Capture of liquid hydrogen boiloff with metal hydride absorbers

A procedure which uses metal hydrides to capture some of this low pressure (,1 psig) hydrogen for subsequent reliquefaction is described. Of the five normally occurring sources of boil-off vapor the stream associated with the off-loading of liquid tankers during dewar refill was identified as the most cost effective and readily recoverable. The design, fabrication and testing of a proof-of-concept capture device, operating at a rate that is commensurate with the evolution of vapor by the target stream, is described. Liberation of the captured hydrogen gas at pressure .15 psig at normal temperatures (typical liquefier compressor suction pressure) are also demonstrated. A payback time of less than three years is projected

Universal interface width distributions at the depinning threshold

We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well approximated by a generalized Gaussian theory of independant modes which decay with a characteristic propagator G(q)=1/q^(d+2 zeta); zeta, the roughness exponent, is computed independently. A functional renormalization analysis explains this result and allows to compute the small deviations, i.e. a universal kurtosis ratio, in agreement with numerics. We stress the importance of the Gaussian theory to interpret numerical data and experiments.Comment: 4 pages revtex4. See also the following article cond-mat/030146

Free-energy distribution of the directed polymer at high temperature

We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x = T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with $\delta$-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit. The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to Tracy Widom established, 1 figure changed

Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator

We have measured the center-of-mass fluctuations of the height of a contact line at depinning for two different systems: liquid hydrogen on a rough cesium substrate and isopropanol on a silicon wafer grafted with silanized patches. The contact line is subject to a confining quadratic well, provided by gravity. From the second cumulant of the height fluctuations, we measure the renormalized disorder correlator Delta(u), predicted by the Functional RG theory to attain a fixed point, as soon as the capillary length is large compared to the Larkin length set by the microscopic disorder. The experiments are consistent with the asymptotic form for Delta(u) predicted by Functional RG, including a linear cusp at u=0. The observed small deviations could be used as a probe of the underlying physical processes. The third moment, as well as avalanche-size distributions are measured and compared to predictions from Functional RG.Comment: 6 pages, 14 figure

Higher correlations, universal distributions and finite size scaling in the field theory of depinning

Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation functions of the displacement field can be computed. Drastic simplifications occur, unveiling much simpler diagrammatic rules than anticipated. This is applied to the universal scaled width-distribution. The expansion in d=4-epsilon predicts that the scaled distribution coincides to the lowest orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta), zeta being the roughness exponent. The deviations from this Gaussian result are small and involve higher correlation functions, which are computed here for different boundary conditions. Other universal quantities are defined and evaluated: We perform a general analysis of the stability of the fixed point. We find that the correction-to-scaling exponent is omega=-epsilon and not -epsilon/3 as used in the analysis of some simulations. A more detailed study of the upper critical dimension is given, where the roughness of interfaces grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146

Depinning of elastic manifolds

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy, we find values of the roughness exponent between the one-loop and the two-loop functional renormalization group result, in good agreement with earlier cellular automata simulations. We find that the harmonic model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched KPZ class.Comment: 4 pages, 4 figure

Roughness at the depinning threshold for a long-range elastic string

In this paper, we compute the roughness exponent zeta of a long-range elastic string, at the depinning threshold, in a random medium with high precision, using a numerical method which exploits the analytic structure of the problem (`no-passing' theorem), but avoids direct simulation of the evolution equations. This roughness exponent has recently been studied by simulations, functional renormalization group calculations, and by experiments (fracture of solids, liquid meniscus in 4He). Our result zeta = 0.390 +/- 0.002 is significantly larger than what was stated in previous simulations, which were consistent with a one-loop renormalization group calculation. The data are furthermore incompatible with the experimental results for crack propagation in solids and for a 4He contact line on a rough substrate. This implies that the experiments cannot be described by pure harmonic long-range elasticity in the quasi-static limit.Comment: 4 pages, 3 figure

Width distribution of contact lines on a disordered substrate

We have studied the roughness of a contact line of a liquid meniscus on a disordered substrate by measuring its width distribution. The comparison between the measured width distribution and the width distribution calculated in previous works, extended here to the case of open boundary conditions, confirms that the Joanny-de Gennes model is not sufficient to describe the dynamics of contact lines at the depinning threshold. This conclusion is in agreement with recent measurements which determine the roughness exponent by extrapolation to large system sizes.Comment: 4 pages, 3 figure

Shock statistics in higher-dimensional Burgers turbulence

We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.Comment: 4 pages, 8 figure

Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers

We consider three independent Brownian walkers moving on a line. The process terminates when the left-most walker (the `Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D_1 (the Leader), D_2 and D_3 of the three walkers, we compute the probability distribution P(m|y_2,y_3) of the maximum distance m between the Leader and the current right-most particle (the `Laggard') during the process, where y_2 and y_3 are the initial distances between the leader and the other two walkers. The result has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where \delta = (2\pi-\theta)/(\pi-\theta) and \theta = cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also determined exactly