Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy

A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure \mu_{\nu} whose covariance is given in terms of the enstrophy. Pathwise uniqueness for \mu_{\nu}-a.e. initial velocity is proven for solutions having \mu_{\nu} as invariant measure.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000037

Damage in porous media due to salt crystallization

We investigate the origins of salt damage in sandstones for the two most common salts: sodium chloride and sulfate. The results show that the observed difference in damage between the two salts is directly related to the kinetics of crystallization and the interfacial properties of the salt solutions and crystals with respect to the stone. We show that, for sodium sulfate, the existence of hydrated and anhydrous crystals and specifically their dissolution and crystallization kinetics are responsible for the damage. Using magnetic resonance imaging and optical microscopy we show that when water imbibes sodium sulfate contaminated sandstones, followed by drying at room temperature, large damage occurs in regions where pores are fully filled with salts. After partial dissolution, anhydrous sodium sulfate salt present in these regions gives rise to a very rapid growth of the hydrated phase of sulfate in the form of clusters that form on or close to the remaining anhydrous microcrystals. The rapid growth of these clusters generates stresses in excess of the tensile strength of the stone leading to the damage. Sodium chloride only forms anhydrous crystals that consequently do not cause damage in the experiments

Aging of rotational diffusion in colloidal gels and glasses

We study the rotational diffusion of aging Laponite suspensions for a wide range of concentrations using depolarized dynamic light scattering. The measured orientational correlation functions undergo an ergodic to non-ergodic transition that is characterized by a concentration-dependent ergodicity-breaking time. We find that the relaxation times associated with rotational degree of freedom as a function of waiting time, when scaled with their ergodicity-breaking time, collapse on two distinct master curves. These master curves are similar to those previously found for the translational dynamics; The two different classes of behavior were attributed to colloidal gels and glasses. Therefore, the aging dynamics of rotational degree of freedom provides another signature of the distinct dynamical behavior of colloidal gels and glasses.Comment: 12 pages, 7 figure

On the origin of the extremely different solubilities of polyethers in water

The solubilities of polyethers are surprisingly counter-intuitive. The best-known example is the difference between polyethylene glycol ([–CH2–CH2–O–]n) which is infinitely soluble, and polyoxymethylene ([–CH2–O–]n) which is completely insoluble in water, exactly the opposite of what one expects from the C/O ratios of these molecules. Similar anomalies exist for oligomeric and cyclic polyethers. To solve this apparent mystery, we use femtosecond vibrational and GHz dielectric spectroscopy with complementary ab initio calculations and molecular dynamics simulations. We find that the dynamics of water molecules solvating polyethers is fundamentally different depending on their C/O composition. The ab initio calculations and simulations show that this is not because of steric effects (as is commonly believed), but because the partial charge on the O atoms depends on the number of C atoms by which they are separated. Our results thus show that inductive effects can have a major impact on aqueous solubilities

NMR evidence for Friedel-like oscillations in the CuO chains of ortho-II YBa2_2Cu3_3O6.5_{6.5}

Nuclear magnetic resonance (NMR) measurements of CuO chains of detwinned Ortho-II YBa$_2$Cu$_3$O$_{6.5}$ (YBCO6.5) single crystals reveal unusual and remarkable properties. The chain Cu resonance broadens significantly, but gradually, on cooling from room temperature. The lineshape and its temperature dependence are substantially different from that of a conventional spin/charge density wave (S/CDW) phase transition. Instead, the line broadening is attributed to small amplitude static spin and charge density oscillations with spatially varying amplitudes connected with the ends of the finite length chains. The influence of this CuO chain phenomenon is also clearly manifested in the plane Cu NMR.Comment: 4 pages, 3 figures, refereed articl

Failure time and microcrack nucleation

The failure time of samples of heterogeneous materials (wood, fiberglass) is studied as a function of the applied stress. It is shown that in these materials the failure time is predicted with a good accuracy by a model of microcrack nucleation proposed by Pomeau. It is also shown that the crack growth process presents critical features when the failure time is approached.Comment: 13 pages, 4 figures, submitted to Europhysics Letter

Planes, Chains, and Orbits: Quantum Oscillations and High Magnetic Field Heat Capacity in Underdoped YBCO

The underlying physics of the magnetic-field-induced resistive state in high temperature cuprate superconductors remains a mystery. One interpretation is that the application of magnetic field destroys the d-wave superconducting gap to uncover a Fermi surface that behaves like a conventional (i.e.Fermi Liquid) metal (1). Another view is that an applied magnetic field destroys long range superconducting phase coherence, but the superconducting gap amplitude survives (2, 3). By measuring the specific heat of ultra-clean YBa2Cu3O6.56 (YBCO 6.56), we obtain a measure of the quasi-particle density of states from the superconducting state well into the magnetic-field-induced resistive state. We have found that at very high magnetic fields the specific heat exhibits both the conventional temperature dependence and quantum oscillations expected for a Fermi Liquid. On the other hand, the magnetic field dependence of the quasi-particle density of states follows a \sqrt{H} behavior that persists right through the zero-resistance transition, evidencing the fully developed d-wave superconducting gap over the entire magnetic field range measured. The coexistence of these two phenomena pose a rigorous thermodynamic constraint on theories of high-magnetic-field resistive state in the cuprates

Aging dynamics in a colloidal glass of Laponite

The aging dynamics of colloidal suspensions of Laponite, a synthetic clay, is investigated using dynamic light stattering (DLS) and viscometry after a quench into the glassy phase. DLS allows to follow the diffusion of Laponite particles and reveals that there are two modes of relaxation. The fast mode corresponds to a rapid diffusion of particles within "cages" formed by the neighboring particles. The slow mode corresponds to escape from the cages: its average relaxation time increases exponentially fast with the age of the glass. In addition, the slow mode has a broad distribution of relaxation times, its distribution becoming larger as the system ages. Measuring the concomitant increase of viscosity as the system ages, we can relate the slowing down of the particle dynamics to the viscosity.Comment: 9 pages, 8 Postscript figures, submitted to Phys. Rev.