Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order

Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers becomes highly nontrivial. We discuss various topological and geometrical aspects of these materials and present recent progress on finding some exact layer configurations. We also exhibit connections to the study of certain embedded minimal surfaces and briefly summarize some important open problems.Comment: 16 page

Roughening Transition in a Moving Contact Line

The dynamics of the deformations of a moving contact line on a disordered substrate is formulated, taking into account both local and hydrodynamic dissipation mechanisms. It is shown that both the coating transition in contact lines receding at relatively high velocities, and the pinning transition for slowly moving contact lines, can be understood in a unified framework as roughening transitions in the contact line. We propose a phase diagram for the system in which the phase boundaries corresponding to the coating transition and the pinning transition meet at a junction point, and suggest that for sufficiently strong disorder a receding contact line will leave a Landau--Levich film immediately after depinning. This effect may be relevant to a recent experimental observation in a liquid Helium contact line on a Cesium substrate [C. Guthmann, R. Gombrowicz, V. Repain, and E. Rolley, Phys. Rev. Lett. {\bf 80}, 2865 (1998)].Comment: 16 pages, 6 encapsulated figure

Dissipation in Dynamics of a Moving Contact Line

The dynamics of the deformations of a moving contact line is studied assuming two different dissipation mechanisms. It is shown that the characteristic relaxation time for a deformation of wavelength $2\pi/|k|$ of a contact line moving with velocity $v$ is given as $\tau^{-1}(k)=c(v) |k|$. The velocity dependence of $c(v)$ is shown to drastically depend on the dissipation mechanism: we find $c(v)=c(v=0)-2 v$ for the case when the dynamics is governed by microscopic jumps of single molecules at the tip (Blake mechanism), and $c(v)\simeq c(v=0)-4 v$ when viscous hydrodynamic losses inside the moving liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated dominant dissipation mechanism can be experimentally determined using relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T. Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].Comment: REVTEX 8 pages, 9 PS figure

Number of distinct sites visited by N random walkers on a Euclidean lattice

The evaluation of the average number S_N(t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is the volume of a hypersphere of radius (4Dt \ln N)^{1/2}, \Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N, d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the dimension and time. The first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1, 2, and 3. Some implications of these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.

Supercurrent in a mesoscopic proximity wire

Recent experiments on the proximity induced supercurrent in mesoscopic normal wires revealed a surprising temperature dependence. They suggest clean-limit behavior although the wires are strongly disordered. We demonstrate that this unexpected scaling is actually contained in the conventional description of diffusive superconductors and find excellent agreement with the experimental results. In addition we propose a SQUID-like proximity structure for further experimental investigations of the effects in question.Comment: 6 pages LaTeX, 4 postscript figures; to appear in J. Low Temp. Phys. (Proceedings of WSS '96

A Scenario to the Anomalous Hall Effect in the Mixed State of Superconductors

We argue that the motion of vacancies in a pinned vortex lattice may dominate the contribution to the Hall effect in an appropriate parameter regime for a superconductor. Based on this consideration a model is constructed to explain the anomalous Hall effect without any modification of the basic vortex dynamic equation. Quantitative predictions are obtained. Present model can be directly tested by an observation of the vacancy motion.Comment: latex, 6 pages (Presented at the Miami High Tc Conf., Jan 5-11, 1995. To appear at J. Supercond.

Spin diffusion of the t-J model

The spin-diffusion constant of the 2D $t-J$ model is calculated for the first time using an analytical approach at high temperatures and a recently-developed numerical method based on the Lanczos technique combined with random sampling in the intermediate temperature regime. A simple relation, $\sigma = D_s\chi$, between spin conductivity and spin diffusion is established and used to calculate the latter. In the high-temperature and low-doping limit the calculated diffusion constant agrees with known results for the Heisenberg model. At small hole doping, $D_s$ increases approximately linearly with doping, which leads us to an important conclusion that hopping processes enhance spin diffusion at high temperatures. At modest hole doping, $\delta\sim 0.25$, diffusion exhibits a nonmonotonic temperature dependence, which indicates anomalous spin dynamics at small frequencies.Comment: 12 pages with figure

Freezing of Spinodal Decompostion by Irreversible Chemical Growth Reaction

We present a description of the freezing of spinodal decomposition in systems, which contain simultaneous irreversible chemical reactions, in the hydrodynamic limit approximation. From own results we conclude, that the chemical reaction leads to an onset of spinodal decomposition also in the case of an initial system which is completely miscible and can lead to an extreme retardation of the dynamics of the spinodal decomposition, with the probability of a general freezing of this process, which can be experimetally observed in simultaneous IPN formation.Comment: 10 page

Études de magnétisme réalisées avec des neutrons

This paper describes two series of experiments on neutron scattering by magnetic media. Series A gives the antiferromagnetic structure of FeCl 2, and the effect of a magnetic field on the spin orientations as measured with a crystal spectrometer. In series B, the critical magnetic scattering of iron near the Curie Point has been investigated with a time of flight spectrometer. As a result one gets both the range of the spin correlations and the scattering constant which is related to their decay in time.On décrit deux expériences de diffusion des neutrons par des substances magnétiques. Dans la première, on étudie au moyen d'un spectromètre à cristal la structure antiferromagnétique de FeCl2 et l'action d'un champ magnétique extérieur sur la disposition des moments magnétiques. La seconde, effectuée avec un spectromètre à temps de vol, a pour objet la diffusion critique au voisinage du point de Curie du fer. Elle permet de déterminer les deux paramètres caractérisant les fluctuations d'aimantation, la partie des corrélations et leur constante de diffusion