Entropy production is one of the most important characteristics of nonequilibrium steady states. We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of nonequilibrium systems: transport systems and reaction-diffusion systems. The usefulness of the mean entropy production rate and of the large deviation function of the entropy production for characterizing nonequilibrium steady states of interacting many-body systems is discussed. We show that the large deviation function displays a kink-like feature at zero entropy production that is similar to that observed for a single particle driven along a periodic potential. This kink is a direct consequence of the detailed fluctuation theorem fulfilled by the probability distribution of the entropy production and is therefore a generic feature of the corresponding large deviation function.

We determine the critical behavior of a reactive model with many absorbing configurations. Monomers $A$ and $B$ land on the sites of a linear lattice and can react depending on the state of their nearest-neighbor sites. The probability of a reaction depends on temperature of the catalyst as well as on the energy coupling between pairs of nearest-neighbor monomers. We employ Monte Carlo simulations to calculate the moments of the order parameter of the model as a function of temperature. Some ratios between pairs of moments are independent of temperature and are in the same universality class of the contact process. We also find the dynamical critical exponents of the model and we show that they are in the directed percolation universality class whatever the values of temperature.

We report on the erosion of flat linoleum “pebbles” under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels with a digital camera. This reduces digitization noise and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle.

We solve the rotational abrasion model of Roth, Marques, and Durian [Phys. Rev. E 83, 031303 (2011)], a one-dimensional quasilinear partial differential equation resembling the inviscid Burgers equation with the unusual feature of a step function factor as a coefficient. The complexity of the solution is primarily in keeping track of the cases in the piecewise function that results from certain amputation and interpolation processes, so we also extract from it a model of an evolving planar tree graph that tracks the evolution of the coarse features of the contour.

We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size $x_0$, we derive analytical expressions for (i) the distribution $P(t_f|x_0)$ of the first-passage time $t_f$, characterizing the bubble lifetime, (ii) the distribution $P(A|x_0)$ of the area $A$ until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution $P(M)$ of the maximum bubble size $M$ attained before the first-passage time, and (iv) the joint probability distribution $P(M,t_m)$ of the maximum bubble size $M$ and the time $t_m$ of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numerical simulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.

Regular columnar joints that originate from networklike crack patterns can be observed in basalt and, on a much smaller scale, in dried starch slurry. Here, the basalt columns are idealized by a periodic array of parallel cracks driven by steady-state cooling. By means of a bifurcation analysis, the minimal possible crack spacing for sustained propagation of the crack array is calculated. It can be shown qualitatively that the minimal possible crack spacing for sustained propagation increases with decreasing velocity. This is confirmed by numerical calculations. The latent heat released at the solidification front is taken into account in the thermomechanical linear-elastic model of propagating shrinkage. Our calculations show that the solidification front is positioned not far ahead of the crack tips, which influences the result considerably. The results agree reasonably well with new measured data of basalt columns. By use of the analogy between contraction due to cooling and that due to drying the model is applied for columns in dried cornstarch, too, showing good agreement with recent experimental data.

A two-dimensional generalized cubic nonlinear Schrödinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is found that modulation of the latter can lead to sideband formation, wave condensation, collapse, turbulence, and inverse energy cascade, although not all together and not in that order.

An efficient state-specific model of dissociation using a quadrature approach is proposed by considering multiquantum vibration-translation (VT) transitions (between bound and quasibound vibrational levels) according to the forced harmonic oscillator theory. Application of this model to a pure ${\mathrm{N}}_2$ gas flow behind a plane shock wave shows that dissociation has a large influence on intermediate and higher vibrational levels and is characterized by state-specific incubation distances, before which VT energy exchanges remain the dominant mechanism just behind the shock.

We have numerically found periodic collisionless motions of a walking model consisting of linked rigid objects. Unlike previous designs, this model can walk on level ground at noninfinitesimal speed with zero energy input. The model avoids collisional losses by using an internal mode of oscillation: swaying of the upper body coupled to the legs by springs. Appropriate synchronized internal oscillations set the foot-strike collision to zero velocity. The concept might be of use for energy-efficient robots and may also help to explain aspects of human and animal locomotion efficiency.

Label propagation has proven to be a fast method for detecting communities in large complex networks. Recent developments have also improved the accuracy of the approach; however, a general algorithm is still an open issue. We present an advanced label propagation algorithm that combines two unique strategies of community formation, namely, defensive preservation and offensive expansion of communities. The two strategies are combined in a hierarchical manner to recursively extract the core of the network and to identify whisker communities. The algorithm was evaluated on two classes of benchmark networks with planted partition and on 23 real-world networks ranging from networks with tens of nodes to networks with several tens of millions of edges. It is shown to be comparable to the current state-of-the-art community detection algorithms and superior to all previous label propagation algorithms, with comparable time complexity. In particular, analysis on real-world networks has proven that the algorithm has almost linear complexity, $O(m^{1.19})$, and scales even better than the basic label propagation algorithm ($m$ is the number of edges in the network).

We show that including a sufficient description of the target’s rear surface significantly affects the interpretation of a wide range of laser-solid experiments. A simple Debye sheath model will be shown to be adequate. From this the sheath field responsible for ion acceleration has been shown to expand at superluminal speeds, leading to very large ion-emission regions on the target’s rear surface; a new explanation for the dynamics of the ion-accelerating sheath field accounts for this observation and demonstrates the inaccuracy of measuring the angular divergence of the injected electron beam, crucial to fast ignition, from the lateral extent of the ion emission. However, it is shown that on careful probing the sheath field can provide unique insight into details of the fast electron’s distribution function. The relative merits of probing other physical quantities has been examined. The width of the background temperature spot overestimates the divergence by a factor of 2 unless electron recirculation is prevented.

We demonstrate the validity of Landauer’s erasure principle in the strong coupling quantum regime by treating the system-reservoir interaction in a thermodynamic way. We show that the initial coupling to the reservoir modifies both the energy and the entropy of the system, and provide explicit expressions for the latter for a damped quantum harmonic oscillator. These contributions are related to the Hamiltonian of mean force and dominate in the strong damping limit. They need therefore to be fully taken into account in any low temperature thermodynamic analysis of quantum systems.

Since only intersections with lines or planes are usually available to quantify the properties of real fracture networks, a stereological analysis of these intersections is a crucial issue. This article—the second of a series—is devoted to the derivation of the direct relations between the properties and the observable quantities. First, this derivation is achieved for anisotropic networks whose orientations obey a Fisher probability distribution function; second, it is extended to networks which are heterogeneous in space, i.e., whose density decays according to an exponential law. Five major quantities are determined: the excluded volume, the average number of intersections with a line and with a plane, the average trace length and the surface density of trace intersections. Some of these relations are valid for any convex fracture shape and some only for circular disks; however, numerical simulations show that excellent approximations are obtained by considering disks with the same area as the noncircular fractures. All the results are summarized in Table I.

Chua [IEEE Trans. Circuit Theory 1, 507 (1971).] argued that, in addition to the standard resistors, capacitors, and inductors, there must be a fourth fundamental element in electrical circuits, which he called a memory resistor or memristor. Strukov et al. [Nature (London) 453, 80 (2008)] showed how memristive behavior arises in some thin semiconducting films. Unlike other passive elements, however, a memristor with large sizes cannot be fabricated, because scale up of a memristor to dimensions of the order of microns causes loss of the memristive effect by decreasing the width of the doped region relative to the overall size of the memristor. A microscale memristor is, however, essential to most of the potential applications. One way of fabricating such a microscale memristor without losing the memristive effect is to make a network of very small interconnected memristors. We report the results of numerical simulations of electrical currents in such networks of interconnected memristors, as well as memristors and Ohmic conductors. The memristor networks exhibit a rich variety of interesting properties, including weakly and strongly memristive regimes, a possible first-order transition at the connectivity threshold, generation of second harmonics in the strongly memristive regime, and the universal dependence of the network’s strength on the frequency. Moreover, we show that the polarity of the memristors can play an important role in the overall properties of the memristor network, in particular its speed of switching, which may have a potentially important application to faster computers. None of these properties are exhibited by linear resistor networks, or even by nonlinear resistor networks without a memory effect.

We address a fundamental problem for the advance of phononics: the search of a feasible thermal diode. We establish sufficient conditions for the existence of thermal rectification in general graded materials. By starting from simple assumptions satisfied by the usual anharmonic models that describe heat conduction in solids, we derive an expression for the rectification. The analytical formula shows how to increase the rectification, and the conditions to avoid its decay with the system size, a problem present in the recurrent model of diodes given by the sequential coupling of two or three different parts. Moreover, for these graded systems, we show that the regimes of nondecaying rectification and of normal conductivity do not overlap. Our results indicate the graded systems as optimal materials for a thermal diode, the basic component of several devices of phononics.

The shear alignment of an initially disordered lamellar phase is examined using lattice Boltzmann simulations of a mesoscopic model based on a free-energy functional for the concentration modulation. For a small shear cell of width $8\lambda$, the qualitative features of the alignment process are strongly dependent on the Schmidt number $\text{Sc}=\nu /D$ (ratio of kinematic viscosity and mass diffusion coefficient). Here, $\lambda$ is the wavelength of the concentration modulation. At low Schmidt number, it is found that there is a significant initial increase in the viscosity, coinciding with the alignment of layers along the extensional axis, followed by a decrease at long times due to the alignment along the flow direction. At high Schmidt number, alignment takes place due to the breakage and reformation of layers because diffusion is slow compared to shear deformation; this results in faster alignment. The system size has a strong effect on the alignment process; perfect alignment takes place for a small systems of width $8\lambda$ and $16\lambda$, while a larger system of width $32\lambda$ does not align completely even at long times. In the larger system, there appears to be a dynamical steady state in which the layers are not perfectly aligned—where there is a balance between the annealing of defects due to shear and the creation due to an instability of the aligned lamellar phase under shear. We observe two types of defect creation mechanisms: the buckling instability under dilation, which was reported earlier, as well as a second mechanism due to layer compression.

Using a combination of dynamic light scattering and Freedericksz transitions induced in applied magnetic and electric fields, we have determined the absolute magnitudes of the Frank elastic constants and effective orientational viscosities of the bent-core nematic liquid crystal, 4-chloro-1,3-phenylene bis 4-[4’-(9-decenyloxy)benzoyloxy] benzoate. At a fixed temperature $2\hspace{0.5em}{}^{ˆ}$C below the isotropic-nematic transition, we find $K_{11}=3.1\times {10}^{-12}$ N, $K_{22}=0.31\times {10}^{-12}$ N, $K_{33}=0.88\times {10}^{-12}$ N, ${\eta }_{\mathrm{splay}}=1.1$ Pa s, ${\eta }_{\mathrm{twist}}=0.37$ Pa s, and ${\eta }_{\mathrm{bend}}=1.2$ Pa s. The unusual anisotropies of these parameters are discussed in terms of short-range, smectic-C-like correlations among molecules in the nematic phase.

Almost two decades ago, measurements of force versus extension on isolated double-stranded DNA molecules revealed a force plateau. This unusual stretching phenomenon in DNA suggests that the long molecules may be extended from the usual B form into a new conformation. Different models have been proposed to describe the nature of DNA in its stretched form, S-DNA. Using atomic force microscopy combined with a molecular combing method, we identified the structure of λ-phage DNA for different stretching values. We provide strong evidence for the existence of a first-order transition between B form and S form. Beyond a certain extension of the natural length, DNA molecules adopt a new double-helix conformation characterized by a diameter of 1.2 nm and a helical pitch of 18 nm.

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for $d=1,2,$ and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence, and different morphologies are presented. In the $d=1$ and $d=2$ models, we analyze the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the $d=2$ case, one of the transitions seems to be characterized by critical exponents that differ from directed-percolation ones, but this transition could be also weakly discontinuous. In the $d=3$ version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behavior occurs in the present model but only for $d\gtrsim 2$. For $d⩾2$, a steady state depends on the initial configuration in some cases.

The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as the three competing strategies. Fines and costs of pool punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects a payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single- and two-strategy stationary states, a rock-paper-scissors type of cyclic dominance can emerge in strikingly different ways.