The morphology of the solid-vapor interface of a nanoscale thin crystalline film is influenced by many factors including surface diffusion, attachment-detachment, deposition, and interface kinetics. Using a high-order accurate and efficient numerical method, we investigate the dynamics of two dimensional thin films when all of these effects are considered. The observed morphologies consist of facets of constant slope separated by narrow transition intervals: kinks (valleys) and antikinks (hills). The number of kinks and antikinks decreases as the system coarsens in time. Our numerical results confirm that when deposition is present, the only possible coarsening event is the kink-ternary where two kinks meet and annihilate an antikink. We characterize the total amount of coarsening, the time over which the coarsening occurs and the associated coarsening scaling laws when all effects are considered. As found in previous work that considered only attachment-detachment, or surface diffusion, there are three distinct coarsening regimes associated with increasing magnitudes of the deposition flux—fast coarsening, a regime in which periodic structures form with little or no subsequent coarsening, and a regime in which the film surface evolves chaotically. We find that the inclusion of attachment-detachment leads to additional coarsening compared to the dynamics that result from driven surface diffusion alone. When deposition and interface kinetics are both considered, the slowdown of evolution caused by the kinetic effects necessitates a decrease in the deposition flux in order to produce a nonchaotic coarsening regime. Together, these provide testable predictions for experiments of thin-film dynamics.

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics, but also on the length of the observation window over which the correlation is calculated. In this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales, a quantity that provides a convenient proxy for the spike count correlation. Over short time scales, we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference. Our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales. We also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales. These analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type I oscillators transfer correlations more faithfully than do type II over long time scales, while the reverse holds true for the better understood case of short time scales.

Theoretical considerations suggest that the mammalian metabolic rate is linearly proportional to the surface areas of mitochondria, capillary, and alveolar membranes. However, the scaling exponents of these surface areas to the mammals' body mass (approximately 0.9–1) are higher than exponents of the resting metabolic rate (RMR) to body mass (approximately 0.75), although similar to the one of exercise metabolic rate (EMR); the underlying physiological cause of this mismatch remains unclear. The analysis presented here shows that discrepancies between the scaling exponents of RMR and the relevant surface areas may originate from, at least for the system of alveolar membranes in mammalian lungs, the facts that (i) not all of the surface area is involved in the gas exchange and (ii) that larger mammals host a smaller effective surface area that participates in the material exchange rate. A result of these facts is that lung surface areas unused at rest are activated under heavy breathing conditions (e.g., exercise), wherein larger mammals support larger activated surface areas that provide a higher capability to increase the gas-exchange rate, allowing for mammals to meet, for example, the high energetic demands of foraging and predation.

We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit-cell designs for (1) out-of-plane, (2) in-plane, and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space ($\sim$${10}^{40}$ possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band-structure calculations. Focusing on high-symmetry plain-strain square lattices, we report unit-cell designs exhibiting record values of normalized band-gap size for all three categories. For the case of combined polarizations, we reveal a design with a normalized band-gap size exceeding 60%.

The Wang-Landau method of estimating the density of states $g\left(E\right)$ has become a powerful tool in statistical mechanics. Here it is shown that the distribution of random walkers sampled using an estimated density of states can always be used to improve the estimate. Specifically, this can be done without resorting to an auxiliary modification factor $f$, which previously has been used to find $g\left(E\right)$ self-consistently through a procedure that reduces $f$ incrementally toward unity. This straightforward approach is validated for multiple, independent random walkers.

We deal with a system of prisoner's dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation.

Robustness of two coupled networks systems has been studied separately only for dependency coupling [Buldyrev et al., Nature (London) 464, 1025 (2010)] and only for connectivity coupling [Leicht and D’Souza, e-print arXiv:0907.0894]. Here we study, using a percolation approach, a more realistic coupled networks system where both interdependent and interconnected links exist. We find rich and unusual phase-transition phenomena including hybrid transition of mixed first and second order, i.e., discontinuities like in a first-order transition of the giant component followed by a continuous decrease to zero like in a second-order transition. Moreover, we find unusual discontinuous changes from second-order to first-order transition as a function of the dependency coupling between the two networks.

Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these features and find that ensembles of networks with high clustering display both high assortativity by degree and prominent community structure, while ensembles with high assortativity show much less enhancement of the clustering or community structure. Further, clustering can amplify a small homophilic bias for trait assortativity in network ensembles. This marked asymmetry suggests that transitivity could play a larger role than homophily in determining the structure of many complex networks.

A coupling phase is deemed to be crucial in stabilizing behavior in nonlinear systems. In this paper, we study how the coupling phase influences the delay-induced oscillation death (OD) in coupled oscillators. The OD boundaries are identified analytically even in the presence of the coupling phase. We find that OD only occurs for a coupling phase belonging to a certain interval. The optimal coupling phase, under which the largest OD island forms, is characterized well by a power law scaling with respect to the frequency. The coupling phase turns out to be a key parameter that determines a delay-induced OD. Furthermore, the controlling role of the coupling phase generally is proved to hold fairly for networked delay-coupled oscillators.

We investigate numerically the dynamics of a laminar-turbulent interface in a spanwisely extended and streamwisely minimal plane Couette flow. The chosen geometry allows one to suppress the large-scale secondary flow and to focus on the nucleation of streaks near the interface. It is shown that the resulting spanwise motion of the interface is essentially stochastic and can be modeled as a continuous-time random walk. This model corresponds here to a Gaussian diffusion process. The average speed of the interface and the corresponding diffusion coefficient are determined as functions of the Reynolds number $\text{Re}$, as well as the threshold value above which turbulence contaminates the whole domain. For the lowest values of $\text{Re}$, the stochastic dynamics competes with another deterministic regime of growth of the localized perturbations. The latter is interpreted as a depinning process from the homoclinic snaking region of the system.

The Kolmogorov-Zakharov spectrum predicted by the weak turbulence theory remains elusive for wave turbulence of flexural waves at the surface of a thin elastic plate. We report a direct measurement of the nonlinear time scale $T_{\mathit{NL}}$ related to energy transfer between waves. This time scale is extracted from the space-time measurement of the deformation of the plate by studying the temporal dynamics of wavelet coefficients of the turbulent field. The central hypothesis of the theory is the time scale separation between dissipative time scale, nonlinear time scale, and the period of the wave ($T_d\gg T_{\mathit{NL}}\gg T$). We observe that this scale separation is valid in our system. The discrete modes due to the finite size effects are responsible for the disagreement between observations and theory. A crossover from continuous weak turbulence and discrete turbulence is observed when the nonlinear time scale is of the same order of magnitude as the frequency separation of the discrete modes. The Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen before reaching the dissipative regime expected in the theory.

Computer simulation of reactive transport in heterogeneous systems remains a challenge due to the multiscale nature of reactive dynamics and the non-Fickian behavior of transport. This study develops a fully Lagrangian approach via particle tracking to describe the reactive transport controlled by the tempered super- or subdiffusion. In the particle-tracking algorithm, the local-scale reaction is affected by the interaction radius between adjacent reactants, whose motion can be simulated by the Langevin equations corresponding to the tempered stable models. Lagrangian simulation results show that the transient superdiffusion enhances the reaction by enhancing the degree of mixing of the reactants. The proposed particle-tracking scheme can also be extended conveniently to multiscale superdiffusion. For the case of transient subdiffusion, the trapping of solutes in the immobile phase can either decrease or accelerate the reaction rate, depending on the initial condition of the reactant particles. Further practical applications show that the new solver efficiently captures bimolecular reactions observed in laboratories.

Critical comments on the entropic lattice Boltzmann equation (ELBE), by Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, and Wei Zhang in Ref. [1], are based on simulations, which make use of a model that, despite being referred to as the ELBE by the authors, is in fact equivalent to the standard lattice Bhatnagar-Gross-Krook equation for low Mach number simulations. In this Comment, a concise review of the ELBE is provided and illustrated by means of a three-dimensional turbulent flow simulation, which highlights the subgrid features of the ELBE.

Three bent-core nematic liquid crystals having the same core but with different terminal groups, short (C4) and long (C7,C9) tails, are investigated by dielectric and electro-optic contrast spectroscopic techniques. C4 shows sign reversal in the dielectric anisotropy $\Delta {\epsilon }^{\prime }$ as a function of both temperature and frequency, whereas C9 shows only negative $\Delta {\epsilon }^{\prime }$ in the entire mesophasic region. The behavior of C7 is intermediate of the two. Results of a dielectric study show that both C7 and C9 exhibit strong short-range polar correlations normal to the director. The correlation lengths of these interactions are found to be similar to those from the x-ray scattering. An increased hindered rotation for C9 compared to C4 moves the dielectric dispersion for ${\epsilon }_{\parallel }^{\prime }$ to much lower frequencies, such that C9 shows only negative $\Delta {\epsilon }^{\prime }$ over the entire temperature range.

Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the near-core-outer region, where biased migration away from the tumor spheroid core takes place. We suggest non-Markovian switching between the migrating and proliferating phenotypes of tumor cells. Nonlinear master equations for mean densities of cancer cells of both phenotypes are derived. In anomalous switching case we estimate the average size of the near-core-outer region that corresponds to sublinear growth $\langle r\left(t\right)\rangle \sim t^{\mu }$ for $0<\mu <1.$ In model II we consider the outer zone, where the density of cancer cells is very low. We suggest an integrodifferential equation for the total density of cancer cells. For proliferation rate we use the classical logistic growth, while the migration of cells is subdiffusive. The exact formulas for the overall spreading rate of cancer cells are obtained by a hyperbolic scaling and Hamilton-Jacobi techniques.

We consider a pack of independent probes—within a spatially inhomogeneous thermal bath consisting of a vast number of randomly moving particles—which are subjected to an external force. The stochastic dynamics of the probes are governed by Langevin's equation. The probes attain a steady state distribution which, in general, is different than the concentration of the particles in the spatially inhomogeneous thermal bath. In this paper we explore the state of “entropic crowding” in which the probes' distribution and the particles' concentration coincide—thus yielding maximal relative entropies of one with respect to the other. Entropic crowding can be attained by two scenarios which are analyzed in detail: (i) “entropically crowding thermal baths”—in which the particles crowd uniformly around the probes; (ii) “entropically crowding Langevin forces”—in which the probes crowd uniformly amongst the particles. Entropic crowding is equivalent to the optimal stochastic cloaking of the probes within the spatially inhomogeneous thermal bath.

We provide formulas for fidelity decay and parametric energy correlations for random matrix ensembles where time-reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities exists. Fidelity freeze is observed for systems with even and odd spin.

This paper investigates the lift force exerted on an elliptical obstacle immersed in a granular flow through analytical calculations and computer simulations. The results are shown as a function of the obstacle size, orientation with respect to the flow direction (tilt angle), the restitution coefficient and ellipse eccentricity. The theoretical argument, based on the force exerted on the obstacle due to inelastic, frictionless collisions of a very dilute flow, captures the qualitative features of the lift, but fails to reproduce the data quantitatively. The reason behind this disagreement is that the dilute flow assumption on which this argument is built breaks down as a granular shock wave forms in front of the obstacle. More specifically, the shock wave changes the grains impact velocity at the obstacle, decreasing the overall net lift obtained from a very dilute flow.

Salt transport in bulk electrolytes is limited by diffusion and advection, but in microstructures with charged surfaces (e.g., microfluidic devices, porous media, soils, or biological tissues) surface conduction and electro-osmotic flow also contribute to ionic fluxes. For small applied voltages, these effects lead to well known linear electrokinetic phenomena. In this paper, we predict some surprising nonlinear dynamics that can result from the competition between bulk and interfacial transport at higher voltages. When counterions are selectively removed by a membrane or electrode, a “deionization shock” can propagate through the microstructure, leaving in its wake an ultrapure solution, nearly devoid of coions and colloidal impurities. We elucidate the basic physics of deionization shocks and develop a mathematical theory of their existence, structure, and stability, allowing for slow variations in surface charge or channel geometry. Via asymptotic approximations and similarity solutions, we show that deionization shocks accelerate and sharpen in narrowing channels, while they decelerate and weaken, and sometimes disappear, in widening channels. These phenomena may find applications in separations (deionization, decontamination, biological assays) and energy storage (batteries, supercapacitors) involving electrolytes in microstructures.

Kinetic Monte Carlo on coarse-grained systems, such as nucleic acid secondary structure, is advantageous for being able to access behavior at long time scales, even minutes or hours. Transition rates between coarse-grained states depend upon intermediate barriers, which are not directly simulated. We propose an Arrhenius rate model and an intermediate energy model that incorporates the effects of the barrier between simulated states without enlarging the state space itself. Applying our Arrhenius rate model to DNA hairpin folding, we demonstrate improved agreement with experiment compared to the usual kinetic Monte Carlo model. Further improvement results from including rigidity of single-stranded stacking.