Mathematical and computational studies of equilibrium capillary free surfaces

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated

On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Experimental Signals of Phase Transition

The connection between the thermodynamics of charged finite nuclear systems and the asymptotically measured partitions is presented. Some open questions, concerning in particular equilibrium partitions are discussed. We show a detailed comparison of the decay patterns in Au+ C,Cu,Au central collisions and in Au quasi-projectile events. Observation of abnormally large fluctuations in carefully selected samples of data is reported as an indication of a first order phase transition (negative heat capacity) in the nuclear equation of state.Comment: 8 pages, 8th International Conference on Nucleus-Nucleus Collisions, Moscow 200

Cytomegalovirus MicroRNA Expression Is Tissue Specific and Is Associated with Persistence

MicroRNAs (miRNAs) are a class of small noncoding RNAs involved in posttranscriptional regulation. miRNAs are utilized in organisms ranging from plants to higher mammals, and data have shown that DNA viruses also use this method for host and viral gene regulation. Here, we report the sequencing of the small RNAs in rat cytomegalovirus (RCMV)-infected fibroblasts and persistently infected salivary glands. We identified 24 unique miRNAs that mapped to hairpin structures found within the viral genome. While most miRNAs were detected in both samples, four were detected exclusively in the infected fibroblasts and two were specific for the infected salivary glands. The RCMV miRNAs are distributed across the viral genome on both the positive and negative strands, with clusters of miRNAs at a number of locations, including near viral genes r1 and r111. The RCMV miRNAs have a genomic positional orientation similar to that of the miRNAs described for mouse cytomegalovirus, but they do not share any substantial sequence conservation. Similar to other reported miRNAs, the RCMV miRNAs had considerable variation at their 3′ and 5′ ends. Interestingly, we found a number of specific examples of differential isoform usage between the fibroblast and salivary gland samples. We determined by real-time PCR that expression of the RCMV miRNA miR-r111.1-2 is highly expressed in the salivary glands and that miR-R87-1 is expressed in most tissues during the acute infection phase. Our study identified the miRNAs expressed by RCMV in vitro and in vivo and demonstrated that expression is tissue specific and associated with a stage of viral infection

Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations

Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible charge-to-mass ratio, the black hole quasi-normal mode spectrum is characterized entirely by the black hole mass and angular momentum and is unique to black holes. In a different theory of gravity, or if the observed radiation arises from a different source (e.g., a neutron star, strange matter or boson star), the spectrum will be inconsistent with that predicted for general relativistic black holes. We give a statistical characterization of the consistency between the noisy observation and the theoretical predictions of general relativity, together with a numerical example.Comment: 19 pages, 7 figure

Tidal deformations of neutron stars: The role of stratification and elasticity

We discuss the response of neutron stars to the tidal interaction in a compact binary system, as encoded in the Love number associated with the induced deformation. This problem is of interest for gravitational-wave astronomy as there may be a detectable imprint on the signal from the late stages of binary coalescence. Previous work has focussed on simple barotropic neutron star models, providing an understanding of the role of the stellar compactness and overall density profile. We add realism to the discussion by developing the framework required to model stars with varying composition and an elastic crust. These effects are not expected to be significant for the next generation of detectors but it is nevertheless useful to be able to quantify them. Our results show that (perhaps surprisingly) internal stratification has no impact whatsoever on the Love number. We also show that crust elasticity provides a (predictably) small correction to existing models.Comment: 16 pages, RevTeX, 3 eps figure

Higher derivative type II string effective actions, automorphic forms and E11

By dimensionally reducing the ten-dimensional higher derivative type IIA string theory effective action we place constraints on the automorphic forms that appear in the effective action in lower dimensions. We propose a number of properties of such automorphic forms and consider the prospects that E11 can play a role in the formulation of the higher derivative string theory effective action.Comment: 34 page

Virtual Texture Generated using Elastomeric Conductive Block Copolymer in Wireless Multimodal Haptic Glove.

Haptic devices are in general more adept at mimicking the bulk properties of materials than they are at mimicking the surface properties. This paper describes a haptic glove capable of producing sensations reminiscent of three types of near-surface properties: hardness, temperature, and roughness. To accomplish this mixed mode of stimulation, three types of haptic actuators were combined: vibrotactile motors, thermoelectric devices, and electrotactile electrodes made from a stretchable conductive polymer synthesized in our laboratory. This polymer consisted of a stretchable polyanion which served as a scaffold for the polymerization of poly(3,4-ethylenedioxythiophene) (PEDOT). The scaffold was synthesized using controlled radical polymerization to afford material of low dispersity, relatively high conductivity (0.1 S cm-1), and low impedance relative to metals. The glove was equipped with flex sensors to make it possible to control a robotic hand and a hand in virtual reality (VR). In psychophysical experiments, human participants were able to discern combinations of electrotactile, vibrotactile, and thermal stimulation in VR. Participants trained to associate these sensations with roughness, hardness, and temperature had an overall accuracy of 98%, while untrained participants had an accuracy of 85%. Sensations could similarly be conveyed using a robotic hand equipped with sensors for pressure and temperature

An Effective Search Method for Gravitational Ringing of Black Holes

We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it will be a direct confirmation of the existence of a black hole. Assuming that the ringdown waves are dominated by the fundamental mode with least imaginary part, we consider matched filtering and develop an optimal method to search for the ringdown waves that have damped sinusoidal wave forms. When we use the matched filtering method, the data analysis with a lot of templates required. Here we have to ensure a proper match between the filter as a template and the real wave. It is necessary to keep the detection efficiency as high as possible under limited computational costs. First, we consider the white noise case for which the matched filtering can be studied analytically. We construct an efficient method for tiling the template space. Then, using a fitting curve of the TAMA300 DT6 noise spectrum, we numerically consider the case of colored noise. We find our tiling method developed for the white noise case is still valid even if the noise is colored.Comment: 17 pages, 9 figures. Accepted to Phys. Rev. D, Note correction to Eq. (3-25), A few comments added and minor typos correcte