We consider a class of self-trapped spatiotemporal solitons: spatiotemporal necklace-ring solitons, whose intensities are azimuthally periodically modulated. We reveal numerically that the spatiotemporal necklace-ring solitons carrying zero, integer, and even fractional angular momentum can be self-trapped over a huge propagation distance in the three-dimensional cubic-quintic complex Ginzburg-Landau equation, even in the presence of random perturbations.

We study the evolution of fronts in a nonlinear wave equation with global feedback. This equation generalizes the Klein-Gordon and sine-Gordon equations. Extending previous work, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the classical case (with no global feedback), leading in most cases to a localized solution; i.e., the stabilization of one phase inside the other. The nature of the localized solution depends on the strength of the global feedback as well as on other parameters of the model.

We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. [Phys. Rev. E 60, 5657 (1999)] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in the experiments are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the “rheologically relevant” linear segment length is smaller than that estimated from the experimental results. We use a numerical method based on a tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior—which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, the contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches a Rouse-like value.

We report results for the potential of mean force (PMF) and the defect structures that arise when spherocylindrical nanoparticles are immersed in a nematic liquid crystal. Using a dynamic field theory for the tensor order parameter $\mathbf{Q}$ of the liquid crystal, we analyzed configurations, including one, two, and three elongated particles, with strong homeotropic anchoring at their surfaces. For systems with one nanoparticle, the most stable configuration is achieved when the spherocylinder is placed with its long axis perpendicular to the far-field director, for which the defect structure consists of an elongated Saturn ring. For systems with two or three nanoparticles with their long axes placed perpendicular to the far-field director, at small separations the defect structures consist of incomplete Saturn rings fused with new disclination rings orthogonal to the original ones, in analogy to results previously observed for spherical nanoparticles. The shape of these orthogonal rings depends on the nanoparticles’ configuration, i.e., triangular, linear, or parallel with respect to their long axis. A comparison of the PMFs indicates that the latter configuration is the most stable. The stability of the different arrays depends on whether orthogonal disclination rings form or not, their size, and the curvature effects in the interparticle regions. Our results suggest that the one-elastic-constant approximation is valid for the considered systems; similar results were obtained when a three-constant expression is used to represent the elastic free energy. The attractive interactions between the elongated particles were compared to those observed for spheres of similar diameters. Similar interparticle energies were observed for linear arrays; in contrast, parallel and triangular arrays of spherocylinders yielded interactions that were up to 3.4 times stronger than those observed for spherical particles.

With the advent of digital media, people are increasingly resorting to online channels for commercial transactions. The online auction is a prototypical example. In such online transactions, the pattern of bidding activity is more complex than traditional offline transactions; this is because the number of bidders participating in a given transaction is not bounded and the bidders can also easily respond to the bidding instantaneously. By using the recently developed network theory, we study the interaction patterns between bidders (items) who (that) are connected when they bid for the same item (if the item is bid by the same bidder). The resulting network is analyzed by using the hierarchical clustering algorithm, which is used for clustering analysis for expression data from DNA microarrays. A dendrogram is constructed for the item subcategories; this dendrogram is compared to a traditional classification scheme. The implication of the difference between the two is discussed.

Composite materials, with statistically distributed thresholds for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution $D\left(\Delta \right)$ of the magnitude $\Delta$ of such avalanches. The distribution is typically a power law $D\left(\Delta \right)\propto {\Delta }^{-\xi }$. For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent $\xi$ in the vicinity of complete breakdown and a larger exponent $\xi$ for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case $\xi =3∕2$ near the breakdown point and $\xi =5∕2$ away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find $\xi =2$ near the catastrophic failure and $\xi =3$ away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

We study spatiotemporal intermittency (STI) in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes with STI of both the directed percolation (DP) and non-DP class. STI with synchronized laminar behavior belongs to the DP class. The regimes of non-DP behavior show spatial intermittency (SI), where the temporal behavior of both the laminar and burst regions is regular, and the distribution of laminar lengths scales as a power law. The regular temporal behavior for the bursts seen in these regimes of spatial intermittency can be periodic or quasiperiodic, but the laminar length distributions scale with the same power law, which is distinct from the DP case. STI with traveling wave laminar states also appears in the phase diagram. Solitonlike structures appear in this regime. These are responsible for crossovers with accompanying nonuniversal exponents. The soliton lifetime distributions show power-law scaling in regimes of long average soliton lifetimes, but peak at characteristic scales with a power-law tail in regimes of short average soliton lifetimes. The signatures of each type of intermittent behavior can be found in the dynamical characterizers of the system viz. the eigenvalues of the stability matrix. We discuss the implications of our results for behavior seen in other systems which exhibit spatiotemporal intermittency.

Synchronization of chaotic systems has been studied extensively, and especially, the possible applications to the communication systems motivated many research areas. We demonstrate the effect of the frequency bandwidth limitations in the communication channel on the synchronization of two unidirectionally coupled Mackey-Glass (MG) analog circuits, both numerically and experimentally. MG system is known to generate high dimensional chaotic signals. The chaotic signal generated from the drive MG system is modified by a low pass filter and is then transmitted to the response MG system. Our results show that the inclusion of the dominant frequency component of the original drive signals is crucial to achieve synchronization between the drive and response circuits. The maximum cross correlation and the corresponding time shift reveal that the frequency-dependent coupling introduced by the low pass filtering effect in the communication channel change the quality of synchronization.

From particle tracking velocimetry we present an experimental measure of the ratio between backwards and forwards relative dispersion in an intermediate Reynolds number turbulent flow. Lack of time-reversal symmetry implies that their ratio may be different from 1. From a stochastic model, this has recently been studied by Sawford et al. [Phys. Fluids 17, 095109 (2005)] giving ratios between 5 and 20. We find a value of approximately 2 and discuss it in the context of the characteristics of the rate of strain tensor $s_{ij}$. An analysis of a direct numerical simulation by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004) and Phys. Fluids 17, 021701 (2004)] gives the same result.

We have demonstrated that the strong and far-field focusing of a point source and a plane wave in a two-dimensional photonic-crystal-based concave lens by the use of the standard finite-difference time-domain simulations. The effect of the distance between the point source and the lens on the focusing is discussed. The far-field focus of a plane wave is shown. In addition, a plane wave is formed with placing the source at the focus point. According to the calculation, the strong and good quality far-field focusing of the transmitted wave, explicitly following the well-known wave beam negative refraction law, can be realized. Moreover, the spatial frequencies information of the Bloch mode in multiple Brillouin zones is investigated in order to indicate the wave propagation in two different regions.

We provide an exact solution to the ideal-gas-like models studied in econophysics to understand the microscopic origin of Pareto law. In these classes of models the key ingredient necessary for having a self-organized scale-free steady-state distribution is the trading or collision rule where agents or particles save a definite fraction of their wealth or energy and invest the rest for trading. Using a Gibbs ensemble approach we could obtain the exact distribution of wealth in this model. Moreover we show that in this model (a) good savers are always rich and (b) every agent poor or rich invests the same amount for trading. Nonlinear trading rules could alter the generic scenario observed here.

The analytical expressions for the time-dependent friction and diffusion coefficients are presented for the case of coupling in coordinates between the collective subsystem and a squeezed heat bath. The effects of initial phase-sensitive and -insensitive correlations of the heat bath on the diffusion coefficients, fluctuations, and decoherence are studied. The interplay between friction and decoherence is discussed.

The densities of Yang-Lee zeros for the Ising ferromagnet on the $L\times L$ square lattice are evaluated from the exact grand partition functions $(L=3\sim 16)$. The properties of the density of Yang-Lee zeros are discussed as a function of temperature $T$ and system size $L$. The three different classes of phase transitions for the Ising ferromagnet—first-order phase transition, second-order phase transition, and Yang-Lee edge singularity—are clearly distinguished by estimating the magnetic scaling exponent $y_h$ from the densities of zeros for finite-size systems. The divergence of the density of zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which has been detected only by the series expansion until now for the square-lattice Ising ferromagnet, is obtained from the finite-size data. The identification of the orders of phase transitions in small systems is also discussed using the density of Yang-Lee zeros.

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit $(N-1)$ singular (nonanalytic) microscopic phase transitions of the formal order $N∕2$, separating $N$ energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.

We study unbinding transitions of a nonequilibrium Kardar-Parisi-Zhang interface in the presence of long-ranged substrates. Both attractive and repulsive substrates, as well as positive and negative Kardar-Parisi-Zhang nonlinearities, are considered, leading to four different physical situations. A detailed comparison with equilibrium wetting transitions as well as with nonequilibrium unbinding transitions in systems with short-ranged forces is presented, yielding a comprehensive picture of unbinding transitions and of their classification into universality classes. These nonequilibrium transitions may play a crucial role in the dynamics of the wetting or growth of systems with intrinsic anisotropies.

We investigate analytically the behavior of the Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alignment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.

We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Lévy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Lévy parameter.

A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

An interfacial liquid crystal model is formulated and used to derive a membrane shape equation that takes into account pressure, tension, bending, torsion, and flexoelectric forces. Flexoelectricity introduces electric field-induced curvature and is of relevance to the study and characterization of biological membranes. It is shown that flexoelectricity renormalizes the membrane mechanical tension, shear, and bending effects, and hence it offers diverse pathways to manipulate the membrane’s shape. The derived electroelastic shape equation provides systematic guidance on how to use electric fields in membrane studies.

Biology is complex. However, it is not clear how much of this complexity must necessarily translate into complicated mathematical models of biological processes. Simple models can be appealing to physicists but are usually deceiving for biologists. Complicated models, on the other hand, depend on too many parameters whose values are frequently unknown. Therefore, complicated models, although in principle more realistic, can lead to erroneous results if they are sensitive to these unknown parameter values. Intracellular calcium signals provide an example of utmost biological importance in which the issue of “simple vs complex” can be explored. In this paper we show that simple models describing the dynamics of intracellular calcium can be directly inferred from experimental data, without no a priori information on unknown parameters. A similar approach can be followed to study other reaction-diffusion systems. In spite of their simplicity, these models can provide quantitative information on some of the processes that shape calcium signals, such as the calcium current that underlies an experimental observation. This shows that simple models of biological systems are not limited to qualitative descriptions.