The flashing ratchet and unidirectional transport of matter

We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor really performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain.Comment: 11 page

Dynamics of filaments during the isotropic-smectic A phase transition

Summary. We study the dynamics of filaments formed when certain materials undergo the isotropic-smectic A phase transition. The basis of this work is a solidification model derived from first principles, taking into account elastic, hydrodynamic, and thermodynamic effects. The permeation process, which is solely responsible for the growth of the filament, is analyzed in detail. Various characteristics of the filament, such as growth rates, velocity profile inside the filament, and transport along the filament, are calculated by studying the asymptotic limit of a slender body problem. We also derive, in this limit, the equation governing the dynamics of the centerline of the filament

Optical, magnetic and dielectric properties of non-liquid crystalline elastomers doped with magnetic colloids

Magnetic nanoparticles from magnetic colloidal suspensions were incorporated in the urethane/urea elastomer (PU/PBDO) by swelling fully crosslinked elastomer samples with a toluene and ferrofluid mixture. It is shown that ferrofluid grains can be efficiently incorporated into the matrix of elastomers. The dependence of the birefringence of both the pure and ferrofluid-doped elastomer samples on strain is linear. The ratio of birefringence to strain of the ferrofluid-doped samples is greater than that of the pure elastomer samples, indicating that ferrofluid grains are oriented by the strained polymer network. We propose that this strain-induced orientation is due to the shape anisotropy of the nanoparticles.publishersversionpublishe

Polymerization-Induced Phase-Separation in a Liquid-Crystal-Polymer Mixture

We have used light scattering to study the kinetics of polymerization-induced phase separation in a liquid-crystal-polymer mixture. The evolution of the structure factor is compared with scaling predictions for thermally quenched systems. We have also observed a cascading phenomenon where phase separated domains become unstable and undergo phase separation for a second time

The Complex Ginzburg-Landau Equation for Beginners

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Ferrofluids as thermal ratchets

Colloidal suspensions of ferromagnetic nano-particles, so-called ferrofluids, are shown to be suitable systems to demonstrate and investigate thermal ratchet behavior: By rectifying thermal fluctuations, angular momentum is transferred to a resting ferrofluid from an oscillating magnetic field without net rotating component. Via viscous coupling the noise driven rotation of the microscopic ferromagnetic grains is transmitted to the carrier liquid to yield a macroscopic torque. For a simple setup we analyze the rotation of the ferrofluid theoretically and show that the results are compatible with the outcome of a simple demonstration experiment.Comment: 4 pages, 3 figures, corrected version, improved figures, to be published in Phys. Rev. Let

Lorentz-Lorenz Coefficient, Critical Point Constants, and Coexistence Curve of 1,1-Difluoroethylene

We report measurements of the Lorentz-Lorenz coefficient density dependence, the critical temperature, and the critical density, of the fluid 1,1-difluoroethylene. Lorentz-Lorenz coefficient data were obtained by measuring refractive index and density of the same fluid sample independently of one another. Accurate determination of the Lorentz-Lorenz coefficient is necessary for transformation of refractive index data into density data from optics-based experiments on critical phenomena of fluid systems done with different apparatus, with which independent measurement of the refractive indes and density is not possible. Measurements were made along the coexistence curve of the fluid and span the density range 0.01 to 0.80 g/cc. The Lorentz-Lorenz coefficient results show a stronger density dependence along the coexistence curve than previously observed in other fluids, with a monotonic decrease from a density of about 0.2 g/cc onwards, and an overall variation of about 2.5% in the density range studied. No anomaly in the Lorentz-Lorenz coefficient was observed near the critical density. The critical temperature is measured at Tc=(302.964+-0.002) K (29.814 C) and the measured critical density is (0.4195+-0.0018)g/cc.Comment: 14 pages, 6 figures, MikTeX 2.4, submitted to Physical Review

n-atic Order and Continuous Shape Changes of Deformable Surfaces of Genus Zero

We consider in mean-field theory the continuous development below a second-order phase transition of $n$-atic tangent plane order on a deformable surface of genus zero with order parameter $\psi = \langle e^{i n \theta} \rangle$. Tangent plane order expels Gaussian curvature. In addition, the total vorticity of orientational order on a surface of genus zero is two. Thus, the ordered phase of an $n$-atic on such a surface will have $2n$ vortices of strength $1/n$, $2n$ zeros in its order parameter, and a nonspherical equilibrium shape. Our calculations are based on a phenomenological model with a gauge-like coupling between $\psi$ and curvature, and our analysis follows closely the Abrikosov treatment of a type II superconductor just below $H_{c2}$.Comment: REVTEX, 12 page