The role of string-like, supramolecular assemblies in reentrant supernematic liquid crystals

Using a combination of isothermal-isobaric Monte Carlo and microcanonical molecular dynamics we investigate the relation between structure and self-diffusion in various phases of a model liquid crystal using the Gay-Berne-Kihara potential. These molecules are confined to a mesoscopic slit-pore with atomically smooth substrate surfaces. As reported recently [see M. G. Mazza {\em et al.}, Phys. Rev. Lett. {\bf 105}, 227802 (2010)], a reentrant nematic (RN) phase may form at sufficiently high pressures/densities. This phase is characterized by a high degree of nematic order and a substantially enhanced self-diffusivity in the direction of the director $\hat{\bm{n}}$ which exceeds that of the lower-density nematic and an intermittent smectic A phase by about an order of magnitude. Here we demonstrate that the unique transport behavior in the RN phase may be linked to a confinement-induced packing effect which causes the formation of supramolecular, string-like conformations. The strings consist of several individual molecules that are capable of travelling in the direction of $\hat{\bm{n}}$ as individual "trains" consisting of chains of molecular "cars". Individual trains run in parallel and may pass each other at sufficiently high pressures.Comment: 24 page

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $\Omega \subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Late

Gluing Initial Data Sets for General Relativity

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Secondly, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.Comment: Final published version - PRL, 4 page

Advanced composite applications for sub-micron biologically derived microstructures

A major thrust of advanced material development is in the area of self-assembled ultra-fine particulate based composites (micro-composites). The application of biologically derived, self-assembled microstructures to form advanced composite materials is discussed. Hollow 0.5 micron diameter cylindrical shaped microcylinders self-assemble from diacetylenic lipids. These microstructures have a multiplicity of potential applications in the material sciences. Exploratory development is proceeding in application areas such as controlled release for drug delivery, wound repair, and biofouling as well as composites for electronic and magnetic applications, and high power microwave cathodes

Liquid n-hexane condensed in silica nanochannels: A combined optical birefringence and vapor sorption isotherm study

The optical birefringence of liquid n-hexane condensed in an array of parallel silica channels of 7nm diameter and 400 micrometer length is studied as a function of filling of the channels via the vapor phase. By an analysis with the generalized Bruggeman effective medium equation we demonstrate that such measurements are insensitive to the detailed geometrical (positional) arrangement of the adsorbed liquid inside the channels. However, this technique is particularly suitable to search for any optical anisotropies and thus collective orientational order as a function of channel filling. Nevertheless, no hints for such anisotropies are found in liquid n-hexane. The n-hexane molecules in the silica nanochannels are totally orientationally disordered in all condensation regimes, in particular in the film growth as well as in the the capillary condensed regime. Thus, the peculiar molecular arrangement found upon freezing of liquid n-hexane in nanochannel-confinement, where the molecules are collectively aligned perpendicularly to the channels' long axes, does not originate in any pre-alignment effects in the nanoconfined liquid due to capillary nematization.Comment: 7 pages, 5 figure

The Jang equation, apparent horizons, and the Penrose inequality

The Jang equation in the spherically symmetric case reduces to a first order equation. This permits an easy analysis of the role apparent horizons play in the (non)existence of solutions. We demonstrate that the proposed derivation of the Penrose inequality based on the Jang equation cannot work in the spherically symmetric case. Thus it is fruitless to apply this method, as it stands, to the general case. We show also that those analytic criteria for the formation of horizons that are based on the use of the Jang equation are of limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte

Results of special mechanical analyses of Luna 16 material

The studies carried out on the Luna 16 regolith have confirmed the data that were already published internationally. By means of activation analysis under irradiation in the reactor, activation analysis with a 14 MeV U-generator, and mass spectroscopy on samples of 10 or 20 mg, six main and 63 trace elements were quantitatively determined and compared with known data

On Static n-body Configurations in Relativity

The static n-body problem of General Relativity states that there are, under a reasonable energy condition, no static $n$-body configurations for $n > 1$, provided the configuration of the bodies satisfies a suitable separation condition. In this paper we solve this problem in the case that there exists a closed, noncompact, totally geodesic surface disjoint from the bodies. This covers the situation where the configuration has a reflection symmetry across a noncompact surface disjoint from the bodies.Comment: 10 pages; result generalized to allow for more than one asymptotically flat en

Statistically designed experiments to screen chemical mixtures for possible interactions.

For the accurate analysis of possible interactive effects of chemicals in a defined mixture, statistical designs are necessary to develop clear and manageable experiments. For instance, factorial designs have been successfully used to detect two-factor interactions. Particularly useful for this purpose are fractionated factorial designs, requiring only a fraction of all possible combinations of a full factorial design. Once the potential interaction has been detected with a fractionated design, a more accurate analysis can be performed for the particular binary mixtures to ensure and characterize these interactions. In this paper this approach is illustrated using an in vitro cytotoxicity assay to detect the presence of mixtures of Fusarium mycotoxins in contaminated food samples. We have investigated interactions between five mycotoxin species (Trichothecenes, Fumonisins, and Zearalenone) using the DNA synthesis inhibition assay in L929 fibroblasts. First, a central composite design was applied to identify possible interactive effects between mycotoxins in the mixtures (27 combinations from 5(5) possible combinations). Then two-factor interactions of particular interest were further analyzed by the use of a full factorial design (5 x 5 design) to characterize the nature of those interactions more precisely. Results show that combined exposure to several classes of mycotoxins generally results in effect addition with a few minor exceptions indicating synergistic interactions. In general, the nature of the interactions characterized in the full factorial design was similar to the nature of those observed in the central composite design. However, the magnitude of interaction was relatively small in the full factorial design

Lower bounds for nodal sets of eigenfunctions

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.Comment: To appear in Communications in Mathematical Physics; revised to include two additional references and update bibliographic informatio