For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called “border-blocking” models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux; however, this approximation dramatically fails in the wet or unjamming limit where the bubbles become close-packed spheres and coarsening proceeds even though there are no films. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We compute that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling by numerical solution of the diffusion equation. We similarly consider transport across inflated vertices and surface Plateau borders in quasi-two-dimensional foams. And we show how the $dA/dt=K_0(n-6)$ von Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scales. Finally, we use the modified von Neumann law to compute the growth rate of the average bubble area, which is not constant.

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number $z_c$ of cohesive contacts and particle volume fraction $\varphi$ of the initial states. We focus on discerning the role of $z_c$ and $\varphi$ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ${\nu }_c=z_c\varphi$ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Passive filters allowing the exchange of particles in a narrow band of energy are currently used in microrefrigerators and energy transducers. In this Rapid Communication, we analyze their thermal properties using linear irreversible thermodynamics and kinetic theory, and discuss a striking phenomenon: the possibility of simultaneously increasing or decreasing the temperatures of two systems without any supply of energy. This occurs when the filter induces a flow of particles whose energy is between the average energies of the two systems. Here we show that this selective transfer of particles does not need the action of any sort of Maxwell demon and can be carried out by passive filters without compromising the second law of thermodynamics. This phenomenon allows us to design cycles between two reservoirs at temperatures $T_1<T_2$ that are able to reach temperatures below $T_1$ or above $T_2$.

We investigate the nonequilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and intercrystal Coulomb interactions and the asymmetric population of the potential wells, we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other. The study and analysis of the latter processes constitutes the main focus of this work. In particular, we examine the dependence of the observed ion transfers on the quench amplitude performing an analysis for different crystalline configurations ranging from one-dimensional ion chains via two-dimensional zigzag chains and ring structures to three-dimensional spherical structures. Such an analysis provides us with the means to extract the general principles governing the ion transfer dynamics and we gain some insight on the structural disorder caused by the quench of the barrier height.

Epidemics, neural cascades, power failures, and many other phenomena can be described by a diffusion process on a network. To identify the causal origins of a spread, it is often necessary to identify the triggering initial node. Here, we define a new morphological operator and use it to detect the origin of a diffusive front, given the final state of a complex network. Our method performs better than algorithms based on distance (closeness) and Jordan centrality. More importantly, our method is applicable regardless of the specifics of the forward model, and therefore can be applied to a wide range of systems such as identifying the patient zero in an epidemic, pinpointing the neuron that triggers a cascade, identifying the original malfunction that causes a catastrophic infrastructure failure, and inferring the ancestral species from which a heterogeneous population evolves.

A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during retina growth, against the geometrically equivalent circular stripe pattern. The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, which find that the successive emergence of local defects plays a critical role in the realization of the wild-type pattern.

The unbinding dynamics of a nanosized sphere-and-cavity assembly under the pulling of constant force and constant loading rate is explored by dissipative particle dynamics simulations. The formation of this matched lock-and-key pair in a polymer solution is driven by the depletion attraction. The two-dimensional free energy landscape $U$($x,z$) associated with this assembly is constructed. Our results indicate that the unbinding pathway along the orientation of the assembly is unfavorable due to the relatively high energy barrier compared to that along the tortuous minimum path whose energy barrier is not high. It is also found that the dissociation rate depends on the direction of the external force ($\theta$) with respect to the assembly orientation. The presence of the force component perpendicular to the assembly orientation can reduce the bond lifetime significantly by driving the key particle to approach the minimum path. Moreover, the dissociation dynamics can be facilitated even by a pushing force compared to the spontaneous dissociation (without forces). To elucidate the effective pathway under pulling, the escaping position is analyzed and its mean direction with respect to the assembly orientation rises generally with increasing $\theta$, revealing that the presence of the force component along the minimum pathway is helpful. The importance of the direction of the external pulling has been demonstrated in our simple system. Therefore, this effect should be considered in more complicated unbinding experiments.

An intruder penetrating into a granular column experiences a depth-dependent friction force $F\left(z\right)$. Different regimes of $F\left(z\right)$ have been measured depending on the experimental design: a nearly linear dependence for shallow penetrations, total saturation at large depths, and an exponential increase when the intruder approaches the bottom of the granular bed. We report here an experiment that allows us to measure the different regimes in a single run during the quasistatic descent of a sphere in a light granular medium. From the analysis of the resistance in the saturation zone, it was found that $F\left(z\right)$ follows a cube-power-law dependence on the intruder diameter and an exponential increase with the packing fraction of the bed. Moreover, we determine the critical mass $m_c$ required to observe infinite penetration and its dependence on the above parameters. Finally, we use our results to estimate the final penetration depth reached by intruders of masses $m<m_c$. The results indicate that an intruder of any density (larger than the density of the granular bed) can sink indefinitely into the granular medium if the bed packing fraction is smaller than a critical value.

This study contributes to the evaluation of the robustness and accuracy of Green's function reconstruction from cross-correlation of strongly dispersed reverberated signals, with disentangling of the respective roles of ballistic and reverberated (“coda”) contributions. We conduct a suite of experiments on a highly reverberating thin duralumin plate, where an approximately diffuse flexural wave field is generated by taking advantage of the plate reverberation and wave dispersion. A large number of impulsive sources that cover the whole surface of the plate are used to validate ambient-noise theory through comparison of the causal and anticausal (i.e., positive- and negative-time) terms of the cross-correlation to one another and to the directly measured Green's function. To quantify the contribution of the ballistic and coda signals, the cross-correlation integral is defined over different time windows of variable length, and the accuracy of the reconstructed Green's function is studied as a function of the initial and end times of the integral. We show that even cross-correlations measured over limited time windows converge to a significant part of the Green's function. Convergence is achieved over a wide time window, which includes not only direct flexural-wave arrivals, but also the multiply reverberated coda. We propose a model, based on normal-mode analysis, that relates the similarity between the cross-correlation and the Green's function to the statistical properties of the plate. We also determine quantitatively how incoherent noise degrades the estimation of the Green's function.

Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free (Fickian) diffusion with no steric constraints on the maximum particle number per lattice site as well as the case of diffusion under steric constraints imposing a maximum particle concentration. We find, for both transient and asymptotic regimes, excellent agreement between the DLEs and kinetic Monte Carlo simulations of the MEs. The DLEs provide a computationally efficient method for predicting the (average) distribution of randomly diffusing particles in inhomogeneous media, with the number of DLEs associated with a given system being independent of the number of particles in the system. From the DLEs we obtain general analytic expressions for the steady-state particle distributions for free diffusion and, in special cases, diffusion under steric constraints in inhomogeneous media. We find that, in the steady state of the system, the average fraction of particles in a given domain is independent of most system properties, such as the arrangement and shape of domains, and only depends on the number of lattice sites in each domain, the particle hopping rates, the number of distinct particle species in the system, and the total number of particles of each particle species in the system. Our results provide general insights into the role of spatially inhomogeneous particle hopping rates in setting the particle distributions in inhomogeneous media.

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

In additive white Gaussian noise channel, chaos has been shown to be the optimal coherent communication waveform in the sense of using a very simple matched filter to maximize the signal-to-noise ratio. Recently, Lyapunov exponent spectrum of the chaotic signals after being transmitted through a wireless channel has been shown to be unaltered, paving the way for wireless communication using chaos. In wireless communication systems, inter-symbol interference caused by multipath propagation is one of the main obstacles to achieve high bit transmission rate and low bit-error rate (BER). How to resist the multipath effect is a fundamental problem in a chaos-based wireless communication system (CWCS). In this paper, a CWCS is built to transmit chaotic signals generated by a hybrid dynamical system and then to filter the received signals by using the corresponding matched filter to decrease the noise effect and to detect the binary information. We find that the multipath effect can be effectively resisted by regrouping the return map of the received signal and by setting the corresponding threshold based on the available information. We show that the optimal threshold is a function of the channel parameters and of the information symbols. Practically, the channel parameters are time-variant, and the future information symbols are unavailable. In this case, a suboptimal threshold is proposed, and the BER using the suboptimal threshold is derived analytically. Simulation results show that the CWCS achieves a remarkable competitive performance even under inaccurate channel parameters.

We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k\ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the distribution of $k$-values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their $k$-values are compared, and with probability $p$ the agent with the lower value adopts the opinion of the one with the higher value, while with probability $1-p$ the opposite happens. The agent that keeps its opinion (winning agent) increments its $k$-value by one. We study the dynamics of the system in the entire $0\le p\le 1$ range and compare with the case $p=1/2$, in which opinions are decoupled from the $k$-values and the dynamics is equivalent to that of the standard voter model. When $0\le p<1/2$, agents with higher $k$-values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time $\tau$ appears to grow logarithmically with the number of agents $N$, and it is greatly decreased relative to the linear behavior $\tau \sim N$ found in the standard voter model. When $1/2<p\le 1$, agents with higher $k$-values are more persuasive, and the system initially relaxes to a state with an even coexistence of opinions, but eventually reaches consensus by finite-size fluctuations. The approach to the coexistence state is monotonic for $1/2<p<p_o\simeq 0.8$, while for $p_o\le p\le 1$ there are damped oscillations around the coexistence value. The final approach to coexistence is approximately a power law $t^{-b\left(p\right)}$ in both regimes, where the exponent $b$ increases with $p$. Also, $\tau$ increases respect to the standard voter model, although it still scales linearly with $N$. The $p=1$ case is special, with a relaxation to coexistence that scales as $t^{-2.73}$ and a consensus time that scales as $\tau \sim N^{\beta }$, with $\beta \simeq 1.45$.

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

We model screened, site-specific charge regulation of the eye lens protein bovine gammaB-crystallin ($\gamma \mathrm{B}$) and study the probability distributions of its proton occupancy patterns. Using a simplified dielectric model, we solve the linearized Poisson-Boltzmann equation to calculate a $54\times 54$ work-of-charging matrix, each entry being the modeled voltage at a given titratable site, due to an elementary charge at another site. The matrix quantifies interactions within patches of sites, including $\gamma \mathrm{B}$ charge pairs. We model intrinsic $p\mathrm{K}$ values that would occur hypothetically in the absence of other charges, with use of experimental data on the dependence of $p\mathrm{K}$ values on aqueous solution conditions, the dielectric model, and literature values. We use Monte Carlo simulations to calculate a model grand-canonical partition function that incorporates both the work-of-charging and the intrinsic $p\mathrm{K}$ values for isolated $\gamma \mathrm{B}$ molecules and we calculate the probabilities of leading proton occupancy configurations, for $4<p\text{H}<8$ and Debye screening lengths from 6 to 20 Å. We select the interior dielectric value to model $\gamma \mathrm{B}$ titration data. At $p\mathrm{H}$ 7.1 and Debye length 6.0 Å, on a given $\gamma \mathrm{B}$ molecule the predicted top occupancy pattern is present nearly 20% of the time, and 90% of the time one or another of the first 100 patterns will be present. Many of these occupancy patterns differ in net charge sign as well as in surface voltage profile. We illustrate how charge pattern probabilities deviate from the multinomial distribution that would result from use of effective $p\mathrm{K}$ values alone and estimate the extents to which $\gamma \mathrm{B}$ charge pattern distributions broaden at lower $p\mathrm{H}$ and narrow as ionic strength is lowered. These results suggest that for accurate modeling of orientation-dependent $\gamma \mathrm{B}-\gamma \mathrm{B}$ interactions, consideration of numerous pairs of proton occupancy patterns will be needed.

We investigate the phase behavior of suspensions of poly($N$-isopropylacrylamide) (pNIPAM) microgels with either bimodal or polydisperse size distribution. We observe a shift of the fluid-crystal transition to higher concentrations depending on the polydispersity or the fraction of large particles in suspension. Crystallization is observed up to polydispersities as high as 18.5%, and up to a number fraction of large particles of 29% in bidisperse suspensions. The crystal structure is random hexagonal close-packed as in monodisperse pNIPAM microgel suspensions. We explain our experimental results by considering the effect of bound counterions. Above a critical particle concentration, these cause deswelling of the largest microgels, which are the softest, changing the size distribution of the suspension and enabling crystal formation in conditions where incompressible particles would not crystallize.

The performance of light-controlled liquid crystal anchoring surfaces depends on the nature of the photosensitive moieties and on the concentration of spacer units. Here, we study the kinetics of photosensitive liquid crystal cells that incorporate an azobenzene-based self-assembled monolayer. We characterize the photoinduced homeotropic-to-planar transition and the subsequent reverse relaxation in terms of the underlying isomerization of the photosensitive layer. We show that the response time can be precisely adjusted by tuning the lateral packing of azobenzene units by means of inert spacer molecules. Using simple kinetic assumptions and a well-known model for the energetics of liquid crystal anchoring we are able to capture the details of the optical microscopy experimental observations. Our analysis provides fitted values for all the relevant material parameters, including the zenithal and the azimuthal anchoring strength.

We study interfaces with periodic boundary conditions in the low-temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with antiperiodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension $\sigma$ and the correlation length $\xi$ obtained in previous work, we determine the universal amplitude ratios $R_{2\mathrm{nd},+}={\sigma }_0{f}_{2\mathrm{nd},+}^2=0.3863\left(6\right), R_{2\mathrm{nd},-}={\sigma }_0{f}_{2\mathrm{nd},-}^2=0.1028\left(1\right)$, and $R_{\exp ,-}={\sigma }_0{f}_{\exp ,-}^2=0.1077\left(3\right)$. Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.

We study the nanoscale terraced topographies that arise when a solid surface is bombarded with a broad ion beam that has a relatively high angle of incidence $\theta$. We find that the surface is not completely flat between the regions in which the surface slope changes rapidly with position: Instead, small-amplitude ripples propagate along the surface. Our analytical work on these ripples yields their propagation velocity as well as the scaling behavior of their amplitude. Our simulations establish that the surfaces exhibit interrupted coarsening, i.e., the characteristic width and height of the surface disturbance grow for a time but ultimately asymptote to finite values as the fully terraced state develops. In addition, as $\theta$ is reduced, the surface can undergo a transition from a terraced morphology that changes little with time as it propagates over the surface to an unterraced state that appears to exhibit spatiotemporal chaos. For different ranges of the parameters, our equation of motion produces unterraced topographies that are remarkably similar to those seen in various experiments, including pyramidal structures that are elongated along the projected beam direction and isolated lenticular depressions.

Granular temperature may control high-speed granular flows, yet it is difficult to measure in laboratory experiments. Here we utilize acoustic energy to measure granular temperature in dense shear flows. We show that acoustic energy captures the anticipated behavior of granular temperature as a function of grain size in quartz sand shear flows. We also find that granular temperature (through its proxy acoustic energy) is nearly linearly proportional to inertial number, and dilation is proportional to acoustic energy raised to the power $0.6\pm 0.2$. This demonstrates the existence of a relationship between granular temperature and dilation. It is also consistent with previous results on dilation due to externally imposed vibration, thus showing that internally and externally induced vibrations have identical results on granular shear flows.