Usually in the presence of a background noise an increased effort put in controlling a system stabilizes its behavior. Rarely it is thought that an increased control of the system can lead to a looser response and, therefore, to a poorer performance. Strikingly there are many systems that show this weird behavior; examples can be drawn form physical, biological, and social systems. Until now no simple and general mechanism underlying such behaviors has been identified. Here we show that such a mechanism, named stochastic resonant damping, can be provided by the interplay between the background noise and the control exerted on the system. We experimentally verify our prediction on a physical model system based on a colloidal particle held in an oscillating optical potential. Our result adds a tool for the study of intrinsically noisy phenomena, joining the many constructive facets of noise identified in the past decades—for example, stochastic resonance, noise-induced activation, and Brownian ratchets.

In this paper, we investigate the dynamics of synchronous totally asymmetric exclusion processes on lattices with a multiple-input–single-output (MISO) junction, which consists of $m$ subchains for the input and one main chain for the output. A MISO junction is a type of complex geometry that is relevant to many biological processes as well as vehicular and pedestrian traffic flow. A mean-field approach is developed to deal with the junction that connects the subchains and the main chain. Theoretical results for stationary particle currents, density profiles, and a phase diagram have been obtained. It is found that the phase boundary moves toward the left in the phase diagram with an increase of the number of subchains. The nonequilibrium stationary states, stationary-state phases, and phase boundaries are determined by the boundary conditions of the system as well as by the number of subchains. The density profiles obtained from computer simulations show very good agreement with our theoretical analysis.

The Green-Kubo relation for two models of granular gases is discussed. In the Maxwell model in any dimension, the effective temperature obtained from the Green-Kubo relation is shown to be frequency independent and equal to the average kinetic energy, known as the granular temperature. In the second model analyzed, a mean-field granular gas, the collision rate of a particle is taken to be proportional to its velocity. The Green-Kubo relation in the high-frequency limit is calculated for this model, and the effective temperature in this limit is shown to be equal to the granular temperature. This result, taken together with previous results showing a difference between the effective temperature at zero frequency (the Einstein relation) and the granular temperature, shows that the Green-Kubo relation for granular gases is violated.

We study the brittle fragmentation of spheres by using a three-dimensional discrete element model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasiperiodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in three-dimensional models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence, and mass distribution, we also have full access to the failure conditions and evolution.

Spin-echo small-angle neutron scattering is able to characterize powders in terms of their density-density correlation function. Here we present a microstructural study on a fine cohesive powder undergoing uniaxial compression. As a function of compression, we measure the autocorrelation function of the density distribution. From these measurements we quantify the typical sizes of the heterogeneities as well as the fractal nature of the powder packing. The fractal dimension increases with increasing stress, creating a more space-filling structure with rougher phase boundaries. The microscopic stress-strain relation showed the same nonlinear behavior as the macroscopic relation. In this way it was possible to link the macroscopic mechanical response with the evolution of microstructure inside the bulk of the cohesive powder. The total macroscopic compressive strain is in agreement with a corresponding decrease in microstructural length scales.

We present extensive Monte Carlo simulations for the thermodynamic and structural properties of a planar bilayer of dipolar hard spheres for a wide range of densities, dipole moments, and layer separations. Expressions for the stress and pressure tensors of the bilayer system are derived. For all thermodynamic states considered, the interlayer energy is shown to be attractive and much smaller than the intralayer contribution to the energy. It vanishes at layer separations of the order of two hard sphere diameters. The normal pressure is negative and decays as a function of layer separation $h$ as $-1/h^5$. Intralayer and interlayer pair distribution functions and angular correlation functions are presented. Despite the weak interlayer energy, strong positional and orientational correlations exist between particles in the two layers.

Lipid membranes play a fundamental role in vital cellular functions such as signal transduction. Many of these processes rely on lateral diffusion within the membrane, generally a complex fluid containing ordered microdomains. However, little attention has been paid to the alterations in transport dynamics of a diffusing species caused by long-range interactions with membrane domains. In this paper, we address the effect of such interactions on diffusive transport by studying lateral diffusion in a phase-separated Langmuir phospholipid monolayer via single-particle tracking. We find that attractive dipole-dipole interactions between condensed phase domains and diffusing probe beads lead to transient confinement at the phase boundaries, causing a transition from two- to one-dimensional diffusion. Using Brownian dynamics simulations, the long-term diffusion constant for such a system is found to have a sensitive, Boltzmann-like, dependence on the interaction strength. In addition, this interaction strength is shown to be a strong function of the ratio of domain to particle size. As similar interactions are expected in biological membranes, the modulation of diffusive transport dynamics by varying interaction strength and/or domain size may offer cells selective spatial and temporal control over signaling processes.

Three-dimensional (3D) ac electro-osmotic (ACEO) pumps have recently been developed that are much faster and more robust than previous planar designs. The basic idea is to create a “fluid conveyor belt” by placing opposing ACEO slip velocities at different heights. Current designs involve electrodes with electroplated steps, whose heights have been optimized in simulations and experiments. Here, we consider changing the boundary conditions—rather than the geometry—and predict that flow rates can be further doubled by fabricating 3D features with nonpolarizable materials. This amplifies the fluid conveyor belt by removing opposing flows on the vertical surfaces, and it increases the slip velocities that drive the flow.

An analytical expression for the synchronization time in coupled-map networks is given. By means of the expression, the synchronization time for any given network can be predicted accurately. Furthermore, for networks in which the distributions of nontrivial eigenvalues of coupling matrices have some unique characteristics, analytical results for the minimal synchronization time are given.

Recent experiments on imbibition in columnar geometries show interfacial fluctuations whose dynamic scaling is not compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

Linear response analysis in the nonequilibrium steady state (Gaussian regime) provides two independent fluctuation-response relations. One, in the form of the symmetric matrix, manifests the departure from the equilibrium formula through the quantity so-called irreversible circulation. The other, in the antisymmetric form, connects the asymmetries in the fluctuation and the response function. These formulas represent characteristic features of fluctuations far from equilibrium, which have no counterparts in thermal equilibrium.

With Monte Carlo simulations, we investigate the relaxation dynamics with a domain wall for magnetic systems at the critical temperature. The dynamic scaling behavior is carefully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surface.

In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar’s celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.

We use the propagator-resolved transverse relaxation exchange experiment to characterize the pore space and fluid behavior of water saturated, tight-packed quartz sand. The experiment uses $T_2$ exchange plots to observe the number of molecules that shift their environment for a range of mixing times. The propagator dimension allows us to determine how far the molecules have moved. The peak intensities are integrated and then plotted as a function of displacement and mixing time. We also model our system using both a probabilistic pore-hopping simulation and a spreading Gaussian model. We use the results of these simulations to interpret the peak intensity plots. From this, we can estimate pore features such as characteristic time, pore radii, and interpore spacing. The tortuosity of the different pore sizes can then be calculated from these values.

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

We present guidelines on how the solution structure of $\pi$-conjugated hairy-rod polyfluorenes is controlled by the side-chain length and branching. First, the semiquantitative mean-field theory is formulated to predict the phase behavior of the system as a function of side-chain beads $\left(N\right)$. The phase transition at $N=N^{\ast }$ separates a lyotropic phase with solvent coexistence $\left(N<N^{\ast }\right)$ and a metastable membrane phase $\left(N>N^{\ast }\right)$. The membrane phase transforms into the isotropic phase of dissolved rodlike polymers at the temperature $T_{\text{mem}}^{\ast }\left(N\right)$, which decreases both with $N$ and with the degree of side-chain branching. This picture is complemented by polymer demixing with the transition temperature $T_{IN}^{\ast }\left(N\right)$, which decreases with $N$. For $N<N^{\ast }$, the lyotropic phase turns isotropic with increasing $T$ at $T_{IN}^{\ast }$. For $N>N^{\ast }$, stable membranes are predicted for $T_{IN}^{\ast }<T<T_{\text{mem}}^{\ast }$ and metastable membranes with nematic coexistence for $T<T_{IN}^{\ast }$. Second, in experiment, samples of poly(9,9-dialkylfluorene) with $N=6–10$ were mixed in methylcyclohexane. For $N=8$ the side-chain branching was controlled by (9,9-dioctylfluorene)/(9,9-bis(2-ethylhexyl)fluorene) (F8/F2/6) random copolymers. The proportion of F8 to F2/6 repeat units was 100:0, 95:5, 90:10, 50:50, and 0:100. In accordance with the theory, lyotropic, membrane, and isotropic phases with the corresponding phase transitions were observed. For $N<N^{\ast }\sim 6$ only the lyotropic phase is present for attainable temperatures. The membrane and isotropic phases are present for $N>N^{\ast }$. $T_{\text{mem}}^{\ast }\left(N\right)$ decreases from 340 K to 280 K for $N\ge 8$. For copolymers, the membrane phase is found when the fraction of F8 units is at least 90%, $T_{\text{mem}}^{\ast }$ decreasing with this fraction. The membrane phase contains three material types: loose sheets of two polymer layers, a better packed $\beta$ phase, and dissolved polymer. For $N\ge 7$ and $T<T_{\text{mem}}^{\ast }$ the tendency for membrane formation becomes stronger with increasing temperature.

We develop coarse-grained models that describe the dynamic encapsidation of functionalized nanoparticles by viral capsid proteins. We find that some forms of cooperative interactions between protein subunits and nanoparticles can dramatically enhance rates and robustness of assembly, as compared to the spontaneous assembly of subunits into empty capsids. For large core-subunit interactions, subunits adsorb onto core surfaces en masse in a disordered manner, and then undergo a cooperative rearrangement into an ordered capsid structure. These assembly pathways are unlike any identified for empty capsid formation. Our models can be directly applied to recent experiments in which viral capsid proteins assemble around functionalized inorganic nanoparticles [Sun et al., Proc. Natl. Acad. Sci. U.S.A. 104, 1354 (2007)]. In addition, we discuss broader implications for understanding the dynamic encapsidation of single-stranded genomic molecules during viral replication and for developing multicomponent nanostructured materials.

We perform Monte Carlo type simulation studies of self-organization of microtubules interacting with molecular motors. We model microtubules as stiff polar rods of equal length exhibiting anisotropic diffusion in the plane. The molecular motors are implicitly introduced by specifying certain probabilistic collision rules resulting in realignment of the rods. This approximation of the complicated microtubule-motor interaction by a simple instant collision allows us to bypass the “computational bottlenecks” associated with the details of the diffusion and the dynamics of motors and the reorientation of microtubules. Consequently, we are able to perform simulations of large ensembles of microtubules and motors on a very large time scale. This simple model reproduces all important phenomenology observed in in vitro experiments: Formation of vortices for low motor density and raylike asters and bundles for higher motor density.

We determine a partition of three-dimensional space into cells by minimization of the sum of the first Laplacian eigenvalues over the cells. This partitioning scheme emerges as a stationary state of a reaction-diffusion process taking place in a system of $n$ different species which mutually annihilate, and simultaneously are duplicated in an autocatalytic reaction, so that the number of particles is kept constant and equal for each species. The system is considered in the limit of strong reactivity, so that the species separate each other into cells with well-defined, sharp boundaries. For a given $n$ and fixed sizes of a periodic simulation box, this partition minimizes the aforementioned sum of eigenvalues. Further minimization is done by changing $n$ and the side ratio of the periodic box. The global minimum is obtained for the structure with A15 symmetry, similar to the Weaire-Phelan foam. Depending on $n$ and the side ratio, there are also many local minima, in particular: hcp (hexagonal close packed), fcc (face centered cubic), the Kelvin structure, and Frank-Kasper sigma phase.

We study annual logarithmic growth rates $R$ of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of $R$ can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation $\sigma \left(R\right)$ on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates $R$ of wages of 161 different occupations, we find a power-law dependence of the standard deviation $\sigma \left(R\right)$ on the average value of the wages with a scaling exponent $\beta \approx 0.14$ close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation $\sigma \left(R\right)$ of the annual logarithmic growth rate $R$ increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of $\sigma \left(R\right)$ on the average payroll with a scaling exponent $\beta \approx -0.08$. Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.