This paper reports the results of an experimental and theoretical study of the segregation of heavy (sand) and light [polyvinyl chloride (PVC)] grains under the action of intense nonlinear water waves, solitons. The tests are carried out with initially carefully mixed grains at the bottom of a wave flume used in resonant mode. Ripples form on the bed and the segregation process is considered after the stopping of the wave paddle. The waves are damped and the PVC grains concentrate in a narrow region close to the ripple crest. A theoretical model explaining this grain density segregation is developed.

Simulations of avascular cancer growth are performed using experimental values of the relevant parameters. This permits a realistic assessment of the influence of these parameters on cancer growth dynamics. In general, an early exponential growth phase is followed by a linear regime (as observed in recent experiments), while the thickness of the viable cell layer remains approximately constant. Contrary to some predictions, a transition to latency is not observed.

We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchrony. These routes seem to be a characteristic feature of coupling asymmetry. We show that they are unaffected by white noise except that the entrainment frequencies are shifted. The probability of occurrence of the routes is determined by phase asymmetry. The identification of these phenomena offers new insight into synchrony between oscillator ensembles and suggest new ways in which it may be controlled.

We here present a method of clearly identifying multipartite subgraphs in a network. The method is based on a recently introduced concept of the communicability, which very clearly identifies communities in a complex network. We here show that, while the communicability at a positive temperature is useful in identifying communities, the communicability at a negative temperature is useful in identifying multipartite subgraphs; the latter quantity between two nodes is positive when the two nodes belong to the same subgraph and is negative when they do not. The method is able to discover “almost” multipartite structures, where intercommunity connections vastly outweigh intracommunity connections. We illustrate the relevance of this work to real-life food web and protein-protein interaction networks.

Community structure and rewiring phenomena exist in many complex networks, particularly in bipartite networks. We construct a model for the degree distribution of the rewiring problem in a multicommunity weight-driven bipartite network (MCWBN). The network consists of many interconnected communities, each of which holds a bipartite graph. The bipartite graph consists of two sets of nodes. We name each node in one set a “producer” and each node in the other set a “consumer.” A weight value matrix defining the trade barrier between any two communities is used to characterize the structure of the communities, which ensures the higher preferential attachment probability in intracommunity than in intercommunity. The size of one producer is defined as the number of consumers connected to it. We find that the nonlinear dynamics of the scale of production, or the total size of all producers in each community is dependent only on the initial scale of production in each community, and independent of the distribution of the producer size. Furthermore, if the nonlinear system of the scale of production in each community is at an equilibrium state, the distribution of the producer size in each community of the MCWBN model is equivalent to that in a one-community model.

We study a class of networks generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary alphabet might generate threshold nets in a similar fashion [A. Hagberg et al., Phys. Rev. E 74, 056116 (2006)]. Just like threshold nets, sequence nets in general possess a modular structure reminiscent of everyday-life nets and are easy to handle analytically (i.e., calculate degree distribution, shortest paths, betweenness centrality, etc.). Exploiting symmetry, we make a full classification of two- and three-letter sequence nets, discovering two classes of two-letter sequence nets. These sequence nets retain many of the desirable analytical properties of threshold nets while yielding richer possibilities for the modeling of everyday-life complex networks more faithfully.

I study the average deformation rate of an amorphous material submitted to an external uniform shear strain rate, in the geometry known as the split-bottom configuration. The material is described using a stochastic model of plasticity at a mesoscopic scale. A shear band is observed to start at the split point at the bottom, and widen progressively towards the surface. In a two-dimensional geometry the average statistical properties of the shear band look similar to those of the directed polymer model. In particular, the surface width of the shear band is found to scale with the system height $H$ as $H^{\alpha }$ with $\alpha =0.68\pm 0.02$. In more realistic three-dimensional simulations the exponent changes to $\alpha =0.60\pm 0.02$ and the bulk profile of the width of the shear band is closer to a quarter of a circle, as it was observed to be the case in recent simulations of granular materials.

The nonlocal elastic response function is crucial for understanding many properties of soft solids. This may be obtained by measuring strain-strain autocorrelation functions. We use computer simulations as well as video microscopy data of superparamagnetic colloids to obtain these correlations for two-dimensional triangular solids. Elastic constants and elastic correlation lengths are extracted by analyzing the correlation functions. We show that to explain our observations displacement fluctuations in a soft solid need to contain affine (strain) as well as nonaffine components.

When the Weniger transformation is systematically used in resumming the asymptotic series arising from the application of the steepest descent method can display dramatic numerical instabilities that prevent it from improving the accuracy achievable via superasymptotics. In the present paper an explanation of such pathologies through the concept of resurgence, introduced by Berry and Howls several years ago within the context of hyperasymptotics, is proposed. In particular, the way the topology of the whole set of the saddles influences the resummation capabilities of the Weniger transformation is here investigated for the integrals defining the lowest-order cuspoid diffraction catastrophes. Eventually, a powerful and easily implementable resummation scheme, based on a joint use of the Weniger transformation and hyperasymptotics, is proposed for taking care of the above pathologies. Such a joint action seems to encompass the main virtues of both approaches, and the preliminary numerical results obtained from its application show that relative errors several orders of magnitude smaller than those achievable via superasymptotics can be achieved with modest implementation efforts.

In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and nonequilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.

We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) that are long-lived but each of which relaxes as a simple function of time. Without the clusters, the relaxation of the background is simply determined by one typical length, which we deduce from an elementary statistical mechanical argument. The total relaxation function (which depends on time in a nontrivial manner) is quantitatively determined as a weighted sum over the clusters and the background. The “fragility” in this system can be understood quantitatively since it is determined by the temperature dependence of the number fractions of the locally favored regions.

We study the self-healing process of materials with embedded “glue”-carrying cells, in the regime of the onset of the initial fatigue. Three-dimensional numerical simulations within the percolation-model approach are reported. The main numerical challenge taken up in the present work has been to extend the calculation of the conductance to three-dimensional lattices. Our results confirm the general features of the process: The onset of material fatigue is delayed, by development of a plateaulike time dependence of the material quality. We demonstrate that, in this low-damage regime, the changes in the conductance and thus in similar transport and response properties of the material can be used as measures of the material quality degradation. A new feature found for three dimensions, where it is much more profound than in earlier-studied two-dimensional systems, is the competition between the healing cells. Even for low initial densities of the healing cells, they interfere with each other and reduce each other’s effective healing efficiency.

We study the long-time tails of the survival probability $P\left(t\right)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move subdiffusively, such that the mean square displacement of each trap grows as $t^{\gamma }$ with $0⩽\gamma ⩽1$. Starting from a continuous time random walk description of the motion of the particle and of the traps, we derive lower and upper bounds for $P\left(t\right)$ and show that for $\gamma ⩽2∕(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $\gamma >2∕(d+2)$ and $d⩽2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $\gamma$ regime no longer coincide, and the decay law for the survival probability of the $A$ particle remains ambiguous.

We consider an anisotropic version of Baxter’s model of “sticky hard spheres,” where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate “dipolar sticky” correction (positive or negative, depending on the mutual orientation of the molecules). The resulting nonuniform adhesion varies continuously, in such a way that in each molecule one hemisphere is “stickier” than the other. We derive a complete analytic solution by extending a formalism [M. S. Wertheim, J. Chem. Phys. 55, 4281 (1971)] devised for dipolar hard spheres. Unlike Wertheim’s solution, which refers to the “mean spherical approximation,” we employ a Percus-Yevick closure with orientational linearization, which is expected to be more reliable. We obtain analytic expressions for the orientation-dependent pair correlation function $g(1,2)$. Only one equation for a parameter $K$ has to be solved numerically. We also provide very accurate expressions which reproduce $K$ as well as some parameters, ${\Lambda }_1$ and ${\Lambda }_2$, of the required Baxter factor correlation functions with a relative error smaller than 1%. We give a physical interpretation of the effects of the anisotropic adhesion on the $g(1,2)$. The model could be useful for understanding structural ordering in complex fluids within a unified picture.

The macroscopic properties of a glass are continually relaxing toward their equilibrium supercooled liquid values. Experimentally, the shape of the relaxation function in a glass is known to depend on the fragility of the supercooled liquid. In this paper, we investigate the impact of fragility on the relaxation behavior of glasses in the enthalpy landscape framework. We show that the fragility of a supercooled liquid is a direct result of the interplay of enthalpic and entropic effects in the enthalpy landscape. Through proper adjustment of the transition barriers in an enthalpy landscape, the fragility of a system can be adjusted while maintaining the same glass transition temperature. By modeling a set of systems with identical glass transition temperatures but varying values of fragility, we show that supercooled liquid fragility has a significant impact on the enthalpy relaxation behavior of a glass. In particular, the magnitude of enthalpy relaxation decreases dramatically with increasing fragility. Finally, we discuss how in the limit of infinite fragility the glass transition becomes an ideal second-order phase transition where no relaxation is possible in the glassy state.

This work aims at a geometrical semimicroscopic model to study the reentrant isotropic-nematic phase transition. It will be assumed that the micellar change of shape in lyotropics can be understood as the deformation of an ellipsoid which is assumed to have the idealized form of a micelle. It will be shown that such deformation is characterized by two kinds of quantities. The first one, which is a scalar determined by the ellipsoidal eccentricity, gives the intensity of the ellipsoidal deformation. The second one, which has a tensorial nature, describes the spatial distribution of such deformation and is proportional to the tensorial nematic order parameter. We construct the invariants of such deformation and couple it with the orientational order parameter to study the reentrant isotropic–nematic phase transition. We determine the thermodynamical characteristics of this phase transition and shown that it is a second-order phase transition. By comparing the theory so constructed with the experimental data, the parameters of the model will be determined.

The static structure of quasi-two-dimensional colloidal mixtures of dumbbells and spheres is studied by optical microscopy. Colloidal dumbbells, produced by aggregation of colloidal spheres, are mixed with spherical particles and confined between two parallel glass walls. The static structural properties of this system are determined for various concentrations of spheres in the dilute limit of dumbbells. The dumbbell-sphere pair correlation function exhibits a strong angular dependence, and also shows that the presence of dumbbells favors the formation of triangular lattices even at sphere concentrations far from close packing.

The present paper considers biaxial nematogenic lattice models, involving particles of $D_{2h}$ symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice. The pair potential is isotropic in orientation space and restricted to nearest neighbors. Let two orthonormal triads define orientations of a pair of interacting particles. The investigated potential models are quadratic with respect to the nine scalar products between the two sets of unit vectors. Actually, based on available geometric identities, these expressions can be reduced to diagonal form containing only the scalar products between corresponding unit vectors and depending on three parameters. Over the years, this comparatively simple functional form has also proven to be rather versatile. By now, various sets of potential parameters capable of producing mesogenic behavior of some kind have been proposed and studied in the literature. A new and simplified form was recently proposed and investigated by Sonnet, Virga, Durand, and De Matteis [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003); G. De Matteis and E. G. Virga, Phys. Rev. E 71, 061703 (2005)] and is known to support a biaxial phase at sufficiently low temperature. Following the idea of the above authors, we have studied a more extended range of parameters, including cases where biaxiality cannot be sustained in the pair ground state. In cases where a biaxial phase survives, an appropriate mean-field analysis may predict the existence of a direct second-order transition to the isotropic phase as well as a second-order sequence isotropic-to-uniaxial-to-biaxial. A second-order phase transition is also predicted, which involves isotropic and uniaxial phases only. Monte Carlo simulations have been carried out as well, for a few points in the parameter space, and found to produce results which partly confirm mean-field predictions.

For cholesteric and chiral smectic liquid crystals a rotation of the helical superstructure can be induced for suitable boundary conditions for external fields such as temperature gradients and electric fields: the Lehmann effect. Here we predict that the inverse effect can lead to a pump for particles and ions on a length scale of microns: When a spatial pattern such as a phase winding pattern or a spiral is generated, for example, for a freely suspended smectic ${\mathrm{C}}^{*}$ film, a concentration current arises. We also point out that this concentration current is, under suitable experimental conditions, accompanied by a heat current and/or an electric current. Similar effects are expected for cholesterics, smectic ${\mathrm{F}}^{*}$ and ${\mathrm{I}}^{*}$ as well as for Langmuir monolayers, since all of these systems share the property of macroscopic chirality.