The raise and peel model is a stochastic model of a fluctuating interface separating a substrate covered with clusters of matter of different sizes and a rarefied gas of tiles. The stationary state is obtained when adsorption compensates the desorption of tiles. This model is generalized to an interface with defects $\left(D\right)$. The defects are either adjacent or separated by a cluster. If a tile hits the end of a cluster with a defect nearby, the defect hops at the other end of the cluster, changing its shape. If a tile hits two adjacent defects, the defects annihilate and are replaced by a small cluster. There are no defects in the stationary state. This model can be seen as describing the reaction $D+D\to 0$, in which the particles (defects) $D$ hop at long distances, changing the medium, and annihilate. Between the hops the medium also changes (tiles hit clusters, changing their shapes). Several properties of this model are presented and some exact results are obtained using the connection of our model with a conformally invariant quantum chain.

We perform an analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears, the probability density functions (PDFs) for the avalanche size differences at different times have fat tails with a $q$-Gaussian shape. This behavior does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. Such a result can be analytically understood if the sizes (released energies) of the avalanches (earthquakes) have no correlations. Our findings support the hypothesis that a self-organized criticality mechanism with long-range interactions is at the origin of seismic events and indicate that it is not possible to predict the magnitude of the next earthquake knowing those of the previous ones.

In statistical mechanical investigations of complex networks, it is useful to employ random graph ensembles as null models to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with asymptotically, scale-free out-degree and compact in-degree. Entries in each row of the adjacency matrix are set to 0 or 1 according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size $n\sim 100$. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs. The technique is easily generalizable to different kinds of graphs.

The effective dynamic properties of composites made of elastic cylindrical fibers randomly distributed in another elastic solid can be evaluated with plane shear-horizontal acoustic waves. In this paper, it is shown that the effective mass density and the effective shear stiffness are complex valued and frequency dependent. Simple formulas are derived for these effective quantities. The low-frequency limit of these formulas is found to be in agreement with physical expectations. The derivation is based on the multiple-scattering approach of Waterman and Truell, where each cylinder of finite cross section is replaced with an equivalent line scatterer. Numerical results are presented for the effective mass density and effective shear stiffness for various values of frequency, cylinder concentration, and elastic properties of the cylinders and matrix.

The radiation spectrum of extreme relativistic electrons and the probability of electron-positron pair production by energetic photons in a strong plasma wakefield are derived in the framework of a semiclassical approach. It is shown that the radiation losses of a relativistic electron in the plasma wakefield scale proportionally to ${\epsilon }^{2∕3}$ in the quantum limit when the energy of the radiated photon becomes close to the electron energy $\epsilon$. The quantum effects will play a key role in future plasma-based accelerators operating at ultrahigh electron energy.

We have derived an equation of motion for coarse-grained particles by using a projection operator. Because the derived coarse-grained equation is based on microscopic description, it can be the basis for models of various coarse-grained simulations. We show that by substitution of random forces into fluctuating forces in the coarse-grained equation, the equations for Brownian dynamics and dissipative particle dynamics are reproduced.

Complete unzipping and rezipping of $\lambda$-phage double-stranded DNA is achieved by applying a constant force. A strong hysteresis is observed at all tested time scales and temperatures. Hysteresis also occurs for partial unzipping, indicating stability for the partially open state over a force range of 2–$5\mathrm{pN}$. Results are compared to nearest-neighbor model simulations, and reasonable agreement is found.

Experimental results for covalent glasses have highlighted the existence of a self-organized phase due to the tendency of glass networks to minimize internal stress. Recently, we have shown that an equilibrated self-organized two-dimensional lattice-based model also possesses an intermediate phase in which a percolating rigid cluster exists with a probability between zero and one, depending on the average coordination of the network. In this paper, we study the properties of this intermediate phase in more detail. We find that microscopic perturbations, such as the addition or removal of a single bond, can affect the rigidity of macroscopic regions of the network, in particular, creating or destroying percolation. This, together with a power-law distribution of rigid cluster sizes, suggests that the system is maintained in a critical state on the rigid-floppy boundary throughout the intermediate phase, a behavior similar to self-organized criticality, but, remarkably, in a thermodynamically equilibrated state. The distinction between percolating and nonpercolating networks appears physically meaningless, even though the percolating cluster, when it exists, takes up a finite fraction of the network. We point out both similarities and differences between the intermediate phase and the critical point of ordinary percolation models without self-organization. Our results are consistent with an interpretation of recent experiments on the pressure dependence of Raman frequencies in chalcogenide glasses in terms of network homogeneity.

The authors have measured the electro-optic Kerr effect in the isotropic phase of a urea derivative. Electric-field-induced birefringence $\mathrm{\Delta }n$ was observed in the isotropic phase even $30°\mathrm{C}$ above the isotropic-columnar phase transition temperature. The induced birefringence is inversely proportional to temperature, as predicted by the Landau–de Gennes theory. Two distinct regions are identified from the proportionality constants in the isotropic phase; optical second-harmonic generation (SHG) is easily observable in the low-temperature region on applying an electric field, whereas SHG activity does not emerge in the higher-temperature region. The structure of molecular assemblies is discussed based on these experimental results.

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science 303, 990 (2004)] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why an isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle $(\overline{Z}=2d_f)$, does not apply to nonspherical particles. We develop first- and second-order conditions for jamming and demonstrate that packings of nonspherical particles can be jammed even though they are underconstrained (hypoconstrained, $\overline{Z}<2d_f$). We apply an algorithm using these conditions to computer-generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings, even close to the sphere point. We also consider packings that are nearly jammed and draw connections to packings of deformable (but stiff) particles. Finally, we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point.

We study the effectiveness of recovery strategies for a dynamic model of failure spreading in networks. These strategies control the distribution of resources based on information about the current network state and network topology. In order to assess their success, we have performed a series of simulation experiments. The considered parameters of these experiments are the network topology, the response time delay, and the overall disposition of resources. Our investigations are focused on the comparison of strategies for different scenarios and the determination of the most appropriate strategy. The importance of prompt response and the minimum sufficient quantity of resources are discussed as well.

A population of coupled nonlinear oscillators may age in such a way that the fraction of non-self-oscillatory elements increases. Following our previous paper [Phys. Rev. Lett. 93, 104101 (2004)], we study the effect of aging in this sense mainly for globally coupled Stuart-Landau oscillators with the emphasis on the structure of the $(K,p)$ phase diagram, where $K$ is the coupling strength and $p$ is the ratio of inactive oscillators. In addition to the aging transition reported previously, such a diagram is shown to be characterized by a hornlike region, which we call a “desynchronization horn,” where active oscillators desynchronize to form a number of clusters, provided that uncoupled active oscillators are sufficiently nonisochronous. We also show that desynchronization in such a region can be captured as a type of diffusion-induced inhomogeneity based on a “swing-by mechanism.” Our results suggest that the desynchronization horn with some curious properties may be a fairly common feature in aging systems of globally and diffusively coupled periodic oscillators.

A cascade model is described based on multiplier distributions determined from three-dimensional (3D) direct numerical simulations (DNS) of turbulent particle laden flows, which include two-way coupling between the phases at global mass loadings equal to unity. The governing Eulerian equations are solved using psuedospectral methods on up to ${512}^3$ computional grid points. DNS results for particle concentration and enstrophy at Taylor microscale Reynolds numbers in the range 34–170 were used to directly determine multiplier distributions on spatial scales three times the Kolmogorov length scale. The multiplier probability distribution functions (PDFs) are well characterized by the $\beta$ distribution function. The width of the PDFs, which is a measure of intermittency, decreases with increasing mass loading within the local region where the multipliers are measured. The functional form of this dependence is not sensitive to Reynolds numbers in the range considered. A partition correlation probability is included in the cascade model to account for the observed spatial anticorrelation between particle concentration and enstrophy. Joint probability distribution functions of concentration and enstrophy generated using the cascade model are shown to be in excellent agreement with those derived directly from our 3D simulations. Probabilities predicted by the cascade model are presented at Reynolds numbers well beyond what is achievable by direct simulation. These results clearly indicate that particle mass loading significantly reduces the probabilities of high particle concentration and enstrophy relative to those resulting from unloaded runs. Particle mass density appears to reach a limit at around 100 times the gas density. This approach has promise for significant computational savings in certain applications.

We evaluate the strain amplitude $\left(\gamma \right)$ dependence of the dynamic storage and loss moduli for polybutadiene elastomers containing carbon black particles of varied size at a constant volume fraction of 0.18. Measurements of the low-strain hysteretic softening (Payne effect or unjamming transition) in both shear and uniaxial extension modes allow the $\gamma$ dependence of Poisson’s ratio $\left(\nu \right)$ to be determined. For elastomers with a fully agglomerated filler network, the breakup of the jammed state with increasing strain induces a transition from $\nu \sim 0.35$ to the limiting value for an incompressible material, $\nu =0.5$. This transition is more marked for samples containing smaller filler particles. The effect is similar to the change caused by temperature in the glass transition zone of amorphous polymers, reflecting the parallel between deformation in jammed systems and temperature (and the volume changes associated with it) in glasses; thus, the Payne effect resembles the glass transition in polymers and molecular liquids. We also show herein that the alleviation of structural arrest in filled rubber occurs at a constant value of strain energy, independent of the size of the reinforcing particles or the nature of the strain (shear vs tension). Contrary to the results for shear or tensile deformation, under hydrostatic pressure (volumetric strain) a value of $\nu =0.5$ is maintained for all magnitudes of strain. Along with the absence of hysteresis in cyclic pressure-volume measurements, this demonstrates the distinct behavior of the filler network for hydrostatic compression, in which there is no relative displacement of polymer and filler.

The electric double layer around fractal electrodes is studied with direct numerical simulations of the Nernst-Planck equation coupled with the Poisson equation. The capacitance and the relaxation time obey a power law as a function of the system size, the temperature, and the concentration. The time evolution of the charging process exhibits a stretched exponential law, and the exponent $\beta$ is numerically evaluated.

The dynamical behavior of ferromagnetic Ising films confined in a $D\times L\times L$ geometry $(D⪡L,1⩽i⩽D)$ is studied by means of Monte Carlo simulations when either short- or long-range competing magnetic fields $H\left(i\right)$ of equal strength but opposite sign are applied at opposite walls, given by the $L\times L$ surfaces. It is well known that, for appropriate choices of the control parameters, these systems exhibit wetting phase transitions that occur in the limit of infinite film thickness at the critical curve $T_w\left(h_w\right)$, where $h_w=H(i=1)$ is the magnitude of the surface field at the wall. Results of the dynamical approach to equilibrium, at criticality and for the complete wetting regime, obtained by starting the systems from different (far-from equilibrium) initial conditions, are presented and discussed. We determine quite accurately a wetting critical point $[T_w=0.8982\left(57\right),h_w=0.555]$ for the case of short-range fields, by measuring the detachment of the wetting layer from a wall, which for this type of field obeys a logarithmic dependence on time. For retarded van der Waals forces we obtained $[T_w=0.8982,h_w=0.449\left(1\right)]$ for the critical point. The scaling behavior of the average position of the interface is also studied for the complete wetting regime at $T=0.8982$ and in the presence of a bulk magnetic field $H=1$. The numerical results are in full agreement with the theoretical expectations for the cases of short-range and long-range (both retarded and nonretarded van der Waals forces) fields, where logarithmic and power-law divergences are found, respectively.

Structural properties of encapsidated flexible polyelectrolytes in viral capsids with dodecahedral charge distribution have been investigated by Monte Carlo simulations using a coarse-grained model. Several capsid charge distributions ranging from a homogeneous surface charge distribution $(\lambda =0)$ to a complete dodecahedral distribution $(\lambda =1)$ at constant total capsid charge and fixed radial location of the capsid charges have been considered. The radial and lateral organizations of the polyelectrolyte have been examined as a function of the polyelectrolyte length and capsid charge distribution. With short polyelectrolytes a single polyelectrolyte layer was formed at the inner capsid surface, whereas at increasing polyelectrolyte length also a uniform polyelectrolyte density inside the surface layer was established. At low $\lambda$, the polyelectrolyte layer was laterally isotropic, but at $\lambda \ge 0.05$ a dodecahedral structure started to appear. At $\lambda =1$, the polyelectrolyte followed essentially a path along the edges of a dodecahedron. With sufficiently long chains, all edges were decorated with polyelectrolyte, facilitated by loop formation. For an undercharged capsid, the capsid counterions inside the capsid also adopted a dodecahedral distribution.

Using analytical calculations and computer simulations, we study binary $AB$ and ternary $ABC$ membranes that respond to an external stimulus by interconverting $A$ and $B$ components. The $C$ component is assumed to be nonreactive and is incompatible with both $A$ and $B$. We also assume that $A$ and $B$ have different spontaneous curvatures. The dynamics of the ternary system is described in terms of three order parameters: two specify the local composition and a third characterizes the local height of the membrane. Our description of the two-component membrane is based on a recent model proposed by Reigada et al. [Phys. Rev. E. 72, 051921 (2005)]; we extend the latter approach by explicitly including the effects of the membrane’s surface tension on the phase behavior of the system. By performing a linear stability analysis, we determine the behavior of the reactive $AB$ membrane for a given bending elasticity and surface tension at different values of the reaction rate coefficients. We also numerically integrate the governing dynamic equations, and the results of these simulations are in agreement with the analytical predictions. For the two-component membranes, we calculate two critical values of the reaction rate coefficients, which define the behavior of the system, and plot the phase diagrams in terms of different parameters. We illustrate that the surface tension of the membrane strongly affects these critical values of the reaction rate coefficients and therefore the location of the phase boundaries. We also pinpoint the regions on the phase diagram where the late-time behavior is affected by the initial fluctuations, i.e., where such a reactive system has some “memory” of its prior state. In the case of the three-component system, we show that the presence of the nonreactive $C$ component strongly affects the composition and topology of the membrane, as well as critically altering the propagation of the traveling waves within the system.

We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional consequences of a given structural feature, for example a scale free architecture. A key step is to construct an algorithm that allows us to efficiently sample from a maximum entropy distribution on the space of Boolean dynamical networks constrained to perform a specific function, or cascade of gene expression. Such a distribution can act as a “functional null model” to test the significance of any given network feature, and can aid in revealing underlying evolutionary selection pressures on various network properties. Although our methods are general, we illustrate them in an analysis of the yeast cell cycle cascade. This analysis uncovers strong constraints on the architecture of the cell cycle regulatory network as well as significant selection pressures on this network to maintain ordered and convergent dynamics, possibly at the expense of sacrificing robustness to structural perturbations.

We experimentally study the dynamical states of a freely moving, floating heat blanket that is coupled with a thermally convecting fluid. This floating boundary modifies the large-scale flow pattern in the bulk and destabilizes the coupled system, leading to spontaneous oscillations. As the moving boundary exceeds a critical size, the system makes a transition from an oscillatory state to a weakly confined state, in which the moving boundary executes only small excursions in response to random bypassing thermal plumes. To explain the observed states and transition, we provide a low-dimensional model that appears to capture the underlying mechanism of this coupled system.