Under an applied external load the global load-sharing fiber bundle model, with individual fiber strength thresholds sampled randomly from a probability distribution, will relax to an equilibrium state, or to complete bundle breakdown. The relaxation can be viewed as taking place in a sequence of steps. In the first step all fibers weaker than the applied stress fail. As the total load is redistributed on the surviving fibers, a group of secondary fiber failures occur, etc. For a bundle with a finite number of fibers the process stops after a finite number of steps, $t_f$. By simulation and theoretical estimates, it is determined how $t_f$ depends upon the stress, the initial load per fiber, both for subcritical and supercritical stress. The two-sided critical divergence is characterized by an exponent $-1∕2$, independent of the probability distribution of the fiber thresholds.

Recently we proposed a phase field model to describe Marangoni convection in a compressible fluid of van der Waals type far from criticality [Eur. Phys. J. B 44, 101 (2005)]. The model previously developed for a two-layer geometry is now extended to drops and bubbles. A randomly distributed initial density evolves towards phase separation and single droplet formation. For a two-component liquid-liquid system we report on numerical simulations for drop Marangoni migration in a vertical thermal gradient.

Bayesian inference has been used widely in physics, biology, and engineering for a variety of experiment- or observation-based estimation problems. Sequential Monte Carlo simulations are effective for realizing Bayesian estimations when the system and observational processes are nonlinear. In realistic applications, large disturbances in the observation, or outliers, may be present. We develop a theory and practical strategy to suppress the effect of outliers in the experimental observation and provide numerical support.

When placed in a crowded environment, a semiflexible tube is forced to fold so as to make a more compact shape. One compact shape that often arises in nature is the tight helix, especially when the tube thickness is of comparable size to the tube length. In this paper we use an excluded volume effect to model the effects of crowding. This gives us a measure of compactness for configurations of the tube, which we use to look at structures of the semiflexible tube that minimize the excluded volume. We focus most of our attention on the helix and which helical geometries are most compact. We found helices of specific pitch to radius ratio 2.512 to be optimally compact. This is the same geometry that minimizes the global curvature of the curve defining the tube. We further investigate the effects of adding a bending energy or multiple tubes to begin to explore the more complete space of possible geometries a tube could form.

The nanoscale cylindrical Couette flow is investigated by means of molecular dynamics simulations, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. We find that the tangential velocity of the flow is inverted when the fluid-wall interaction near the outer cylinder is weak and the fluid density is low. The unusual velocity inversion behavior is shown to be strongly related to the degree of the slip between the fluid and the outer cylinder, which is determined by the presence or absence of the layering of the fluid near the outer wall.

The dissipative collision of two identical viscoelastic disks is studied. By using a known law for the elastic part of the interaction force and the viscoelastic damping model an analytical solution for the coefficient of restitution is given. The coefficient of restitution depends significantly on the impact velocity. It approaches 1 for small velocities and decreases for increasing velocities.

A simple equation of state is derived for a hard-core lattice gas of side length $\lambda$, and compared to the results of Monte Carlo simulations. In the disordered fluid phase, the equation is found to work very well for a two-dimensional lattice gas of hard squares and reasonably well for the three-dimensional gas of hard cubes.

The present work extends our recently published study [Phys. Rev. E 73, 066224 (2006)] on a mechanism of pattern formation in excitable media due to inhomogeneous boundary conditions (BC). To that end, we analyze a pair of coupled excitable and oscillatory cells, a distributed FitzHugh Nagumo model, and a distributed five-variable model that describes $\mathrm{CO}$ catalytic oxidation. For the three systems we determine the structure of the oscillatory domains, composed of bands of complex firing solutions with period-adding bifurcations, and show the commonality of the structures. The obtained results account for the recently reported experimental observations of mixed-mode oscillations showing a period-adding bifurcation during $\mathrm{CO}$ oxidation on a disk-shaped catalytic cloth with imposed cold temperature BC.

We discuss some problems encountered in inference of directionality of coupling, or, in the case of two interacting systems, in inference of causality from bivariate time series. We identify factors and influences that can lead to either decreased test sensitivity or false detections and propose ways to cope with them in order to perform tests with high sensitivity and a low rate of false positive results.

Multiple oil drops bouncing on the surface of a vertically vibrating bath of the same oil exhibit self-organization behavior in two dimensions [S. Protière, Y. Couder, E. Fort, and A. Boudaoud, J. Phys.: Condens. Matter 17, S3529 (2005)]. We describe further the morphology and dynamic behavior of stable assemblies of large bouncing oil drops, for which we find that both the spacing and the lattice structure itself change with frequency, with variants of both square and hexagonal structures being observed. Large “rafts” of drops form soft triangular lattices with faceted boundaries. Small clusters of drops are unstable to coherent, collective spinning under certain driving conditions, manifesting spontaneous rotational symmetry breaking.

We have predicted that weak coherent radiation in the $1–100\mathrm{THz}$ frequency regime can be emitted under some circumstances when a shock wave propagates through a polarizable crystal, like NaCl [Reed et al., Phys. Rev. Lett. 96, 013904 (2006)]. In this work, we present and analyze a new model of a shocked polarizable crystal that is amenable to systematic analytical study and direct numerical solution of Maxwell’s equations to predict emitted coherent field amplitudes and properties. Our simulations and analysis indicate that the field amplitude of the effect decreases rapidly with increasing shock front rise distance. These models establish a fundamental limit of the ratio of emitted terahertz amplitude to the static polarization of a material. While this effect is treated classically in our previous work, we present a quantum perturbation analysis showing that it can also occur in the low-amplitude emission quantum limit.

We report an exact result for the calculation of the probability distribution of the Bernoulli-Malthus-Verhulst model driven by a multiplicative colored noise. We study the conditions under which the probability distribution of the Malthus-Verhulst model can exhibit a transition from a unimodal to a bimodal distribution depending on the value of a critical parameter. Also we show that the mean value of $x\left(t\right)$ in the latter model always approaches asymptotically the value 1.

We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multiparametric probability density. The system information in the formulation enters through two parameters only, namely, system size and the complexity parameter, a function of all system parameters including size. The behavior is contrary to the eigenvalue statistics which is sensitive to the complexity parameter only and shows a single parametric scaling. The existence of a mathematical formulation of both eigenfunctions and eigenvalues common to a wide range of complex systems indicates the possibility of a similar formulation for many physical properties. This also suggests the possibility to classify them in various universality classes defined by the complexity parameter.

Cell colonies of bacteria, tumor cells, and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on an Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilizes the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularization. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.

We propose a theoretical method for the calculation of the interaction energy between macromolecular systems at large distances. The method provides a linear scaling of the computing time with the system size and is considered as an alternative to the well-known fast multipole method. Its efficiency, accuracy, and applicability to macromolecular systems is analyzed and discussed in detail.

Most data concerning the topology of complex networks are the result of mapping projects which bear intrinsic limitations and cannot give access to complete, unbiased datasets. A particularly interesting case is represented by the physical Internet. Router-level Internet mapping projects generally consist of sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the different sources to a set of destinations, leads necessarily to a partial, incomplete map of the Internet. The determination of the real Internet topology characteristics from such sampled maps is therefore, in part, a problem of statistical inference. In this paper we present a twofold contribution in order to address this problem. First, we argue that inference of some of the standard topological quantities is, in fact, a version of the so-called “species” problem in statistics, which is important in categorizing the problem and providing some indication of its inherent difficulties. Second, we tackle the issue of estimating arguably the most basic of network characteristics—its number of nodes—and propose two estimators for this quantity, based on subsampling principles. Numerical simulations, as well as an experiment based on probing the Internet, suggest the feasibility of accounting for measurement bias in reporting Internet topology characteristics.

Spatially self-localized states have been found in a model of vertical-cavity surface-emitting lasers with frequency-selective optical feedback. The structures obtained differ from most known dissipative solitons in optics in that they are localized traveling waves. The results suggest a route to realization of a cavity soliton laser using standard semiconductor laser designs.

The existence of rotating accelerator-mode islands (RAIs), performing quasiregular motion in rotational resonances of order $m>1$ of the standard map, is firmly established by an accurate numerical analysis of all the known data. It is found that many accelerator-mode islands for relatively small nonintegrability parameter $K$ are RAIs visiting resonances of different orders $m⩽3$. For sufficiently large $K$, one finds also “pure” RAIs visiting only resonances of the same order, $m=2$ or $m=3$. RAIs, even quite small ones, are shown to exhibit sufficient stickiness to produce an anomalous chaotic transport. The RAIs are basically different in nature from accelerator-mode islands in resonances of the “forced” standard map which was extensively studied recently in the context of quantum accelerator modes.

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from $0.8\text{to}2.5\mathrm{mm}$ and of driving frequencies from $2.0\text{to}11.5\mathrm{Hz}$. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba et al., Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings $(\mathrm{Re}<{10}^{-1})$, it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.