We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, $\tilde{M}\left(\omega \right)$, of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity. The dominant features of $\tilde{M}\left(\omega \right)$ are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: (a) on a fundamental level, dampening of acoustic modes is dominated by adsorbed films of water at grain-grain contacts, not by global viscous dampening or by attenuation within the grains. (b) These systems may be understood, qualitatively, in terms of a height-dependent and diameter-dependent effective sound speed $\left[\sim 100–300\left(\text{m}\cdot {\text{s}}^{-1}\right)\right]$ and an effective viscosity $\left[\sim 5\times {10}^4\text{Poise}\right]$. (c) There is an acoustic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. (d) There is a monotonically increasing effect of humidity on the dampening of the fundamental resonance within the granular medium which translates to a nonmonotonic, but predictable, variation in dampening within the grain-loaded bar.

Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. In confined geometries, the structural properties of random-packed systems will change. To understand these changes, we study random close packing in finite-sized confined systems, in both two and three dimensions. Each packing consists of a 50-50 binary mixture with particle size ratio of 1.4. The presence of confining walls significantly lowers the overall maximum area fraction (or volume fraction in three dimensions). A simple model is presented, which quantifies the reduction in packing due to wall-induced structure. This wall-induced structure decays rapidly away from the wall, with characteristic length scales comparable to the small particle diameter.

The mechanism for the formation of solid-supported phospholipid membranes during a drying process was investigated. Terracelike multilamellar structures were found to develop from a micellar solution with either spinodal decompositionlike process or nucleation growth, depending on the evaporation rate of an organic solvent. In contrast to the well-known kinetics of phase separation, fast drying induces nucleation while slow drying induces spinodal decompositionlike lipid-film formation. The existing models for the interpretation of phase separation are not sufficient to understand this unexpected kinetics. We suggest a schematic model with which this kinetic feature can be interpreted in terms of a self-assembly pathway in a three-component phase diagram for a phospholipid, organic solvent, and water.

We study the optimal packing of triangular ionic lattices on the surface of nanofibers. We compute the favored orientation of the lattice with respect to the axis of the cylindrical fiber, and we determine the effects of the surface curvature. Electrostatic interactions prefer chiral arrangements only for special families of lattices that depend on the fiber diameter. However, there are families of lattices that energetically promote achiral configurations. Besides the long-range Coulomb interactions we consider the behavior of short-range elastic forces, represented by interconnected springs between neighboring ions. In this case a different family of achiral lattices is always preferred. We also show that varying the stoichiometric composition of charges, as well as including higher-order curvature effects, does not significantly modify such a scenario.

We study the configurational properties of single polymers in a theta solvent by Monte Carlo simulation of the bond fluctuation model. The intramolecular structure factor at the theta point is found to be distinctively different from that of the ideal chain. The structure factor shows a hump around $q\sim 5/R_g$ and a dip around $q\sim 10/R_g$ in the Kratky plot with $R_g$ being the radius of gyration. This feature is apparently similar to that in a melt. The theoretical expression by the simple perturbation expansion to the first order in terms of the Mayer function can be fitted to the obtained structure factor quite well, but the second virial coefficient cannot be set to zero.

We study flexible polymer macromolecules in a crowded (porous) environment, modeling them as self-attracting self-avoiding walks on site-diluted percolative lattices in space dimensions $d=2,3$. The influence of stretching force on the polymer folding and the properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method, we estimate the transition temperature $T_{\Theta }$ between collapsed and extended polymer configurations and construct the phase diagrams of the globule-coil coexistence when varying temperature and stretching force. The transition to a completely stretched state, caused by applying force, is discussed as well.

We use the nonstandard-finite-difference time-domain (NS-FDTD) method to investigate the interaction of light with the complicated microstructures in the Morpho butterfly scales, which produce the well-known brilliant blue coloring. The NS-FDTD algorithm is particularly suitable to analyze such complex structures because the calculation can be performed in a short time with high accuracy on a relatively coarse numerical grid. We analyze (1) the microstructure obtained directly by binarizing an electron microgram of the cross section of a scale, (2) the reflection and diffraction properties of three model structures—flat, alternating, and tree-shaped alternating multilayers, and (3) an array of alternating multilayers with random noise superposed on the height of the structures. We found that the actual microstructure well reproduced the reflection spectrum in a blue region by integrating the reflection intensities over all the reflection angles. Under normal incidence, the flat multilayer mainly stresses on multilayer interference except for shorter wavelengths, while alternating multilayer rather enhances the effect of diffraction grating due to longitudinally repeating structure by strongly suppressing the reflection toward the normal direction. In the array of alternating multilayers, the reflection into larger angles is considerably suppressed and the spectral shape becomes different from that expected for a single alternating multilayer. This suppression mainly comes from the scattering of reflected light by adjacent structures, which is particularly prominent for the TM mode. Thus a clear difference between the TE and TM modes is observed with respect to the origin of spectral shape, though the obtained spectra are similar to each other. Finally, the polarization dependence of the reflection and the importance of the alternating multilayer are discussed.

The gene transcription occurs via the RNA polymerase (RNAP) recruitment on the DNA promoter sequence, formation of a locally open DNA chain, promoter escape, steps of the RNA synthesis, and RNA and RNAP release after reading the final DNA base. Just after the end of the RNA synthesis, RNAP surrounds the closed DNA chain and may diffuse along DNA, desorb, or reach the promoter and start the RNA-synthesis cycle again. We present a generic kinetic model taking the latter steps into account and show analytically and by Monte Carlo simulations that it predicts transcriptional bursts even in the absence of explicit regulation of the transcription by master proteins.

A simple model is presented to describe the variation of the onset of the initial planar instability with surface tension anisotropy during directional solidification. The effect of surface-tension anisotropy on the incubation time and the initial average wavelength of planar instability are predicted by the simple model quantitatively, which are also verified by phase field simulation. Investigation results reveal that surface-tension anisotropy is one of important factors in the dynamic process of planar instability. The contribution of surface-tension anisotropy to the tilting modulation is also analyzed by comparing the results from the present simple model with those from phase field simulation.

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit. The complex resonance wave functions are found to be localized on the fractal classical repeller.

Recently, synchronization of complex networks has attracted increasing attention from various research fields. However, most previous works focused on the stability of synchronization manifold. In this paper, we analyze the time-delay tolerance and converging speed of synchronization. Our theoretical analysis and extensive simulations show that the critical value of time delay for network synchronization is inversely proportional to the largest Laplacian eigenvalue, the converging speed without time delay is proportional to the second least Laplacian eigenvalue, and the time delay could increase the converging speed linearly for heterogeneous networks and significantly for homogeneous networks.

Uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom [Proc. Natl. Acad. Sci. U.S.A. 104, 7327 (2007); Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008)], Blondel et al. [J. Stat. Mech.: Theory Exp. (2008), P10008], and Ronhovde and Nussinov [Phys. Rev. E 80, 016109 (2009)] have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.

Using nonequilibrium molecular dynamics (MD) simulations behavior of three-dimensional (3D) Yukawa system has been studied in the presence of a small amplitude drive along one direction (say $\widehat{z}$). This drive has the general form $V=V_0\text{cos}\left(k_{L}z\right)\Theta \left(t-t_0\right)$, where $\Theta \left(t-t_0\right)$ is a Heaviside step function in time at $t=t_0$ and $k_L=2\pi /L$, $L$ being the size of the system; $V_0$ is considered small compared to average interparticle potential energy. In particular, a 3D equilibrated Yukawa crystal (bcc) near solid-liquid transition is subjected to an external drive at times $t\ge t_0$ at the largest possible scale. For a given $k_L$ it is observed that there exists a critical amplitude $\left(V_0^c\right)$ of the external drive below which the crystalline order is preserved and above which $\left(V_0\ge V_0^c\right)$ the transition from bcc to strongly coupled Yukawa liquid is observed. This critical amplitude $\left(V_0^c\right)$ is sensitive to the location of the Yukawa solid in the $\left(\kappa ,\Gamma \right)$ phase space. Various signatures of melting, transients, and steady state in the presence of this drive are elucidated using extensive MD diagnostics such as loss of long-range crystalline order, change in diffusion from subnormal to normal, and the fall of transversal shear peak in the Fourier transform of the velocity autocorrelation function. The mechanism of heating in the transient state is attributed to the local heating of the system where the forces are maximum. It is shown that these local hot regions dissipate heat into surrounding regions ultimately leading to a uniform temperature throughout the system. Ion streaming due to external field has been neglected.

We test experimentally a Brownian ratchet system suggested by Engel et al. [Phys. Rev. Lett. 91, 060602 (2003)]. This ratchet system is based on a magnetic fluid that contains nanometer sized magnetic particles in a thermal bath of carrier fluid. An external static magnetic field and, perpendicular to it, an oscillatory magnetic field act on the ferrofluid particles; the total magnetic field contains no rotating component. The directed effective rotation of the particles due to the ratchet effect induces a macroscopic torque density of the fluid. The torque on a spherical ferrofluid sample is measured in dependence on the field parameters. A quantitative comparison with predictions from a microscopic and a phenomenological model are given. Both models describe certain aspects of the measurements correctly, but qualitative discrepancies between both models and experiment are found, particularly in the high-frequency range.

We study the critical behavior of the Ising model in annealed scale-free (SF) networks of finite system size with forced upper cutoff in degree. By mapping the model onto the weighted fully connected Ising model, we derive analytic results for the finite-size scaling (FSS) near the phase transition, characterized by the cutoff-dependent two-parameter scaling with four distinct scaling regimes, in highly heterogeneous networks. These results are essentially the same as those found for the nonequilibrium contact process in annealed SF networks, except for an additional complication due to the trivial critical point shift in finite systems. The discrepancy of the FSS theories between annealed and quenched SF networks still remains in the equilibrium Ising model, like some other nonequilibrium models. All of our analytic results are confirmed reasonably well by numerical simulations.

The resonate-and-fire (RF) model is a spiking neuron model which from a dynamical systems perspective is a piecewise smooth system (impact oscillator). We analyze the response of the RF neuron oscillator to periodic stimuli by expressing the firing events in terms of an implicit one-dimensional time map. Based on such a firing map, we describe mode-locked solutions and their stability, leading to the so-called Arnol’d tongues. The boundaries of these tongues correspond to either local bifurcations of the firing time map or grazing bifurcations of the discontinuity of the flow. Despite the fact that the periodically driven RF system shows periodic firing, its behavior may become chaotic when the forcing frequency is near the resonant frequency. We compare these results to numerical simulations of the model undergoing sinusoidal forcing. Furthermore, upon varying a system parameter, the RF system can be reduced to the integrate-and-fire system and in this case we show the consistency of the results on mode-locked solutions.

Neural feedback-triads consisting of two feedback loops with a nonreciprocal lateral connection from one loop to the other are ubiquitous in the brain. We show analytically that the dynamics of this network topology are determined by algebraic combinations of its five synaptic weights. Exploration of network activity over the parameter space demonstrates the importance of the nonreciprocal lateral connection and reveals intricate behavior involving continuous transitions between qualitatively different activity states. In addition, we show that the response to periodic inputs is narrowly tuned around a center frequency determined by the effective synaptic parameters.

We present an experimental study of the effect of an electromagnetically generated vortex flow on parametrically amplified waves at the surface of a vertically vibrated fluid layer. The underlying vortex flow, generated by a periodic Lorentz force, creates spatiotemporal fluctuations that nonlinearly interact with the standing surface waves. We measure the power spectral density of the surface wave amplitude and we characterize the bifurcation diagram by recording the subharmonic response of the surface to the external vibration. We show that the parametric instability is delayed in the presence of spatiotemporal fluctuations due to the vortex flow. In addition, the dependence of the amplitude of the subharmonic response on the distance to the instability threshold is modified. This shows that the nonlinear saturation mechanism of the waves is modified by the vortex flow.

We demonstrate that photoisomerizable liquid-crystal elastomer soft films can be used as tunable holographic gratings. Optomechanical mechanism of imprinting one-dimensional grating structure into the soft matrix by two-beam uv laser interference can be clearly resolved from the time dependence of the reading beam diffraction patterns. We analyze the observed response in terms of cis-trans isomerization-controlled modulation of the grating profile. The grating period can be tuned reversibly by stretching or contraction of the specimen, either thermomechanically or by applying external stress. Temperature-induced modifications of the grating parameters in the vicinity of the nematic-paranematic phase transition are also examined.

The decay form of the time correlation function $U_n\left(t\right)$ of a state variable $u_n\left(t\right)$ with a small wave number $k_n$ has been shown to take the algebraic decay $1/\left\{1+{\left({\gamma }_{na}t\right)}^2\right\}$ in the initial regime $t<{\tau }_n^{\left(\gamma \right)}$ and the exponential decay ${\alpha }_{ne}\text{exp}\left(-{\gamma }_{ne}t\right)$ in the final regime $t>{\tau }_n^{\left(\gamma \right)}$, where ${\tau }_n^{\left(\gamma \right)}$ denotes the decay time of the memory function ${\Gamma }_n\left(t\right)$. This dual structure of $U_n\left(t\right)$ is generated by the deterministic short orbits in the initial regime and the stochastic long orbits in the final regime, thus giving the outstanding features of chaos and turbulence. The $k_n$ dependence of ${\gamma }_{na}$, ${\alpha }_{ne}$, and ${\gamma }_{ne}$ is obtained for the chaotic Kuramoto-Sivashinsky equation, and it is shown that if $k_n$ is sufficiently small, then the dual structure of $U_n\left(t\right)$ obeys a hydrodynamic scaling law in the final regime $t>{\tau }_n^{\left(\gamma \right)}$ with scaling exponent $z=2$ and a dynamic scaling law in the initial regime $t<{\tau }_n^{\left(\gamma \right)}$ with scaling exponent $z=1$. If $k_n$ is increased so that the decay time ${\tau }_n^{\left(u\right)}$ of $U_n\left(t\right)$ becomes equal to the decay time ${\tau }_n^{\left(\gamma \right)}$, then the decay form of $U_n\left(t\right)$ becomes the power-law decay $t^{-3/2}$ in the final regime.