption normal to the target surface. These properties become evident at the rear surface of the target, where they give rise to two spatially separated sources of ions with distinguishable characteristics when ultrashort $\left(40\mathrm{fs}\right)$ high-intensity laser pulses irradiate a foil at $45°$ incidence. The laser pulse intensity and the contrast ratio are crucial. One can establish conditions such that one or the other of the laser energy absorption mechanisms is dominant, and thereby one can control the ion acceleration scenarios. The observations are confirmed by particle-in-cell (PIC) simulations.