The migration of a particle in a system of obstacles under the action of an external field is often modeled using lattice Monte Carlo algorithms. For example, such simulation methods have been used to study the electrophoresis of charged molecules in sieving gels and the separation of particles using ratchet systems. In the case of constant fields or low-frequency alternating fields, the Monte Carlo simulation method can be mapped onto a numerical or algebraic matrix problem that can be solved exactly. In this Rapid Communication, we generalize this matrix approach to treat periodic time-dependent fields. The evolution of the spatial distribution function during a period is computed using a sequence of transfer matrices, and a steady-state closure relation allows us to calculate the exact mean velocity of the particle during a complete cycle. As an example, we examine the properties of a simple spatially asymmetric ratchet system in the presence of periodic alternating fields (symmetric and asymmetric) as well as random telegraph signals.

We study the evolution of cooperation within the spatial prisoner’s dilemma game on a square lattice where a fraction of players $\mu$ can spread their strategy more easily than the rest due to a predetermined larger teaching capability. In addition, players characterized by the larger teaching capability are allowed to temporarily link with distant opponents of the same kind with probability $p$, thus introducing shortcut connections among the distinguished players. We show that these additional temporary connections are able to sustain cooperation throughout the whole range of the temptation to defect. Remarkably, we observe that, as the temptation to defect increases the optimal $\mu$ decreases, and moreover only minute values of $p$ warrant the best promotion of cooperation. Our study thus indicates that influential individuals must be few and sparsely connected in order for cooperation to thrive in a defection-prone environment.

The stability and nonlinear dynamics of two semiconductor lasers coupled side to side via evanescent waves are investigated by using three different models. In the composite-cavity model, the coupling between the lasers is accurately taken into account by calculating electric field profiles (composite-cavity modes) of the whole coupled-laser system. A bifurcation analysis of the composite-cavity model uncovers how different types of dynamics, including stationary phase-locking, periodic, quasiperiodic, and chaotic intensity oscillations, are organized. In the individual-laser model, the coupling between individual lasers is introduced phenomenologically with ad hoc coupling terms. Comparison with the composite-cavity model reveals drastic differences in the dynamics. To identify the causes of these differences, we derive a coupled-laser model with coupling terms which are consistent with the solution of the wave equation and the relevant boundary conditions. This coupled-laser model reproduces the dynamics of the composite-cavity model under weak-coupling conditions.

We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean-field approach to sandpile dynamics by formulating it as a generalization of Itô’s SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters and a drift term reflecting the tendency for small avalanches to grow and large avalanches to be constricted by the finite system size. If one defines avalanching to take place when the toppling activity exceeds a certain threshold, the stochastic model allows us to compute the avalanche exponents in the continum limit as functions of the Hurst exponent of the noise. The results are found to agree well with numerical simulations in the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also provides a method for computing the probability density functions of the fluctuations in the toppling activity itself. We show that the sandpiles do not belong to the class of phenomena giving rise to universal non-Gaussian probability density functions for the global activity. Moreover, we demonstrate essential differences between the fluctuations of total kinetic energy in a two-dimensional turbulence simulation and the toppling activity in sandpiles.

Bartumeus et al. [Phys. Rev. Lett. 88, 097901 (2002)] compared the efficiency of a Lévy random walk predator strategy with a Brownian random walk strategy in a periodic one-dimensional domain with nonrevisitable moving targets. Their findings from numerical simulations conclude that “a Lévy search strategy is the best option in some, but not all, cases for a random search process.” Using the same methodology, we show that the simplest random search strategy of all, ballistic motion in a random direction, outperforms a Lévy strategy in almost every case. We further show that, in the small set of cases where the ballistic strategy is not optimal, the periodic model does not capture the more realistic nonperiodic case. In the nonperiodic case, the ballistic strategy again outperforms the Lévy strategy.

We describe the growth of vesicles, due to the accretion of lipid molecules to their surface, in terms of linear irreversible thermodynamics. Our treatment differs from those previously put forward by consistently including the energy of the membrane in the thermodynamic description. We calculate the critical radius at which the spherical vesicle becomes unstable to a change of shape in terms of the parameters of the model. The analysis is carried out for the case both when the increase in volume is due to the absorption of water and when a solute is also absorbed through the walls of the vesicle.

We consider deflections of a thin rectangular elastic plate that is submerged within a Newtonian fluid. The plate is clamped along one edge and supported horizontally over a plane horizontal wall. We consider both external driving, where the clamped edge is vibrated vertically at high frequencies, and thermal driving, where the plate fluctuates under Brownian motion. In both cases, the amplitude of oscillation is assumed sufficiently small that the resulting flow has little convective inertia, although the oscillation frequency is sufficiently high to generate substantial unsteady inertia in the flow, a common scenario in many nano- and microdevices. We exploit the plate’s thinness to develop an integral-equation representation for the three-dimensional flow (a so-called thin-plate theory) which offers considerable computational savings over a full boundary-integral formulation. Limiting cases of high oscillation frequencies and small wall-plate separation distances are studied separately, leading to further simplified descriptions for the hydrodynamics. We validate these reduced integral representations against full boundary-integral computations, and identify the parameter ranges over which these simplified formulations are valid. Addressing the full flow-structure interaction, we also examine the limits of simpler two-dimensional hydrodynamic models. We compare the responses of a narrow plate under two- and three-dimensional hydrodynamic loading, and report differences in the frequency response curves that occur when the plate operates in water, in contrast to the excellent agreement observed in air.

We derive a general formula for the reduced fidelity susceptibility when the reduced density matrix is $2\times 2$ block diagonal. By using this result and a continuous unitary transformation, we study finite-size scaling of the reduced fidelity susceptibility in the Lipkin-Meshkov-Glick model. It is found that it can well characterize quantum phase transitions, that is, we can extract information about quantum phase transitions from only the fidelity of a subsystem, which is of practical use in experiments.

We present results from four independent models of a granular assembly subjected to tapping. We find that the steady-state packing fraction as a function of the tapping intensity is nonmonotonic. In particular, for high tapping intensities, we observe an increase of the packing fraction with tapping strength. This finding challenges the current understanding of compaction of granular media since the steady-state packing fraction is believed to decrease monotonically with increasing tapping intensity. We propose an explanation of our results based on the properties of the arches formed by the particles.

We examine polymers in the presence of an applied asymmetric sawtooth (ratchet) potential which is periodically switched on and off, using molecular dynamics (MD) simulations with an explicit Lennard-Jones solvent. We show that the distribution of the center of mass for a polymer in a ratchet is relatively wide for potential well depths $U_0$ on the order of several $k_{B}T$. The application of the ratchet potential also deforms the polymer chains. With increasing $U_0$ the Flory exponent varies from that for a free three-dimensional (3D) chain, $\nu =3∕5$ $(U_0=0)$, to that corresponding to a 2D compressed (pancake-shaped) polymer with a value of $\nu =3∕4$ for moderate $U_0$. This has the added effect of decreasing a polymer’s diffusion coefficient from its 3D value $D_{3\mathrm{D}}$ to that of a pancaked-shaped polymer moving parallel to its minor axis $D_{2\mathrm{D}}$. The result is that a polymer then has a time-dependent diffusion coefficient $D\left(t\right)$ during the ratchet off time. We further show that this suggests a different method to operate a ratchet, where the off time of the ratchet, $t_{\text{off}}$, is defined in terms of the relaxation time of the polymer, ${\tau }_R$. We also derive a modified version of the Bader ratchet model [Bader et al., Proc. Natl. Acad. Sci. U.S.A. 96, 13165 (1999)] which accounts for this deformation and we present a simple expression to describe the time dependent diffusion coefficient $D\left(t\right)$. Using this model we then illustrate that polymer deformation can be used to modulate polymer migration in a ratchet potential.

The elasticity and mechanical stability of empty and filled viral capsids under external force loading are studied in a combined analytical and numerical approach. We analyze the influence of capsid structure and chirality on the mechanical properties. We find that generally skew shells have lower stretching energy. For large Föppl–von Kármán numbers $\gamma$ $(\gamma \approx {10}^5)$, skew structures are stiffer in their elastic response than nonchiral ones. The discrete structure of the capsules not only leads to buckling for large $\gamma$ but also influences the breakage behavior of capsules below the buckling threshold: the rupture force shows a ${\gamma }^{1∕4}$ scaling rather than a ${\gamma }^{1∕2}$ scaling as expected from our analytical results for continuous shells. Filled viral capsids are exposed to internal anisotropic pressure distributions arising from regularly packaged DNA coils. We analyze their influence on the elastic properties and rupture behavior and we discuss possible experimental consequences. Finally, we numerically investigate specific sets of parameters corresponding to specific phages such as $\varphi 29$ and cowpea chlorotic mottle virus (CCMV). From the experimentally measured spring constants we make predictions about specific material parameters (such as bending rigidity and Young’s modulus) for both empty and filled capsids.

We investigate the origin of the experimentally observed multifractal scaling of vehicular traffic flows by studying a hydrodynamic model of traffic. We first extend and apply the formalism of generalized Hurst exponents $H\left(q\right)$ to the case of random walkers that not only diffuse but rather also undergo nonlinear convection due to interactions with other walkers. We recover analytically, as expected, that $H\left(q\right)$ equals $1∕2$ for a single random walker starting at the origin whose probability density function satisfies Burger’s equation. Despite this result for a single walker, we find that for a collection of nonlinearly convecting diffusive particles, transient effects can give rise to multiscaling at given time scales for many initial conditions. In the Lighthill-Whitham-Richards hydrodynamic model of traffic, this multiscaling effect becomes more prominent for smaller diffusion constants and larger speed limits. We discuss the relevance of these findings for the realistic scenario of traffic that flows from small roads to large highways and vice versa, where transient effects can be expected to play a significant role.

Prime numbers are the building blocks of our arithmetic; however, their distribution still poses fundamental questions. Riemann showed that the distribution of primes could be given explicitly if one knew the distribution of the nontrivial zeros of the Riemann $\zeta \left(s\right)$ function. According to the Hilbert-Pólya conjecture, there exists a Hermitian operator of which the eigenvalues coincide with the real parts of the nontrivial zeros of $\zeta \left(s\right)$. This idea has encouraged physicists to examine the properties of such possible operators, and they have found interesting connections between the distribution of zeros and the distribution of energy eigenvalues of quantum systems. We apply the Marčhenko approach to construct potentials with energy eigenvalues equal to the prime numbers and to the zeros of the $\zeta \left(s\right)$ function. We demonstrate the multifractal nature of these potentials by measuring the Rényi dimension of their graphs. Our results offer hope for further analytical progress.

This paper analyzes the stability of the amplitude death phenomenon that occurs in a pair of scalar time-delay nonlinear oscillators coupled by static, dynamic, and delayed connections. Stability analysis shows that static connections never induce death in time-delay oscillators. Further, for the case of dynamic and delayed connections, a simple instability condition under which death never occurs is derived. A systematic procedure for estimating the boundary curves of death regions is also provided. These analytical results are then verified by electronic circuit experiments.

We experimentally investigate the flow structures formed when two miscible fluids that have large viscosity contrasts are injected and hydrodynamically focused in plane microchannels. Parallel viscous flows composed of a central stream surrounded by symmetric sheath streams are examined as a function of the flow rates, fluid viscosities, and rates of molecular diffusion. We study miscible interfacial morphologies and show a route for manipulating viscous flow-segregation processes in plane microsystems. The diffusion layer at the boundary of an ensheathed fluid grows as function of the distance downstream and depends on the Péclet number. In particular, we observe diffusion-enhanced viscous ensheathing processes. In the presence of a constriction, we investigate the formation of a lubricated viscous thread in the converging flow and also the buckling morphologies of the thread in the diverging flow. This study, relevant to multifluid flow between a “thick” material and a “thin” solvent, demonstrates the possibility to further control steady and oscillatory miscible fluid microstructures.

Rotating turbulence is characterized by the nondimensional Rossby number Ro, which is a measure of the strength of the Coriolis term relative to that of the nonlinear term. For rapid rotation $(\mathrm{Ro}\to 0)$, nonlinear interactions between inertial waves are weak, and the theoretical approaches used for other weak (wave) turbulence problems can be applied. The important interactions in rotating turbulence at small Ro become those between modes satisfying the resonant and near-resonant conditions. Often, discussions comparing theoretical results and numerical simulations are questioned because of a speculated problem regarding the discreteness of the modes in finite numerical domains versus continuous modes in unbounded continuous theoretical domains. This argument finds its origin in a previous study of capillary waves, for which resonant interactions have a very particular property that is not shared by inertial waves. This possible restriction on numerical simulations of rotating turbulence to moderate Ro has never been quantified. In this paper, we inquire whether the discreteness effects observed in capillary wave turbulence are also present in inertial wave turbulence at small Ro. We investigate how the discreteness effects can affect the setup and interpretation of studies of rapidly rotating turbulence in finite domains. In addition, we investigate how the resolution of finite numerical domains can affect the different types of nonlinear interactions relevant for rotating inertial wave turbulence theories. We focus on Rossby numbers ranging from 0 to 1 and on periodic domains due to their relevance to direct numerical simulations of turbulence. We find that discreteness effects are present for the system of inertial waves for Rossby numbers comfortably smaller than those used in the most recent numerical simulations of rotating turbulence. We use a kinematic model of the cascade of energy via selected types of resonant and near-resonant interactions to determine the threshold of Ro below which discreteness effects become important enough to render an energy cascade impossible.

We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.

Several researchers have analyzed pumps that employ induced-charge electro-osmosis (ICEO) using mainly coplanar electrode array structures in a lateral electric field. We propose ICEO pumps that remove reverse flows using asymmetrically stacked elliptical metal posts and numerically examine the pumping performance. By the boundary element method along with double layer approximation, we find that the asymmetrical stacking configuration efficiently suppresses the unwanted reverse flow and yields velocities of the order of a few millimeters per second, and this configuration is compatible with that of an optimized half-coating pump. Further, we propose a simple model for the stacking pump and predict that the velocity of such a stacking pump with a thin limit is larger than 67% of that of a circular cylindrical half-coating pump of the same length. Using this stacking pump, we can expect to significantly improve the pumping performance.

Previous studies mostly assume deterministic interactions among neighboring individuals for games on graphs. In this paper, we relax this assumption by introducing stochastic interactions into the spatial Prisoner’s dilemma game, and study the effects of interaction stochasticity on the evolution of cooperation. Interestingly, simulation results show that there exists an optimal region of the intensity of interaction resulting in a maximum cooperation level. Moreover, we find good agreement between simulation results and theoretical predictions obtained from an extended pair-approximation method. We also show some typical snapshots of the system and investigate the mean payoffs for cooperators and defectors. Our results may provide some insight into understanding the emergence of cooperation in the real world where the interactions between individuals take place in an intermittent manner.