Pattern Formation from Defect Chaos --- A Theory of Chevrons

For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the tendency to form chevron structures. We show, with the help of a coarse-grained model, that this effect can generally be expected for systems with spontaneously broken isotropy, that is lifted by a small external perturbation. The linearized model as well as a nonlinear extension are compared to simulations of a system of coupled amplitude equations which generate chevrons out of defect chaos. The mechanism of chevron formation is similar to the development of Turing patterns in reaction diffusion systems.Comment: 17 pages, Latex, 11 PS-figures, submitted to Physica

Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy

Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly nonlinear analysis leading to amplitude equations which couple the short-wavelength patterning mode with the Goldstone mode resulting from the broken isotropy. The new coefficients in these equations are calculated from the hydrodynamics. Simulations exhibit a new type of spatio-temporal chaos at onset. The results are compared with experiments.Comment: 4 pages, RevTeX, 4 PS-figures, to appear in PR

Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory.Comment: 11 pages, 4 figures, submitted to Europhys. Let

Information Content in B→VVB \to VV Decays and the Angular Moments Method

The time-dependent angular distributions of decays of neutral $B$ mesons into two vector mesons contain information about the lifetimes, mass differences, strong and weak phases, form factors, and CP violating quantities. A statistical analysis of the information content is performed by giving the ``information'' a quantitative meaning. It is shown that for some parameters of interest, the information content in time and angular measurements combined may be orders of magnitude more than the information from time measurements alone and hence the angular measurements are highly recommended. The method of angular moments is compared with the (maximum) likelihood method to find that it works almost as well in the region of interest for the one-angle distribution. For the complete three-angle distribution, an estimate of possible statistical errors expected on the observables of interest is obtained. It indicates that the three-angle distribution, unraveled by the method of angular moments, would be able to nail down many quantities of interest and will help in pointing unambiguously to new physics.Comment: LaTeX, 34 pages with 9 figure

Axial symmetry and conformal Killing vectors

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, we prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others mush vanish or else the symmetry is larger than that originally considered. The results are completely general and do not depend on Einstein's equations or any particular matter content.Comment: 15 pages, Latex, no figure

Long term monitoring of mode switching for PSR B0329+54

The mode switching phenomenon of PSR B0329+54 is investigated based on the long-term monitoring from September 2003 to April 2009 made with the Urumqi 25m radio telescope at 1540 MHz. At that frequency, the change of relative intensity between the leading and trailing components is the predominant feature of mode switching. The intensity ratios between the leading and trailing components are measured for the individual profiles averaged over a few minutes. It is found that the ratios follow normal distributions, where the abnormal mode has a wider typical width than the normal mode, indicating that the abnormal mode is less stable than the normal mode. Our data show that 84.9% of the time for PSR B0329+54 was in the normal mode and 15.1% was in the abnormal mode. From the two passages of eight-day quasi-continuous observations in 2004, and supplemented by the daily data observed with 15 m telescope at 610 MHz at Jodrell Bank Observatory, the intrinsic distributions of mode timescales are constrained with the Bayesian inference method. It is found that the gamma distribution with the shape parameter slightly smaller than 1 is favored over the normal, lognormal and Pareto distributions. The optimal scale parameters of the gamma distribution is 31.5 minutes for the abnormal mode and 154 minutes for the normal mode. The shape parameters have very similar values, i.e. 0.75^{+0.22}_{-0.17} for the normal mode and 0.84^{+0.28}_{-0.22} for the abnormal mode, indicating the physical mechanisms in both modes may be the same. No long-term modulation of the relative intensity ratios was found for both the modes, suggesting that the mode switching was stable. The intrinsic timescale distributions, for the first time constrained for this pulsar, provide valuable information to understand the physics of mode switching.Comment: 31 pages,12 figures, Accepted by the Ap