Dynamical approach to chains of scatterers

Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the transport through the chain to the spectral properties of individual scatterers. For a single-scattering channel case some new light is shed on known transport properties of disordered and noisy chains, whereas translationally invariant case can be studied analytically in terms of a simple deterministic dynamical map. The many-channel case was studied numerically by examining the statistical properties of scatterers that correspond to a certain type of transport of the chain i.e. ballistic or (partially) localised.Comment: 16 pages, 7 figure

Temporal Modulation of Traveling Waves in the Flow Between Rotating Cylinders With Broken Azimuthal Symmetry

The effect of temporal modulation on traveling waves in the flows in two distinct systems of rotating cylinders, both with broken azimuthal symmetry, has been investigated. It is shown that by modulating the control parameter at twice the critical frequency one can excite phase-locked standing waves and standing-wave-like states which are not allowed when the system is rotationally symmetric. We also show how previous theoretical results can be extended to handle patterns such as these, that are periodic in two spatial direction.Comment: 17 pages in LaTeX, 22 figures available as postscript files from http://www.esam.nwu.edu/riecke/lit/lit.htm

Random-mass Dirac fermions in an imaginary vector potential: Delocalization transition and localization length

One dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. Especially we numerically calculate both the "typical" and "mean" localization lengths as a function of energy and the correlation length of the random mass. To this end we introduce an imaginary vector potential as suggested by Hatano and Nelson and solve the eigenvalue problem. Numerical calculations are in good agreement with the results of the analytical calculations.Comment: 4 page

External-field-induced tricritical point in a fluctuation-driven nematic-smectic-A transition

We study theoretically the effect of an external field on the nematic-smectic-A (NA) transition close to the tricritical point, where fluctuation effects govern the qualitative behavior of the transition. An external field suppresses nematic director fluctuations, by making them massive. For a fluctuation-driven first-order transition, we show that an external field can drive the transition second-order. In an appropriate liquid crystal system, we predict the required magnetic field to be of order 10 T. The equivalent electric field is of order $1 V/\mu m$.Comment: revtex, 4 pages, 1 figure; revised version, some equations have been modifie

Tkachenko waves, glitches and precession in neutron star

Here I discuss possible relations between free precession of neutron stars, Tkachenko waves inside them and glitches. I note that the proposed precession period of the isolated neutron star RX J0720.4-3125 (Haberl et al. 2006) is consistent with the period of Tkachenko waves for the spin period 8.4s. Based on a possible observation of a glitch in RX J0720.4-3125 (van Kerkwijk et al. 2007), I propose a simple model, in which long period precession is powered by Tkachenko waves generated by a glitch. The period of free precession, determined by a NS oblateness, should be equal to the standing Tkachenko wave period for effective energy transfer from the standing wave to the precession motion. A similar scenario can be applicable also in the case of the PSR B1828-11.Comment: 6 pages, no figures, accepted to Ap&S

Smectic ordering in liquid crystal - aerosil dispersions II. Scaling analysis

Liquid crystals offer many unique opportunities to study various phase transitions with continuous symmetry in the presence of quenched random disorder (QRD). The QRD arises from the presence of porous solids in the form of a random gel network. Experimental and theoretical work support the view that for fixed (static) inclusions, quasi-long-range smectic order is destroyed for arbitrarily small volume fractions of the solid. However, the presence of porous solids indicates that finite-size effects could play some role in limiting long-range order. In an earlier work, the nematic - smectic-A transition region of octylcyanobiphenyl (8CB) and silica aerosils was investigated calorimetrically. A detailed x-ray study of this system is presented in the preceding Paper I, which indicates that pseudo-critical scaling behavior is observed. In the present paper, the role of finite-size scaling and two-scale universality aspects of the 8CB+aerosil system are presented and the dependence of the QRD strength on the aerosil density is discussed.Comment: 14 pages, 10 figures, 1 table. Companion paper to "Smectic ordering in liquid crystal - aerosil dispersions I. X-ray scattering" by R.L. Leheny, S. Park, R.J. Birgeneau, J.-L. Gallani, C.W. Garland, and G.S. Iannacchion

Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability

A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - Bénard convection

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

Influence of Shear-Thinning Rheology on the Mixing Dynamics in Taylor-Couette Flow

Non‐Newtonian rheology can have a significant effect on mixing efficiency, which remains poorly understood. The effect of shear‐thinning rheology in a Taylor‐Couette reactor is studied using a combination of particle image velocimetry and flow visualization. Shear‐thinning is found to alter the critical Reynolds numbers for the formation of Taylor vortices and the higher‐order wavy instability, and is associated with an increase in the axial wavelength. Strong shear‐thinning and weak viscoelasticity can also lead to sudden transitions in wavelength as the Reynolds number is varied. Finally, it is shown that shear‐thinning causes an increase in the mixing time within vortices, due to a reduction in their circulation, but enhances the axial dispersion of fluid in the reactor