Air is injected locally at the base of an immersed granular bed. The gas, which is forced to flow gently through the material, creates several paths between the grains. We observe that the latter gas venting results in the emission of bubbles in a localized region at the free surface. Additional experiments, performed in two dimensions, permit a direct visualization of the paths, and a theoretical approach shows that the typical size of the region at the free surface can be accounted for by a diffusionlike process. The diffusion coefficient is expressed as a function of the system parameters.

We study interactions between shocks and standing-wave patterns in vertically oscillated layers of granular media using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order. We simulate a layer of grains atop a plate that oscillates sinusoidally in the direction of gravity. Standing waves form stripe patterns when the accelerational amplitude of the plate’s oscillation exceeds a critical value. Shocks also form with each collision between the layer and the plate; we show that pressure gradients formed by these shocks cause the flow to reverse direction within the layer. This reversal leads to an oscillatory state of the pattern that is subharmonic with respect to the plate’s oscillation. Finally, we study the relationship between shocks and patterns in layers oscillated at various frequencies and show that the pattern wavelength increases monotonically as the shock strength increases.

Starting from the hypothesis that the decay of coherent signals observed in ${}^1\mathrm{H}$ NMR experiments is driven by quantum interference, irreversible decoherence, and nonidealities in the experiment, we design an experiment to isolate and identify the irreversible attenuation of multiple-quantum coherences toward quasiequilibrium states of dipolar order in nematic liquid crystals (LCs). The experiment combines the well-known “magic sandwich” pulse sequence with preparation of dipolar ordered states and encoding of multiple-quantum coherences. The spin system composed of the dipole-coupled protons of a LC molecule provides an example of a small cluster of strongly interacting spins. We study decoherence rates under a sequence that reverses time evolution with the secular dipolar Hamiltonian to compensate coherent evolution of a closed quantum system. In this way, the time scale is made evident where irreversible decoherence takes place, providing insight into the nature of the processes responsible for the attainment of quasiequilibrium. The behavior of single- and double-quantum-coherence amplitudes with reversal time is interpreted as evidence of the quantum character (as opposed to stochastic character) of the processes that drive irreversible decoherence. The experimental method proposed is useful for probing the action of the environment on materials with quantum information processing potential.

The molecular motor gliding assay, in which a microtubule or other filament moves across a surface coated with motors, has provided much insight into how molecular motors work. The kinesin-microtubule system is also a strong candidate for the job of nanoparticle transporter in nanotechnology devices. In most cases, several motors transport each filament. Each motor serves both to bind the microtubule to a stationary surface and to propel the microtubule along the surface. By applying a uniform transverse force of 4–19 pN to a superparamagnetic bead attached to the trailing end of the microtubule, we have measured the distance $d$ between binding points (motors). The average value of $d$ was determined as a function of motor surface density $\mathit{\sigma }$. The measurements agree well with the scaling model of Duke, Holy, and Liebler, which predicts that $\langle d\rangle ~{\mathit{\sigma }}^{-2/5}$ if $0.05⩽\mathit{\sigma }⩽20\hspace{0.5em}\mu {\mathrm{m}}^{-2}$ [Phys. Rev. Lett. 74, 330 (1995)]. The distribution of $d$ fits an extension of the model. The radius of curvature of a microtubule bent at a binding point by the force of the magnetic bead was ≈1 μm, 5000-fold smaller than the radius of curvature of microtubules subjected only to thermal forces. This is evidence that at these points of high bending stress, generated by the force on the magnetic bead, the microtubule is in the more flexible state of a two-state model of microtubule bending proposed by Heussinger, Schüller, and Frey [Phys. Rev. E 81, 021904 (2010)].

We extend the concept of symbolic transfer entropy to enable the time-resolved investigation of directional relationships between coupled dynamical systems from short and transient noisy time series. For our approach, we consider an observed ensemble of a sufficiently large number of time series as multiple realizations of a process. We derive an index that quantifies the preferred direction of transient interactions and assess its significance using a surrogate-based testing scheme. Analyzing time series from noisy chaotic systems, we demonstrate numerically the applicability and limitations of our approach. Our findings obtained from an analysis of event-related brain activities underline the importance of our method to improve understanding of gross neural interactions underlying cognitive processes.

A useful perspective to take when studying anomalous diffusion processes is that of a continuous-time random walk and its associated generalized master equation. We derive the generalized master equations for continuous-time random walks that are restricted to a bounded domain and compare numerical solutions with kernel-density estimates of the probability-density function computed from simulations. The numerical solution of the generalized master equation represents a powerful tool in the study of continuous-time random walks on bounded domains.

How a network breaks up into subnetworks or communities is of wide interest. Here we show that vertices connected to many other vertices across a network can disturb the community structures of otherwise ordered networks, introducing noise. We investigate strategies to identify and remove noisy vertices (“violators”) and develop a quantitative approach using statistical breakpoints to identify when the largest enhancement to a modularity measure is achieved. We show that removing nodes thus identified reduces noise in detected community structures for a range of different types of real networks in software systems and in biological systems.

An iterated function system is used to generate fractal-like ramified graph networks of absorbers, which are optimized for desalination performance. The diffusion equation is solved for the boundary case of constant pressure difference at the absorbers and a constant ambient salt concentration far from the absorbers, while constraining both the total length of the network and the total area of the absorbers to be constant as functions of generation $G.$ A linearized form of the solution was put in dimensionless form which depends only on a dimensionless membrane resistance, a dimensionless inverse svelteness ratio, and $G$. For each of the first nine generations $G=2,\dots ,10,$ the optimal graph shapes were obtained. Total water production rate increases parabolically as a function of generation, with a maximum at $G=7$. Total water production rate is shown to be approximately linearly related to the power consumed, for a fixed generation. Branching ratios which are optimal for desalination asymptote decreasingly to $r=0.510$ for large $G$, while branching angles which are optimal for desalination asymptote decreasingly to 1.17 radians. Asymmetric graphs were found to be less efficient for desalination than symmetric graphs. The geometry which is optimal for desalination does not depend strongly on the dimensionless parameters, but the optimal water production does. The optimal generation was found to increase with the inverse svelteness ratio.

We examine long-time properties of the ideal dynamics of three-dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases, the results agree with the isotropic predictions stemming from statistical mechanics. No accumulation of excitation occurs in the large scales, although, in the dissipative rotating case, anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two dimensionalization of the flow undergoing strong rotation as advocated by several authors.

The recognition of phenomena emerging from fluid-structure interaction represents a central problem in applied fluid mechanics, especially relevant in those biological systems when the tissue properties are not measurable with accuracy. The problem of an oscillatory flow over a wall-mounted leaflet is studied here with the objective to better define the role of inertia. A numerical model based on time-dependent conformal transformation is introduced to ensure an accurate solution and an intrinsic fluid-solid coupling. The results evidence the development of long wave modulation whose amplitude and frequency depend on the leaflet inertia. When inertia is above a certain threshold, the modulation becomes large enough that the leaflet ends impacting on the wall. The potential relevance in terms of mechanical valves design, or long-term testing of natural systems subjected to period forcing, is briefly discussed.

On-lattice particle simulation is one of the most common types of Monte Carlo simulations used in studying the dynamics of film growth. We report the observation of a large artificial anisotropic growth rate variation owing to the fixed arrangement of particles in an on-lattice simulation of oblique angle deposition. This unexpectedly large anisotropy is not reported in previous literatures and substantially affects the simulation outcomes such as column angle and porosity, two of the most essential quantities in obliquely deposited nanostructures. The result of our finding is of interest to all on-lattice simulations in obliquely deposited films or nanostructures.

The osmotic second virial coefficients $B_2$ are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions $B_2$ of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated $B_2$ are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions.

Using an optimized combination of tethered particle motion method, total internal reflection, and a gold nanobead, we measured the three-dimensional distribution of the free end of a tethered DNA molecule. The distribution along the axial $z$ direction (perpendicular to the surface) is found to be Rayleigh-like, in agreement with wormlike chain and freely jointed chain simulations. Using these simulations, we show that the presence of the wall increases the correlations between the orientations of neighboring chain segments compared to free DNA. While the measured and the simulated planar ($\mathit{xy}$) distributions always agree with that of a Gaussian-random-walk (GRW) model, for short DNA lengths (1 μm) studied in our experiment, the corresponding axial ($z$) distributions deviate from those predicted for a GRW confined to half-space.

Species in nature are typically mobile over diverse distance scales, examples of which range from bacteria run to long-distance animal migrations. These behaviors can have a significant impact on biodiversity. Addressing the role of migration in biodiversity microscopically is fundamental but remains a challenging problem in interdisciplinary science. We incorporate both intra- and inter-patch migrations in stochastic games of cyclic competitions and find that the interplay between the migrations at the local and global scales can lead to robust species coexistence characterized dynamically by the occurrence of remarkable target-wave patterns in the absence of any external control. The waves can emerge from either mixed populations or isolated species in different patches, regardless of the size and the location of the migration target. We also find that, even in a single-species system, target waves can arise from rare mutations, leading to an outbreak of biodiversity. A surprising phenomenon is that target waves in different patches can exhibit synchronization and time-delayed synchronization, where the latter potentially enables the prediction of future evolutionary dynamics. We provide a physical theory based on the spatiotemporal organization of the target waves to explain the synchronization phenomena. We also investigate the basins of coexistence and extinction to establish the robustness of biodiversity through migrations. Our results are relevant to issues of general and broader interest such as pattern formation, control in excitable systems, and the origin of order arising from self-organization in social and natural systems.

The study of morphology and shape development has gained considerable interest in certain sciences, notably biology and geology. Liesegang experiments producing Co(OH)${}_2$ stratification are performed here, in one, two, and three dimensions for comparison of the pattern morphologies. We obtain well-resolved bands in one dimension, target patterns (rings) in two dimensions, and onion patterns (spherical shells) in three dimensions. The morphological characteristics of the various patterns (spacing coefficients, rate of growth of ring spacing with distance) were measured. The spacing ratio of the strata in the different spatial dimensions was found to be anticorrelated with the surface-to-volume ratio of the gel domain. Some studies featuring the importance of morphology in Liesegang systems are briefly surveyed.

The emergence of uncorrelated growing networks is proved when nodes are removed either uniformly or under the preferential survival rule recently observed in the World Wide Web evolution. To this aim, the rate equation for the joint probability of degrees is derived, and stationary symmetrical solutions are obtained, by passing to the continuum limit. When a uniformly random removal of extant nodes and linear preferential attachment of new nodes are at work, we prove that the only stationary solution corresponds to uncorrelated networks for any removal rate $r\in (0,1)$. In the more general case of preferential survival of nodes, uncorrelated solutions are also obtained. These results generalize the uncorrelatedness displayed by the (undirected) Barabási-Albert network model to models with uniformly random and selective (against low degrees) removal of nodes.

We define an opinion formation model of agents in a one-dimensional ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other agents. While the dynamics of the agent’s opinion is described with an appropriate differential equation, from time to time pairs of agents are allowed to change their locations to improve the homogeneity of opinion (or comfort feeling) with respect to their short-range environment. In this way the timescale of transaction dynamics and that of environment update are well separated and controlled by a single parameter. By varying this parameter we discovered a phase change in the number of undecided individuals. This phenomenon arises from the fact that too frequent location exchanges among agents result in frustration in their opinion formation. Our mean field analysis supports this picture.

We study a problem of failure of two interdependent networks in the case of identical degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency links establishing a one-to-one correspondence between the nodes of the two networks in a such a way that the mutually dependent nodes have the same number of connectivity links; i.e., their degrees coincide. This implies that both networks have the same degree distribution $P(k)$. We call such networks correspondently coupled networks (CCNs). We assume that the nodes in each network are randomly connected. We define the mutually connected clusters and the mutual giant component as in earlier works on randomly coupled interdependent networks and assume that only the nodes that belong to the mutual giant component remain functional. We assume that initially a $1-p$ fraction of nodes are randomly removed because of an attack or failure and find analytically, for an arbitrary $P(k)$, the fraction of nodes $\mu (p)$ that belong to the mutual giant component. We find that the system undergoes a percolation transition at a certain fraction $p=p_c$, which is always smaller than $p_c$ for randomly coupled networks with the same $P(k)$. We also find that the system undergoes a first-order transition at $p_c>0$ if $P(k)$ has a finite second moment. For the case of scale-free networks with $2<\lambda ⩽3$, the transition becomes a second-order transition. Moreover, if $\lambda <3$, we find $p_c=0$, as in percolation of a single network. For $\lambda =3$ we find an exact analytical expression for $p_c>0$. Finally, we find that the robustness of CCN increases with the broadness of their degree distribution.

The Sznajd model for opinion dynamics has attracted a large interest as a simple realization of the psychological principle of social validation. As its most salient feature, it has been claimed that the Sznajd model is qualitatively different from other ordering processes because it is the only one featuring outflow of information as opposed to inflow. We show that this claim is unfounded by presenting a generalized zero-temperature Glauber type of dynamics, which yields results indistinguishable from those of the Sznajd model. In one dimension, we also derive an exact expression for the exit probability of the Sznajd model, which turns out to coincide with the result of an analytical approach based on the Kirkwood approximation. This observation raises interesting questions about the applicability and limitations of this approach.

We investigate a model for pattern formation in the presence of Galilean symmetry proposed by Matthews and Cox [Phys. Rev. E 62, R1473 (2000)], which has the form of coupled generalized Burgers- and Ginzburg-Landau-type equations. With only the system size $L$ as a parameter, we find distinct “small-$L$” and “large-$L$” regimes exhibiting clear differences in their dynamics and scaling behavior. The long-time statistically stationary state contains a single $L$-dependent front, stabilized globally by spatiotemporally chaotic dynamics confined away from the front. For sufficiently large domains, the transient dynamics include a state consisting of several viscous shocklike structures that coarsens gradually, before collapsing to a single front when one front absorbs the others.