Snow is a porous disordered medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of an assemblage of grains, ice matrix, initially arranged over a random load bearing skeleton. The quantitative relationship between density and morphological characteristics of different snow microstructures is still an open issue. In this work, a three-dimensional fractal description of density corresponding to different snow microstructure is put forward. First, snow density is simulated in terms of a generalized Menger sponge model. Then, a fully three-dimensional compact stochastic fractal model is adopted. The latter approach yields a quantitative map of the randomness of the snow texture, which is described as a three-dimensional fractional Brownian field with the Hurst exponent $H$ varying as continuous parameters. The Hurst exponent is found to be strongly dependent on snow morphology and density. The approach might be applied to all those cases where the morphological evolution of snow cover or ice sheets should be conveniently described at a quantitative level.

In this work we studied the combined action of chemical and electrical synapses in small networks of Hindmarsh-Rose (HR) neurons on the synchronous behavior and on the rate of information produced (per time unit) by the networks. We show that if the chemical synapse is excitatory, the larger the chemical synapse strength used the smaller the electrical synapse strength needed to achieve complete synchronization, and for moderate synaptic strengths one should expect to find desynchronous behavior. Otherwise, if the chemical synapse is inhibitory, the larger the chemical synapse strength used the larger the electrical synapse strength needed to achieve complete synchronization, and for moderate synaptic strengths one should expect to find synchronous behaviors. Finally, we show how to calculate semianalytically an upper bound for the rate of information produced per time unit (Kolmogorov-Sinai entropy) in larger networks. As an application, we show that this upper bound is linearly proportional to the number of neurons in a network whose neurons are highly connected.

We present an experimental realization of time-delayed feedback control proposed by Schöll and Fiedler. The scheme enables us to stabilize torsion-free periodic orbits in autonomous systems, and to overcome the so-called odd number limitation. The experimental control performance is in quantitative agreement with the bifurcation analysis of simple model systems. The results uncover some general features of the control scheme which are deemed to be relevant for a large class of setups.

Using a combined analytical/molecular dynamics approach, we study the current fluctuation spectra and longitudinal and transverse collective mode dispersions of the classical two-dimensional (point) dipole system (2DDS) characterized by the ${\varphi }_D\left(r\right)={\mu }^2/r^3$ repulsive interaction potential; $\mu$ is the electric dipole strength. The interest in the 2DDS is twofold. First, the quasi-long-range $1/r^3$ interaction makes the system a unique classical many-body system, with a remarkable collective mode behavior. Second, the system may be a good model for a closely spaced semiconductor electron-hole bilayer, a system that is in the forefront of current experimental interest. The longitudinal collective excitations, which are of primary interest for the liquid phase, are acoustic at long wavelengths. At higher wave numbers and for sufficiently high coupling strength, we observe the formation of a deep minimum in the dispersion curve preceded by a sharp maximum; this is identical to what has been observed in the dispersion of the zero-temperature bosonic dipole system, which in turn emulates so-called roton-maxon excitation spectrum of the superfluid ${}^4\text{H}\text{e}$. The analysis we present gives an insight into the emergence of this apparently universal structure, governed by strong correlations. We study both the liquid and the crystalline solid state. We also observe the excitation of combination frequencies, resembling the roton-roton, roton-maxon, etc. structures in ${}^4\text{H}\text{e}$.

We study the heat conduction problem in two-dimensional (2D) lattice models of disk shape consisting of two circular heat baths with radius $r_1$ and $r_2$ $\left(r_1<r_2\right)$, located concentrically at the center and the edge of the disk. Compared with the lattice models of rectangle shape adopted in previous studies, the main advantage of the disk models is that they have an unambiguous 2D dimensionality. The Fermi-Pasta-Ulam interaction of $\beta$ type and the ${\varphi }^4$ system are considered, respectively, as momentum conserving and nonconserving prototypes. In the former we find that in the range of the system size investigated, the heat conductivity $\kappa$ depends on the system size $L=r_2-r_1$ as $\kappa \sim {\left(\text{ln}L\right)}^{\alpha }$ with $\alpha$ being a function of $r_1/r_2$. In particular, in the limit of $r_1/r_2\to 1$ we have $\alpha \to 1$, i.e., a logarithmic dependence of $\kappa$ on $L$, which is in agreement with the prediction of existing theories. In the momentum nonconserving ${\varphi }^4$ system the heat conductivity converges to a finite value as the system size is increased.

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error-free manner when working at nonzero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error-free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error-free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.

The principal signatures of deterministic dynamics in the statistical properties of the range and normalized range of sums are identified. Substantial differences from the classical statistical theory are found. Analytical expressions are derived, compared to those of the classical theory, and applied to generic classes of dynamical systems giving rise to chaotic and intermittent chaotic behavior.

A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the optimal solution of the problem is characterized by the solution of the Bellman equation obtained by numerical algorithms. Second, the solution is used as a benchmark to value how far from the optimum other heuristics that can be applied to larger systems are. This approach is the first attempt on the direction of schemes for controlling self-organized criticality that are based on optimization principles that consider explicitly a tradeoff between the size of the avalanches and the cost of intervention.

A model of soft frictionless disks in two dimensions at zero temperature is simulated with a shearing dynamics to study various kinds of asymmetries in sheared systems. We examine both single particle properties, the spatial velocity correlation function, and a correlation function designed to separate clockwise and counterclockwise rotational fields from one another. Among the rich and interesting behaviors we find that the velocity correlation along the two different diagonals corresponding to compression and dilation, respectively, are almost identical and, furthermore, that a feature in one of the correlation functions is directly related to irreversible plastic events.

The structural behavior of hard spheres interacting with repulsive (screened Coulomb) interaction in narrow constrictions is investigated using Brownian dynamics simulations. The system of particles adapts to the confining potential and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of planes throughout the three-dimensional channel. The presence of hard walls leads to structural deviations from the unbounded (infinite) crystal. The arrangement of the particles is perturbed by diffusion and an external driving force leading to a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of planes if it is energetically favorable. This reduction in the number of planes is analogous to the reduction in the number of layers in two-dimensional systems. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior.

In globally coupled networks composed of oscillatory and nonoscillatory elements, the balance between the subpopulations plays an important role in network dynamics and phase transitions. To extend this framework, we investigate mixed populations consisting of two types of self-oscillatory elements with different periods, particularly given by limit cycle oscillators and period-doubled ones. Phase transitions in the mixed populations are elucidated by numerical bifurcation analyses of a reduced system. We numerically confirm a formula determining the critical balance between the subpopulations for a phase transition at sufficiently large coupling strength.

Recently, the existence of extremely energetic hydrogen atoms in electrical discharges has been proposed in the literature with large controversy, from the analysis of the anomalous broadening of hydrogen Balmer lines. In this paper, the velocity distribution of H atoms and the profiles of the emitting atom lines created by the exothermic reaction $\text{H}_2{}^{+}+{\text{H}}_2\to \text{H}_3{}^{+}+\text{H}+\Delta E$ are calculated, as a function of the internal energy defect $\Delta E$. The shapes found for the non-Maxwell-Boltzmann distributions resulting in non-Gaussian line profiles raise serious arguments against the existence of hot and superhot H atoms as it has been proposed, at least with those temperatures.

A contactless pumping mechanism is realized in a layer of ferrofluid via a spatiotemporally modulated magnetic field. The resulting pressure gradient leads to a liquid ramp, which is measured by means of x-rays. The transport mechanism works best if a resonance of the surface waves with the driving is achieved. The behavior can be understood by considering the magnetically influenced dispersion relation of the fluid.

In this paper we develop a theoretical framework to study the hydrodynamic interactions in the presence of a nonflat and no-slip boundary. We calculate the influence of a small amplitude and sinusoidal deformations of a boundary wall in the self-mobility and the two-body hydrodynamic interactions for spherical particles. We show that the surface roughness enhances the self-mobility of a sphere in a way that, for motion in front of a local hump of the surface, the mobility strength decreases while it increases for the motion above a local deep of the rough surface. The influence of the surface roughness in the two-body hydrodynamic interactions is also analyzed numerically.

Currently, simulation is usually used to estimate network degree distribution $P\left(k\right)$ and to examine if a network model predicts a scale-free network when an analytical formula does not exist. An alternative Markovian chain-based numerical method was proposed by Shi et al. [Phys. Rev. E 71, 036140 (2005)] to compute time-dependent degree distribution $P\left(k,t\right)$. Although the numerical results demonstrate a quick convergence of $P\left(k,t\right)$ to $P\left(k\right)$ for the Barabási-Albert model, the crucial issue on the rate of convergence has not been addressed formally. In this paper, we propose a simpler Markovian iterative method to compute $P\left(k,t\right)$ for a class of growing network models. We also provide an upper bound estimation of the error of using $P\left(k,t\right)$ to represent $P\left(k\right)$ for sufficiently large $t$, and we show that with the iterative method, the rate of convergence of $P\left(k,t\right)$ is root linear.

The effect of finite temperature $T$ and finite strain rate $\dot{\gamma }$ on the statistical physics of plastic deformations in amorphous solids made of $N$ particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, $T<T_{\text{cross}}\left(N\right)$, and the strain is quasistatic. In this regime the elastoplastic steady state exhibits highly correlated plastic events whose statistics are characterized by anomalous exponents. In the second regime $T_{\text{cross}}\left(N\right)<T<T_{\text{max}}\left(\dot{\gamma }\right)$ the system-size dependence of the stress fluctuations becomes normal, but the variance depends on the strain rate. The physical mechanism of the crossover is different for increasing temperature and increasing strain rate, since the plastic events are still dominated by the mechanical instabilities (seen as an eigenvalue of the Hessian matrix going to zero), and the effect of temperature is only to facilitate the transition. A third regime occurs above the second crossover temperature $T_{\text{max}}\left(\dot{\gamma }\right)$ where stress fluctuations become dominated by thermal noise. Throughout the paper we demonstrate that scaling concepts are highly relevant for the problem at hand, and finally we present a scaling theory that is able to collapse the data for all the values of temperatures and strain rates, providing us with a high degree of predictability.

We present the results of three-dimensional discrete element simulations of global normal stresses in quasi-two-dimensional sandpiles formed by pouring monodispersed cohesionless spherical grains into a vertical granular Hele-Shaw cell. We observe the Janssen effect which is the phenomenon of pressure saturation at the bottom of the container. Simulation of cells with different thicknesses shows that the Janssen coefficient $\kappa$ is a function of the cell thickness. Dependence of global normal stresses as well as $\kappa$ on the friction coefficients between the grains $\left({\mu }_p\right)$ and with walls $\left({\mu }_w\right)$ are also studied. The results show that in the range of our simulations $\kappa$ usually increases with the wall-grain friction coefficient. Meanwhile by increasing ${\mu }_p$ while the other system parameters are fixed, we witness a gradual increase in $\kappa$ to a parameter dependent maximal value.

Controlled vertical drying deposition method was used to make high-quality single crystal close-packed colloidal films formed of different radii polystyrene latex spheres on glass substrates coming from a low concentration water suspension (0.1% volume fraction). Regardless of the spheres radii the film thickness was about 6.3 microns. However, cracks destroyed the crystalline film structure during the colloidal film growth. The effect of particle radius (85–215 nm range) on film cracking was systematically studied using in situ optical fracture monitoring. Primary parallel cracks run along the vertical growth direction, later followed by secondary branched cracks in-between the primary cracks due to residual water evaporation. Quantitative theoretical relationship between the cracks spacing and particles radius was derived and shows good agreement with experimental observations. Normalized cracks spacing is related to a reciprocal ratio of the dimensionless particle radius.

The effect of confinement by crystals on the $\alpha$ relaxation, observed by dielectric broadband spectroscopy, in isotropic as well as in oriented semicrystalline poly(vinilydene fluoride), is analyzed on the basis of a new thermodynamic model. In both samples, it has been found that the average free-energy barrier, $\Delta F$, for conformational rearrangements is of the same order of the dispersion barrier heights, $\delta \left(\Delta F\right)$, around $\Delta F$, i.e., the increase in the barrier height in conformational rearrangement is accompanied by an increase in the heterogeneity of constraining conditions. At a given temperature $T$, the readjustment free energy is larger in the oriented sample. This fact might be ascribed to either an enhanced effectiveness of confinement in the amorphous region due to the decrease of the amorphous layer thickness in the stacks, or to a change of the mean chain orientation or both. In addition, it is worth noting that in oriented poly(vinilydene fluoride) the regions of cooperative rearrangement are significantly larger. Moreover, independent of orientation, the size of these readjusting regions increase upon decreasing $T$. This feature, which underlies the Adam-Gibbs approach for liquids, is pointed out for the first time from direct data analysis in the case of confinement enhanced cooperativity. In addition to the above analysis, the samples have been characterized by differential scanning calorimetry, wide angle x-ray scattering, and small angle x-ray scattering.

We present the results of molecular-dynamics simulations on the salt concentration dependence of the formation of polyelectrolyte bundles in thermodynamic equilibrium. Extending our results on salt-free systems we investigate here deficiency or excess of trivalent counterions in solution. Our results reveal that the trivalent counterion concentration significantly alters the bundle size and size distribution. The onset of bundle formation takes place at earlier Bjerrum length values with increasing trivalent counterion concentration. For the cases of 80%, 95%, and 100% charge compensation via trivalent counterions, the net charge of the bundles decreases with increasing size. We suggest that competition among two different mechanisms, counterion condensation and merger of bundles, leads to a nonmonotonic change in line-charge density with increasing Bjerrum length. The investigated case of having an abundance of trivalent counterions by 200% prohibits such a behavior. In this case, we find that the difference in effective line-charge density of different size bundles diminishes. In fact, the system displays an isoelectric point, where all bundles become charge neutral.