A number of current theories of plasticity in amorphous solids assume at their basis that plastic deformations are spatially localized. We present in this paper a series of numerical experiments to test the degree of locality of plastic deformation. These experiments increase in terms of the stringency of the removal of elastic contributions to the observed elastoplastic deformations. It is concluded that for all our simulational protocols the plastic deformations are not localized, and their scaling is subextensive. We offer a number of measures of the magnitude of the plastic deformation, all of which display subextensive scaling characterized by nontrivial exponents. We provide some evidence that the scaling exponents governing the subextensive scaling laws are nonuniversal, depending on the degree of disorder and on the parameters of the systems. Nevertheless, understanding what determines these exponents should shed considerable light on the physics of amorphous solids.

A simulation study of the magnetic electron drift vortex (MEDV) mode turbulence in a magnetoplasma in the presence of inhomogeneities in the plasma temperature and density, as well as in the external magnetic field, is presented. The study shows that the influence of the magnetic field inhomogeneity is to suppress streamerlike structures observed in previous simulation studies without background magnetic fields. The MEDV mode turbulence exhibits nonuniversal (non-Kolmogorov-type) spectra for different sets of the plasma parameters. In the presence of an inhomogeneous magnetic field, the spectrum changes to a 7/3 power law, which is flatter than without magnetic field gradients. The relevance of this work to laser-produced plasmas in the laboratory is briefly mentioned.

We study a two-lane model of two species of particles that perform biased diffusion. Extensive numerical simulations show that when bias $q$ is strong enough, oppositely drifting particles form some clusters that block each other. Coarsening of such clusters is very slow and their size increases logarithmically in time. For smaller $q$, particles collapse essentially on a single cluster whose size seems to diverge at a certain value of $q=q_c$. Simulations show that despite slow coarsening, the model has rather large power-law cooling-rate effects. It makes its dynamics different from glassy systems but similar to some three-dimensional Ising-type models (gonihedric models).

A molecular dynamics calculation of the amino acid polar requirement is used to score the canonical genetic code. Monte Carlo simulation shows that this computational polar requirement has been optimized by the canonical genetic code, an order of magnitude more than any previously known measure, effectively ruling out a vertical evolution dynamics. The sensitivity of the optimization to the precise metric used in code scoring is consistent with code evolution having proceeded through the communal dynamics of statistical proteins using horizontal gene transfer, as recently proposed. The extreme optimization of the genetic code therefore strongly supports the idea that the genetic code evolved from a communal state of life prior to the last universal common ancestor.

Myelin figures are interfacial structures formed when certain surfactants swell in excess water. Here, I present data and model calculations suggesting the formation and growth of myelins is due to the fluid flow of surfactant, driven by the hydration gradient at the dry surfactant/water interface; a simple model based on this idea qualitatively reproduces various myelin growth behaviors observed in different experiments. From a detailed experimental observation of how myelins develop from a planar precursor structure, I identify a mechanical instability that may underlie myelin formation. These results indicate the mixed mechanical character of the surfactant lamellar structure, where fluid and elastic properties coexist, is what enables the formation and growth of myelins.

In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of $a$-dependent mutation rate $m\left(a\right)$, where $a$ is the parent’s age. The mutation rate $m\left(a\right)$ is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that $m\left(a\right)$ increases with age $a$. As compared with the reference case of the standard Penna model based on a constant mutation rate $m$, the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality $q\left(a\right)$, a fraction of items eliminated from the population when we go from age $\left(a\right)$ to $\left(a+1\right)$ in simulated transition from time $\left(t\right)$ to next time $\left(t+1\right)$. The experimentally observed $q\left(a\right)$ dependence essentially follows the Gompertz exponential law for $a$ above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate $m$ with age $a$ discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe et al. [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe et al.

Nacre is a natural composite material which has been studied because of its remarkable structure and its strength. In this paper, we revisit a layered model of nacre proposed previously [K. Okumura and P. G. de Gennes, Eur. Phys. J. E 4, 121 (2001)] in order to understand the physical reasons for the toughening via numerical simulation. We construct a two-dimensional lattice model which reflects the layered structure and perform a numerical study. This grid model reproduces the essential features predicted by the analytical solutions to the previous model and the results elucidate the reasons why the tip-stress concentration is reduced and tip displacement is enhanced in the layered system.

Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general situation (but with a constraint) where all the coefficients of the error equation corresponding to the synchronization manifold are time dependent. These analytical results are also confirmed by the numerical simulation of paradigmatic examples.

Calculations of force and torque on a sphere with inhomogeneous slip boundary conditions are presented. A theoretical approach introduced previously is employed to explicitly explore two types of azimuthally symmetric boundary-condition patterning of high practical importance. The first is a discontinuous binary surface while the second involves continuously varying slip patterned in stripes, with arbitrary periodicity. These geometries mimic anisotropic spheres, as well as superhydrophobic surfaces applied to a sphere. The dynamics apply for unbounded uniform flow and pure rotational flow of a Newtonian fluid at low Reynolds number. In unbounded uniform flow, torque is maximized for an ideal Janus sphere with a discontinuous equatorial transition between regions of slip and no slip.

In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to nonequilibrium thermodynamics. An outcome of these calculations is that Eckart’s version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic nonequilibrium thermodynamics. The answer will clearly require deeper examination of this problem.

In this work, we establish some fluctuation relations for a classical two-dimensional system of independent charged harmonic oscillators in the presence of an electromagnetic field. The main fluctuation relation quantifies irreversible behavior by comparing probabilities of observing particular trajectories during forward and backward processes and is expressed in terms of the work performed by the externally time-dependent electric field when the system is driven away from equilibrium. In the absence of a harmonic force and assuming a constant electric field, our theoretical results reduce to the fluctuation relations for a classical two-dimensional system of noninteracting electrons under the influence of externally crossed electric and magnetic fields, which were recently studied [D. Roy and N. Kumar, Phys. Rev. E 78, 052102 (2008)]. Finally, by considering the dragging of the center of the harmonic trap potential given by the presence of the arbitrary time-dependent electric field, the work-fluctuation theorem and the Jarzynski equality are verified.

Many time series in natural and social sciences can be seen as resulting from an interplay between exogenous influences and an endogenous organization. We use a simple epidemic-type aftershock model of events occurring sequentially, in which future events are influenced (partially triggered) by past events to ask the question of how well can one disentangle the exogenous events from the endogenous ones. We apply both model-dependent and model-independent stochastic declustering methods to reconstruct the tree of ancestry and estimate key parameters. In contrast with previously reported positive results, we have to conclude that declustered catalogs are rather unreliable for the synthetic catalogs that we have investigated, which contains of the order of thousands of events, typical of realistic applications. The estimated rates of exogenous events suffer from large errors. The branching ratio $n$, quantifying the fraction of events that have been triggered by previous events, is also badly estimated in general from declustered catalogs. We find, however, that the errors tend to be smaller and perhaps acceptable in some cases for small triggering efficiency and branching ratios. The high level of randomness together with the long memory makes the stochastic reconstruction of trees of ancestry and the estimation of the key parameters perhaps intrinsically unreliable for long-memory processes. For shorter memories (larger “bare” Omori exponent), the results improve significantly.

Isothermal-isobaric simulations on the ordering behavior of hard spheres upon confinement are presented. The radii of the confining cylinders go from 1.1 to 2 in units of the diameters of the hard spheres adsorbed. In all the range of pressures considered the spheres were located in concentric layers, as many as the radius of the hard cylinder would permit. When the pressure increases, the hard spheres go from being loosely arranged to the formation of ordered structures. This change is marked in all cases by a distinct break in the density of spheres in a narrow pressure range. When the tube radius is smaller than 1.5, the high-pressure ordering is determined by the number of coplanar spheres you can have within a circle of radius equal to that of the confining tube. For wider tubes, the change upon compression is determined by the formation of defected two-dimensional triangular lattices wrapped to fit inside the particular cylinder we are considering.

We derive the scaling dimension associated with crossing bonds in the random-cluster representation of the two-dimensional Potts model by means of a mapping on the Coulomb gas. The scaling field associated with crossing bonds appears to be irrelevant on the critical as well as on the tricritical branch. The latter result stands in a remarkable contrast with the existing result for the tricritical $\text{O}\left(n\right)$ model that crossing bonds are relevant. Although the O(1) model is equivalent with the $q=2$ random-cluster model, the crossing-bond exponents obtained for these two models appear to be different. We provide an explanation of this peculiar observation. In order to obtain an independent confirmation of the Coulomb gas result for the crossing-bond exponent, we perform a finite-size-scaling analysis based on numerical transfer-matrix calculations.

A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes have been investigated in scale-free small-world networks, analytical research about random walks on such networks is much less. In this paper, we will study analytically the scaling of the mean first-passage time (MFPT) for random walks on scale-free small-world networks. To this end, we first map the classical Koch fractal to a network, called Koch network. According to this proposed mapping, we present an iterative algorithm for generating the Koch network; based on which we derive closed-form expressions for the relevant topological features, such as degree distribution, clustering coefficient, average path length, and degree correlations. The obtained solutions show that the Koch network exhibits scale-free behavior and small-world effect. Then, we investigate the standard random walks and trapping issue on the Koch network. Through the recurrence relations derived from the structure of the Koch network, we obtain the exact scaling for the MFPT. We show that in the infinite network order limit, the MFPT grows linearly with the number of all nodes in the network. The obtained analytical results are corroborated by direct extensive numerical calculations. In addition, we also determine the scaling efficiency exponents characterizing random walks on the Koch network.

Surface effects cause tilted molecular arrangements in smectic layers near the surface of a free-standing liquid-crystal film in which the bulk of the film is in the smectic-$A$ phase. One recent work has shown that the tilt directions in adjacent surface layers may be nonplanar. In this paper we study films with thicknesses of two to six smectic layers. Surface effects dominate in these very thin films. We show that the molecular tilts are nonplanar even in these very thin films.

We present a model for nonlinear hydrodynamic instabilities of interfaces and the formation of bubbles driven by time-dependent accelerations $g\left(t\right)$. To obtain analytic solutions, we map the equation for the bubble amplitude $\eta \left(t\right)$ onto the Schrödinger equation and solve it as an initial value $\left({\eta }_0,{\dot{\eta }}_0\right)$ problem in time instead of an eigenvalue problem in space. Very good agreement is obtained with full hydrodynamic simulations. We then apply the WKB approximation to derive scaling with $s=\int \sqrt{g\left(t\right)}dt$. Bubbles scale while spikes do not. Zitterbewegung, meaning rapid oscillations of $g\left(t\right)$ around an average value, has little effect on $\eta \left(t\right)$.

Formation of giant waves in sea states with two spectral maxima centered at close wave vectors ${\mathbf{k}}_0\pm \Delta \mathbf{k}/2$ in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle $\theta$ between the vectors ${\mathbf{k}}_0$ and $\Delta \mathbf{k}$, which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If $\theta \lesssim \text{arctan}\left(1/\sqrt{2}\right)$, then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular ${\mathbf{k}}_0$ and $\Delta \mathbf{k}$, the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.

The recent boom of large-scale online social networks (OSNs) both enables and necessitates the use of parallelizable and scalable computational techniques for their analysis. We examine the problem of real-time community detection and a recently proposed linear time—$O\left(m\right)$ on a network with $m$ edges—label propagation, or “epidemic” community detection algorithm. We identify characteristics and drawbacks of the algorithm and extend it by incorporating different heuristics to facilitate reliable and multifunctional real-time community detection. With limited computational resources, we employ the algorithm on OSN data with $1\times {10}^6$ nodes and about $58\times {10}^6$ directed edges. Experiments and benchmarks reveal that the extended algorithm is not only faster but its community detection accuracy compares favorably over popular modularity-gain optimization algorithms known to suffer from their resolution limits.

Previous work [Gong and Brumer, Phys. Rev. Lett. 97, 240602 (2006)] motivates this study as to how asymmetry-driven quantum ratchet effects can persist despite a corresponding fully chaotic classical phase space. A simple perspective of ratchet dynamics, based on the Heisenberg picture, is introduced. We show that ratchet effects are in principle of common origin in classical and quantum mechanics, although full chaos suppresses these effects in the former but not necessarily the latter. The relationship between ratchet effects and coherent dynamical control is noted.