Flexoelectricity and pattern formation in nematic liquid crystals

We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $\omega$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic which describes the elasticity with respects to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $\omega \to 0$ is highly singular. In distinct contrast to the dc-case, where the patterns are stationary and time-independent, they appear at finite, small $\omega$ periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electro-hydrodynamic instability in nematics, which presents a non-equilibrium dissipative transition. It will be demonstrated that $\omega$ is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes

Galactic Rotation Parameters from Data on Open Star Clusters

Currently available data on the field of velocities Vr, Vl, Vb for open star clusters are used to perform a kinematic analysis of various samples that differ by heliocentric distance, age, and membership in individual structures (the Orion, Carina--Sagittarius, and Perseus arms). Based on 375 clusters located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the Galactic rotation parameters Wo =-26.0+-0.3 km/s/kpc, W'o = 4.18+-0.17 km/s/kpc^2, W''o=-0.45+-0.06 km/s/kpc^3, the system contraction parameter K = -2.4+-0.1 km/s/kpc, and the parameters of the kinematic center Ro =7.4+-0.3 kpc and lo = 0+-1 degrees. The Galactocentric distance Ro in the model used has been found to depend significantly on the sample age. Thus, for example, it is 9.5+-0.7 kpc and 5.6+-0.3 kpc for the samples of young (50 Myr) clusters, respectively. Our study of the kinematics of young open star clusters in various spiral arms has shown that the kinematic parameters are similar to the parameters obtained from the entire sample for the Carina-Sagittarius and Perseus arms and differ significantly from them for the Orion arm. The contraction effect is shown to be typical of star clusters with various ages. It is most pronounced for clusters with a mean age of 100 Myr, with the contraction velocity being Kr = -4.3+-1.0 km/s.Comment: 14 pages, 4 figures, 2 table

Anomalous Negative Magnetoresistance Caused by Non-Markovian Effects

A theory of recently discovered anomalous low-field magnetoresistance is developed for the system of two-dimensional electrons scattered by hard disks of radius $a,$ randomly distributed with concentration $n.$ For small magnetic fields the magentoresistance is found to be parabolic and inversely proportional to the gas parameter, $\delta \rho_{xx}/\rho \sim - (\omega_c \tau)^2 / n a^2.$ With increasing field the magnetoresistance becomes linear $\delta \rho_{xx}/\rho \sim - \omega_c \tau$ in a good agreement with the experiment and numerical simulations.Comment: 4 pages RevTeX, 5 figure

Evolution of the Velocity Ellipsoids in the Thin Disk of the Galaxy and the Radial Migration of Stars

Data from the revised Geneva--Copenhagen catalog are used to study the influence of radial migration of stars on the age dependences of parameters of the velocity ellipsoids for nearby stars in the thin disk of the Galaxy, assuming that the mean radii of the stellar orbits remain constant. It is demonstrated that precisely the radial migration of stars, together with the negative metallicity gradient in the thin disk,are responsible for the observed negative correlation between the metallicities and angular momenta of nearby stars, while the angular momenta of stars that were born at the same Galactocentric distances do not depend on either age or metallicity. (abridged)Comment: Astronomy Reports, Vol. 86 No. 9, P.1117-1126 (2009

Flexoelectricity in an oxadiazole bent-core nematic liquid crystal

We have determined experimentally the magnitude of the difference in the splay and bend flexoelectric coefficients, |e1 - e3|, of an oxadiazole bent-core liquid crystal by measuring the critical voltage for the formation of flexodomains together with their wave number. The coefficient |e1 - e3| is found to be a factor of 2-3 times higher than in most conventional calamitic nematic liquid crystals, varying from 8 pCm-1 to 20 pCm-1 across the ∼60 K - wide nematic regime. We have also calculated the individual flexoelectric coefficients e1 and e3, with the dipolar and quadrupolar contributions of the bent-core liquid crystal by combining density functional theory calculations with a molecular field approach and atomistic modelling. Interestingly, the magnitude of the bend flexoelectric coefficient is found to be rather small, in contrast to common expectations for bent-core molecules. The calculations are in excellent agreement with the experimental values, offering an insight into how molecular parameters contribute to the flexoelectric coefficients and illustrating a huge potential for the prediction of flexoelectric behaviour in bent-core liquid crystals

Electron-electron interaction at decreasing kFlk_Fl

The contribution of the electron-electron interaction to conductivity is analyzed step by step in gated GaAs/InGaAs/GaAs heterostructures with different starting disorder. We demonstrate that the diffusion theory works down to $k_F l\simeq 1.5-2$, where $k_F$ is the Fermi quasimomentum, $l$ is the mean free paths. It is shown that the e-e interaction gives smaller contribution to the conductivity than the interference independent of the starting disorder and its role rapidly decreases with $k_Fl$ decrease.Comment: 5 pages, 6 figure

Galactic Kinematics from OB3 Stars with Distances determined from Interstellar Ca II Lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation {\Omega}'0 and the external reconciliation with Humphreys's distance scale for OB associations refined by Mel'nik and Dambis show that the initial distances should be reduced by \approx 20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6-2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R0=8 kpc, has allowed the following parameters to be determined:(1) the solar peculiar velocity components (U_o,V_o,W_o)=(8.9,10.3,6.8)\pm(0.6,1.0,0.4) km/s;(2) the Galactic rotation parameters {\Omega}_o=-31.5\pm0.9 km/s/kpc, {\Omega}'_o=+4.49\pm0.12 km/s/kpc^2, {\Omega}"_o=-1.05\pm0.38 km/s/kpc^3, (the corresponding Oort constants are A=17.9\pm0.5 km/s/kpc, B=-13.6\pm1.0 km/s/kpc and the circular rotation velocity of the solar neighborhood is |V_o|=252\pm14 km/s); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f_R = -12.5\pm1.1 km/s and f_{\theta}=2.0\pm1.6 km/s; the pitch angle for the two-armed spiral pattern i=-5.3\pm0.3 degrees, with the wavelength of the spiral density wave at the solar distance being {\lambda}=2.3\pm0.2 kpc; the Sun's phase in the spiral wave {\chi}_o=-91\pm4 degrees.Comment: 14 pages, 4 figures, 3 table

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem