Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom that can be eliminated locally (cell-wise), thereby significantly reducing the size of the global problem. Although the linear system becomes more complex to analyze after static condensation of these element degrees-of-freedom, the pressure Schur complement of the original and reduced problem are the same. Using this fact, we prove spectral equivalence of this Schur complement to two simple matrices, which is then used to formulate optimal preconditioners for the statically condensed problem. Numerical simulations in two and three spatial dimensions demonstrate the good performance of the proposed preconditioners

An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field, pointwise satisfaction of the continuity equation and \emph{a priori} error estimates for the velocity that are independent of the pressure. The embedded--hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees-of-freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers. The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show computational efficiency gains over a full hybridized formulation

Intonation development from five to thirteen

Research undertaken to date suggests that important developments in the understanding and use of intonation may take place after the age of 5;0. The present study aims to provide a more comprehensive account of these developments. A specially designed battery of prosodic tasks was administered to four groups of thirty children, from London (U.K.), with mean ages of 5;6, 8;7, 10;10 and 13;9. The tasks tap comprehension and production of functional aspects of intonation, in four communicative areas: CHUNKING (i.e. prosodic phrasing), AFFECT, INTERACTION and FOCUS. Results indicate that there is considerable variability among children within each age band on most tasks. The ability to produce intonation functionally is largely established in five-year-olds, though some specific functional contrasts are not mastered until C.A. 8;7. Aspects of intonation comprehension continue to develop up to C.A. 10;10, correlating with measures of expressive and receptive language development

An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system

We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the whole domain. In the proposed scheme, coupling between the Stokes and Darcy domains is achieved naturally through the EDG-HDG facet variables. \emph{A priori} error analysis shows optimal convergence rates, and that the velocity error does not depend on the pressure. The error analysis is verified through numerical examples on unstructured grids for different orders of polynomial approximation

Quantised vortices and mutual friction in relativistic superfluids

We consider the detailed dynamics of an array of quantised superfluid vortices in the framework of general relativity, as required for quantitative modelling of realistic neutron star cores. Our model builds on the variational approach to relativistic (multi-) fluid dynamics, where the vorticity plays a central role. The description provides a natural extension of, and as it happens a better insight into, existing Newtonian models. In particular, we account for the mutual friction associated with scattering of a second "normal" component in the mixture off of the superfluid vortices.Comment: 9 pages, RevTe

Life Science Payloads Planning Study Integration Facility Survey: Executive Summary

Analyses of proposed life science shuttle era payload operations are discussed. A summary of results from a survey conducted to: (1) examine facility and equipment resources needed for life science payload integration, checkout, test and mission support activities; (2) identify presently available resources; and (3) determine methods by which operational era status may be implemented based on currently available resources, is presented

Random matrices and quantum spin chains

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the density of states when $n \rightarrow\infty$, giving explicit bounds on the rate of approach to the limit. Universality within a class of probability measures and the extension to more general interaction geometries are established. The level spacing distributions of the Gaussian Orthogonal, Unitary and Symplectic Ensembles are observed numerically for the energy levels in these ensembles.Comment: Updated figures, as accepted in 'Markov Processes and Related Fields' on 3 March 201

Spectra and eigenstates of spin chain Hamiltonians

We prove that translationally invariant Hamiltonians of a chain of $n$ qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $n\rightarrow\infty$ we show that any translationally invariant Hamiltonian of a chain of $n$ qubits has an eigenbasis such that almost all eigenstates have maximal entanglement between fixed-size sub-blocks of qubits and the rest of the system; in this sense these eigenstates are like those of completely general Hamiltonians (i.e. Hamiltonians with interactions of all orders between arbitrary groups of qubits). Secondly in the limit $n\rightarrow\infty$ we show that any nearest-neighbour Hamiltonian of a chain of $n$ qubits has a Gaussian density of states; thus as far as the eigenvalues are concerned the system is like a non-interacting one. The comparison applies to chains of qubits with translationally invariant nearest-neighbour interactions, but we show that it is extendible to much more general systems (both in terms of the local dimension and the geometry of interaction). Numerical evidence is also presented which suggests that the translational invariance condition may be dropped in the case of nearest-neighbour chains.Comment: Updated figures, as accepted in 'Communications in Mathematical Physics' on 5 January 201

Automated code generation for discontinuous Galerkin methods

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates efficient code in a standard programming language. This facilitates the rapid generation of efficient code for general equations in varying spatial dimensions. Key concepts underlying the compiler approach and the automated generation of computer code are elaborated. The approach is demonstrated for a range of common problems, including the Poisson, biharmonic, advection--diffusion and Stokes equations

Gluino decays with heavier scalar superpartners

We compute gluino decay widths in supersymmetric theories with arbitrary flavor and CP violation angles. Our emphasis is on theories with scalar superpartner masses heavier than the gluino such that tree-level two-body decays are not allowed, which is relevant, for example, in split supersymmetry. We compute gluino decay branching fractions in several specific examples and show that it is plausible that the only accessible signal of supersymmetry at the LHC could be four top quarks plus missing energy. We show another example where the only accessible signal for supersymmetry is two gluon jets plus missing energy.Comment: 17 pages, 8 figures. Added references and minor typos and errors corrected (no change in numerical results