Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions

We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some uniform bounds on some hydrodynamic quantities. This lower bound is independent of time and space. When the collision kernel satisfies Grad's cutoff assumption, the lower bound is a global Maxwellian and its asymptotic behavior in velocity is optimal, whereas for non-cutoff collision kernels the lower bound we obtain decreases exponentially but faster than the Maxwellian. Our results cover solutions constructed in a spatially homogeneous setting, as well as small-time or close-to-equilibrium solutions to the full Boltzmann equation in the torus. The constants are explicit and depend on the a priori bounds on the solution.Comment: 37 page

Modeling planar degenerate wetting and anchoring in nematic liquid crystals

We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at lowest order in the tensorial Landau-de Gennes order-parameter, fourth-order terms must be included. We analyze the anchoring and wetting properties of this surface potential. In the nematic phase, we find the desired degenerate planar anchoring, with positive scalar order-parameter and some surface biaxiality. In the isotropic phase, we find, in agreement with experiments, that the wetting layer may exhibit a uniaxial ordering with negative scalar order-parameter. For large enough anchoring strength, this negative ordering transits towards the planar degenerate state

The Generation of Magnetic Fields Through Driven Turbulence

We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical resolution of up to $144^3$ collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so that the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale, and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor which increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?

Nematic-Wetted Colloids in the Isotropic Phase: Pairwise Interaction, Biaxiality and Defects

We calculate the interaction between two spherical colloidal particles embedded in the isotropic phase of a nematogenic liquid. The surface of the particles induces wetting nematic coronas that mediate an elastic interaction. In the weak wetting regime, we obtain exact results for the interaction energy and the texture, showing that defects and biaxiality arise, although they are not topologically required. We evidence rich behaviors, including the possibility of reversible colloidal aggregation and dispersion. Complex anisotropic self-assembled phases might be formed in dense suspensions.Comment: 4 pages, 6 figure

Prefix-Projection Global Constraint for Sequential Pattern Mining

Sequential pattern mining under constraints is a challenging data mining task. Many efficient ad hoc methods have been developed for mining sequential patterns, but they are all suffering from a lack of genericity. Recent works have investigated Constraint Programming (CP) methods, but they are not still effective because of their encoding. In this paper, we propose a global constraint based on the projected databases principle which remedies to this drawback. Experiments show that our approach clearly outperforms CP approaches and competes well with ad hoc methods on large datasets

Bi-defects of Nematic Surfactant Bilayers

We consider the effects of the coupling between the orientational order of the two monolayers in flat nematic bilayers. We show that the presence of a topological defect on one bilayer generates a nontrivial orientational texture on both monolayers. Therefore, one cannot consider isolated defects on one monolayer, but rather associated pairs of defects on either monolayer, which we call bi-defects. Bi-defects generally produce walls, such that the textures of the two monolayers are identical outside the walls, and different in their interior. We suggest some experimental conditions in which these structures could be observed.Comment: RevTeX, 4 pages, 3 figure

Fourfold oscillations and anomalous magnetic irreversibility of magnetoresistance in the non-metallic regime of Pr1.85Ce0.15CuO4

Using magnetoresistance measurements as a function of applied magnetic field and its direction of application, we present sharp angular-dependent magnetoresistance oscillations for the electron-doped cuprates in their low-temperature non-metallic regime. The presence of irreversibility in the magnetoresistance measurements and the related strong anisotropy of the field dependence for different in-plane magnetic field orientations indicate that magnetic domains play an important role for the determination of electronic properties. These domains are likely related to the stripe phase reported previously in hole-doped cuprates.Comment: 11 pages, 5 figure

Reply to Comment on:"Nonmonotonic d_{x^2-y^2} Superconducting Order Parameter in Nd_{2-x}Ce_xCuO_4"

We confirm that all the results of scanning SQUID, tunneling, ARPES, penetration depth and Raman experiments are consistent with a nonmonotonic d_{x^2-y^2} superconducting order parameter proposed in Phys. Rev. Lett., 88, 107002 (2002).Comment: Reply to Comment by F. Venturini, R. Hackl, and U. Michelucci cond-mat/020541