21,009 research outputs found
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 -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 distinguishable spin-half
particles with nearest-neighbour interactions. We prove a central limit theorem
for the density of states when , 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 qubits
with nearest-neighbour interactions have two seemingly contradictory features.
Firstly in the limit we show that any translationally
invariant Hamiltonian of a chain of 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
we show that any nearest-neighbour Hamiltonian of a chain
of 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
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