We simulate by the lattice Boltzmann method the steady shearing of a binary fluid mixture with full hydrodynamics in three dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite correlation lengths in all three spatial directions. Using large simulations, we obtain at moderately high Reynolds numbers apparent scaling exponents comparable to those found by us previously in two dimensions (2D). However, in 3D there may be a crossover to different behavior at low Reynolds number: accessing this regime requires even larger computational resources than used here.

We study the nonlinear response of a noisy bistable system to a biperiodic signal through experiments with an electronic circuit (Schmitt trigger). The signal we use is a biharmonic one, i.e., a superposition of low and high frequency harmonic components. It is shown that the mean switching frequency (MSF) of the system can be locked at both low and high frequencies. Moreover, the phenomenon of MSF locking at the lower frequency can be induced and enhanced by the higher frequency excitation. Thus high frequency bias can control synchronization at the low frequency.

We treat a one-dimensional binary mixture of hard-core particles that possess nonadditive diameters. For this model, a density functional theory is constructed following similar principles as an earlier extension of Rosenfeld’s fundamental measure theory to three-dimensional nonadditive hard-sphere mixtures. The theory applies to arbitrary positive and moderate negative nonadditivity and reduces to Percus’ exact functional in the additive case. Bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional. Results for the partial pair correlation functions in bulk, as calculated via the Ornstein-Zernike route and using the direct correlation functions as input, show very good agreement with results from our Monte Carlo computer simulations of the mixture.

We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (nongrowing) self-organizing networks, preferentially growing networks, and (preferentially) rewiring networks. Further, it exhibits a natural random graph limit. The proposed model generalizes network dynamics to rewiring and growth modes which depend on internal topology as well as on a metric imposed by the space they are embedded in. In all of the networks emerging from the presented model we find $q$-exponential degree distributions over a large parameter space. We comment on the parameter dependence of the corresponding entropic index $q$ for the degree distributions, and on the behavior of the clustering coefficients and neighboring connectivity distributions.

Some statistical properties of finite-time stability exponents in the standard map can be estimated analytically. The mean exponent averaged over the entire phase space behaves quite differently from all the other cumulants. Whereas the mean carries information about the strength of the interaction and only indirect information about dynamical correlations, the higher cumulants carry information about dynamical correlations and essentially no information about the interaction strength. In particular, the variance and higher cumulants of the exponent are very sensitive to dynamical correlations and easily detect the presence of very small islands of regular motion via their anomalous time scalings. The average of the stability matrix’ inverse trace is even more sensitive to the presence of small islands and has a seemingly fractal behavior in the standard map parameter. The usual accelerator modes and the small islands created through double saddle node bifurcations, which come halfway between the positions in interaction strength of the usual accelerator modes, are clearly visible in the variance, whose time scaling is capable of detecting the presence of islands as small as 0.01% of the phase space. We study these quantities with a local approximation to the trace of the stability matrix which significantly simplifies the numerical calculations as well as allows for generalization of these methods to higher dimensions. We also discuss the nature of this local approximation in some detail.

Recently the general form of a translation-covariant quantum Boltzmann equation has been derived, which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full three-dimensional Monte Carlo simulations of this equation. The simulation method is used to study the approach to equilibrium for various scattering cross sections and to determine dynamical deviations from Gaussian statistics through an investigation of higher-order cumulants. Moreover, we examine the loss of coherence of superpositions of momentum eigenstates and determine the corresponding decoherence time scales to quantify the transition from quantum to classical behavior of the state of the test particle.

In this paper, a method is proposed to enhance the traffic handling capacity of scale-free networks by closing or cutting some links between some large-degree nodes, for both local routing strategy and global shortest-path routing strategy. The traffic capacity of networks is found to be considerably improved after applying the link-closing strategy, especially in the case of global routing. Due to the strongly improved network capacity, easy realization on networks, and low cost, the strategy may be useful for modern communication networks.

Transport of electron pairs in a superconducting junction device with spatiotemporal noise is investigated. It is shown that, in a superconducting junction device, spatiotemporal noise can appear and induce a nonzero current due to the symmetry breaking induced by the correlation of the spatiotemporal noise with the phase difference. We found that there is a negative current for the electron pairs, exhibiting a well with increasing thermal noise strength. Our results can provide a theoretical foundation for the further investigation of superconducting junctions.

In an ensemble of noninteracting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium under strongly nonequilibrium conditions.

The Stokes-Einstein relation between shear viscosity, diffusion constant, and temperature holds in many liquids, but there are certain examples where the relation fails. In this study, we consider liquids where the interaction potential is bounded, and we find that a different behavior of the Stokes-Einstein relation is possible, where the relation between shear viscosity, diffusion constant, and temperature grows linearly with the viscosity. This special behavior occurs when the potential is bounded and full overlap between the particles is possible. We try to show that the peculiar departure from the classical Stokes-Einstein relation can be explained by this possible overlap of particles by using a hydrodynamic model. Then we compare our result with molecular dynamics simulations for the Gaussian core model liquid.

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%).

Equilibrium aspects of the molecular recognition of rigid biomolecules are investigated using coarse-grained lattice models. The analysis is carried out in two stages. First, an ensemble of probe molecules is designed with respect to the target biomolecule. The recognition ability of the probe ensemble is then investigated by calculating the free energy of association. The influence of cooperative and anticooperative effects accompanying the association of the target and probe molecules is studied. Numerical findings are presented and compared to analytical results which can be obtained in the limit of dominating cooperativity and in the mean-field formulation of the models.

A method describing NMR-signal formation in inhomogeneous tissue is presented which covers all diffusion regimes. For this purpose, the frequency distribution inside the voxel is described. Generalizing the results of the well-known static dephasing regime, we derive a formalism to describe the frequency distribution that is valid over the whole dynamic range. The expressions obtained are in agreement with the results obtained from Kubos line-shape theory. To examine the diffusion effects, we utilize a strong collision approximation, which replaces the original diffusion process by a simpler stochastic dynamics. We provide a generally valid relation between the frequency distribution and the local Larmor frequency inside the voxel. To demonstrate the formalism we give analytical expressions for the frequency distribution and the free induction decay in the case of cylindrical and spherical magnetic inhomogeneities. For experimental verification, we performed measurements using a single-voxel spectroscopy method. The data obtained for the frequency distribution, as well as the magnetization decay, are in good agreement with the analytic results, although experiments were limited by magnetic field gradients caused by an imperfect shim and low signal-to-noise ratio.

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasistatic evolution of the helical pitch with cell growth, as well as time scales of helix turnover and de novo establishment. We find that while the body of a polarized MreB helix treadmills toward its slow-growing end, the fast-growing tips of laterally associated protofilaments move toward the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.

A fully atomistic model of B-DNA using the CHARMM (chemistry at Harvard molecular mechanics) force field is presented. Molecular dynamics simulations were used to prepare an equilibrium structure. The Hessian of interatomic forces obtained from CHARMM for the equilibrium structure was used as input to a large scale phonon calculation. The calculated dispersion relations at low frequency are compared with recently published experimental data, which shows the model to have good accuracy for the low frequency, vibrational modes of DNA. These are discussed in the context of base-pair opening. In addition to the widely reported modes at, or below, $\sim 12.5\mathrm{meV}$, a continuous band of modes with strong base-pair opening character is found up to $40\mathrm{meV}$, which coincides with the typical denaturation temperature of DNA.

Electron attachment to perfluoromethylcyclohexane $\left({\mathrm{C}}_7{\mathrm{F}}_{14}\right)$ and sulfur hexafluoride $\left({\mathrm{SF}}_6\right)$ is studied in a Q machine which produces a thermally ionized potassium plasma at an electron temperature $T_e\simeq 0.2\mathrm{eV}$ $\left(2300\mathrm{K}\right)$. Negative ion formation is observed by Langmuir probe measurements of the reduction in electron density as electrons attach to ${\mathrm{C}}_7{\mathrm{F}}_{14}$ to form ${\mathrm{C}}_7{\mathrm{F}}_{14}^{-}$ or to ${\mathrm{SF}}_6$ to produce ${\mathrm{SF}}_6^{-}$. In ${\mathrm{C}}_7{\mathrm{F}}_{14}$ at a pressure $\sim 3\times {10}^{-5}\mathrm{Torr}$, a nearly electron-free plasma is formed with a residual electron-to-ion density ratio $n_e∕n_{+}<{10}^{-4}$. Formation of the ${\mathrm{C}}_7{\mathrm{F}}_{14}^{-}$ negative ion was confirmed by the presence of the ${\mathrm{C}}_7{\mathrm{F}}_{14}^{-}$ electrostatic ion cyclotron wave mode in the power spectrum of current-driven plasma oscillations. Measurements of the negative ion-to-electron density ratio, $n_{-}∕n_e$ for different pressures in both ${\mathrm{C}}_7{\mathrm{F}}_{14}$ and ${\mathrm{SF}}_6$ indicate that for thermal electrons at $2300\mathrm{K}$ larger values of $n_{-}∕n_e$ are obtained in ${\mathrm{C}}_7{\mathrm{F}}_{14}$ at a lower pressure than in ${\mathrm{SF}}_6$.

Systems governed by the standard mechanisms of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find an analogy with classical thermodynamic systems. In particular, we can demonstrate the existence of several distinct phases of evolutionary dynamics: a phase of fast growing diversity, one of stationary, finite diversity, and one of rapidly decaying diversity. While the first two phases have been subject to previous work, here we focus on the destructive aspects—in particular the phase diagram—of evolutionary dynamics. The main message is that within a critical region, massive loss of diversity can be triggered by very small external fluctuations. We further propose a dynamical model of diversity which captures spontaneous creation and destruction processes fully respecting the phase diagrams of evolutionary systems. The emergent time series show rich diversity dynamics, including power laws as observed in actual economical data, e.g., firm bankruptcy data. We believe the present model presents a possibility to cast the famous qualitative picture of Schumpeterian economic evolution, into a quantifiable and testable framework.

The ground state of an externally confined one-component Yukawa plasma is derived analytically using the local density approximation (LDA). In particular, the radial density profile is computed. The results are compared with the recently obtained mean-field (MF) density profile [Henning et al., Phys. Rev. E 74, 056403 (2006)]. While the MF results are more accurate for weak screening, the LDA with correlations included yields the proper description for large screening. By comparison with first-principles simulations for three-dimensional spherical Yukawa crystals, we demonstrate that the two approximations complement each other. Together they accurately describe the density profile in the full range of screening parameters.

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional $N$-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the $\mu$ (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.