A geometrical argument is used to account for the exponent of 1/3 describing the isotropic-(para)nematic phase boundary of sheared carbon nanotube dispersions [E. K. Hobbie and D. J. Fry, Phys. Rev. Lett. 97, 036101 (2006)]. Through simplifying assumptions motivated by the effects of concentration and attractive interactions, the behavior is explained by relating the mean strain-induced alignment to the average distance between nanotubes for the scenario of limited anisotropy in non-Brownian suspensions.

A scaling analysis of conductance for photons in two dimensions is carried out and, contrary to widely held belief, we find strong evidence of a mobility edge. Such behavior is compatible with the existence of an Anderson transition for electronic systems under symplectic symmetry, and indeed we show that the transfer matrix in the photonic system we have modelled has such a symmetry. We verify single parameter scaling of the conductance and demonstrate the transition from the metallic phase to localization. Key parameters, including the critical disorder, the conductance, and the critical exponent of the localization length are calculated, and it is shown that the value of the critical exponent is similar to that for electronic systems with symplectic symmetry.

Fractal scaling—a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box—is studied. We introduce a box-covering algorithm that is a modified version of the original algorithm introduced by Song et al. [Nature (London) 433, 392 (2005)]; this algorithm enables easy implementation. Fractal networks are viewed as comprising a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a special type of spanning tree based on the edge betweenness centrality; it provides a scaffold for the fractality of the network. When the skeleton is regarded as a branching tree, it exhibits a plateau in the mean branching number as a function of the distance from a root. For nonfractal networks, on the other hand, the mean branching number decays to zero without forming a plateau. Based on these observations, we construct a fractal network model by combining a random branching tree and local shortcuts. The scaffold branching tree can be either critical or supercritical, depending on the small worldness of a given network. For the network constructed from the critical (supercritical) branching tree, the average number of vertices within a given box grows with the lateral size of the box according to a power-law (an exponential) form in the cluster-growing method. The critical and supercritical skeletons are observed in protein interaction networks and the World Wide Web, respectively. The distribution of box masses, i.e., the number of vertices within each box, follows a power law $P_m\left(M\right)\sim M^{-\eta }$. The exponent $\eta$ depends on the box lateral size ${\ell }_B$. For small values of ${\ell }_B$, $\eta$ is equal to the degree exponent $\gamma$ of a given scale-free network, whereas $\eta$ approaches the exponent $\tau =\gamma ∕(\gamma -1)$ as ${\ell }_B$ increases, which is the exponent of the cluster-size distribution of the random branching tree. Finally, we study the perimeter $H_{\alpha }$ of a given box $\alpha$, i.e., the number of edges connected to different boxes from a given box $\alpha$ as a function of the box mass $M_{B,\alpha }$. It is obtained that the average perimeter over the boxes with box mass $M_B$ is likely to scale as $⟨H\left(M_B\right)⟩\sim M_B$, irrespective of the box size ${\ell }_B$.

In this paper we explore the functional correlation approach to operational risk. We consider networks with heterogeneous a priori conditional and unconditional failure probability. In the limit of sparse connectivity, self-consistent expressions for the dynamical evolution of order parameters are obtained. Under equilibrium conditions, expressions for the stationary states are also obtained. Consequences of the analytical theory developed are analyzed using phase diagrams. We find coexistence of operational and nonoperational phases, much as in liquid-gas systems. Such systems are susceptible to discontinuous phase transitions from the operational to nonoperational phase via catastrophic breakdown. We find this feature to be robust against variation of the microscopic modeling assumptions.

A solution of the Euler equations with Boussinesq approximation is derived by considering unbounded flows subjected to spatially uniform density stratification and shear rate that are time dependent $\left[S\right(t)=\partial U_3∕\partial x_2]$. In addition to vertical stratification with constant strength $N_v^2$, this base flow includes an additional, horizontal, density gradient characterized by $N_h^2\left(t\right)$. The stability of this flow is then analyzed: When the vertical stratification is stabilizing, there is a simple harmonic motion of the horizontal stratification $N_h^2\left(t\right)$ and of the shear rate $S\left(t\right)$, but this flow is unstable to certain disturbances, which are amplified by a Floquet mechanism. This analysis may involve an additional Coriolis effect with Coriolis parameter $f$, so that governing dimensionless parameters are a modified Richardson number, $R=\left[S\right(0{)}^2+N_h^4\left(0\right)∕N_v^2{]}^{1∕2}$, and $f_v=f∕N_v$, as well as the initial phase of the periodic shear rate. Parametric resonance between the inertia-gravity waves and the oscillating shear is demonstrated from the dispersion relation in the limit $R\to 0$. The parametric instability has connection with both baroclinic and elliptical flow instabilities, but can develop from a very different base flow.

Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear Schrödinger (DNLS) equations with damping and strong rapid drive are investigated. The averaged equations have the forms of the parametric AL and DNLS equations. An additional type of parametric bright discrete soliton and cnoidal waves are found and the stability properties are analyzed. The analytical predictions of the perturbed inverse scattering transform are confirmed by the numerical simulations of the AL and DNLS equations with rapidly varying drive and damping.

We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays, and mechanical systems, where the active elements are turned on one by one. The resulting model is analytically tractable and predicts that both first and second order phase transitions are possible, depending upon the value of a new parameter that tunes the coupling among the oscillators. Numerical simulations of the model are in accordance with the analytical estimates, and in qualitative agreement with the behavior of Josephson junctions coupled via a cavity.

We consider long-term correlated data with several distribution densities (Gaussian, exponential, power law, and log normal) and various correlation exponents $\gamma$ $(0<\gamma <1)$, and study the statistics of the return intervals $r_j$ between events above some threshold $q$. We show that irrespective of the distribution, the return intervals are long-term correlated in the same way as the original record, but with additional uncorrelated noise. Due to this noise, the correlations are difficult to observe by the detrended fluctuation analysis (which exhibits a crossover behavior) but show up very clearly in the autocorrelation function. The distribution $P_q\left(r\right)$ of the return intervals is characterized at large scales by a stretched exponential with exponent $\gamma$, and at short scales by a power law with exponent $\gamma -1$. We discuss in detail the occurrence of finite-size effects for large threshold values for all considered distributions. We show that finite-size effects are most pronounced in exponentially distributed data sets where they can even mask the stretched exponential behavior in records of up to ${10}^6$ data points. Finally, in order to quantify the clustering of extreme events due to the long-term correlations in the return intervals, we study the conditional distribution function and the related moments. We find that they show pronounced memory effects, irrespective of the distribution of the original data.

We investigate a tethered (i.e., fixed connectivity) surface model on spherical surfaces with many holes by using the canonical Monte Carlo simulations. Our result in this paper reveals that the model has only a collapsing transition at finite bending rigidity, where no surface fluctuation transition can be seen. The first-order collapsing transition separates the smooth phase from the collapsed phase. Both smooth and collapsed phases are characterized by Hausdorff dimension $H\simeq 2$, consequently, the surface becomes smooth in both phases. The difference between these two phases can be seen only in the size of surface. This is consistent with the fact that we can see no surface fluctuation transition at the collapsing transition point. These two types of transitions are well known to occur at the same transition point in the conventional surface models defined on the fixed connectivity surfaces without holes.

We solve a model of self-avoiding walks with up to two monomers per site on the Bethe lattice. This model, inspired in the Domb-Joyce model, was recently proposed to describe the collapse transition observed in interacting polymers [J. Krawczyk et al., Phys. Rev. Lett. 96, 240603 (2006)]. When immediate self-reversals are allowed (reversion-allowed model), the solution displays a phase diagram with a polymerized phase and a nonpolymerized phase, separated by a phase transition which is of first order for a nonvanishing statistical weight of doubly occupied sites. If the configurations are restricted forbidding immediate self-reversals (reversion-forbidden model), a richer phase diagram with two distinct polymerized phases is found, displaying a tricritical point and a critical end point.

In this paper we demonstrate the feasibility and utility of an augmented version of the Gibbs ensemble Monte Carlo method for computing the phase behavior of systems with strong, extremely short-ranged attractions. For generic potential shapes, this approach allows for the investigation of narrower attractive widths than those previously reported. Direct comparison to previous self-consistent Ornstein-Zernike approximation calculations is made. A preliminary investigation of out-of-equilibrium behavior is also performed. Our results suggest that the recent observations of stable cluster phases in systems without long-ranged repulsions are intimately related to gas-crystal and metastable gas-liquid phase separation.

We propose a macroscopic approach toward realistic simulations of the population activity of hippocampal pyramidal neurons, based on the known refractory density equation with a different hazard function and on a different single-neuron threshold model. The threshold model is a conductance-based model taking into account adaptation-providing currents, which is reduced by omitting the fast sodium current and instead using an explicit threshold criterion for action potential events. Compared to the full pyramidal neuron model, the threshold model well approximates spike-time moments, postspike refractory states, and postsynaptic current integration. The dynamics of a neural population continuum are described by a set of one-dimensional partial differential equations in terms of the distributions of the refractory density (where the refractory state is defined by the time elapsed since the last action potential), the membrane potential, and the gating variables of the voltage-dependent channels, across the entire population. As the source term in the density equation, the probability density of firing, or hazard function, is derived from the Fokker-Planck (FP) equation, assuming that a single neuron is governed by a deterministic average-across-population input and a noise term. A self-similar solution of the FP equation in the subthreshold regime is obtained. Responses of the ensemble to stimulation by a current step and oscillating current are simulated and compared with individual neuron simulations. An example of interictal-like activity of a population of all-to-all connected excitatory neurons is presented.

Much recent empirical evidence shows that community structure is ubiquitous in the real-world networks. In this paper we propose a growth model to create scale-free networks with the tunable strength (noted by $Q$) of community structure and investigate the influence of community strength upon the collective synchronization induced by Susceptive-Infected-Recovery-Susceptive (SIRS) epidemiological process. Global and local synchronizability of the system is studied by means of an order parameter and the relevant finite-size scaling analysis is provided. The numerical results show that a phase transition occurs at $Q_c\simeq 0.835$ from global synchronization to desynchronization and the local synchronization is weakened in a range of intermediately large $Q$. Moreover, we study the impact of mean degree $⟨k⟩$ upon synchronization on scale-free networks.

In the traditional Drossel-Schwabl forest fire model (DS model), the frequency distributions of fire size and fire interval follow a power law and an exponential law, respectively. However, it is found that the frequency-interval distribution of actual forest fires is not exponential, but a power law with periodical fluctuations which may be caused by the daily cycle of weather parameters. Therefore, a weather driven forest fire model (WD model) is built considering actual hourly weather records, with which the fire igniting probability is calculated. The simulation results indicate that the frequency-interval distribution of the WD model agrees with that of actual forest fire data and, at the same time, the frequency-size distributions of the WD and the DS models are in accordance with each other. In the further analysis of the temporal property of weather data, it is found that the change of weather data also exhibits a power-law relation with periodic fluctuations, implying that the external driving from weather parameters is the essential reason for the power-law distribution of fire intervals. The results suggest that natural systems may be coupled with each other and that the decoupling of systems is important to identifying system characteristics.

Recently there has been much attention devoted to exploring the complicated possibly chaotic dynamics in pseudoperiodic time series. Two methods [Zhang et al., Phys. Rev. E 73, 016216 (2006); Zhang and Small, Phys. Rev. Lett. 96, 238701 (2006)] have been forwarded to reveal the chaotic temporal and spatial correlations, respectively, among the cycles in the time series. Both these methods treat the cycle as the basic unit and design specific statistics that indicate the presence of chaotic dynamics. In this paper, we verify the validity of these statistics to capture the chaotic correlation among cycles by using the surrogate data method. In particular, the statistics computed for the original time series are compared with those from its surrogates. The surrogate data we generate is pseudoperiodic type (PPS), which preserves the inherent periodic components while destroying the subtle nonlinear (chaotic) structure. Since the inherent chaotic correlations among cycles, either spatial or temporal (which are suitably characterized by the proposed statistics), are eliminated through the surrogate generation process, we expect the statistics from the surrogate to take significantly different values than those from the original time series. Hence the ability of the statistics to capture the chaotic correlation in the time series can be validated. Application of this procedure to both chaotic time series and real world data clearly demonstrates the effectiveness of the statistics. We have found clear evidence of chaotic correlations among cycles in human electrocardiogram and vowel time series. Furthermore, we show that this framework is more sensitive to examine the subtle changes in the dynamics of the time series due to the match between PPS surrogate and the statistics adopted. It offers a more reliable tool to reveal the possible correlations among cycles intrinsic to the chaotic nature of the pseudoperiodic time series.

A computer algorithm for the visualization of sample paths of anomalous diffusion processes is developed. It is based on the stochastic representation of the fractional Fokker-Planck equation describing anomalous diffusion in a nonconstant potential. Monte Carlo methods employing the introduced algorithm will surely provide tools for studying many relevant statistical characteristics of the fractional Fokker-Planck dynamics.

Measurement of energy dissipation in small nonequilibrium systems is generally a difficult task. Recently, Harada and Sasa [Phys. Rev. Lett. 95, 130602 (2005)] derived an equality relating the energy dissipation rate to experimentally accessible quantities in nonequilibrium steady states described by the Langevin equation. Here, we show an experimental test of this new relation in an optically driven colloidal system. We find that this equality is validated to a fairly good extent, thus the irreversible work of a small system is estimated from readily obtainable quantities.

We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a function of the size change are obtained. Results are compared with approximate analytical solutions.

We simulate advective transport in bond percolation clusters at the critical point. We compute the histogram of flow speeds in each bond of the backbone and find the multifractal spectrum for two-dimensional lattices with linear dimension $L⩽2000$ and in three dimensions for $L⩽250$. We demonstrate that in the limit of large systems all the negative moments of the velocity distribution become ill-defined. However, to model transport, the velocity histogram should be weighted by the flux to obtain a well-defined mean travel time. Finally, we use continuous time random walk theory to demonstrate that anomalous transport is observed whose characteristics can be related to the multifractal properties of the system.