We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for degree-degree correlations to be irrelevant for critical singularities. We present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents.

We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their persistent directionality through the crosslinks. A Monte Carlo scheme is employed to obtain isotropic, homogeneous networks that minimize the free energy and for which all of the relevant parameters can be varied: the persistence length and the contour length as well as the crosslinking length may be chosen at will. We also provide an initial survey of the mechanical properties of our networks subjected to shear strains, showing them to display the expected nonlinear stiffening behavior. Also, a key role for nonaffinity and its relation to order in the network is uncovered.

The state of a collection of phase-locked oscillators is determined by a single phase variable or cyclic coordinate. This paper presents a computational method, Phaser, for estimating the phase of phase-locked oscillators from limited amounts of multivariate data in the presence of noise and measurement errors. Measurements are assumed to be a collection of multidimensional time series. Each series consists of several cycles of the same or similar systems. The oscillators within each system are not assumed to be identical. Using measurements of the noise covariance for the multivariate input, data from the individual oscillators in the system are combined to reduce the variance of phase estimates for the whole system. The efficacy of the algorithm is demonstrated on experimental and model data from biomechanics of cockroach running and on simulated oscillators with varying levels of noise.

The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of elastic nonlinearities in fracture dynamics. We study two simple one-dimensional models of fracture in order to gain insights about the role of elastic nonlinearities and the implications of their exclusion in the common linear elastic approximation. In one model we consider the decohesion of a nonlinear elastic membrane from a substrate. In a second model we follow the philosophy of linear elastic fracture mechanics and study a linearized version of the nonlinear model. By analyzing the steady state solutions, the velocity-load relations and the response to perturbations of the two models we show that the linear approximation fails at finite crack tip velocities. We highlight certain features of the breakdown of the linear theory and discuss possible implications of our results to higher dimensional systems.

A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

The dynamics of planar and outward propagating cylindrical flames has been studied in terms of exact solutions of the Sivashinsky equation with a random force term. The force term models the computational roundoff errors or a variety of perturbations of physical origins. In contrast to noiseless conditions, the number of poles in the system does not conserve and new poles appear due to the external forcing. It was found that modification of the pole solutions taking into account the appearance of new poles captures the features typical for the hydrodynamically unstable flames, which cannot be detected by the pole solutions with a fixed number of poles. Investigations based on the pole solutions make it possible to exclude the uncontrolled numerical noise that is always present in direct computations of the Sivashinsky equation, and to examine the interplay between noises and hydrodynamic instability. The study clearly demonstrates that the presence of noises is a necessary condition for flame acceleration.

Proton beams generated from thin aluminum and Mylar foil targets that are irradiated by a $30\mathrm{fs}$ Ti:sapphire laser pulse with an intensity of $2.2\times {10}^{18}\mathrm{W}∕{\mathrm{cm}}^2$ were investigated. Protons from the Mylar targets were observed to have an energy higher by a factor of 2 and were higher in number by an order of magnitude as compared with those generated from the aluminum targets. The maximum proton energy of $1.3\pm 0.12\mathrm{MeV}$ obtained from the Mylar target was found to be similar with previous observations that used laser pulses with different intensities. To address the anomalous behavior of the maximum proton energy for plastic targets, an acceleration model is proposed. In this model, the protons are accelerated by a resistively induced electric field in the front of the target, which can account for the experimental observations.

We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.

A theoretical model for vesicle fission induced by particle adsorption and aggregation on a membrane surface is presented. The bulk fluid contains particles that are adsorbed reversibly to the membrane. Adsorbed particles aggregate on the membrane, forming particle-rich domains. Domains at a critical size which contains $n_v$ particles become vesicles and leave the membrane. We find that for parameters that correspond to typical experimental situations, vesicle formation is energetically favored except for a possible energy barrier for domain nucleation at small $n$, where $n$ is the number of particles in a domain. We also find that in typical experimental situations a particle-rich domain grows without being affected strongly by neighboring domains, and the vesicle formation rate is proportional to adsorption rate $j_{\mathrm{on}}$ when $j_{\mathrm{on}}$ is large; when $j_{\mathrm{on}}$ is small the vesicle formation rate scales like $j_{\mathrm{on}}^2$. Because the diffusion flux is small for domains with small in-plane radius $R_n$, in the time-independent state the densities of domains with $n∕n_v⪡1$ and $1-n∕n_v⪡1$ are large.

Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.

We solve the escape problem for the Heston random diffusion model from a finite interval of span $L$. We obtain exact expressions for the survival probability (which amounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless of volatility. We consider these results in terms of the dimensionless normal level of volatility—a ratio of the three parameters that appear in the Heston model—and analyze their form in several asymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower, depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparently paradoxical way, increases survival and prolongs the escape time. We finally observe that the model is able to describe the main exit-time statistics of the Dow-Jones daily index.

We describe a simple continuous-time flow such that Lyapunov exponents fail to exist at nearly every point in the phase space ${\mathbb{R}}^2$, despite the fact that the flow admits a unique natural measure. This example illustrates that the existence of Lyapunov exponents is a subtle question for systems that are not conservative.

We report results of collisions between coaxial vortex solitons with topological charges $\pm S$ in the complex cubic-quintic Ginzburg-Landau equation. With the increase of the collision momentum, merger of the vortices into one or two dipole or quadrupole clusters of fundamental solitons (for $S=1$ and 2, respectively) is followed by the appearance of pairs of counter-rotating “unfinished vortices,” in combination with a soliton cluster or without it. Finally, the collisions become elastic. The clusters generated by the collisions are very robust, while the “unfinished vortices,” eventually split into soliton pairs.

We propose a simple method to evaluate the approximation of separation of variables in molecular dynamics (MD) and related fields. It is based on a point-by-point evaluation of the difference between the true potential and the corresponding potential where the separation of variables is applied. The major advantage of such an approach is the fact that it requires only the analytical form of the potential as provided in most of the MD codes. We provide two examples of application, namely, a diatomic molecule adsorbing on a flat surface and an alkane (aliphatic) chain.

We compare quantitatively two experimental situations concerning injection of a miscible fluid into an initially jammed granular medium saturated with the same fluid, confined in a Hele-Shaw cell. The two experiments are identical, apart from the interstitial and injected fluid, which is in one case air injected into a dry granular packing, and in the other case silicone oil injected into a dense suspension. In spite of the strong differences regarding the nature of the two fluids, strikingly similar dynamical and geometrical features are identified as functions of the control parameters: cell thickness and applied fluid injection pressure. In both cases an initial hydrodynamically driven decompaction process controls the unjamming and prepares the final displacement process characterized by fingerlike patterns empty of grains. The pattern shapes are comparable. In addition, the mobilities of the coupled fluid-grain flow, rescaled by the interstitial fluid viscosity and grain diameter squared, are of the same range and behave comparably. The mobility proves to depend on the initial solid fraction of the medium. Subtle differences are observed in geometrical aspects like the finger width with respect to the control parameters.

We report an experimental investigation of time dependent anisotropic light scattering by an aqueous suspension of tetramethyl ammonium hydroxide coated ${\mathrm{Fe}}_3{\mathrm{O}}_4$ nanoparticles $(\sim 6\mathrm{nm})$ under the ON-OFF transient of an external dc magnetic field. The study employs the synchronized recording and measurement of the two magnetic-field-induced light-scattering patterns produced by two identical orthogonal He-Ne laser beams passing through the ferrofluid sample and propagating parallel and perpendicular to the applied field, respectively. From these patterns, we extract the time dependence of the induced optical anisotropy, which provides a measure of the characteristic time scale and kinematic response for field-induced structure formation in the sample. We propose that the time evolution of the scattering patterns, which is very fast at short times and significantly slower at long times, can be explained using a model based on a two-stage chain formation and coarsening processes.

Density fluctuation structures of supercritical carbon dioxide along the isothermal and isochoric lines were observed with small-angle neutron scattering (SANS). All the scattering intensities in the low-$Q$ range were well described with the Ornstein-Zernike (OZ) equation. It was confirmed that there exists a locus where the OZ correlation length and scattering intensity at $Q=0$ exhibit extrema on the isothermal lines: this locus, named the ridge, was interpreted as the boundary by which the supercritical state is divided into liquidlike and gaslike phases. In order to clarify the difference of the fluctuation structure between the liquidlike and the gaslike phases, a real-space molecular distribution was obtained with a reverse Monte Carlo (RMC) method. Number density distributions of $\mathrm{C}{\mathrm{O}}_2$ molecules at all measured states were calculated with the real-space molecular distributions obtained. In addition, the statistical parameters of the number density distributions, the standard deviations, and the skewnesses, were examined. The standard deviations of the number density distributions almost coincide with the results of the OZ analysis. On the other hand, the skewnesses, which describe the asymmetric nature of the number density distribution, clearly showed a difference between the two phases: the skewness became negative in the liquidlike phase, positive in the gaslike phase, and almost zero at the nearest state to the ridge in all isotherms. It was proved with simple equations of statistical mechanics that the skewness is described as the first differential of the magnitude of the density fluctuation with respect to the pressure. We conclude that the skewness, obtained with a RMC analysis for SANS data, is an important structural parameter distinguishing between the liquidlike and gaslike phases.

In this paper, we propose a simple statistical mechanical model to study the conformation transition between the $\alpha$ helix, $\beta$ sheet, and random coil in homopolypeptides. In our model, five parameters are introduced to obtain the partition function. There are two factors for helical propagation and initiation, which are the same as those used in the Zimm-Bragg model, and three newly introduced parameters for $\beta$ structures: the strand propagation factor for residues in $\beta$ strands and two correction factors for the initiation effect of the $\beta$ strand and $\beta$ sheet. Our model shows that the variation of these parameters may induce conformation transition from $\alpha$ helix or random coil to $\beta$ sheet. The sharpness of the transition depends on the initiation factors.