We study antisymmetric components of matrices characterizing pair interactions in multistrategy evolutionary games. Based on the dyadic decomposition of matrices we distinguish cyclic and starlike hierarchical dominance in the appropriate components. In the symmetric matrix games the strengths of these elementary components are determined. The general features and intrinsic symmetries of these interactions are represented by directed graphs. It is found that the variation of a single matrix component modifies simultaneously the strengths of two starlike hierarchical basis games and many other independent rock-paper-scissors type cyclic basis games. The application of the related concepts is illustrated by discussing the three-strategy voluntary prisoner's dilemma.

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

For many power-limited networks, such as wireless sensor networks and mobile ad hoc networks, maximizing the network lifetime is the first concern in the related designing and maintaining activities. We study the network lifetime from the perspective of network science. In our model, nodes are initially assigned a fixed amount of energy moving in a square area and consume the energy when delivering packets. We obtain four different traffic regimes: no, slow, fast, and absolute congestion regimes, which are basically dependent on the packet generation rate. We derive the network lifetime by considering the specific regime of the traffic flow. We find that traffic congestion inversely affects network lifetime in the sense that high traffic congestion results in short network lifetime. We also discuss the impacts of factors such as communication radius, node moving speed, routing strategy, etc., on network lifetime and traffic congestion.

Collective behavior of bacterial colonies plays critical roles in adaptability, survivability, biofilm expansion and infection. We employ an individual-based model of an interstitial biofilm to study emergent pattern formation based on the assumptions that rod-shaped bacteria furrow through a viscous environment and excrete extracellular polymeric substances which bias their rate of motion. Because the bacteria furrow through their environment, the substratum stiffness is a key control parameter behind the formation of distinct morphological patterns. By systematically varying this property (which we quantify with a stiffness coefficient $\gamma$), we show that subtle changes in the substratum stiffness can give rise to a stable state characterized by a high degree of local order and long-range pattern formation. The ordered state exhibits characteristics typically associated with bacterial fitness advantages, even though it is induced by changes in environmental conditions rather than changes in biological parameters. Our findings are applicable to a broad range of biofilms and provide insights into the relationship between bacterial movement and their environment, and basic mechanisms behind self-organization of biophysical systems.

This study explores the significance of geometric angle shifts, which we call geometric somersaults, arising from cyclic twisting motions of a polymer chain. A five-bead polymer chain serves as a concise and minimal model of a molecular shaft throughout this study. We first show that this polymer chain can change its orientation about its longitudinal axis largely, e.g., ${120}^{\circ }$, under conditions of zero total angular momentum by changing the two dihedral angles in a cyclic manner. This phenomenon is an example of the so-called “falling cat” phenomenon, where a falling cat undergoes a geometric somersault by changing its body shape under conditions of zero total angular momentum. We then extend the geometric somersault of the polymer chain to a noisy and viscous environment, where the polymer chain is steered by external driving forces. This extension shows that the polymer chain can achieve an orientation change keeping its total angular momentum and total external torque fluctuating around zero in a noisy and viscous environment. As an application, we argue that the geometric somersault of the polymer chain by ${120}^{\circ }$ may serve as a prototypical and coarse-grained model for the rotary motion of the central shaft of ATP synthase (${\mathrm{F}}_{\mathrm{O}}{\mathrm{F}}_1$-ATPase). This geometric somersault is in clear contrast to the standard picture for the rotary motion of the central shaft as a rigid body, which generally incurs nonzero total angular momentum and nonzero total external torque. The power profile of the geometric somersault implies a preliminary mechanism for elastic power transmission. The results of this study may be of fundamental interest in twisting and rotary motions of biomolecules.

Triboelectric charging, the phenomenon by which electrical charge is exchanged during contact between two surfaces, has been known to cause significant charge separation in granular mixtures, even between chemically identical grains. This charging is a stochastic size-dependent process resulting from random collisions between grains. The prevailing models and experimental results suggest that, in most cases, larger grains in a mixture of dielectric grains acquire a positive charge, while smaller grains charge negatively. These models are typically restricted to mixtures of two discrete grain sizes, which are not representative of most naturally occurring granular mixtures, and neglect the effect of grain size on individual charging events. We have developed a model that predicts the average charge distribution in a granular mixture, for any continuous size distribution of dielectric grains of a single material. Expanding to continuous size distributions enables the prediction of charge separation in many natural granular phenomena, including terrestrial dust storms and industrial powder handling operations. The expanded model makes predictions about the charge distribution, including specific conditions under which the usual size-dependent polarity is reversed such that larger grains charge negatively.

Here we investigate, using relativistic fluid theory and Vlasov-Maxwell simulations, the local heating of a dense plasma by two crossing electron beams. Heating occurs as an instability of the electron beams drives Langmuir waves, which couple nonlinearly into damped ion-acoustic waves. Simulations show a factor 2.8 increase in electron kinetic energy with a coupling efficiency of 18%. Our results support applications to the production of warm dense matter and as a driver for inertial fusion plasmas.

We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e., rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks relevant to various real-world systems.

A recent theoretical study [Phys. Rev. Lett. 112, 037202 (2014)] has revealed that systems such as uranium ferromagnetic superconductors obey conserved dynamics. To capture the critical behavior near the paramagnetic to ferromagnetic phase transition of these compounds, we study the conserved critical dynamics of a nonlocal Ginzburg-Landau model. A dynamic renormalization-group calculation at one-loop order yields the critical indices in the leading order of $\epsilon =d_c-d$, where $d_c=4-2\rho$ is the upper critical dimension, with $\rho$ an exponent in the nonlocal interaction. The predicted static critical exponents are found to be comparable with the available experimentally observed critical exponents for strongly uniaxial uranium ferromagnetic superconductors. The corresponding dynamic exponent $z$ and linewidth exponent $w$ are found to be $z=4-\rho \epsilon /4+O\left({\epsilon }^2\right)$ and $w=1+\rho +3\epsilon /4+O\left({\epsilon }^2\right)$.

Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the Kardar–Parisi–Zhang (KPZ) equation in $1+1$ dimensions. Here we notice that, at or above a critical dimension, the finite-time one-point height distribution is ill defined in a broad class of linear surface growth models unless the model is regularized at small scales. The regularization via a system-dependent small-scale cutoff leads to a partial loss of universality. As a possible alternative, we introduce a local average height. For the linear models, the probability density of this quantity is well defined in any dimension. The weak-noise theory for these models yields the “optimal path” of the interface conditioned on a nonequilibrium fluctuation of the local average height. As an illustration, we consider the conserved Edwards–Wilkinson (EW) equation, where, without regularization, the finite-time one-point height distribution is ill defined in all physical dimensions. We also determine the optimal path of the interface in a closely related problem of the finite-time height-difference distribution for the nonconserved EW equation in $1+1$ dimension. Finally, we discuss a UV catastrophe in the finite-time one-point distribution of height in the (nonregularized) KPZ equation in $2+1$ dimensions.

We obtain an exact solution for the cluster-size distributions in a closed system described by nonlinear rate equations for irreversible homogeneous growth with size-linear agglomeration rates of the form $K_s=D(a+s-1)$ for all $s\ge 1$, where $D$ is the diffusion coefficient, $s$ is the size, and $a$ is a positive constant. The size spectrum is given by the Pólya distribution times a factor that normalizes the first moment of the distribution to unity and zeroes out the monomer concentration at $t\to \infty$. We show that the $a$ value sets a maximum mean size that equals $e$ for large $a$ and tends to infinity only when $a\to 0$. The size distributions are monotonically decreasing in the initial stage, converting to different monomodal shapes with a maximum at $s=2$ in the course of growth. The variance of the distribution is narrower than Poissonian at large $a$ and broader than Poissonian at small $a$, with the threshold occurring at $a\cong 1$. In most cases, the sizes present in the distributions are small and hence can hardly be described by continuum equations.

The understanding of interacting dynamics is important for the characterization of real-world networks. In general, real-world networks are heterogeneous in the sense that each node of the network is a dynamics with different properties. For coupled nonidentical dynamics symmetric interactions are not straightforwardly defined from the coupling strength values. Thus, a challenging issue is whether we can define a symmetric interaction in this asymmetric setting. To address this problem we introduce the notion of the coupling impact. The coupling impact considers not only the coupling strength but also the energy of the individual dynamics, which is conveyed via the coupling. To illustrate this concept, we follow a data-driven approach by analyzing signals from pairs of coupled model dynamics using two different connectivity measures. We find that the coupling impact, but not the coupling strength, correctly detects a symmetric interaction between pairs of coupled dynamics regardless of their degree of asymmetry. Therefore, this approach allows us to reveal the real impact that one dynamics has on the other and hence to define symmetric interactions in pairs of nonidentical dynamics.

Given any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. In this work, we use the Darboux transformation to prove, in a unified manner and without knowing the analytical form of the background solution, that the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background, irrespective of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background. Generalizations to more extended nonlinear Schrödinger equations, such as the Hirota equation, are indicated.

In this paper we experimentally examine evaporation flux distributions and modes of interfacial energy transport for continuously fed evaporating spherical sessile water droplets in a regime that is relevant for applications, particularly for evaporative cooling systems. The contribution of the thermal conduction through the vapor phase was found to be insignificant compared to the thermal conduction through the liquid phase for the conditions we investigated. The local evaporation flux distributions associated with thermal conduction were found to vary along the surface of the droplet. Thermal conduction provided a majority of the energy required for evaporation but did not account for all of the energy transport, contributing $64\pm 3\%, 77\pm 3\%$, and $77\pm 4\%$ of the energy required for the three cases we examined. Based on the temperature profiles measured along the interface we found that thermocapillary flow was predicted to occur in our experiments, and two convection cells were consistent with the temperature distributions for higher substrate temperatures while a single convection cell was consistent with the temperature distributions for a lower substrate temperature.

Calculations of translational self-diffusion coefficient in free-standing smectic films during a series of layer-thinning transitions as the temperature is raised above the bulk smectic-$A$–isotropic transition have been carried out. A molecular model based upon the random walk theory is applied for calculating the translational diffusion coefficient (TDC) $D_{\parallel }$ across the smectic film both in the bulk of the film, as well as in the vicinity of the bounding surfaces. Calculations of $D_{\parallel }$ require the set of the orientational and translational order parameters (OPs) which have been obtained by using the extended McMillan approach with anisotropic forces. The effect of $\mathbf{\text{E}}$ on the orientational and translational OPs, as well as on the TDC of smectic films has been investigated. A reasonable agreement between the theoretically predicted and the experimentally obtained data on the TDC in the bulk of the partially fluorinated H10F5MOPP film has been obtained. We also found, in agreement with the experimentally observed behavior of $D_{\parallel }\left(\mathrm{N}\right)(N=25,13,11,10)$, that the translational diffusion coefficient in the bulk of the film gradually increases as the film thickness $N$ is decreased.

While flame propagation through obstacles is often associated with turbulence and/or shocks, Bychkov et al. [V. Bychkov et al., Phys. Rev. Lett. 101, 164501 (2008)] have revealed a shockless, conceptually laminar mechanism of extremely fast flame acceleration in semiopen obstructed pipes (one end of a pipe is closed; a flame is ignited at the closed end and propagates towards the open one). The acceleration is devoted to a powerful jet flow produced by delayed combustion in the spaces between the obstacles, with turbulence playing only a supplementary role in this process. In the present work, this formulation is extended to pipes with both ends open in order to describe the recent experiments and modeling by Yanez et al. [J. Yanez et al., arXiv:1208.6453] as well as the simulations by Middha and Hansen [P. Middha and O. R. Hansen, Process Safety Prog. 27, 192 (2008)]. It is demonstrated that flames accelerate strongly in open or vented obstructed pipes and the acceleration mechanism is similar to that in semiopen ones (shockless and laminar), although acceleration is weaker in open pipes. Starting with an inviscid approximation, we subsequently incorporate hydraulic resistance (viscous forces) into the analysis for the sake of comparing its role to that of a jet flow driving acceleration. It is shown that hydraulic resistance is actually not required to drive flame acceleration. In contrast, this is a supplementary effect, which moderates acceleration. On the other hand, viscous forces are nevertheless an important effect because they are responsible for the initial delay occurring before the flame acceleration onset, which is observed in the experiments and simulations. Accounting for this effect provides good agreement between the experiments, modeling, and the present theory.

$\gamma$-ray flash generation in near-critical-density target irradiated by four symmetrical colliding laser pulses is numerically investigated. With peak intensities about ${10}^{23}$ $\mathrm{W}/{\mathrm{cm}}^2$, the laser pulses boost electron energy through direct laser acceleration, while pushing them inward with the ponderomotive force. After backscattering with counterpropagating laser, the accelerated electron is trapped in the electromagnetic standing waves or the ponderomotive potential well created by the coherent overlapping of the laser pulses, and emits $\gamma$-ray photons in a multiple-laser-scattering regime, where electrons act as a medium transferring energy from the laser to $\gamma$ rays in the ponderomotive potential valley.

We define a “$k$-booklet” to be a set of $k$ semi-infinite planes with $-\infty <x<\infty$ and $y\ge 0$, glued together at the edges (the “spine”) $y=0$. On such booklets we study three critical phenomena: self-avoiding random walks, the Ising model, and percolation. For $k=2$, a booklet is equivalent to a single infinite lattice, and for $k=1$ to a semi-infinite lattice. In both these cases the systems show standard critical phenomena. This is not so for $k\ge 3$. Self-avoiding walks starting at $y=0$ show a first-order transition at a shifted critical point, with no power-behaved scaling laws. The Ising model and percolation show hybrid transitions, i.e., the scaling laws of the standard models coexist with discontinuities of the order parameter at $y\approx 0$, and the critical points are not shifted. In the case of the Ising model, ergodicity is already broken at $T=T_c$, and not only for $T<T_c$ as in the standard geometry. In all three models, correlations (as measured by walk and cluster shapes) are highly anisotropic for small $y$.

We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.

We report that population dynamics in fluctuating environments is characterized by a mathematically equivalent structure to steady-state thermodynamics. By employing the structure, population growth in fluctuating environments is decomposed into housekeeping and excess parts. The housekeeping part represents the integral of the stationary growth rate for each condition during a history of the environmental change. The excess part accounts for the excess growth induced by environmental fluctuations. Focusing on the excess growth, we obtain a Clausius inequality, which gives the upper bound of the excess growth. The equality is shown to be achieved in quasistatic environmental changes. We also clarify that this bound can be evaluated by the “lineage fitness”, which is an experimentally observable quantity.