We derive a lattice Boltzmann model of a ternary fluid mixture, one component of which consists of amphiphilic molecules with a rotational degree of freedom. The model was first introduced elsewhere where it was constructed on the basis of the earlier Shan-Chen type lattice Boltzmann model for binary fluids. We provide a rigorous derivation of the model from an underlying continuum kinetic theory. In particular, we show how the model can be interpreted as a discretization of a Vlasov-Boltzmann type kinetic theory for a fluid composed of two species of oppositely charged monopoles and a composite, dipolar molecule. We also derive a free-energy functional for the model, including the contribution from the amphiphiles, and confirm that the free energy is lowered during phase separation and during the formation of a stable emulsion.

We investigate the generalized contact process with two absorbing states in one space dimension by means of large-scale Monte Carlo simulations. Treating the creation rate of active sites between inactive domains as an independent parameter leads to a rich phase diagram. In addition to the conventional active and inactive phases we find a parameter region where the simple contact process is inactive, but an infinitesimal creation rate at the boundary between inactive domains is sufficient to take the system into the active phase. Thus, the generalized contact process has two different phase transition lines. The point separating them shares some characteristics with a multicritical point. We also study in detail the critical behaviors of these transitions and their universality.

Low-frequency signal transmission in one-way coupled bistable systems subject to a high-frequency force is studied. Two cases including the high-frequency force on all sites (case 1) and only on the first site (case 2) are considered. In these two cases, vibrational resonance induced by the high-frequency force can play an active role to effectively improve the signal transmission, and undamped signal transmission can be found in a broad parameter region. The combinative action of injected low-frequency signal, high-frequency driving, and coupling is of importance. Our findings suggest that high-frequency signal could be properly used in low-frequency signal transmission, and especially the implementation of high-frequency force simply on the first site for case 2 is meaningful for its simplicity and high efficiency.

We investigate the effect of an external torque, applied in the vorticity direction, to particles in a sheared non-Brownian suspension confined by rigid walls. At volume fractions of $\varphi =0.48–0.52$ such suspension flows undergo an ordering transition, developing a hexagonal structure of particle strings in the velocity gradient-vorticity plane. The hexagonal structure is disturbed by negative torques, leading to an increase in the shear viscosity. Positive torque has a favorable effect on the ordered state. However, if the magnitude of the positive torque exceeds a certain threshold, the hexagonal order begins to be weakened. Due to the significant changes in suspension microstructures, rheological parameters such as the shear and vortex viscosities exhibit nonlinear responses to the external torques. On the other hand, at lower volume fractions $\varphi \le 0.40$, where ordered structures are not developed, suspension microstructure is not sensitive to an external torque and the apparent viscosity is a linear function of the torque.

Here, we report on numerical simulations showing that chemotaxis will take a body through a maze via the shortest possible route to the source of a chemoattractant. This is a robust finding that does not depend on the geometrical makeup of the maze. The predictions are supported by recent experimental studies which have shown that by moving down gradients in $p\text{H}$, a droplet of organic solvent can find the shortest of multiple possible paths through a maze to an acid-soaked exit. They are also consistent with numerical and experimental evidence that plant-parasitic nematodes take the shortest route through the labyrinth of air-filled pores within soil to preferred host plants that produce volatile chemoattractants. The predictions support the view that maze-solving is a robust property of chemotaxis and is not specific to particular kinds of maze or to the fractal structure of air-filled channels within soils.

We present an instability in vertically vibrated dilute wormlike micellar solutions. Above a critical driving acceleration the fluid forms elongated solitary domains of high amplitude waves. We model this instability using a Mathieu equation modified to account for the non-Newtonian character of the fluid. We find that our model successfully reproduces the observed transitions.

Within the framework of paraxial approximation it is shown that in an anisotropic plasma with sloshing ions confined an open-ended system a magnetic hole is formed near the turning point of the sloshing ions above the threshold of the mirror instability. The magnetic field experiences a jump at the hole boundary from the side of the magnetic mirror. For a small excess over the mirror instability threshold, the surface of the discontinuity has the shape of a truncated paraboloid, and the magnitude of the magnetic field jump at the system axis is proportional to the radius of the hole and gradually decreases to zero away of the axis. It is argued that disappearance of the magnetic hole because of the widening of the sloshing ions angular spread in the course of the neutral beam injection results in abrupt anticorrelated changes of the diamagnetic signals measured near the turning point of the sloshing ions and near the midplane of the gas-dynamic trap.

Consider $N$ sites randomly and uniformly distributed in a $d$-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last $\mu$ (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory ${\mu }_1={\text{log}}_{2}N$. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter $T$ (temperature). In this case, the walker movement is driven by a probability density function parameterized by $T$ and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

The effect of optical gradient force from a focused laser beam on the fluorescence correlation spectroscopy (FCS) was investigated by a computing method based on Brownian dynamics simulation. A series of calculations revealed that, in relatively shallow optical force potential up to $1.0k{T}_R$ $\left(T_R=298.15\text{K}\right)$, the conventional theoretical model of FCS without consideration of the optical gradient force could evaluate the increase in the average number of molecules and the diffusion time in the potential. On the other hand, large deviation between the simulated fluorescence correlation curve and the theoretical model was observed under the potential depth $>1.0k{T}_R$. In addition, by integrating the optical force potential with the temperature elevation under optical trapping condition, it was deduced that the temperature rise does not seriously affect the average number of particles in the sampling area, but the average residence time is more sensitively affected by the temperature elevation. The present study using the simulation also provides a method to experimentally estimate molecular polarizabilities from FCS measurements.

We investigate the effective viscosity of a nematic-liquid-crystal (NLC) for viscosity measurement using a shear horizontal (SH) wave propagating through a glass substrate loaded with the NLC. The phase measurement of the SH wave determines the NLC viscosity because SH wave propagation depends on loaded material viscosity. Using this viscosity measurement, we can also determine the viscosity anisotropy of the NLC with director reorientation. In experiment, phase shifts are detected when voltages are applied to a NLC layer. The measured phases show an unpredictable shift which cannot be explained by conventional director angular dependence of viscosity. To analyze the phase shifts quantitatively, we introduce average effective viscosity for the viscosity measurement using SH wave. This effective viscosity is calculated considering the NLC director configuration and SH wave penetration into the NLC layer. The phase shifts calculated from the effective viscosity well agree with the measured phase shifts. The use of effective viscosity enables quantitative analysis for NLC viscosity measurement using the SH wave and also clarifies the mechanism of the unpredictable SH wave phase shift with director reorientation.

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distribution. We study the distribution empirically and show that the tail is much better described by a log-normal than a power law, indicating less concentration than, for example, personal income. The results are highly statistically significant and are consistent across fifteen years. This contradicts a recent theory concerning the origin of the power law tails of the trading volume distribution. Based on the analysis in a companion paper, the log-normality is to be expected, and indicates that the distribution of mutual funds remains perpetually out of equilibrium.

The question of how clustering (nonzero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modeling highly clustered networks are employed here to analytically study the bond percolation threshold. In comparison to the threshold in an unclustered network with the same degree distribution and correlation structure, the presence of triangles in these model networks is shown to lead to a larger bond percolation threshold (i.e. clustering increases the epidemic threshold or decreases resilience of the network to random edge deletion).

Pattern formation in reaction-diffusion systems is an important self-organizing mechanism in nature. Dynamics of systems with normal diffusion do not always reflect the processes that take place in real systems when diffusion is enhanced by a fluid flow. In such reaction-diffusion-advection systems diffusion might be anomalous for certain time and length scales. We experimentally study the propagation of a chemical wave occurring in a Belousov-Zhabotinsky reaction subjected to a quasi-two-dimensional chaotic flow created by the Faraday experiment. We present a novel analysis technique for the local expansion of the active wave front and find evidence of its superdiffusivity. In agreement with these findings the variance ${\sigma }^2\left(t\right)\propto t^{\gamma }$ of the reactive wave grows supralinear in time with an exponent $\gamma >2$. We study the characteristics of the underlying flow with microparticles. By statistical analysis of particle trajectories we derive flight time and jump length distributions and find evidence that tracer-particles undergo complex trajectories related to Lévy statistics. The propagation of active and passive media in the flow is compared.

The Floquet spectra of a class of driven SU(2) systems have been shown to display butterfly patterns with multifractal properties. The implication of such critical spectral behavior for the Floquet eigenstate statistics is studied in this work. Following the methodologies for understanding the fractal behavior of energy eigenstates of time-independent systems on the Anderson transition point, we analyze the distribution profile, the mean value, and the variance of the logarithm of the inverse participation ratio of the Floquet eigenstates associated with multifractal Floquet spectra. The results show that the Floquet eigenstates also display fractal behavior but with features markedly different from those in time-independent Anderson-transition models. This motivated us to propose random unitary matrix ensemble, called “power-law random banded unitary matrix” ensemble, to illuminate the Floquet eigenstate statistics of critical driven systems. The results based on the proposed random matrix model are consistent with those obtained from our dynamical examples with or without time-reversal symmetry.

We propose to take advantage of using the Wiener path integrals as the formal solution for the joint probability densities of coupled Langevin equations describing particles suspended in a fluid under the effect of viscous and random forces. Our obtained formal solution, giving the expression for the Lyapunov exponent, (i) will provide the description of all the features and the behavior of such a system, e.g., the aggregation phenomenon recently studied in the literature using appropriate approximations, (ii) can be used to determine the occurrence and the nature of the aggregation-nonaggregation phase transition which we have shown for the one-dimensional case, and (iii) allows the use of a variety of approximative methods appropriate for the physical conditions of the problem such as instanton solutions in the WKB approximation in the aggregation phase for the one-dimensional case as presented in this paper. The use of instanton approximation gives the same result for the Lyapunov exponent in the aggregation phase, previously obtained by other authors using a different approximative method. The case of nonaggregation is also considered in a certain approximation using the general path integral expression for the one-dimensional case.

We consider globally coupled random frequency oscillators under thermal noise, and explore the synchronization transition with its critical behavior near the transition. In particular, we focus on the finite-size scaling behavior of the synchronization, and investigate how the thermal noise affects the correlation size exponent $\overline{\nu }$ of the synchronized oscillators. Extensive numerical simulations as well as mean-field analysis have been performed. We find that the correlation size exponent changes from $\overline{\nu }=5/2$ without thermal noise to $\overline{\nu }=2$ with strong thermal noise, where the value $\overline{\nu }=2$ is the same as that for the usual equilibrium systems described by the Ginzburg-Landau mean-field theory. In order to see the effects of thermal fluctuation further, we remove the frequency-disorder fluctuations originating from the different realizations of natural frequencies of the oscillators, and examine the finite-size scaling behavior for the case only with the thermal fluctuation. It is found that $\overline{\nu }$ becomes 2 at much weak thermal noise strength, which implies that even very weak thermal fluctuations may lead to $\overline{\nu }=2$ when frequency-disorder fluctuations are absent.

We study the statistical topology of folding configurations of hand folded paper balls. Specifically, we are studying the distribution of two sides of the sheet along the ball surface and the distribution of sheet fragments when the ball is cut in half. We found that patterns obtained by mapping of ball surface into unfolded flat sheet exhibit the fractal properties characterized by two fractal dimensions which are independent on the sheet size and the ball diameter. The mosaic patterns obtained by sheet reconstruction from fragments of two parts (painted in two different colors) of the ball cut in half also possess a fractal scale invariance characterized by the box fractal dimension $D_{BF}=1.68\pm 0.04$, which is independent on the sheet size. Furthermore, we noted that $D_{BF}$, at least numerically, coincide with the universal fractal dimension of the intersection of hand folded paper ball with a plane. Some other fractal properties of folding configurations are recognized.

This paper is concerned with ionic currents from an electrolyte solution into a charge selective solid, such as an electrode, an ion exchange membrane or an array of nanochannels in a microfluidic system. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization—formation of solute concentration gradients under the passage of a dc current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, superfast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed nonequilibrium electro-osmotic instability, result from formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface or, rather, from the peculiar features of the extended space charge distinguishing it from that of a common diffuse electrical double layer. In this paper we discuss the nature and origin of the extended space charge and analyze its peculiar steady state and time-dependent properties important for understanding nonequilibrium electrokinetic phenomena in ionic systems.

We analytically examine the pair interaction for parallel discrete helices of charge. Symmetry arguments allow for the free energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier expansions of these terms are shown to provide effective free energy expressions that are valid under very general circumstances. These expressions are used to briefly examine and characterize the azimuthal interactions within F-actin and A-DNA aggregates.

In view of the important role helix-sheet transitions play in protein aggregation, we introduce a simple model to study secondary structural transitions of helix-coil-sheet systems using a Potts model starting with an effective Hamiltonian. This energy function depends on four parameters that approximately describe entropic and enthalpic contributions to the stability of a polypeptide in helical and sheet conformations. The sheet structures involve long-range interactions between residues which are far in sequence, but are in contact in real space. Such contacts are included in the Hamiltonian. Using standard statistical mechanical techniques, the partition function is solved exactly using transfer matrices. Based on this model, we study thermodynamic properties of polypeptides, including phase transitions between helix, sheet, and coil structures.