Orientational fluctuations of colloidal particles with magnetic moments may be rectified with the help of external magnetic fields with suitably chosen time dependence. As a result a noise-driven rotation of particles occurs giving rise to a macroscopic torque per volume of the carrier liquid. We investigate the influence of mutual interactions between the particles on this ratchet effect by studying a model system with mean-field interactions. The stochastic dynamics may be described by a nonlinear Fokker-Planck equation for the collective orientation of the particles which we solve approximately by using the effective field method. We determine an interval for the ratio between coupling strength and noise intensity for which a self-sustained rectification of fluctuations becomes possible. The ratchet effect then operates under conditions for which it was impossible in the absence of interactions.

We study the consequences of the interplay between electrostatic forces, mechanical contact forces, and frictional properties of grains upon the bulk frictional properties of charged granular media subjected to quasistatic shearing. We show that, the variations in short-range electrostatic forces between the grains (which are often ignored in the existing studies) dominantly affect the bulk friction. Charging enhances the fabric anisotropy of heavily loaded contacts—this enhances the bulk friction, more significantly, in the case of low frictional granular systems.

Granular mixtures immersed in a liquid (slurries) show segregation dynamics which are quantitatively and qualitatively different from those of dry systems. The principal mechanisms of the segregation dynamics in slurries, as well as the relevant material parameters that must be taken into account in a dynamic description are not sufficiently understood so far. We investigate experimentally the influence of the viscosity of the interstitial liquid on the coarsening of axial segregation patterns in a horizontally rotating mixer. It is found that not only the characteristic time scales but also fundamental structural features of these patterns are influenced by the viscous properties of the liquid component.

We examine random matrix systems driven by an external field in view of optimal control theory (OCT). By numerically solving OCT equations, we can show that there exists a smooth transition between two states called “moving bases” which are dynamically related to initial and final states. In our previous work [J. Phys. Soc. Jpn. 73, 3215 (2004); Adv. Chem. Phys. 130A, 435 (2005)], they were assumed to be orthogonal, but in this paper, we introduce orthogonal moving bases. We can construct a Rabi-oscillation-like representation of a wave packet using such moving bases, and derive an analytic optimal field as a solution of the OCT equations. We also numerically show that the newly obtained optimal field outperforms the previous one.

We consider the dynamics when traveling pulses encounter heterogeneities in a three-component reaction diffusion system of one-activator–two-inhibitor type, which typically arises as a qualitative model of a gas-discharge system. We focused on the case where one of the kinetic coefficients changes similar to a smoothed step function, which is basic for more general heterogeneity as in periodic or random media. Since the heterogeneity is introduced to the kinetic part in an additive way, it causes the system to produce various types of localized structures smoothing the jump heterogeneity called the defects at the jump point, which makes a sharp contrast with the multiplicative heterogeneous case for the Gray-Scott model. The main issue is to study the collision dynamics between traveling pulses and defects, and show that their global bifurcation structure plays a key role in clarifying the underlying mechanism. Five outputs are observed after collisions including annihilation, rebound, and pinning. Unstable steady states are identified as separators between two different dynamic regimes: penetration and rebound, the role of which is very close to that of scattors arising in collision process. An organizing center producing the traveling pulses, defects, and scattors via unfolding with respect to the parameters is also presented.

The fast boiling dynamics of superheated surface layers of bulk water cavitating under near-spinodal conditions during nanosecond $\mathrm{C}{\mathrm{O}}_2$ laser heating pulses was studied using contact broad-band photoacoustic spectroscopy. Characteristic pressure-tension cycles recorded by an acoustic transducer at different incident laser fluences represent (a) weak random oscillations of transient nanometer-sized near-critical bubbles-precursors and (b) well-defined stimulated oscillations of micron-sized supercritical bubbles and their submicrosecond coalescence products. These findings provide an important insight into basic thermodynamic parameters, spatial and temporal scales of bubble nucleation during explosive liquid/vapor transformations in absorbing liquids ablated by short laser pulses in the thermal confinement regime.

We study a ferrofluid in a horizontal Hele-Shaw geometry subjected to a vertical magnetic field. Specifically, we calculate the energy of a single ferrofluid finger using an idealized model for the finger. By minimizing this energy, we find the preferred finger width as a function of the applied field. Our model predicts a first order transition as the fluid abruptly transforms from a circular drop to a finite finger. This behavior arises because of a double energy minimum that yields two different stable configurations for the system. Interestingly, this system exhibits hysteresis as the circle-to-finger (increasing field) transition occurs at a different applied field than the finger-to-circle (decreasing field) transition. We carry out a simple experiment and observe good overall agreement with the theoretical predictions.

The dielectric response of a polymer matrix composite can be substantially modified and tuned within a broad frequency band by integrating within the material an artificial plasmon medium composed of periodically distributed, very thin, electrically conducting wires. In the microwave regime, such plasmon/polymer composites have been studied analytically, computationally, and experimentally. This work reports the design, fabrication, and characterization of similar composites for operation at terahertz frequencies. Such composites require significant reduction in the thickness and spacing of the wires. We used numerical modeling to design artificial effective plasmonic media with turn-on frequencies in the terahertz range. Prototype samples were produced by lithographically embedding very thin gold strips into a PDMS [poly(dimethylsiloxane)] matrix. These samples were characterized with a Fourier-transform infrared interferometer using the frequency-dependent transmission and Kramers-Kronig relations to determine the electromagnetic properties. We report the characterization results for a sample, demonstrating excellent agreement between theory, computer design, and experiment. To our knowledge this is the first demonstration of the possibility of creating composites with tuned dielectric response at terahertz frequencies.

We extend our studies of thermal diffusion of nontopological solitons to anharmonic Fermi-Pasta-Ulam-type chains with additional long-range couplings. The observed superdiffusive behavior in the case of nearest-neighbor interaction turns out to be the dominating mechanism for the soliton diffusion on chains with long-range interactions. Using a collective variable technique in the framework of a variational analysis for the continuum approximation of the chain, we derive a set of stochastic integrodifferential equations for the collective variables (CVs) soliton position and the inverse soliton width. This set can be reduced to a statistically equivalent set of Langevin-type equations for the CV, which shares the same Fokker-Planck equation. The solution of the Langevin set and the Langevin dynamics simulations of the discrete system agree well and demonstrate that the variance of the soliton increases stronger than linearly with time (superdiffusion). This result for the soliton diffusion on anharmonic chains with long-range interactions reinforces the conjecture that superdiffusion is a generic feature of nontopological solitons.

We simulate time harmonic flows by the lattice Boltzmann method. We propose a general scheme to choose simulation parameters, under the constraints of fixed Reynolds and Womersley numbers, and with a specified simulation error. Under these constraints parameters are chosen to minimize the execution time. Numerical stability is studied in a range of Reynolds and Womersley numbers. As an example of time harmonic flow simulations, results of blood flow in a human abdominal aorta are presented.

We propose a level dynamics approach to the large deviation statistical characteristic function $\varphi \left(q\right)$ for temporal series of dynamical variable $V$, which is the largest eigenvalue of the generalized evolution operator $H_q(\equiv H+qV)$. This is done first by deriving “equations of motion” for the eigenvalues and the eigenstates of $H_q$ with the initial conditions determined by those of $H$, the true evolution operator for the dynamical variable under consideration, and then by solving these equations. Furthermore, utilizing simple solvable models, it is shown that the eigenvalues and eigenstates satisfy the equations of motion derived in this paper.

We consider the Brownian motion of a colloidal particle in a symmetric, periodic potential, whose potential barriers are subjected to temporal oscillations. Experimentally, the potential is generated by two arrays of trapped, negatively charged particles whose positions are periodically modulated with light forces. This results in a structured channel geometry of locally variable width. If all potential barriers are oscillating in synchrony, a resonancelike peak of the effective diffusion coefficient upon variation of the oscillation period is observed. For asynchronously oscillating barriers, the particle can be steered with great reliability into one or the other direction by properly choosing the oscillation periods of the different barriers along the channel.

We study the effect of precollisional velocity correlations on granular shear flow by molecular dynamics simulations of an inelastic hard sphere system. Comparison of the simulations with kinetic theory reveals that the theory overestimates both the energy dissipation rate and the normal stress in the dense flow region. We find that the relative normal velocity of colliding particles is smaller than that expected from random collisions, and the discrepancies in the dissipation and the normal stress can be adjusted by introducing the idea of the collisional temperature, from which we conclude that the velocity correlation neglected in the kinetic theory is responsible for the discrepancies. Our analysis of the distributions of the precollisional velocity suggests that the correlation grows through multiple inelastic collisions during the time scale of the inverse of the shear rate. As for the shear stress, the discrepancy is also found in the dense region, but it depends strongly on the particle inelasticity.

Some years ago it was shown that gas-fluidized powders may transit from solidlike to fluidlike fluidization prior to bubbling, shedding light on a long-standing controversy on the nature of “homogeneous” fluidization. In this paper it is shown that some gas-fluidized powders may also transit from the fluidlike regime to elutriation, with full suppression of the bubbling regime. We provide a diagram that can be used to predict these types of fluidization exhibited by cohesive powders based on simple phenomenological equations in which particle aggregation due to attractive forces is a key ingredient.

Using inverse statistical-mechanical optimization techniques, we have discovered isotropic pair interaction potentials with strongly repulsive cores that cause the tetrahedrally coordinated diamond and wurtzite lattices to stabilize, as evidenced by lattice sums, phonon spectra, positive-energy defects, and self-assembly in classical molecular dynamics simulations. These results challenge conventional thinking that such open lattices can only be created via directional covalent interactions observed in nature. Thus, our discovery adds to fundamental understanding of the nature of the solid state by showing that isotropic interactions enable the self-assembly of open crystal structures with a broader range of coordination number than previously thought. Our work is important technologically because of its direct relevance generally to the science of self-assembly and specifically to photonic crystal fabrication.

We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical framework, except for a linear contribution to the memory kernel which adds to the usual quadratic term. The coupling coefficients involve structural quantities which are specific of fluids evolving in random environments and have expressions which are consistent with those found in related problems. Numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios, which are either continuous or discontinuous and include the possibility of higher-order singularities and glass-glass transitions. The main features of the dynamics in the two most generic cases are reviewed and illustrated with detailed computations. Moreover, a reentry phenomenon is predicted in the low fluid-high matrix density regime and is interpreted as the signature of a decorrelation mechanism by fluid-fluid collisions competing with the localization effect of the solid matrix.

We present a simple model for dipolar elastic membranes that gives lattice-bound point dipoles complete orientational freedom as well as translational freedom along one coordinate (out of the plane of the membrane). There is an additional harmonic term which binds each of the dipoles to the six nearest neighbors on either triangular or distorted lattices. The translational freedom of the dipoles allows triangular lattices to find states that break out of the normal orientational disorder of frustrated configurations and which are stabilized by long-range antiferroelectric ordering. In order to break out of the frustrated states, the dipolar membranes form corrugated or “rippled” phases that make the lattices effectively nontriangular. We observe three common features of the corrugated dipolar membranes: (1) the corrugated phases develop easily when hosted on triangular lattices, (2) the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis, and (3) on triangular lattices, the dipole director axis is found to be parallel to any of the three equivalent lattice directions.

A statistical theory for the dipole flexoelectric (FE) polarization in liquid crystals is derived in the thermodynamic limit at small distortions and a small density. General microscopic expressions for the FE coefficients are rederived in the case of the uniaxial nematic phase. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. It is shown that, for wedge-shaped polar molecules, the FE coefficients are proportional to the longitudinal component of the molecule dipole moment. The FE coefficients include a term linear in $⟨P_2⟩$ and a quadratic form in $⟨P_j⟩$ ($j$-even). The theory is used to calculate the temperature dependence of the elastic constants and the FE coefficients for a system of rigid molecules similar to cones.

We present a phase model of a repetitively firing neuron possessing a phase-dependent stochastic response to periodic inhibition. We analyze the dynamics in terms of a stochastic phase map and determine the invariant phase distribution. We use the latter to compute both the distribution of interspike intervals (ISIs) and the stochastic winding number (mean firing rate) as a function of the input frequency. We show that only low-order phase locking persists in the presence of weak phase dependence, and is characterized statistically by a multimodal ISI distribution and a nonmonotonic variation in the stochastic winding number as a function of input frequency.