Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface

Theoretical flow regime diagrams for the AGCE

The major criterion for the design of the Atmospheric General Circulation Experiment is that it be possible to realize strong baroclinic instability in the apparatus. A spherical annulus configuration which allows only steady basic state flows was chosen for the first set of stability analyses. Baroclinic instability was found for this configuration and few results suggest a regime diagram very different from the cylindrical annulus regime diagram

Optical second harmonic generation probe of two-dimensional ferroelectricity

Optical second harmonic generation (SHG) is used as a noninvasive probe of two-dimensional (2D) ferroelectricity in Langmuir-Blodgett (LB) films of copolymer vinylidene fluoride with trifluorethylene. The surface 2D ferroelectric-paraelectric phase transition in the topmost layer of LB films and a thickness independent (almost 2D) transition in the bulk of these films are observed in temperature studies of SHG.Comment: 9 pages, 2 figures, Optics Letters, in prin

Dynamics of First Order Transitions with Gravity Duals

A first order phase transition usually proceeds by nucleating bubbles of the new phase which then rapidly expand. In confining gauge theories with a gravity dual, the deconfined phase is often described by a black hole. If one starts in this phase and lowers the temperature, the usual description of how the phase transition proceeds violates the area theorem. We study the dynamics of this phase transition using the insights from the dual gravitational description, and resolve this apparent contradiction.Comment: 11 pages, 1 figure. v2: minor clarifications, reference adde

Construction of a deep shaft for Crossrail

An 8·2 m diameter, 37·5 m deep shaft has been successfully constructed from within the basement of a new development, Moorhouse, near Moorgate in the City of London. Programme constraints led to the shaft being constructed after completion of the foundations, basements and most of the superstructure for the development. At its closest point the shaft is less than 2 m from the large-diameter piles that support Moorhouse, and the presence of these foundations placed tight constraints on acceptable ground movements associated with construction of the shaft. The depth of the shaft is such that it penetrates through stiff London Clay and is founded at the bottom of the Lambeth Group. The paper describes the contingency measures to deal with potentially difficult ground conditions, including the water-bearing layers of the Lambeth Group. The construction processes included a complex temporary works dewatering system around the shaft, with the option to carry out additional dewatering from within the shaft during excavation. Provision was also made for radial grouting to ‘restress’ the ground, to prevent long-term settlement of the Moorhouse piles, should the need arise. The success of the project was due, in no small part, to the detailed planning and consideration of contingency measures to deal with perceived risk

Analysis of Sub-threshold Short Gamma-ray Bursts in Fermi GBM Data

The Fermi Gamma-ray Burst Monitor (GBM) is currently the most prolific detector of Gamma-Ray Bursts (GRBs). Recently the detection rate of short GRBs (SGRBs) has been dramatically increased through the use of ground-based searches that analyze GBM continuous time tagged event (CTTE) data. Here we examine the efficiency of a method developed to search CTTE data for sub-threshold transient events in temporal coincidence with LIGO/Virgo compact binary coalescence triggers. This targeted search operates by coherently combining data from all 14 GBM detectors by taking into account the complex spatial and energy dependent response of each detector. We use the method to examine a sample of SGRBs that were independently detected by the Burst Alert Telescope on board the Neil Gehrels Swift Observatory, but which were too intrinsically weak or viewed with unfavorable instrument geometry to initiate an on-board trigger of GBM. We find that the search can successfully recover a majority of the BAT detected sample in the CTTE data. We show that the targeted search of CTTE data will be crucial in increasing the GBM sensitivity, and hence the gamma-ray horizon, to weak events such as GRB 170817A. We also examine the properties of the GBM signal possibly associated with the LIGO detection of GW150914 and show that it is consistent with the observed properties of other sub-threshold SGRBs in our sample. We find that the targeted search is capable of recovering true astrophysical signals as weak as the signal associated with GW150914 in the untriggered data.Comment: 10 pages, 9 figures, 1 table, submitted to Ap

Particle-scale structure in frozen colloidal suspensions from small angle X-ray scattering

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has mostly concentrated on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle-scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small angle X-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by any standard inter-particle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium or steady-state densification processes

Structure of boson systems beyond the mean-field

We investigate systems of identical bosons with the focus on two-body correlations. We use the hyperspherical adiabatic method and a decomposition of the wave function in two-body amplitudes. An analytic parametrization is used for the adiabatic effective radial potential. We discuss the structure of a condensate for arbitrary scattering length. Stability and time scales for various decay processes are estimated. The previously predicted Efimov-like states are found to be very narrow. We discuss the validity conditions and formal connections between the zero- and finite-range mean-field approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz, and the present method. We compare numerical results from present work with mean-field calculations and discuss qualitatively the connection with measurements.Comment: 26 pages, 6 figures, submitted to J. Phys. B. Ver. 2 is 28 pages with modified figures and discussion

Cold Bose gases with large scattering lengths

We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive s-wave scattering length $a$. At high densities, $n>>a^{-3}$, the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to $n^{2/3}$, as in Fermi systems.Comment: 4 pages, 3 figure

Random billiards with wall temperature and associated Markov chains

By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard domain, gives the probability distribution of the post-collision velocity for a given pre-collision velocity. A random billiard with microstructure (RBM) is a random billiard for which P is derived from a choice of geometric/mechanical structure on the boundary of the billiard domain. RBMs provide simple and explicit mechanical models of particle-surface interaction that can incorporate thermal effects and permit a detailed study of thermostatic action from the perspective of the standard theory of Markov chains on general state spaces. We focus on the operator P itself and how it relates to the mechanical/geometric features of the microstructure, such as mass ratios, curvatures, and potentials. The main results are as follows: (1) we characterize the stationary probabilities (equilibrium states) of P and show how standard equilibrium distributions studied in classical statistical mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine law, arise naturally as generalized invariant billiard measures; (2) we obtain some basic functional theoretic properties of P. Under very general conditions, we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert space. In a simple but illustrative example, we show that P is a compact (Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of eigenvalues of P to the features of the microstructure;(3) we explore the latter issue both analytically and numerically in a few representative examples;(4) we present a general algorithm for simulating these Markov chains based on a geometric description of the invariant volumes of classical statistical mechanics