In an effort to investigate the link between failure mechanisms and the geometry of fractures of compacted grains materials, a detailed statistical analysis of the surfaces of fractured Fontainebleau sandstones has been achieved. The roughness of samples of different widths $W$ is shown to be self-affine with an exponent $\zeta =0.46\pm 0.05$ over a range of length scales ranging from the grain size $d$ up to an upper cutoff length $\xi \simeq 0.15W$. This low $\zeta$ value is in agreement with measurements on other sandstones and on sintered materials. The probability distributions ${\pi }_{\delta z}\left(\delta h\right)$ of the variations of height over different distances $\delta z>d$ can be collapsed onto a single Gaussian distribution with a suitable normalization and do not display multiscaling features. The roughness amplitude, as characterized by the height-height correlation over fixed distances $\delta z$, does not depend on the sample width, implying that no anomalous scaling of the type reported for other materials is present. It is suggested, in agreement with recent theoretical work, to explain these results by the occurrence of brittle fracture (instead of damage failure in materials displaying a higher value of $\zeta \simeq 0.8$).

We propose a criterion to detect determinism in short time series. This criterion is based on the estimation of the parameter $E_2$ defined by the averaged false neighbors method for analyzing time series [Cao, Physica D 110, 43 (1997)]. Using surrogate data testing with several chaotic and stochastic simulated time series, we show that the variation coefficient of $E_2$ over a few values of the embedding dimension $d$ defines a suitable statistic to detect determinism in short data sequences. This result holds for a time series generated by a high-dimensional chaotic system such as the Mackey-Glass one. Different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real-world data. We also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise.

We examine the evolution of the ground state of a Bose-Einstein condensate in a two-dimensional circular box, the wall of which is initially at rest and then recedes with large and constant speed. The final state of the condensate depends on the rapidity of the expansion of the box. If the number of atoms in the condensate is small compared to the dimensionless speed of the wall, then the condensate becomes a mixture of excitations and follows the expansion of the box, leaving empty though an increasingly larger region between the condensate boundary and the wall. If, on the other hand, the number of atoms is large compared to the dimensionless speed of the wall, then the condensate is always in the ground state and spreads uniformly in all of the expanding box, the condensate boundary always coinciding with the receding wall. Approximate analytic expressions are found for the evolving wave function.

A system very similar to a dielectric barrier discharge, but with a simple stationary dc voltage, can be realized by sandwiching a gas discharge and a high-ohmic semiconductor layer between two planar electrodes. In experiments this system forms spatiotemporal and temporal patterns spontaneously, quite similarly to, e.g., Rayleigh-Bénard convection. Here it is modeled with a simple discharge model with space charge effects, and the semiconductor is approximated as a linear conductor. In previous work, this model has reproduced the phase transition from homogeneous stationary to homogeneous oscillating states semiquantitatively. In the present work, the formation of spatial patterns is investigated through linear stability analysis and through numerical simulations of the initial value problem; the methods agree well. They show the onset of spatiotemporal patterns for high semiconductor resistance. The parameter dependence of temporal or spatiotemporal pattern formation is discussed in detail.

A form for the two-point third-order structure function has been calculated for three-dimensional (3D) homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalization of the 3D incompressible turbulence owing to rotation.

We investigate the occurrence of $1∕f$ spectra of low-frequency fluctuations in numerical simulations of three-dimensional hydrodynamic and magnetohydrodynamic turbulence driven by a random forcing with a controlled correlation time. A range of one decade of $1∕f$ spectrum is observed when a strong background magnetic field is present. The frequency spectra of individual Fourier modes is also analyzed and it is observed that the $1∕f$ range is present in the largest available wavelength mode for the magnetohydrodynamic simulations with and without a background magnetic field and it is not observed (or is less clear) for the hydrodynamic case. The presence of $1∕f$ spectra of low-frequency fluctuations is also analyzed for two-dimensional magnetohydrodynamic and hydrodynamic turbulence simulations and it is observed in both cases. The origin of these long period fluctuations is discussed.

We propose a derivation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statistical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each velocity direction occupied by many particles. We show that the most probable state of this model corresponds to the usual equilibrium distribution of the lattice Boltzmann equation. Thermal fluctuations about this equilibrium are controlled by the mean number of particles at a lattice site. Stochastic collision rules are described by a Monte Carlo process satisfying detailed balance. This allows for a straightforward derivation of discrete Langevin equations for the fluctuating modes. It is shown that all nonconserved modes should be thermalized, as first pointed out by Adhikari et al. [Europhys. Lett. 71, 473 (2005)]; any other choice violates the condition of detailed balance. A Chapman-Enskog analysis is used to derive the equations of fluctuating hydrodynamics on large length and time scales; the level of fluctuations is shown to be thermodynamically consistent with the equation of state of an isothermal, ideal gas. We believe this formalism will be useful in developing new algorithms for thermal and multiphase flows.

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. Yeong and Torquato [Phys. Rev. E 57, 495 (1998)] introduced a stochastic optimization technique that enables one to generate realizations of heterogeneous materials from a prescribed set of correlation functions. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function $S_2\left(\mathbf{r}\right)$ and formulate a conjecture. In particular, we argue that given a complete two-point correlation function space, $S_2\left(\mathbf{r}\right)$ of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide examples of realizable two-point correlation functions and suggest a set of analytical basis functions. We also discuss an exact mathematical formulation of the (re)construction problem and prove that $S_2\left(\mathbf{r}\right)$ cannot completely specify a two-phase heterogeneous material alone. Moreover, we devise an efficient and isotropy-preserving construction algorithm, namely, the lattice-point algorithm to generate realizations of materials from their two-point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions. We will mainly focus on basic principles in this paper. The algorithmic details and applications of the general scheme are given in the second part of this series of two papers.

An extension of a recently introduced one-dimensional model, the necklace model, is used to study the reptation of a chain of $N$ particles in a two-dimensional square lattice. The mobilities of end and middle particles of a chain are governed by three free parameters. This new model mimics the behavior of a long linear and flexible polymer in a gel. Noninteracting and self-avoiding chains are considered. For both cases, analytical approximations for the diffusion coefficient of the center of mass of the chain, for all values of $N$, are proposed. The validity of these approximations for different values of the free parameters is verified by means of Monte Carlo simulations. Extensions to higher dimensions are also discussed.

We study the multipulse formation in passive mode locking in the framework of the statistical light-mode dynamics theory. It is a many-body theory that treats the complex many-mode laser system by statistical mechanics. We give a detailed theory and experimental verification for the important case of multiple-pulse formation in the laser cavity. We follow and extend our former work on the subject. We give a detailed analysis with a rigorous calculation of the partition function, the free energy, and the order parameter in the coarse-graining method within the mean-field theory that is exact in the light-mode system. The outcome is a comprehensive picture of multipulse formation and annihilation, pulse after pulse, in an almost quantized manner, as the noise (“temperature”) or the light power is varied. We obtain the phase diagram of the system, showing a series of first-order phase transitions, each belonging to a different number of pulses. We also study the hysteresis behavior, typical for such thermodynamic systems. We elaborate on the role of the saturable absorber structure in determining the multipulse formation. The theoretical results are compared to experimental measurements that we obtained with mode-locked fiber lasers, and we find an excellent agreement.

Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some “mobility” field. The identity of this “mobility” field has remained elusive due to the lack of coarse-graining procedures to obtain these models from a more microscopic point of view. Here we exhibit a scheme to map the dynamics of a two-dimensional soft disk glass former onto a kinetically constrained spin model, providing an attempt at bridging these two approaches.

We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation time scales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that the entire distribution of relaxation times scales identically with age. Despite large changes in mobility, we observe comparatively little structural change except for a weak logarithmic increase in the degree of short-range order that may be correlated with an observed decrease in aging with increasing load.

In the study a model of training of neuronal networks built of integrate-and-fire neurons is investigated. Neurons are assembled into complex networks of Watts-Strogatz type. Every neuronal network contains a single receptor neuron. The receptor neuron, stimulated by an external signal, evokes spikes in equal time intervals. The spikes generated by the receptor neuron induce subsequent activity of a whole network. The depolarization signals, traveling the network, modify synaptic couplings according to a kick-and-delay rule, whose process is termed “training.” It is shown that the training decreases the mean length of paths along which a depolarization signal is transmitted from the receptor neuron. Consequently, the training also decreases the reaction time and the energy expense necessary for the network to react to the external stimulus. It is shown that the initial distribution of synaptic couplings crucially determines the performance of trained networks.

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams, stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces (“stretching”). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of “floppy modes”—low-energy bending excitations that retain a high degree of nonaffinity. The length scale characterizing the emergent nonaffinity is given by the “fiber length” $l_f$, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.

The tortoise beetle Charidotella egregia is able to modify the structural color of its cuticle reversibly, when disturbed by stressful external events. After field observations, measurements of the optical properties in the two main stable color states and scanning electron microscope and transmission electron microscope investigations, a physical mechanism is proposed to explain the color switching of this insect. It is shown that the gold coloration displayed by animals at rest arises from a chirped multilayer reflector maintained in a perfect coherent state by the presence of humidity in the porous patches within each layer, while the red color displayed by disturbed animals results from the destruction of this reflector by the expulsion of the liquid from the porous patches, turning the multilayer into a translucent slab that leaves an unobstructed view of the deeper-lying, pigmented red substrate. This mechanism not only explains the change of hue but also the change of scattering mode from specular to diffuse. Quantitative modeling is developed in support of this analysis.

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.

Microrheological measurements have been carried out on ionotropic gels made from an important cell wall polysaccharide, using diffusing wave spectroscopy and multiple particle tracking. These gels were formed by the interaction of calcium ions with negatively charged groups on the polymer backbone, which is a copolymer of charged and uncharged sugars, galacturonic acid, and its methylesterified analog, respectively. The results suggest that semiflexible networks are formed in these systems, with a low frequency, frequency independent storage modulus $(G^{\prime }>G^{″})$, and a high frequency scaling of both $G^{\prime }$ and $G^{″}$ with ${\omega }^{3∕4}$. The differences observed between gels obtained using polysaccharide samples with different amounts and patterns of the charged ion-binding groups could comfortably be accommodated within this theoretical framework, assuming that the elementary semiflexible elements of the network are filaments consisting of two polymer chains bridged with calcium. In particular, a sample that was engineered to possess a blockwise intramolecular distribution of calcium chelating moieties clearly exhibited the high frequency scaling of both moduli with ${\omega }^{3∕4}$ across some three orders of magnitude, and the concentration dependences of the elastic modulus, at both high and low frequency, were found to follow power laws with predicted exponents. Furthermore, quantitative agreement of the moduli with theory was found for realistic estimates of the molecular parameters, suggesting that the physics of semiflexible networks is not only exploited by protein components of the cytoskeleton but also by polysaccharides in plant cell walls.

Community detection and analysis is an important methodology for understanding the organization of various real-world networks and has applications in problems as diverse as consensus formation in social communities or the identification of functional modules in biochemical networks. Currently used algorithms that identify the community structures in large-scale real-world networks require a priori information such as the number and sizes of communities or are computationally expensive. In this paper we investigate a simple label propagation algorithm that uses the network structure alone as its guide and requires neither optimization of a predefined objective function nor prior information about the communities. In our algorithm every node is initialized with a unique label and at every step each node adopts the label that most of its neighbors currently have. In this iterative process densely connected groups of nodes form a consensus on a unique label to form communities. We validate the algorithm by applying it to networks whose community structures are known. We also demonstrate that the algorithm takes an almost linear time and hence it is computationally less expensive than what was possible so far.

We generalize a sampling algorithm for lattice animals (connected clusters on a regular lattice) to a Monte Carlo algorithm for “graph animals,” i.e., connected subgraphs in arbitrary networks. As with the algorithm in [N. Kashtan et al., Bioinformatics 20, 1746 (2004)], it provides a weighted sample, but the computation of the weights is much faster (linear in the size of subgraphs, instead of superexponential). This allows subgraphs with up to ten or more nodes to be sampled with very high statistics, from arbitrarily large networks. Using this together with a heuristic algorithm for rapidly classifying isomorphic graphs, we present results for two protein interaction networks obtained using the tandem affinity purification (TAP) method: one of Escherichia coli with 230 nodes and 695 links, and one for yeast (Saccharomyces cerevisiae) with roughly ten times more nodes and links. We find in both cases that most connected subgraphs are strong motifs ($Z$ scores $>10$) or antimotifs ($Z$ scores $<-10$) when the null model is the ensemble of networks with fixed degree sequence. Strong differences appear between the two networks, with dominant motifs in E. coli being (nearly) bipartite graphs and having many pairs of nodes that connect to the same neighbors, while dominant motifs in yeast tend towards completeness or contain large cliques. We also explore a number of methods that do not rely on measurements of $Z$ scores or comparisons with null models. For instance, we discuss the influence of specific complexes like the 26S proteasome in yeast, where a small number of complexes dominate the $k$ cores with large $k$ and have a decisive effect on the strongest motifs with 6–8 nodes. We also present Zipf plots of counts versus rank. They show broad distributions that are not power laws, in contrast to the case when disconnected subgraphs are included.

In the present paper, molecular dynamics simulations are performed to explore the effects of wall lattice-fluid interactions on the hydrodynamic characteristics in nanochannels. Couette and Poiseuille flows of liquid argon with channel walls of face-centered cubic (fcc) lattice structure are employed as the model configurations. Truncated and shifted Lennard-Jones (LJ) 12-6 potentials for evaluations of fluid-fluid and wall-fluid interactions, and a nonlinear spring potential for wall-wall interaction, are used as interatomistic or molecular models. The hydrodynamics at various flow orientation angles with respect to channel walls of lattice planes (111), (100), and (110) are explored. The present work discloses that the effects of key parameters, such as wall density, lattice plane, flow orientation, and LJ interaction energy, have a very significant impact on the nanochannel flow characteristics. The related interfacial phenomena and the underlying physical mechanisms are explored and interpreted. These results are significant in the understanding of nanoscale hydrodynamics, as well as in various applications where an accurate nanoscale flow rate control is necessary.