Depletion forces near a soft surface

We investigate excluded-volume effects in a bidisperse colloidal suspension near a flexible interface. Inspired by a recent experiment by Dinsmore et al. (Phys. Rev, Lett. 80, 409 (1998)), we study the adsorption of a mesoscopic bead on the surface and show that depletion forces could in principle lead to particle encapsulation. We then consider the effect of surface fluctuations on the depletion potential itself and construct the density profile of a polymer solution near a soft interface. Surprisingly we find that the chains accumulate at the wall, whereas the density displays a deficit of particles at distances larger than the surface roughness. This non-monotonic behavior demonstrates that surface fluctuations can have major repercusions on the properties of a colloidal solution. On average, the additional contribution to the Gibbs adsorbance is negative. The amplitude of the depletion potential between a mesoscopic bead and the surface increases accordingly.Comment: 10 pages, 5 figure

Surface-mediated attraction between colloids

We investigate the equilibrium properties of a colloidal solution in contact with a soft interface. As a result of symmetry breaking, surface effects are generally prevailing in confined colloidal systems. In this Letter, particular emphasis is given to surface fluctuations and their consequences on the local (re)organization of the suspension. It is shown that particles experience a significant effective interaction in the vicinity of the interface. This potential of mean force is always attractive, with range controlled by the surface correlation length. We suggest that, under some circumstances, surface-induced attraction may have a strong influence on the local particle distribution

Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

Ablation debris control by means of closed thick film filtered water immersion

The performance of laser ablation generated debris control by means of open immersion techniques have been shown to be limited by flow surface ripple effects on the beam and the action of ablation plume pressure loss by splashing of the immersion fluid. To eradicate these issues a closed technique has been developed which ensured a controlled geometry for both the optical interfaces of the flowing liquid film. This had the action of preventing splashing, ensuring repeatable machining conditions and allowed for control of liquid flow velocity. To investigate the performance benefits of this closed immersion technique bisphenol A polycarbonate samples have been machined using filtered water at a number of flow velocities. The results demonstrate the efficacy of the closed immersion technique: a 93% decrease in debris is produced when machining under closed filtered water immersion; the average debris particle size becomes larger, with an equal proportion of small and medium sized debris being produced when laser machining under closed flowing filtered water immersion; large debris is shown to be displaced further by a given flow velocity than smaller debris, showing that the action of flow turbulence in the duct has more impact on smaller debris. Low flow velocities were found to be less effective at controlling the positional trend of deposition of laser ablation generated debris than high flow velocities; but, use of excessive flow velocities resulted in turbulence motivated deposition. This work is of interest to the laser micromachining community and may aide in the manufacture of 2.5D laser etched patterns covering large area wafers and could be applied to a range of wavelengths and laser types

A Smirnov-Bickel-Rosenblatt theorem for compactly-supported wavelets

In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the supremum norm of the variance term is asymptotically distributed as a Gumbel random variable. In the following, we prove a version of this result for estimators using compactly-supported wavelets, a popular tool in nonparametric statistics. Our result relies on an assumption on the nature of the wavelet, which must be verified by provably-good numerical approximations. We verify our assumption for Daubechies wavelets and symlets, with N = 6, ..., 20 vanishing moments; larger values of N, and other wavelet bases, are easily checked, and we conjecture that our assumption holds also in those cases

Finite-difference distributions for the Ginibre ensemble

The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of real and imaginary parts of second difference, as well as of its radius and of its argument (angle). For the generic N-dimensional Ginibre ensemble an exact analytical formula for second difference's distribution is derived. The comparison with real valued random variable of second difference of adjacent real valued energy levels for Gaussian orthogonal, unitary, and symplectic, ensemble of random matrices as well as for Poisson ensemble is provided.Comment: 8 pages, a number of small changes in the tex

Robust Estimators in Generalized Pareto Models

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.Comment: 26pages, 6 figure

Ab-initio study of BaTiO3 surfaces

We have carried out first-principles total-energy calculations of (001) surfaces of the tetragonal and cubic phases of BaTiO3. Both BaO-terminated (type I) and TiO2-terminated (type II) surfaces are considered, and the atomic configurations have been fully relaxed. We found no deep-gap surface states for any of the surfaces, in agreement with previous theoretical studies. However, the gap is reduced for the type-II surface, especially in the cubic phase. The surface relaxation energies are found to be substantial, i.e., many times larger than the bulk ferroelectric well depth. Nevertheless, the influence of the surface upon the ferroelectric order parameter is modest; we find only a small enhancement of the ferroelectricity near the surface.Comment: 8 pages, two-column style with 4 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#pad_sur