On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedeness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka: we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other

Geothermal studies - Yellowstone National Park /test site 11/, Wyoming

Summary report of diamond drilling in thermal areas of Yellowstone National Park, and method for determining heat flow in thermal area

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

Low-temperature phonon thermal conductivity of cuprate single crystals

The effect of sample size and surface roughness on the phonon thermal conductivity $\kappa_p$ of Nd$_2$CuO$_4$ single crystals was studied down to 50 mK. At 0.5 K, $\kappa_p$ is proportional to $\sqrt{A}$, where $A$ is the cross-sectional area of the sample. This demonstrates that $\kappa_p$ is dominated by boundary scattering below 0.5 K or so. However, the expected $T^3$ dependence of $\kappa_p$ is not observed down to 50 mK. Upon roughing the surfaces, the $T^3$ dependence is restored, showing that departures from $T^3$ are due to specular reflection of phonons off the mirror-like sample surfaces. We propose an empirical power law fit, to $\kappa_p \sim T^{\alpha}$ (where $\alpha < 3$) in cuprate single crystals. Using this method, we show that recent thermal conductivity studies of Zn doping in YBa$_2$Cu$_3$O$_y$ re-affirm the universal heat conductivity of d-wave quasiparticles at $T \to 0$.Comment: 4 pages, 4 figure

Shear strength properties of wet granular materials

We investigate shear strength properties of wet granular materials in the pendular state (i.e. the state where the liquid phase is discontinuous) as a function of water content. Sand and glass beads were wetted and tested in a direct shear cell and under various confining pressures. In parallel, we carried out three-dimensional molecular dynamics simulations by using an explicit equation expressing capillary force as a function of interparticle distance, water bridge volume and surface tension. We show that, due to the peculiar features of capillary interactions, the major influence of water content over the shear strength stems from the distribution of liquid bonds. This property results in shear strength saturation as a function of water content. We arrive at the same conclusion by a microscopic analysis of the shear strength. We propose a model that accounts for the capillary force, the granular texture and particle size polydispersity. We find fairly good agreement of the theoretical estimate of the shear strength with both experimental data and simulations. From numerical data, we analyze the connectivity and anisotropy of different classes of liquid bonds according to the sign and level of the normal force as well as the bond direction. We find that weak compressive bonds are almost isotropically distributed whereas strong compressive and tensile bonds have a pronounced anisotropy. The probability distribution function of normal forces is exponentially decreasing for strong compressive bonds, a decreasing power-law function over nearly one decade for weak compressive bonds and an increasing linear function in the range of tensile bonds. These features suggest that different bond classes do not play the same role with respect to the shear strength.Comment: 12 page

Theory of Thermoelectric Power in High-Tc Superconductors

We present a microscopic theory for the thermoelectric power (TEP) in high-Tc cuprates. Based on the general expression for the TEP, we perform the calculation of the TEP for a square lattice Hubbard model including all the vertex corrections necessary to satisfy the conservation laws. In the present study, characteristic anomalous temperature and doping dependences of the TEP in high-Tc cuprates, which have been a long-standing problem of high-Tc cuprates, are well reproduced for both hole- and electron-doped systems, except for the heavily under-doped case. According to the present analysis, the strong momentum and energy dependences of the self-energy due to the strong antiferromagnetic fluctuations play an essential role in reproducing experimental anomalies of the TEP.Comment: 5 pages, 8 figures, to appear in J. Phys. Soc. Jpn. 70 (2001) No.10. Figure 2 has been revise

Coupling between Smectic and Twist Modes in Polymer Intercalated Smectics

We analyse the elastic energy of an intercalated smectic where orientationally ordered polymers with an average orientation varying from layer to layer are intercalated between smectic planes. The lowest order terms in the coupling between polymer director and smectic layer curvature are added to the smectic elastic energy. Integration over the smectic degrees of freedom leaves an effective polymer twist energy that has to be included into the total polymer elastic energy leading to a fluctuational renormalization of the intercalated polymer twist modulus. If the polymers are chiral this in its turn leads to a renormalization of the cholesteric pitch.Comment: 8 pages, 1 fig in ps available from [email protected] Replaced version also contains title and abstract in the main tex

Substitution Effect by Deuterated Donors on Superconductivity in κ\kappa-(BEDT-TTF)2_2Cu[N(CN)2_2]Br

We investigate the superconductivity in the deuterated BEDT-TTF molecular substitution system $\kappa$-[(h8-BEDT-TTF)$_{1-x}$(d8-BEDT-TTF)$_x$]$_2$Cu[N(CN)$_2$]Br, where h8 and d8 denote fully hydrogenated and deuterated molecules, respectively. Systematic and wide range ($x$ = 0 -- 1) substitution can control chemical pressure finely near the Mott boundary, which results in the modification of the superconductivity. After cooling slowly, the increase of $T_{\textrm{c}}$ observed up to $x \sim$ 0.1 is evidently caused by the chemical pressure effect. Neither reduction of $T_{\textrm{c}}$ nor suppression of superconducting volume fraction is found below $x \sim$ 0.5. This demonstrates that the effect of disorder by substitution is negligible in the present system. With further increase of $x$, both $T_{\textrm{c}}$ and superconducting volume fraction start to decrease toward the values in $x$ = 1.Comment: J. Phys. Soc. Jp