Evaporation waves in superheated dodecane

We have observed propagating adiabatic evaporation waves in superheated liquid dodecane, C_(12)H_(26). Experiments were performed with a rapid decompression apparatus at initial temperatures of 180–300°C. Saturated dodecane in a tube was suddenly depressurized by rupturing a diaphragm. Motion pictures and still photographic images, and pressure and temperature data were obtained during the evaporation event that followed depressurization. Usually, a front or wave of evaporation started at the liquid free surface and propagated into the undisturbed regions of the metastable liquid. The evaporation wave front moved with a steady mean velocity but the front itself was unstable and fluctuating in character. At low superheats, no waves were observed until a threshold superheat was exceeded. At moderate superheats, subsonic downstream states were observed. At higher superheats, the downstream flow was choked, corresponding to a Chapman–Jouguet condition. At the most extreme superheat tested, a vapour content of over 90% was estimated from the measured data, indicating a nearly complete evaporation wave. Our results are interpreted by modelling the evaporation wave as a discontinuity, or jump, between a superheated liquid state and a two-phase liquid–vapour downstream state. Reasonable agreement is found between the model and observations; however, there is a fundamental indeterminacy that prevents the prediction of the observed wave speeds

Signatures of the self-modulation instability of relativistic proton bunches in the AWAKE experiment

We investigate numerically the detection of the self-modulation instability in a virtual detector located downstream from the plasma in the context of AWAKE. We show that the density structures, appearing in the temporally resolving virtual detector, map the transverse beam phase space distribution at the plasma exit. As a result, the proton bunch radius that appears to grow along the bunch in the detector results from the divergence increase along the bunch, related with the spatial growth of the self-modulated wakefields. In addition, asymmetric bunch structures in the detector are a result of asymmetries of the bunch divergence, and do not necessarily reflect asymmetric beam density distributions in the plasma.Comment: Accepted for publication in NIM-A for the proceedings of the 3rd European Advanced Accelerator Workshop. 5 pages, 2 figure

Coupling theory for counterion distributions based in Tsallis statistics

It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB approach to account for coupling of arbitrary strength by making use of Tsallis q-exponential distributions. Both the weak coupling and the strong coupling limits are reproduced. For arbitrary coupling we also provide simple analytical expressions which are compared to recent Monte Carlo simulations by A. G. Moreira and R. R. Netz [Europhys. Lett. 52 (2000) 705]. Excellent agreement with these is obtained.Comment: 17 pages, 2 figures, 1 table. Final version, accepted for publication in Physica

Asymptotic power of sphericity tests for high-dimensional data

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and contiguous alternatives, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643-1697] the limiting process is degenerate, and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the limiting process is nondegenerate, and the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial (i.e., equals the asymptotic size), whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1100 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal Inference in Regression Models with Nearly Integrated Regressors

This paper considers the problem of conducting inference on the regression coefficient in a bivariate regression model with a highly persistent regressor. Gaussian power envelopes are obtained for a class of testing procedures satisfying a conditionality restriction. In addition, the paper proposes feasible testing procedures that attain these Gaussian power envelopes whether or not the innovations of the regression model are normally distributed.

Optimal Inference in Regression Models with Nearly Integrated Regressors

This paper considers the problem of conducting inference on the regression coeffcient in a bivariate regression model with a highly persistent regressor. Gaussian power envelopes are obtained for a class of testing procedures satisfying a conditionality restriction. In addition, the paper proposes feasible testing procedures that attain these Gaussian power envelopes whether or not the innovations of the regression model are normally distributed.