We study inelastic collapse in a one-dimensional $N$-particle system when the system is driven from below under gravity. We investigate the hard-sphere limit of inelastic soft-sphere systems by numerical simulations to find how the collision rate per particle $n_{\mathrm{coll}}$ increases as a function of the elastic constant of the sphere $k$ when the restitution coefficient $e$ is kept constant. For systems with large enough $N\gtrsim 20$, we find three regimes in $e$ depending on the behavior of $n_{\mathrm{coll}}$ in the hard-sphere limit: (i) an uncollapsing regime for $1\ge e>e_{c1}$, where $n_{\mathrm{coll}}$ converges to a finite value, (ii) a logarithmically collapsing regime for $e_{c1}>e>e_{c2}$, where $n_{\mathrm{coll}}$ diverges as $n_{\mathrm{coll}}\sim \log k$, and (iii) a power-law collapsing regime for $e_{c2}>e>0$, where $n_{\mathrm{coll}}$ diverges as $n_{\mathrm{coll}}\sim k^{\alpha }$ with an exponent $\alpha$ that depends on $N$. The power-law collapsing regime shrinks as $N$ decreases and seems not to exist for the system with $N=3$, while, for large $N$, the size of the uncollapsing and the logarithmically collapsing regime decreases as $e_{c1}\simeq 1$–$2.6/N$ and $e_{c2}\simeq 1$–$3.0/N$. We demonstrate that this difference between large and small systems exists already in the inelastic collapse without external drive and gravity.

Optical birefringence and light absorption measurements reveal four regimes for the thermotropic behavior of a nematogen liquid (7CB) upon sequential filling of parallel-aligned capillaries of 12 nm diameter in a monolithic, mesoporous silica membrane. No molecular reorientation is observed for the first adsorbed monolayer. In the film-condensed state (up to 1 nm thickness), a weak, continuous paranematic-to-nematic (P-N) transition is found, which is shifted by 10 K below the discontinuous bulk transition at $T_{\mathrm{IN}}=305$ K. The capillary-condensed state exhibits a more pronounced, albeit still continuous P-N reordering, located 4 K below $T_{\mathrm{IN}}$. This shift vanishes abruptly upon complete filling of the capillaries. It could originate in competing anchoring conditions at the free inner surfaces and at the pore walls or result from the 10-MPa tensile pressure release associated with the disappearance of concave menisci in the confined liquid upon complete filling. The study documents that the thermo-optical properties of nanoporous systems (or single nanocapillaries) can be tailored over a surprisingly wide range simply by variation of the filling fraction with liquid crystals.

We analyze the problem of agents' interactions in a given population. The purpose of this paper is twofold. Starting from a scheme proposed by Galam [Physica A 320, 571 (2003)], which is based on a majority rule to treat the individuals’ interactions, we first study some of its relevant properties. Then, we introduce special individuals, called opinion leaders, who play a key role in information spreading in several practical applications. Opinion leaders have the special feature of strongly interfering with the process based on the majority rule, speeding up the diffusion. We consider a model describing agents’ interactions, which encompasses Galam's proposal, where opinion leaders are included as special agents. Then we study its specific properties which significantly recast and extend some conclusions drawn for the models given by Galam and Ellero, Fasano, and Sorato [Physica A 388, 3901 (2009)]. Finally, we provide theoretical and numerical results concerning the dynamics of our model, showing that a small percentage of opinion leaders may both accelerate and/or even reverse the overall consensus among all the agents.

Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address these questions is the percolation model, where the resilience of the system is quantified by the dependence of the size of the largest cluster on the number of failures. Numerically, the major challenge is the identification of this cluster and the calculation of its size. Here, we propose an efficient algorithm to tackle this problem. We show that the algorithm scales as $O\left(N\log N\right)$, where $N$ is the number of nodes in the network, a significant improvement compared to $O\left(N^2\right)$ for a greedy algorithm, which permits studying much larger networks. Our new strategy can be applied to any network topology and distribution of interdependencies, as well as any sequence of failures.

A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest-neighbor spin couplings and then evaluating the Pfaffian of the matrix. Utilizing this technique and other more recent developments in evaluating elements of inverse matrices and exact sampling, a method and computer code for studying two-dimensional Ising models is developed. The formulation of this method is convenient and fast for computing the partition function and spin correlations. It is also useful for exact sampling, where configurations are directly generated with probability given by the Boltzmann distribution. These methods apply to Ising model samples with arbitrary nearest-neighbor couplings and can also be applied to general dimer models. Example results of computations are described, including comparisons with analytic results for the ferromagnetic Ising model, and timing information is provided.

We describe an algorithm for simulating ultrasound propagation in random one-dimensional media, mimicking different microstructures by choosing physical properties such as domain sizes and mass densities from probability distributions. By combining a detrended fluctuation analysis (DFA) of the simulated ultrasound signals with tools from the pattern-recognition literature, we build a Gaussian classifier which is able to associate each ultrasound signal with its corresponding microstructure with a very high success rate. Furthermore, we also show that DFA data can be used to train a multilayer perceptron which estimates numerical values of physical properties associated with distinct microstructures.

Can we change the average state of a resistor by simply applying white noise? We show that the answer to this question is positive if the resistor has memory of its past dynamics (a memristive system). We also prove that, if the memory arises only from the charge flowing through the resistor—an ideal memristor—then the current flowing through such memristor cannot charge a capacitor connected in series and, therefore, cannot produce useful work. However, the memristive system may skew the charge probability density on the capacitor, an effect that can be measured experimentally.

In this work, we adopt a statistical-mechanics approach to investigate basic, systemic features exhibited by adaptive immune systems. The lymphocyte network made by B cells and T cells is modeled by a bipartite spin glass, where, following biological prescriptions, links connecting B cells and T cells are sparse. Interestingly, the dilution performed on links is shown to make the system able to orchestrate parallel strategies to fight several pathogens at the same time; this multitasking capability constitutes a remarkable, key property of immune systems as multiple antigens are always present within the host. We also define the stochastic process ruling the temporal evolution of lymphocyte activity and show its relaxation toward an equilibrium measure allowing statistical-mechanics investigations. Analytical results are compared with Monte Carlo simulations and signal-to-noise outcomes showing overall excellent agreement. Finally, within our model, a rationale for the experimentally well-evidenced correlation between lymphocytosis and autoimmunity is achieved; this sheds further light on the systemic features exhibited by immune networks.

We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network.

We introduce a system of two parallel-coupled discrete nonlinear Schrödinger inhomogeneous chains. Each one favors the unidirectional transmission of incident packets, in the opposite directions with respect to each other. Two different configurations of the diode-antidiode pair are considered, i.e., a ladder and a plaquette. They feature, respectively, the uniform transverse linear coupling or the coupling limited to the central nonlinear segment of the system. In the case of weak linear coupling, the symmetry breaking is observed (i.e., the pair still features the diode behavior), while the moderately strong coupling restores the symmetry, making the transmission effectively bidirectional. In the case of the ladder, an oscillatory dependence of the transmission on the strength of the coupling is observed and qualitatively explained.

Spatiotemporal excitation patterns in the FitzHugh-Nagumo model are studied, which result from the disturbance of a primary pacemaker by a secondary pacemaker. The primary and secondary pacemakers generate regular waves with frequencies $f_{\mathrm{pace}}$ and $f_{\mathrm{pert}}$, respectively. The pacemakers are spatially separated, but waves emanating from them encounter each other via a small bridge. This leads to three different types I–III of irregular excitation patterns in disjunct domains of the $f_{\mathrm{pace}}-f_{\mathrm{pert}}$ plane. Types I and II are caused by detachments of waves coming from the two pacemakers at corners of the bridge. Type III irregularities are confined to a boundary region of the system and originate from a partial penetration of the primary waves into a space, where circular wave fronts from the secondary pacemaker prevail. For this type, local frequencies can significantly exceed $f_{\mathrm{pace}}$ and $f_{\mathrm{pert}}$. The degree of irregularity found for the three different types is quantified by the entropy of the local frequency distribution and an order parameter for phase coherence.

The emergence of order in far-from-equilibrium systems is often accompanied by the formation of spatially asymmetric patterns. About 30 years ago, a general mechanism to select a chiral solution by coupling a reaction-diffusion system to an external chiral electric field was proposed by Nicolis and Prigogine [Proc. Natl. Acad. Sci. USA 78, 659 (1981)]. However, no experimental or even numerical evidence in reaction-diffusion systems has been reported yet. Here we report a chiral symmetry-breaking phenomenon in a reaction-diffusion system coupled to a circularly polarized electric field (CPEF). Specifically, we show that the CPEF breaks the zero-rotation chiral symmetry between clockwise and counterclockwise spiral defects and that ordered spiral waves with preferred chirality arise from defect-mediated turbulence. The occurrence of such chiral symmetry breaking can be understood by the competition between spiral defects with opposite chirality.

We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number $M_A$. We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence. Sufficiently strong fields ($M_A<6$) completely suppress vortex formation. Maximum jet deceleration, and viscous dissipation, occur for intermediate vortex-disruptive fields, while electromagnetic energy is maximized for the strongest fields which allow vortex formation. Highly relativistic flows destabilize the system, supporting modes with near-maximum growth at smaller wavelengths than the shear width of the velocity. This helps to explain early numerical breakdown of highly relativistic simulations using numerical viscosity, a long-standing problem. While magnetic fields generally stabilize the system, we have identified many features of the complex and turbulent reorganization that occur for sufficiently weak fields in RMHD flows, and have described the transition from disruptive to stabilizing fields at $M_A\approx 6$. Our results are qualitatively similar to observations of numerous jets, including M87, whose knots may exhibit vortex-like behavior. Furthermore, in both the linear and nonlinear analyses, we have successfully unified the HD, MHD, RHD, and RMHD regimes.

We investigate the motion of a two-dimensional wedge-shaped object (a granular Brownian motor), which is restricted to move along the $x$ axis and cannot rotate as gas particles collide with it. We show that its steady-state drift, resulting from inelastic gas-motor collisions, is dramatically affected by anisotropy in the velocity distribution of the gas. We identify the dimensionless parameter providing the dependence of this drift on shape, masses, inelasticity, and anisotropy: The anisotropy leads to dramatically enhanced drift of the motor, which should easily be visible in experimental realizations.

The twist-bend nematic, an enantiomorphic liquid-crystalline phase, exhibited by the structurally symmetric liquid-crystal dimer CB7CB is induced to form a single domain of uniform handedness, in the bulk, by the addition of the dopant chiral solute ($S$)-1-phenylethanol. Addition of a nonracemic (or scalemic) mixture of both $R$ and $S$ enantiomers of this solute produced equal volumes of $P$ and $M$ chiral domains for the twist-bend nematic phase. This seeding of the domains in an enantiomorphic nematic conglomerate is revealed using deuterium NMR spectroscopy.

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping, and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament numbers. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth-order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, these mechanisms allow cells to grow stable actin networks over a large range of different conditions.

It has been proposed [Ginelli et al., Phys. Rev. E 71, 026121 (2005)] that, unlike the short-range contact process, the long-range counterpart may lead to the existence of a discontinuous phase transition in one dimension. Aiming to explore such a link, here we investigate thoroughly a family of long-range contact processes. They are introduced through the transition rate $1+a{\ell }^{-\sigma }$, where $\ell$ is the length of inactive islands surrounding particles. In the former approach we reconsider the original model (called the $\sigma$-contact process) by considering distinct mechanisms of weakening the long-range interaction toward the short-range limit. In addition, we study the effect of different rules, including creation and annihilation by clusters of particles and distinct versions with infinitely many absorbing states. Our results show that for all examples presenting a single absorbing state, a discontinuous transition is possible for small $\sigma$. On the other hand, the presence of infinite absorbing states leads to a distinct scenario depending on the interactions at the perimeter of inactive sites.

A recently proposed rational-function approximation [Phys. Rev. E 84, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar nonadditive hard wall. The theory is assessed by comparison with $NVT$ Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonadditive mixture with a nonadditive wall. It is observed that, while the theory tends to underestimate the local densities at contact (especially in the case of the big spheres) it captures very well the initial decay of the densities with increasing separation from the wall and the subsequent oscillations.

Previous work [J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, Phys. Rev. Lett. 106, 128701 (2011)] has reported that explosive synchronization can be achieved in heterogeneous networks with a microscopic correlation between the structural and dynamical properties of the networks. This phenomenon, however, cannot be observed in all heterogeneous networks even if this structure-dynamics correlation is preserved. It is therefore of particular interest to identify the general topological factors that can induce the first order synchronization transition and to understand the underlying mechanisms. Here we investigate this issue using the scenario of the smooth transformation from homogeneous Erdös-Rènyi networks to heterogeneous Barabàsi-Albert networks. Specifically, we scrutinize how local and global properties of the network change during this process, and how these properties are associated with the emergence of explosive synchronization. We find that the local degree-degree correlation in the network contributes primarily to explosive synchronization, other than the global topological property or starlike subgraphs. We furthermore demonstrate that the degree of disassortative mixing also has a great effect in the presence of explosive synchronization.

We present a detailed theoretical and numerical study of combustion waves in a discrete one-dimensional disordered system. The distances between neighboring reaction cells were modeled with a gamma distribution. The results show that the random structure of the microheterogeneous system plays a crucial role in the dynamical and statistical behavior of the system. This is a consequence of the nonlinear interaction of the random structure of the system with the thermal wave. An analysis of the experimental data on the combustion of a gasless system (Ti + $x$Si) and a wide range of thermite systems was performed in view of the developed model. We have shown that the burning rate of the powder system sensitively depends on its internal structure. The present model allows for reproducing theoretically the experimental data for a wide range of pyrotechnic mixtures. We show that Arrhenius’ macrokinetics at combustion of disperse systems can take place even in the absence of Arrhenius’ microkinetics; it can have a purely thermal nature and be related to their heterogeneity and to the existence of threshold temperature. It is also observed that the combustion of disperse systems always occurs in the microheterogeneous mode according to the relay-race mechanism.