We focus on polymer networks with a scale-free topology. In the framework of generalized Gaussian structures, by making use of the eigenvalue spectrum of the connectivity matrix, we determined numerically the averaged monomer displacement under external forces and the mechanical relaxation moduli (storage and loss modulus). First, we monitor these physical quantities and additionally the eigenvalue spectrum for structures of different sizes, but with the same $\gamma$, which is a parameter that measures the connectivity of the structure. Second, we vary the parameter $\gamma$, and we keep constant the size of the structures. This allows us to study in detail the crossover behavior from a simple linear chain to a starlike structure. As expected we encounter a more chainlike behavior for high values of $\gamma$, while for small values of $\gamma$ a more starlike behavior is observed. In the intermediate time (frequency) domain, we encounter regions of constant slope for some intermediate values of $\gamma$.

We show how to use a fractional autoregressive integrated moving average (FARIMA) model to a statistical analysis of the subdiffusive dynamics. The discrete time FARIMA$(1,d,1)$ model is applied in this paper to the random motion of an individual fluorescently labeled mRNA molecule inside live E. coli cells in the experiment described in detail by Golding and Cox [Phys. Rev. Lett. 96, 098102 (2006)] as well as to the motion of fluorescently labeled telomeres in the nucleus of live human cells (U2OS cancer) in the experiment performed by Bronstein et al. [Phys. Rev. Lett. 103, 018102 (2009)]. It is found that only the memory parameter $d$ of the FARIMA model completely detects an anomalous dynamics of the experimental data in both cases independently of the observed distribution of random noises.

We develop a spectral method for computing the probability density function for delayed random walks; for such problems, the method is exact to machine precision and faster than existing approaches. In conjunction with a step function approximation and the weak Euler-Maruyama discretization, the spectral method can be applied to nonlinear stochastic delay differential equations (SDDE). In essence, this means approximating the SDDE by a delayed random walk, which is then solved using the spectral method. We carry out tests for a particular nonlinear SDDE that show that this method captures the solution without the need for Monte Carlo sampling.

Existence and properties of the Shapiro steps in the presence of noise have been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. The results have shown that the influence of noise on interference phenomena is determined by the presence and the size of half-integer steps. Since half-integer steps are more affected by noise, and the properties of harmonic steps are directly correlated with the size of half-integer steps, noise will have completely different effects on the harmonic steps if half-integer steps are present. As temperature increases, in the amplitude dependence of the step width, deviation from the well-known Bessel-like oscillations has been observed, and three different types of behavior have been classified. In the influence of noise on the frequency dependence of the steps, appearance of oscillations and strong influence of half-integer steps on their form have been observed.

In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.

In this article we investigate the electrical conductance of an insulating porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.g., brine), usually described using the Archie cementation exponent. We show how the electrical conductance depends on changes in the drift velocity and the length of the electric field lines, in addition to the porosity and the conductance of the electrolyte. We characterize the length of the electric field lines by a tortuosity and the changes in drift velocity by a constriction factor. Both the tortuosity and the constriction factor are descriptors of the pore microstructure. We define a conductance reduction factor to measure the local contributions of the pore microstructure to the global conductance. It is shown that the global conductance reduction factor is the product of the tortuosity squared divided by the constriction factor, thereby proving that the combined effect of tortuosity and constriction, in addition to the porosity and conductance of the electrolyte, fully describes the effective electrical conductance of a porous medium. We show that our tortuosity, constriction factor, and conductance reduction factor reproduce the electrical conductance for idealized porous media. They are also applied to Bentheimer sandstone, where we describe a microstructure-related correlation between porosity and conductivity using both the global conductance reduction factor and the distinct contributions from tortuosity and constriction. Overall, this work shows how the empirical Archie cementation exponent can be substituted by more descriptive, physical parameters, either by the global conductance reduction factor or by tortuosity and constriction.

Spherically collapsing cavitation bubbles produce a shock wave followed by a rebound bubble. Here we present a systematic investigation of the energy partition between the rebound and the shock. Highly spherical cavitation bubbles are produced in microgravity, which suppresses the buoyant pressure gradient that otherwise deteriorates the sphericity of the bubbles. We measure the radius of the rebound bubble and estimate the shock energy as a function of the initial bubble radius ($2–5.6\mathrm{mm}$) and the liquid pressure ($10–80\mathrm{kPa}$). Those measurements uncover a systematic pressure dependence of the energy partition between rebound and shock. We demonstrate that these observations agree with a physical model relying on a first-order approximation of the liquid compressibility and an adiabatic treatment of the noncondensable gas inside the bubble. Using this model we find that the energy partition between rebound and shock is dictated by a single nondimensional parameter $\xi =\Delta p{\gamma }^6/\left[{p_{g0}}^{1/\gamma }{\left(\rho c^2\right)}^{1-1/\gamma }\right]$, where $\Delta p=p_{\infty }-p_v$ is the driving pressure, $p_{\infty }$ is the static pressure in the liquid, $p_v$ is the vapor pressure, $p_{g0}$ is the pressure of the noncondensable gas at the maximal bubble radius, $\gamma$ is the adiabatic index of the noncondensable gas, $\rho$ is the liquid density, and $c$ is the speed of sound in the liquid.

The ionized gas in Hall-effect plasma accelerators spans a wide range of spatial and temporal scales, and exhibits diverse physics some of which remain elusive even after decades of research. Inside the acceleration channel a quasiradial applied magnetic field impedes the current of electrons perpendicular to it in favor of a significant component in the $\mathbf{E}\times \mathbf{B}$ direction. Ions are unmagnetized and, arguably, of wide collisional mean free paths. Collisions between the atomic species are rare. This paper reports on a computational approach that solves numerically the 2D axisymmetric vector form of Ohm's law with no assumptions regarding the resistance to classical electron transport in the parallel relative to the perpendicular direction. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations on a computational mesh that is aligned with the applied magnetic field. This approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction and encompasses the cathode boundary where the lines of force can become nonisothermal. It also allows for the self-consistent solution of the plasma conservation laws near the anode boundary, and for simulations in accelerators with complex magnetic field topologies. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for the ion drag in the momentum equation due to ion-neutral (charge-exchange) and ion-ion collisions. The density of the atomic species is determined using an algorithm that eliminates the statistical noise associated with discrete-particle methods. Numerical simulations are presented that illustrate the impact of the above-mentioned features on our understanding of the plasma in these accelerators.

Granular media, whose features range from the particle scale to the force-chain scale and the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with each of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures to determine their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of mesoscale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by mesoscale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.

A phase-field model is developed for quantitative simulation of bubble growth in the diffusion-controlled regime. The model accounts for phase change and surface tension effects at the liquid-vapor interface of pure substances with large property contrast. The derivation of the model follows a two-fluid approach, where the diffuse interface is assumed to have an internal microstructure, defined by a sharp interface. Despite the fact that phases within the diffuse interface are considered to have their own velocities and pressures, an averaging procedure at the atomic scale, allows for expressing all the constitutive equations in terms of mixture quantities. From the averaging procedure and asymptotic analysis of the model, nonconventional terms appear in the energy and phase-field equations to compensate for the variation of the properties across the diffuse interface. Without these new terms, no convergence towards the sharp-interface model can be attained. The asymptotic analysis also revealed a very small thermal capillary length for real fluids, such as water, that makes impossible for conventional phase-field models to capture bubble growth in the millimeter range size. For instance, important phenomena such as bubble growth and detachment from a hot surface could not be simulated due to the large number of grids points required to resolve all the scales. Since the shape of the liquid-vapor interface is primarily controlled by the effects of an isotropic surface energy (surface tension), a solution involving the elimination of the curvature from the phase-field equation is devised. The elimination of the curvature from the phase-field equation changes the length scale dominating the phase change from the thermal capillary length to the thickness of the thermal boundary layer, which is several orders of magnitude larger. A detailed analysis of the phase-field equation revealed that a split of this equation into two independent parts is possible for system sizes ranging from micrometers and above. The split of the phase-field equation leads to two equations controlling independently the phase change and the shape of the phase-field profile across the diffuse interface. A new algorithm is presented to solve a fully coupled model, including advection, phase change, and surface tension effects. Good agreement is found among numerical simulations, analytical solutions, and experimental results.

We study numerically the formation of localized superlattices in spatially distributed systems. We predict that in wide regions of the parameter space, stable localized, either bright or dark, superlattices may form in reaction-diffusion systems. Localized superlattices are patterns which consist of a piece of superlattice. Each single ring is surrounded by spots. The number of rings and their spatial distribution are determined by the initial conditions. The peak concentration remains unaltered for fixed values of the parameters.

Optical microscopy was used to visualize the flow of two phases [British Petroleum (BP) oil and an aqueous surfactant phase] in confined space, three-dimensional, transparent, natural porous media. The porous media consisted of water-wet cryolite grains packed inside cylindrical, glass microchannels, thus producing microscopic packed beds. Primary drainage of BP oil displacing an aqueous surfactant phase was studied at capillary numbers that varied between ${10}^{-6}$ and ${10}^{-2}$. The confinement space had a significant effect on the flow behavior. Phenomena of burst motion and capillary fingering were observed for low capillary numbers due to the domination of capillary forces. It was discovered that breakthrough time and capillary number bear a log-log scale linear relationship, based on which a generalized correlation between oil travel distance $x$ and time $t$ was found empirically.

In this work we investigate the critical behavior of the three-dimensional simple-cubic majority voter model. Using numerical simulations and a combination of two different cumulants, we evaluated the critical point with a higher accuracy than the previous numerical result found by Yang, Kim, and Kwak [Phys. Rev. E 77, 051122 (2008)]. Using standard finite-size scaling theory and scaling corrections, we find that the critical exponents $\nu \text{,}\gamma$, and $\beta$ are the same as those of the three-dimensional Ising model.

We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters ($N$-clusters) with well-defined structures. We use Brownian dynamics to model the assembly of $N$-clusters varying in size from two to twelve outer spheres and free energy calculations to predict the expected cluster sizes and shapes as a function of temperature and inner particle diameter. We show that the arrangements of outer spheres at finite temperatures are related to spherical codes, an ideal mathematical sequence of points corresponding to the densest possible sphere packings. We demonstrate that temperature and the ratio of the diameters of the inner and outer spheres dictate cluster morphology. We present a surprising result for the equilibrium structure of a 5-cluster, for which the square pyramid arrangement is preferred over a more symmetric structure. We show this result using Brownian dynamics, a Monte Carlo simulation, and a free energy approximation. Our results suggest a promising way to assemble anisotropic building blocks from constituent colloidal spheres.

Recent work has shown that different theoretical approaches to the dynamics of the susceptible-infected-susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size $N$. We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with $N$ with the correct exponent, but often failing to capture the correct prefactor.

There are two distinct approaches for deriving the canonical ensemble. The canonical ensemble either follows as a special limit of the microcanonical ensemble or alternatively follows from the maximum entropy principle. We show the equivalence of these two approaches by applying the maximum entropy formulation to a closed universe consisting of an open system plus bath. We show that the target function for deriving the canonical distribution emerges as a natural consequence of partial maximization of the entropy over the bath degrees of freedom alone. By extending this mathematical formalism to dynamical paths rather than equilibrium ensembles, the result provides an alternative justification for the principle of path entropy maximization as well.

We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase and at its boundaries. This indicates that the systemwide sampling at equal times, characteristic of the instantaneous activity, overshadows the subtler effects which come about from nonequal time correlations, and are responsible for anomalous scaling. We show that apparently conflicting results concerning asymmetry (skewness) of the corresponding distributions can in fact be reconciled, and that (apart from a few well-understood exceptional cases) for both activity and local current one has positive skew deep within the low-current phase, and negative skew everywhere else.

We study the vertex-cover problem, which is a nondeterministic polynomial-time hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, such as Erdős-Rényi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g., for the ER ensemble at connectivity $c=e\approx 2.7183$ from replica symmetric to replica-symmetry broken. For the vertex-cover problem, the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, also changes close to this phase transition from “easy” to “hard.” In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach; hence the algorithm operates in a space outside the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an easy-hard transition around $c=e$, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.

Experimental evidence shows that a variety of photosynthetic systems can preserve quantum beats in the process of electronic energy transfer, even at room temperature. However, whether this quantum coherence arises in vivo and whether it has any biological function have remained unclear. Here we present a theoretical model that suggests that the creation and recreation of coherence under natural conditions is ubiquitous. Our model allows us to theoretically demonstrate a mechanism for a ratchet effect enabled by quantum coherence, in a design inspired by an energy transfer pathway in the Fenna-Matthews-Olson complex of the green sulfur bacteria. This suggests a possible biological role for coherent oscillations in spatially directing energy transfer. Our results emphasize the importance of analyzing long-range energy transfer in terms of transfer between intercomplex coupling states rather than between site or exciton states.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized $\left[N\right]pT$ ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the $\left[N\right]pT$ ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.