We consider phononic energy transport between nanoparticles mediated by a quantum particle. The nanoparticles are considered as thermal reservoirs described by ensembles of finite numbers of harmonic oscillators within the Drude-Ullersma model having, in general, unequal mode spacings ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$, which amount to different numbers of atoms in the nanoparticles. The quasistatic energy transport between the nanoparticles on the time scale $t\sim 1/{\mathrm{\Delta }}_{1,2}$ is investigated using the generalized quantum Langevin equation. We find that double degeneracy of system's eigenfrequencies, which occurs in the case of identical nanoparticles, is removed when the mode spacings become unequal. The equations describing the dynamics of the averaged eigenmode energies are derived and solved, and the resulting expression for the energy current between the nanoparticles is obtained and explored. Unlike the case when the thermodynamic limit is assumed resulting in time-independent energy current, finite-size effects result in temporal behavior of the energy current that evinces reversibility features combined with decay and possesses peculiarities at time moments $t=2\pi n/{\mathrm{\Delta }}_1+2\pi m/{\mathrm{\Delta }}_2$ for non-negative integers $n$ and $m$. When ${\mathrm{\Delta }}_{1,2}\to 0$, an expression for the heat current obtained previously under assumption of the thermodynamic limit is reproduced. The energy current between two platinum nanoparticles mediated by a carbon oxide molecule is considered as an application of the developed model.

We study extreme value statistics of multiple sequences of random variables. For each sequence with $N$ variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of $m$ independent sequences and investigate the probability $S_N$ that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability $S_N$ is universal: it does not depend on the distribution from which the random variables are drawn. For two sequences, $S_N\sim N^{-1/2}$, and in general, the decay is algebraic, $S_N\sim N^{-{\sigma }_m}$, for large $N$. We analytically obtain the exponent ${\sigma }_3\cong 1.302931$ as root of a transcendental equation. Furthermore, the exponents ${\sigma }_m$ grow with $m$, and we show that ${\sigma }_m\sim m$ for large $m$.

Drops of active liquid crystal have recently shown the ability to self-propel, which was associated with topological defects in the orientation of active filaments [Sanchez et al., Nature 491, 431 (2013)]. Here, we study the onset and different aspects of motility of a three-dimensional drop of active fluid on a planar surface. We analyze theoretically how motility is affected by orientation profiles with defects of various types and locations, by the shape of the drop, and by surface friction at the substrate. In the scope of a thin drop approximation, we derive exact expressions for the flow in the drop that is generated by a given orientation profile. The flow has a natural decomposition into terms that depend entirely on the geometrical properties of the orientation profile, i.e., its bend and splay, and a term coupling the orientation to the shape of the drop. We find that asymmetric splay or bend generates a directed bulk flow and enables the drop to move, with maximal speeds achieved when the splay or bend is induced by a topological defect in the interior of the drop. In motile drops the direction and speed of self-propulsion is controlled by friction at the substrate.

Shape measurements after the coalescence of isotropic droplets embedded in a thin sample of a homeotropic nematic phase provides a tool to measure the nematic-isotropic surface tension. In addition, this experiment allows us to check the scaling laws recently given by Brun et al. [P.-T. Brun, M. Nagel, and F. Gallaire, Phys. Rev. E 88, 043009 (2013)] to explain the relaxation of ellipsoidal droplets in a Hele-Shaw cell.

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.

We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself, but the activity provided initially is sustained within the collective of interacting agents. In contrast to existing models of self-sustaining activity that are caused by (long) loops present in the network, here we focus on treelike structures and examine activation mechanisms that are due to temporal memory of the nodes. This approach is motivated by applications in social media, where long network loops are rare or absent. Our results suggest that under a weak behavioral noise, the nodes robustly split into several clusters, with partial synchronization of nodes within each cluster. We also study the randomly weighted version of the models where the nodes are allowed to change their connection strength (this can model attention redistribution) and show that it does facilitate the self-sustained activity.

The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust, and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the hierarchical mutual information, which is a generalization of the traditional mutual information and makes it possible to compare hierarchical partitions and hierarchical community structures. The normalized version of the hierarchical mutual information should behave analogously to the traditional normalized mutual information. Here the correct behavior of the hierarchical mutual information is corroborated on an extensive battery of numerical experiments. The experiments are performed on artificial hierarchies and on the hierarchical community structure of artificial and empirical networks. Furthermore, the experiments illustrate some of the practical applications of the hierarchical mutual information, namely the comparison of different community detection methods and the study of the consistency, robustness, and temporal evolution of the hierarchical modular structure of networks.

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.

We numerically analyze the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem, we compute the linear stability of the log-rolling orbit at small shear Reynolds number ${\mathrm{Re}}_a$. As ${\mathrm{Re}}_a\to 0$ and as the box size of the system tends to infinity, we find good agreement between the numerical results and earlier analytical predictions valid to linear order in ${\mathrm{Re}}_a$ for the case of an unbounded shear. The numerical stability analysis indicates that there are substantial finite-size corrections to the analytical results obtained for the unbounded system. We also compare the analytical results to results of lattice Boltzmann simulations to analyze the stability of the tumbling orbit at shear Reynolds numbers of order unity. Theory for an unbounded system at infinitesimal shear Reynolds number predicts a bifurcation of the tumbling orbit at aspect ratio ${\lambda }_{\mathrm{c}}\approx 0.137$ below which tumbling is stable (as well as log rolling). The simulation results show a bifurcation line in the $\lambda \text{−}{\mathrm{Re}}_a$ plane that reaches $\lambda \approx 0.1275$ at the smallest shear Reynolds number $\left({\mathrm{Re}}_a=1\right)$ at which we could simulate with the lattice Boltzmann code, in qualitative agreement with the analytical results.

Many physical systems can be modeled as large sets of domains “glued” together along boundaries—biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth.

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the $n\mathrm{th}$ topological neighbor; the specific value of $n$ being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for $n$ = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period $t_c$, then switches over to the ordered state and remains in this state ever after. For $n$ = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for $n\ge 3$. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase $n$. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of $n$, which match well with their simulated values.

Random searches often take place in fragmented landscapes. Also, in many instances like animal foraging, significant benefits to the searcher arise from visits to a large diversity of patches with a well-balanced distribution of targets found. Up to date, such aspects have been widely ignored in the usual single-objective analysis of search efficiency, in which one seeks to maximize just the number of targets found per distance traversed. Here we address the problem of determining the best strategies for the random search when these multiple-objective factors play a key role in the process. We consider a figure of merit (efficiency function), which properly “scores” the mentioned tasks. By considering random walk searchers with a power-law asymptotic Lévy distribution of step lengths, $p\left(\ell \right)\sim {\ell }^{-\mu }$, with $1<\mu \le 3$, we show that the standard optimal strategy with ${\mu }_{\text{opt}}\approx 2$ no longer holds universally. Instead, optimal searches with enhanced superdiffusivity emerge, including values as low as ${\mu }_{\text{opt}}\approx 1.3$ (i.e., tending to the ballistic limit). For the general theory of random search optimization, our findings emphasize the necessity to correctly characterize the multitude of aims in any concrete metric to compare among possible candidates to efficient strategies. In the context of animal foraging, our results might explain some empirical data pointing to stronger superdiffusion ($\mu <2$) in the search behavior of different animal species, conceivably associated to multiple goals to be achieved in fragmented landscapes.

A zero-dimensional system that is affected by field-dependent fluctuations evolves toward the field's values in which the fluctuations' effect is minimized. For a high enough noise intensity, it causes an exchange of roles between the stable and unstable state. In this paper, we report symmetry breaking in two stable states, but one of them stabilized by the fluctuations while exchanging its role with a previously stable state.

The equations of fluctuating nonlinear hydrodynamics for a two component mixture are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. Using these nonlinear equations we construct the basic equations of the mode coupling theory (MCT) and consequent ergodic-nonergodic (ENE) transition in a binary mixture. The model is also analyzed in the one component limit of the mixture to study the dynamics of a tagged particle in the sea of identical particles. According to the existing MCT, dynamics of the single-particle correlation is slaved to that of the collective density fluctuations and, hence, both correlations freeze simultaneously at the ENE transition. We show here from a nonperturbative approach that at the ENE transition, characterized by the freezing of the long time limit of the dynamic correlation of collective density fluctuations to a nonzero value, the tagged-particle correlation still decays to zero. Our result implies that the point at which simulation or experimental data of the self-diffusion constant extrapolate to zero would not correspond to the ENE transition of simple MCT.

The ergodicity-nonergodicity (ENE) transition of the self-consistent mode-coupling theory (MCT) is marked by the point at which the time correlation of collective density fluctuations is not zero in the long-time limit. The nonergodic state, reaching beyond the ENE transition of simple MCT, is characterized by a finite shear modulus. The MCT, formulated in the current set of papers, predicts that the single-particle density correlation, unlike the collective density correlation, decays to zero at long times on either side of the ENE transition. The self-diffusion coefficient remains finite. This differs from the existing MCT results in which both collective and single-particle correlations are simultaniously frozen at the ENE transition. We discuss in this paper mechanisms by which a sharp fall in self-diffusion coefficient may occur within the present model. This overdamping or the so-called adiabatic approximation for the supercooled state does not maintain microscopic momentum conservation. Within this approximation, the self-diffusion constant approaches zero at the ENE transition point. This approximate result, which is similar to the prediction of the existing MCT models, further illustrates the process of cage formation with increase of density. At a qualitative level, our analysis shows that the self-diffusion process depends on the structure as well as short-time transport properties of the supercooled liquid. We solve the integral equations for the nonergodicity parameters to analyze the full implications of the adiabatic approximation.

In the present paper, flows of granular materials impacting wall-like obstacles down inclines are described by depth-averaged analytic solutions. Particular attention is paid to extending the existing depth-averaged equations initially developed for frictionless and incompressible fluids down a horizontal plane. The effects of the gravitational acceleration along the slope, and of the retarding acceleration caused by friction as well, are systematically taken into account. The analytic solutions are then used to revisit existing data on rigid walls impacted by granular flows. This approach allows establishing a complete phase diagram for granular flow-wall interaction.

Smectic liquid crystals vividly illustrate the subtle interplay of broken translational and orientational symmetries, by exhibiting defect structures forming geometrically perfect confocal ellipses and hyperbolas. Here, we develop and numerically implement an effective theory to study the dynamics of focal conic domains in smectic-$A$ liquid crystals. We use the information about the smectic's structure and energy density provided by our simulations to develop several novel visualization tools for the focal conics. Our simulations accurately describe both simple and extensional shear, which we compare to experiments, and provide additional insight into the coarsening dynamics of focal conic domains.

Actomyosin actively generates contractile forces that provide the plasma membrane with the deformation stresses essential to carry out biological processes. Although the contractile property of purified actomyosin has been extensively studied, to understand the physical contribution of the actomyosin contractile force on a deformable membrane is still a challenging problem and of great interest in the field of biophysics. Here, we reconstitute a model system with a cell-sized deformable interface that exhibits anomalous curvature-dependent wrinkling caused by the actomyosin cortex underneath the spherical closed interface. Through a shape analysis of the wrinkling deformation, we find that the dominant contributor to the wrinkled shape changes from bending elasticity to stretching elasticity of the reconstituted cortex upon increasing the droplet curvature radius of the order of the cell size, i.e., tens of micrometers. The observed curvature dependence is explained by the theoretical description of the cortex elasticity and contractility. Our present results provide a fundamental insight into the deformation of a curved membrane induced by the actomyosin cortex.

Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering and regularity of network connections. While many existing network characterizations rely on constructing benchmark networks for comparison or fail to describe the structural properties of relatively densely connected networks, our classification relies only on the intrinsic network structure and is quite robust with respect to changes in connection density, producing stable results across network realizations. Using this framework, we analyze several real-world networks and reveal new structural properties, which are often indiscernible by previously established characterizations of network connectivity.

Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a vanishingly small seed fraction can spread to a finite fraction of an infinitely large network through local infections. In social and economic networks, however, individuals' behavior is often influenced not only by what their direct neighbors are doing, but also by what the majority of people are doing as a trend. A trend affects individuals' behavior while individuals' behavior creates a trend. To analyze such a complex interplay between local- and global-scale phenomena, I generalize the standard threshold model by introducing a type of node called global nodes (or trend followers), whose activation probability depends on a global-scale trend, specifically the percentage of activated nodes in the population. The model shows that global nodes play a role as accelerating cascades once a trend emerges while reducing the probability of a trend emerging. Global nodes thus either facilitate or inhibit cascades, suggesting that a moderate share of trend followers may maximize the average size of cascades.