In this study we investigate electrical conduction in finite rectangular random resistor networks in quasione and two dimensions far away from the percolation threshold $p_c$ by the use of a bond percolation model. Various topologies such as parallel linear chains in one dimension, as well as square and triangular lattices in two dimensions, are compared as a function of the geometrical aspect ratio. In particular we propose a linear approximation for conduction in two-dimensional systems far from $p_c$, which is useful for engineering purposes. We find that the same scaling function, which can be used for finite-size scaling of percolation thresholds, also applies to describe conduction away from $p_c$. This is in contrast to the quasi-one-dimensional case, which is highly nonlinear. The qualitative analysis of the range within which the linear approximation is legitimate is given. A brief link to real applications is made by taking into account a statistical distribution of the resistors in the network. Our results are of potential interest in fields such as nanostructured or composite materials and sensing applications.

Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatiotemporal structures in a self-organized manner, such as temporal rhythms, switching phenomena, and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field. Based on the present model, we discuss the underlying physical principles that are independent of the details of biomolecular reactions. We also discuss the framework of spatial discreteness based on the reaction-diffusion model in relation to a cellular array, by comparison with an actual experimental observation.

We consider the dynamics of polymer translocation out of confined environments. Analytic scaling arguments lead to the prediction that the translocation time scales like $\tau \sim N^{\beta +{\nu }_{2D}}{R}^{1+\left(1-{\nu }_{2D}\right)/\nu }$ for translocation out of a planar confinement between two walls with separation $R$ into a three-dimensional (3D) environment, and $\tau \sim N^{\beta +1}R$ for translocation out of two strips with separation $R$ into a two-dimensional (2D) environment. Here, $N$ is the chain length, $\nu$ and ${\nu }_{2D}$ are the Flory exponents in 3D and 2D, and $\beta$ is the scaling exponent of translocation velocity with $N$, whose value for the present choice of parameters is $\beta \approx 0.8$ based on Langevin dynamics simulations. These scaling exponents improve on earlier predictions.

Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.

We present a method for the calculation of asymptotic operators for nonequilibrium steady-state quantum systems. The asymptotic steady-state operator is obtained by averaging the corresponding operator in Heisenberg representation over infinitely long time. Several examples are considered to demonstrate the utility of our method. The results obtained within our approach are compared to those obtained within the Schwinger-Keldysh nonequilibrium Green’s functions.

Natural time $\chi$ enables the distinction of two origins of self-similarity, i.e., the process memory and the process increments infinite variance. Employing multiplicative cascades in natural time, the most probable value of the variance ${\kappa }_1\left(\equiv ⟨{\chi }^2⟩-{⟨\chi ⟩}^2\right)$ is explicitly related with the parameter $b$ of the Gutenberg-Richter law of randomly shuffled earthquake data. Moreover, the existence of temporal and magnitude correlations is studied in the original earthquake data. Magnitude correlations are larger for closer in time earthquakes, when the maximum interoccurrence time varies from half a day to 1 min.

A protean topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here, we present a minimal and local continuum model that can explain many of the features of the phyllotactic soliton, such as locked speed, screw shift, energy transport, and—for Wigner crystal on a nanotube—charge transport. The treatment is general and should apply to other spiraling systems. Unlike, e.g., sine-Gordon-like systems, our soliton can exist between nondegenerate structures and its dynamics extends to the domains it separates; we also predict pulses, both static and dynamic. Applications include charge transport in Wigner Crystals on nanotubes or $A$- to $B$-DNA transitions.

Natural convection within an enclosed circular annular cavity formed by two concentric vertical cylinders is of fundamental interest and practical importance. Generally, the assumption of axisymmetric thermal flow is adopted for simulating such natural convections and the validity of the assumption of axisymmetric thermal flow is still held even for some turbulent convection. Usually the Rayleigh numbers (Ra) of realistic flows are very high. However, the work to design suitable and efficient lattice Boltzmann (LB) models on such flows is quite rare. To bridge the gap, in this paper a simple LB subgrid-scale (SGS) model, which is based on our recent work [S. Chen, J. Tölke, and M. Krafczyk, Phys. Rev. E 79, 016704 (2009); S. Chen, J. Tölke, S. Geller, and M. Krafczyk, Phys. Rev. E 78, 046703 (2008)], is proposed for simulating convectional flow with high Ra within an enclosed circular annular cavity. The key parameter for the SGS model can be quite easily and efficiently evaluated by the present model. The numerical experiments demonstrate that the present model works well for a large range of Ra and Prandtl number (Pr). Though in the present study a popularly used static Smagorinsky turbulence model is adopted to demonstrate how to develop a LB SGS model for simulating axisymmetric thermal flows with high Ra, other state-of-the-art turbulence models can be incorporated into the present model in the same way. In addition, the present model can be extended straightforwardly to simulate other axisymmetric convectional flows with high Ra, for example, turbulent convection with internal volumetric heat generation in a vertical cylinder, which is an important simplified representation of a nuclear reactor.

It is shown that magnetic fields can be generated in a warm plasma by the nonstationary ponderomotive force of a large-amplitude electromagnetic wave. In the present Brief Report, we derive simple and explicit results that can be useful for understanding the origin of the magnetic fields that are produced in intense laser-plasma interaction experiments.

We investigated cluster formation in model colloids where the interparticle potential beyond the collision diameter includes a short-ranged attraction and a longer-ranged repulsion. The structure and thermodynamic properties of the model system can be accurately described by the first-order mean-spherical approximation (FMSA) and a perturbation theory for bulk phases and by a nonlocal density-functional theory (DFT) for stable/metastable clusters. In corroboration with recent experiments and molecular simulations, we predicted that the bulk to cluster transition may occur at both one-phase and two-phase regions of the colloidal phase diagram. While formation of colloidal clusters appears uncorrelated with the bulk phase transitions, the local phenomena may nevertheless play an important role in the dynamics of stable colloids and the kinetics of colloidal phase transitions.

The onset of electroconvection in binary mixtures of a bent-core and a rodlike nematic has been characterized by measuring the threshold voltage $U_c$ and the critical wave number of the pattern in a wide range of frequencies $f$. In the mixtures rich in bent-core molecules, a “conductive-prewavy2-patternless-prewavy1” morphological sequence has been detected with an unusual negative slope of $U_c\left(f\right)$ at high frequencies. This latter scenario seems to be related to the bent-core component, as it disappears with increasing the concentration of rodlike molecules. In addition, one of the parameters most relevant for electroconvection, the electrical conductivity, has also been varied by ionic salt doping. It has been found that the above effect of the banana-shaped molecules on the electroconvection scenarios can be suppressed by the conductivity.

Spatial games are crucial for understanding patterns of cooperation in nature (and to some extent society). They are known to be more sensitive to local symmetries than, e.g., spin models. This paper concerns the evolution of the prisoner’s dilemma game on regular lattices with three different types of neighborhoods—the von Neumann, Moore, and kagomé types. We investigate two kinds of dynamics for the players to update their strategies (that can be unconditional cooperator or defector). Depending on the payoff difference, an individual can adopt the strategy of a random neighbor [a voter-model-like dynamics (VMLD)] or impose its strategy on a random neighbor, i.e., invasion-process-like dynamics (IPLD). In particular, we focus on the effects of noise, in combination with the strategy dynamics, on the evolution of cooperation. We find that VMLD, compared to IPLD, better supports the spreading and sustaining of cooperation. We see that noise has nontrivial effects on the evolution of cooperation: maximum cooperation density can be realized either at a medium noise level, in the limit of zero noise or in both these regions. The temptation to defect and the local interaction structure determine the outcome. Especially, in the low noise limit, the local interaction plays a crucial role in determining the fate of cooperators. We elucidate these both by numerical simulations and mean-field cluster approximation methods.

We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation in the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occurs. We fill this gap by perturbatively incorporating classes of spatially varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity, apply the method to the spherical pore with a simple hemispherical binary distribution of the depletion strength, and obtain bounds for the induced change in the slowest relaxation mode.

The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first- and second-order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erdös-Rényi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis.

The occurrence of single-site or multisite localized vibrational modes, also called discrete breathers, in two-dimensional hexagonal dusty plasma lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized by a negative coupling parameter $\epsilon$ in account of its inverse dispersive behavior. A theoretical analysis is performed in order to establish the possibility of existence of single as well as three-site discrete breathers in such systems. The study is complemented by a numerical investigation based on experimentally provided potential forms. This investigation shows that a dusty plasma lattice can support single-site discrete breathers, while three-site in phase breathers could exist if specific conditions, about the intergrain interaction strength, would hold. On the other hand, out of phase and vortex three-site breathers cannot be supported since they are highly unstable.

A class of reptiles known as sand swimmers adapts to hot environments by submerging beneath desert sands during the day and so provide a unique probe into the dynamics of intruders in granular beds. To understand the mechanism for swimming in an otherwise solid bed, we study a simple model of periodic contraction and extension of large intruders in a granular bed. Using an event-driven simulation, we find optimal conditions that idealized swimmers must use to critically fluidize a sand bed so that it is rigid enough to support a load when needed, but fluid enough to permit motion with minimal resistance. Swimmers—or other intruders—that agitate the bed too rapidly produce large voids that prevent traction from being achieved, while swimmers that move too slowly cannot travel before the bed resolidifies around them, i.e., the swimmers locally probe the fundamental time scale in a granular packing.

Gold nanorods are generated spontaneously in a surfactant solution. We developed an experimental setup where the growth of gold nanorods can be completely stopped at any instant. With this method, a time series of the growth process of gold nanorods was determined by the direct observation of nanorods with transmission electron microscopy. We estimated the growth rate of nanorods from the change in the average long-axis length over time. To understand the experimental results, we developed a mathematical model for the growth of nanorods. The present results should help to clarify the mechanism of the growth of gold nanorods.

Knowing which mode of combinatorial regulation (typically, AND or OR logic operation) that a gene employs is important for determining its function in regulatory networks. Here, we introduce a dynamic cross-correlation function between the output of a gene and its upstream regulator concentrations for signatures of combinatorial regulation in gene expression noise. We find that such a correlation function with respect to the correlation time near the peak close to the point of the zero correlation time is always upward convex in the case of AND logic whereas is always downward convex in the case of OR logic, whichever sources of noise (intrinsic or extrinsic or both). In turn, this fact implies a means for inferring regulatory synergies from available experimental data. The extensions and applications are discussed.

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks, corresponding to consensus formation in society, we observe two distinct phases: (i) ordering within each module at a critical temperature followed by (ii) global ordering at a lower temperature. This indicates polarization of society into groups having contrary opinions can persist indefinitely even when mutual interactions between agents favor consensus.