A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio $r$ is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than ${(1/2)}^{1/3}$ for a fixed value of branching number $n$, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number $n_c$ when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of $r$ is close to ${(1/2)}^{1/3}$.

We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction, and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behavior can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.

We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly $50000$ individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate $\left[\right(1–5)\times {10}^{-5}$ ${\mathrm{s}}^{-1}]$ to maximum macroscopic strains $\left(5\%–10\%\right)$ and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.

The radical pair mechanism can help to explain avian orientation and navigation. Some evidence indicates that the intensity of external magnetic fields plays an important role in avian navigation. In this paper, using a two-stage model, we demonstrate that birds could reasonably detect the directions of geomagnetic fields and gradients of these fields using a yield-based chemical compass that is sensitive enough for navigation. Also, we find that the lifetime of entanglement in this proposed compass is angle dependent and long enough to allow adequate electron transfer between molecules.

We investigate the influence of chain rigidity on the dynamics of polymer translocation in the presence of binding particles (BPs) through a nanopore using two-dimensional Langevin dynamics simulations. With increasing chain rigidity $\kappa$, the mean translocation time $\langle \tau \rangle$ increases monotonically due to an increase in the radius of gyration and a decrease in the center of mass velocity. Particularly for weak binding, we further find that $\langle \tau \rangle$ shows a power-law behavior with the persistence length $l_p$. Analysis indicates a scaling relation between the average velocity of the center of mass of a chain $\langle v_{\text{c.m.}}\rangle$ and $l_p$. As the chain becomes stiffer, the distribution of the translocation time $\tau$ approximates the Gaussian distribution and gets broader with the peak position being shifted towards longer translocation time. The corresponding translocation coordinate $s_{\text{max}}$ of the maximum waiting time gets smaller with increasing chain rigidity. Finally, under an extremely low BP concentration, $\langle \tau \rangle$ shows a minimum for small $\kappa$, while it decreases monotonically for large $\kappa$ with increasing binding energy. Our results suggest a nontrivial effect of the intrinsic property of chains on the dynamics of polymer translocation driven by BPs.

Most of the complex social, technological, and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored small-world and scale-free properties of these networks. Despite the large interest in characterizing the community structures of real networks, not enough attention has been devoted to the detection of universal mechanisms able to spontaneously generate networks with communities. Triadic closure is a natural mechanism to make new connections, especially in social networks. Here we show that models of network growth based on simple triadic closure naturally lead to the emergence of community structure, together with fat-tailed distributions of node degree and high clustering coefficients. Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation. Communities are the more pronounced, the sparser the graph, and disappear for high values of link density and randomness in the attachment procedure. By introducing a fitness-based link attractivity for the nodes, we find a phase transition where communities disappear for high heterogeneity of the fitness distribution, but a different mesoscopic organization of the nodes emerges, with groups of nodes being shared between just a few superhubs, which attract most of the links of the system.

Crack patterns of drying paste and their statistical properties are investigated through smoothed particle hydrodynamics, which is one method for solving continuum equations in the Lagrangian description. In addition to reproducing a realistic crack pattern, we also find that the average area of a fragment decays inversely with time in the case of linearly increasing desiccation stress. We find that the distribution can be scaled with the average area of the fragment over the corresponding time, even though the distribution function of the fragment area changes the functional form during evolution.

We use synthetic turbulence simulations to study how inertial particles cluster in a turbulent flow, for a wide range of Stokes numbers. Two different types of synthetic turbulence are used: one Gaussian, where the time evolution of the velocity field is a simple phase shift, and one non-Gaussian, where convection is used to evolve the velocity field in time. In both flow types we observe significant particle clustering over a wide range of scales and Stokes numbers. The clustering found at low Stokes numbers can be attributed to the vortex centrifuge effect, where heavy particles are expelled from regions dominated by vorticity. This mechanism is much more effective in the non-Gaussian turbulence, because local flow structures are convected with the particles. The preferential sampling of regions with low vorticity is almost negligible in the Gaussian turbulence. At higher Stokes numbers, caustics are formed in a very similar manner in both Gaussian and non-Gaussian synthetic turbulence. In non-Gaussian turbulence, heavy particles cluster in regions of low fluid kinetic energy, while the opposite is true in Gaussian turbulence. Our results show that synthetic simulations cannot correctly predict how the particle clustering correlates with local fluid flow properties, without including convection.

We investigate regular configurations of a small number of non-Brownian particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle approximation. A family of regular configurations is found with periodic oscillations of all the settling particles. The oscillations are shown to be robust under some out-of-phase rearrangements of the particles. In the presence of an additional particle above such a regular configuration, the particle periodic trajectories are horizontally repelled from the symmetry axis, and flattened vertically. The results are used to propose a mechanism of how a spherical cloud, made of a large number of particles distributed at random, evolves and destabilizes.

Starting from preferences on $N$ proposed policies obtained via questionnaires from a sample of the electorate, an Ising spin-glass model in a field can be constructed from which a political party could find the subset of the proposed policies which would maximize its appeal, form a coherent choice in the eyes of the electorate, and have maximum overlap with the party's existing policies. We illustrate the application of the procedure by simulations of a spin glass in a random field on scale-free networks.

Recently, as the controllability of complex networks attracts much attention, how to design and optimize the controllability of networks has become a common and urgent problem in the field of controlling complex networks. Previous work focused on the structural perturbation and neglected the role of edge direction to optimize the network controllability. In a recent work [Phys. Rev. Lett. 103, 228702 (2009)], the authors proposed a simple method to enhance the synchronizability of networks by assignment of link direction while keeping network topology unchanged. However, the controllability is fundamentally different from synchronization. In this work, we systematically propose the definition of assigning direction to optimize controllability, which is called the edge orientation for optimal controllability problem (EOOC). To solve the EOOC problem, we construct a switching network and transfer the EOOC problem to find the maximum independent set of the switching network. We prove that the principle of our optimization method meets the sense of unambiguity and optimum simultaneously. Furthermore, the relationship between the degree-degree correlations and EOOC are investigated by experiments. The results show that the disassortativity pattern could weaken the orientation for optimal controllability, while the assortativity pattern has no correlation with EOOC. All the experimental results of this work verify that the network structure determines the network controllability and the optimization effects.

We investigate cluster synchronization in coupled map networks in the presence of heterogeneous delays. We find that while the parity of heterogeneous delays plays a crucial role in determining the mechanism of cluster formation, the cluster synchronizability of the network gets affected by the amount of heterogeneity. In addition, heterogeneity in delays induces a rich cluster pattern as compared to homogeneous delays. The complete bipartite network stands as an extreme example of this richness, where robust ideal driven clusters observed for the undelayed and homogeneously delayed cases dismantle, yielding versatile cluster patterns as heterogeneity in the delay is introduced. We provide arguments behind this behavior using a Lyapunov function analysis. Furthermore, the interplay between the number of connections in the network and the amount of heterogeneity plays an important role in deciding the cluster formation.

By using compressive sensing (CS) theory, a broad class of static signals can be reconstructed through a sequence of very few measurements in the framework of a linear system. For networks with nonlinear and time-evolving dynamics, is it similarly possible to recover an unknown input signal from only a small number of network output measurements? We address this question for pulse-coupled networks and investigate the network dynamics necessary for successful input signal recovery. Determining the specific network characteristics that correspond to a minimal input reconstruction error, we are able to achieve high-quality signal reconstructions with few measurements of network output. Using various measures to characterize dynamical properties of network output, we determine that networks with highly variable and aperiodic output can successfully encode network input information with high fidelity and achieve the most accurate CS input reconstructions. For time-varying inputs, we also find that high-quality reconstructions are achievable by measuring network output over a relatively short time window. Even when network inputs change with time, the same optimal choice of network characteristics and corresponding dynamics apply as in the case of static inputs.

We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however it has the same binary correlator, the general theory is absent. Thus, we consider the case when only one channel is open and all others are closed. For this situation we suggest a semianalytical approach which is quite effective for the description of the total transmission coefficient. Our numerical data confirm the validity of this approach.

We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the ${\mathrm{Airy}}_1$ process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom [Commun. Math. Phys. 177, 727 (1996)].

We consider a phenomenological continuum theory for an active nematic fluid and show that there exists a universal, model-independent instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools we show that, in the vicinity of a critical point, this instability leads to a phase-separated state in which the ordered regions form bands in which the direction of nematic order is perpendicular to the direction of the density gradient. We argue that the underlying mechanism that leads to this phase separation is a universal feature of active fluids of different symmetries.

The characteristic relaxation time $\tau$ of protein hydration water exhibits a strong hydration level $h$ dependence. The dynamic crossover is observed when $h$ is higher than the monolayer hydration level $h_c=0.2$–0.25 and becomes more visible as $h$ increases. When $h$ is lower than $h_c$, $\tau$ only exhibits Arrhenius behavior in the measured temperature range. The activation energy of the Arrhenius behavior is insensitive to $h$, indicating a local-like motion. Moreover, the $h$ dependence of the crossover temperature shows that the protein dynamic transition is not directly or solely induced by the dynamic crossover in the hydration water.