The Wigner transform of the master equation describing the reduced dynamics of the system, of a harmonic oscillator coupled to an oscillator bath, was obtained by Karrlein and Grabert [Phys. Rev. E 55, 153 (1997)]. It was shown that for some special correlated initial conditions the master equation reduces, in the classical limit, to the corresponding classical Fokker-Planck equation obtained by Adelman [J. Chem Phys. 64, 124 (1976)]. However, for separable initial conditions the Adelman equations were not recovered. We resolve this problem by showing that, for separable initial conditions, the classical Langevin equations are somewhat different from the one considered by Adelman. We obtain the corresponding Fokker-Planck equation and show that they exactly match the classical limit of the evolution of the Wigner function obtained from the master equation for separable initial conditions. We also discuss why thermal initial conditions correspond to Adelman’s solution.

This paper examines the impact of shear on the drainage of liquid through a foam. The effect on drainage of changes in the Plateau border network brought about by shear is examined. This effect of shear was modeled using both a detailed three-dimensional simulation of foam structure, and an idealized two-dimensional hexagonal foam. The main phenomenon that has been discovered is that shear induces an anisotropy in the drainage of liquid through the foam. If the foam is strained and liquid flows under gravity either perpendicular or parallel to the shear direction, a net liquid flow in the direction perpendicular to the direction of gravity is induced. It was found that the degree of anisotropy increases nearly linearly with increasing strain until the foam yields, after which the degree of flow anisotropy remains roughly constant. This is not a small effect, with the flow in the direction perpendicular to gravity being up to about 20% of the flow in the direction of gravity at the yield strain. This shear-induced anisotropy provides a potential explanation for the hitherto puzzling phenomenon of the convective roll in foam. The other two effects examined are the effect of shear on the length of Plateau borders per volume of foam, which increases as strain increases, and the resistance of the foam to flow in the direction of gravity, which increases if the strain direction is perpendicular to gravity, but decreases if the strain is parallel to gravity.

We numerically study the behavior of a collection of overdamped Brownian particles in a channel, in the presence of a flow field applied on similar but slower particles in a wide chamber in contact with the channel. For a suitable range of shear rates, we find that the flow field induces a unidirectional drift in the confined particles, and is stronger for narrower channels. The average drift velocity initially rises with increasing shear rate, then shows saturation for a while, thereafter starts decreasing, in qualitative agreement with recent theoretical studies [Phys. Rev. B 70, 205423 (2004)] based on Brownian drag and “loss of grip.” Interestingly, if the sign of the interspecies interaction is reversed, the direction of the induced drift remains the same, but the flow rate at which loss of grip occurs is lower, and the level of fluctuations is higher.

Time-resolved small-angle x-ray scattering measurements reveal that a long-lived intermediate bcc state forms when a poly(styrene-$b$-isoprene) diblock copolymer solution in an isoprene selective solvent is rapidly cooled from the disordered micellar fluid at high temperature to an equilibrium fcc state. The kinetics of the epitaxial growth of the [111] fcc peak from the [110] bcc peak was obtained by fitting the scattering data to a simple model of the transformation. The growth of the [111] fcc peak agrees with the Avrami model of nucleation and growth kinetics with an exponent $n=1.4$, as does the initial decay of the [110] bcc peak, with an exponent $n=1.3$. The data were also found to be in good agreement with the Cahn model of grain boundary nucleation and growth.

The early-stage roughening of the interface between thin deuterated poly(methyl methacrylate) (d-PMMA) layers on thick polystyrene (PS) films was studied as a function of the temperature using real-time specular neutron reflectivity. By measuring the growth of the interface roughness as a precursor of the dewetting, the characteristic time constant of the early stages of the process was studied as a function of the temperature approaching the glass transition temperature $\left(T_g\right)$ of the two polymers from above and compared with the prediction of the growth of the interface by the spinodal process. Both solid and liquid regimes were probed, in which the viscosity of the thin film or the substrate dominates respectively. The characteristic growth time of the process also depends on the upper film thickness to a power of 5 or 6 in the solid or liquid regimes, respectively, as predicted by the theory of spinodal dewetting.

The dynamics of long DNA moving through microfluidic arrays of micron-sized posts under a moderate electric field are modeled by a Scher-Lax continuous-time random walk. The microscale model consists of a repetitive sequence of three steps: (i) collision with the post and extension into two arms, (ii) electric-field-driven unhooking from the post, and (iii) uniform translation until the next collision. The model features two random variables: the initial offset between the two arms of the polymer during a given collision and the distance traveled between collisions. For experimentally realistic values of the electric field strength and DNA molecular weight, scaling laws indicate that the chain will generally be in a stem-flower conformation when unhooking from the post. Compared to a taut-chain model at the same field strength, the stem-flower conformation reduces the time engaged with the post and increases the collision frequency. Analytical expressions for the mean velocity and dispersivity are derived as a function of the post density, post spacing, free-solution mobility, Kuhn length, and sequence length. The incomplete extension of the chain does not strongly affect the mean velocity, but tends to increase the dispersivity relative to a taut chain. As a result, the separation resolution decreases as the field decreases for a moderate field, in agreement with experiments. The quantitative agreement between the model and experimental data is satisfactory, especially considering that the model contains no adjustable parameters.

The dynamics of intracellular ${\mathrm{Ca}}^{2+}$ is driven by random events called ${\mathrm{Ca}}^{2+}$ puffs, in which ${\mathrm{Ca}}^{2+}$ is liberated from intracellular stores. We show that the emergence of ${\mathrm{Ca}}^{2+}$ puffs can be mapped to an escape process. The mean first passage times that correspond to the stochastic fraction of puff periods are computed from a novel master equation and two Fokker-Planck equations. Our results demonstrate that the mathematical modeling of ${\mathrm{Ca}}^{2+}$ puffs has to account for the discrete character of the ${\mathrm{Ca}}^{2+}$ release sites and does not permit a continuous description of the number of open channels.

We propose an approach for analyzing the basic relation between correlation properties of the original signal and its magnitude fluctuations by decomposing the original signal into its positive and negative fluctuation components. We use this relation to understand the following phenomenon found in many naturally occurring time series: the magnitude of the signal exhibits long-range correlation, whereas the original signal is short-range correlated. The applications of our approach to heart rate variability signals and high-frequency foreign exchange rates reveal that the difference between the correlation properties of the original signal and its magnitude fluctuations is induced by the time organization structure of the correlation function between the magnitude fluctuations of positive and negative components. We show that this correlation function can be described well by a stretched-exponential function and is related to the nonlinearity and the multifractal structure of the signals.

An exact derivation of the surface magnetizations of the two phases $m_1^I$ and $m_1^{II}$ coexisting below the bulk critical temperature for the semi-infinite two-dimensional Ising ferromagnet subject to a surface field is given. The surface critical behavior of the difference $m_1^I-m_1^{II}$ is that of the ordinary transition only in a limit of a weak surface field below the wetting temperature.

We apply periodic-orbit theory to calculate the integrated density of states $N\left(k\right)$ of the quantum mechanical eigenvalues from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the density of states obtained from numerical solutions of the Schrödinger equation that about the first 100 eigenvalues can be obtained directly from the periodic-orbit calculations with good accuracy.

The influence of the horizontal component of the temperature gradient on nonlinear regimes of oscillatory Marangoni convection in a real symmetric three-layer system is investigated. The transitions between different flow regimes have been studied. The general diagram of regimes is constructed.

When a liquid droplet experiences a temperature inhomogeneity along its bounding surface, a surface energy gradient is engendered, which when, in a continuous sense, exceeding a threshold, results in a convective flow dissipating the energy. If the associated temperature gradients are sustained by the interface between the liquid and a supporting substrate, the induced flow can result in the lateral motion of the droplet overcoming the viscosity and inertia. Recently, pico-liter adsorbed and applied droplets were shown experimentally to be transported, and divided by the decay of optically excited surface plasmons into phonons in a thin gold foil. The decaying events locally modify the temperature of the liquid-solid interface, establishing microscale thermal gradients of sufficient magnitude for the droplet to undergo thermocapillary flow. We present experimental evidence of such gradients resulting in local surface modification associated with the excitation of surface plasmons. We show theoretically that the observed effect is due to Marangoni forces, and computationally visualize the flow characteristics for the experimental parameters. As an application based on our results, we propose a method for an all-optical modulation of light by light mediated by the droplet oscillations. Furthermore, the results have important consequences for microfluidics, droplet actuation, and simultaneous surface plasmon resonance sensing and spectroscopy.

Coupling between magnetic and mechanical rotational degrees of freedom of fine ferromagnetic grains is provided by the energy of their magnetic anisotropy. In the limiting case of strong anisotropy, an applied stationary magnetic field induces the greatest obstacles to the “rigid dipole” spin in a vortex ferrofluid flow, while in the opposite ideal case, the “soft dipoles” twist freely with the liquid. As a result, the field-dependent part of the ferrofluids viscosity depends not only on the external magnetic field strength but also on the particle magnetic anisotropy. An explicit expression coming from simple physical arguments and describing both these dependencies of magnetoviscosity is derived and discussed.

By an extended plane-wave-based transfer-matrix method, the photonic band structure and the corresponding transmission spectrum have been calculated for a two-dimensional photonic crystal composed of negative-phase-velocity-medium (NPVM) cylindrical rods. Dispersionless anticrossing bands in the two-dimensional NPVM periodic structure are generated by the couplings among surface polaritons localized in the NPVM rods. In part of the negative-phase-velocity frequency region, the photonic band structures of the NPVM photonic crystal are characterized by a topographical continuous dispersion relationship accompanied by many anticrossing bands. The effect of the filling fraction of the NPVM rods on the optical properties of photonic crystals has also been studied.

A slip-flow boundary condition has been developed in the lattice Boltzmann model combining an interpolation method and a simple slip boundary condition for straight walls placed at arbitrary distance from the last fluid node. An analytical expression has been derived to connect the model parameters with the slip velocity for Couette and Poiseuille flows in the nearly continuum limit. The proposed interpolation method ensures that the slip velocity is independent of the wall position in first order of the Knudsen number. Computer simulations have been carried out to validate the model. The Couette and Poiseuille flows agree with the analytical results to machine order. Numerical simulation of a moving square demonstrates the accuracy of the model for walls moving in both the tangential and normal directions.

A recent reformulation [Phys. Rev. E 73, 016705 (2006)] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite-temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a spatial lattice by including additional bosonic fields. For large systems, the Monte Carlo algorithm proposed in the above-cited work becomes inefficient due to a low acceptance rate for particle moves in a fixed background multiboson field. We show here how this problem can be circumvented by use of a coupled particle-multiboson update procedure that improves acceptance rates on large lattices by orders of magnitude. The method is tested on a one-component plasma with neutral dielectric particles for a variety of system sizes.

We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion-broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed and find their shape. Quantitatively, the tubes are characterized by the distribution of trajectories that, after escape, pass through a given point in phase space for a given modulation phase. This distribution may display several peaks separated by the modulation period. Analytical results agree with the results of simulations of a Brownian particle in a model modulated potential.

We present methodologies for calculating the direct correlation function $c(1,2)$, the cavity function $y(1,2)$, and the bridge function $b(1,2)$, for molecular liquids, from Monte Carlo simulations. As an example we present results for the isotropic hard spheroid fluid with elongation $e=3$. The simulation data are compared with the results from integral equation theory. In particular, we solve the Percus-Yevick and hypernetted chain equations. In addition, we calculate the first two terms in the virial expansion of the bridge function and incorporate this into the closure. At low densities, the bridge functions calculated by theory and from simulation are in good agreement, lending support to the correctness of our numerical procedures. At higher densities, the hypernetted chain results are brought into closer agreement with simulation by incorporating the approximate bridge function, but significant discrepancies remain.

Transcription-factor proteins bind to specific DNA sequences to regulate gene expression in cells. DNA-binding sites are often identified using weight matrices calculated from multiple known binding sites. However, in many cases the number of examples is limited. Here, we report on an atomistic method that starts from an x-ray co-crystal structure of the protein bound to one particular DNA sequence, and infers other binding sites, which are used to construct a weight matrix. The emphasis of the paper is on using the Wang-Landau Monte Carlo algorithm to efficiently sample high-affinity binding sites, which demonstrates that sampling can produce accurate weight matrices in analogy to bioinformatics approaches. For cases of low complexity, we compare to the exhaustive (but slow) dead-end elimination algorithm. To recover crystal binding sites, it is important to include bound water in the protein-DNA interface. Our approach can, in principle, even be applied when no native protein-DNA co-crystal structure is available, only the structure of a closely related homologous protein whose amino-acid sequence is changed to the protein of interest.

We consider maximization of the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. By extending the master stability formalism to all possible network structures, we show that, unless some oscillator is linked to all the others, maximally synchronizable networks are necessarily nondiagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The results provide insights into hierarchical structures observed in complex networks in which synchronization is important.