4,323 research outputs found
Efficient Decomposition of Dense Matrices over GF(2)
In this work we describe an efficient implementation of a hierarchy of
algorithms for the decomposition of dense matrices over the field with two
elements (GF(2)). Matrix decomposition is an essential building block for
solving dense systems of linear and non-linear equations and thus much research
has been devoted to improve the asymptotic complexity of such algorithms. In
this work we discuss an implementation of both well-known and improved
algorithms in the M4RI library. The focus of our discussion is on a new variant
of the M4RI algorithm - denoted MMPF in this work -- which allows for
considerable performance gains in practice when compared to the previously
fastest implementation. We provide performance figures on x86_64 CPUs to
demonstrate the viability of our approach
Topologically massive gravito-electrodynamics: exact solutions
We construct two classes of exact solutions to the field equations of
topologically massive electrodynamics coupled to topologically massive gravity
in 2 + 1 dimensions. The self-dual stationary solutions of the first class are
horizonless, asymptotic to the extreme BTZ black-hole metric, and regular for a
suitable parameter domain. The diagonal solutions of the second class, which
exist if the two Chern-Simons coupling constants exactly balance, include
anisotropic cosmologies and static solutions with a pointlike horizon.Comment: 15 pages, LaTeX, no figure
Consistent local projection stabilized finite element methods
This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while gives rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macro-element grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results
A theorem on topologically massive gravity
We show that for three dimensional space-times admitting a hypersurface
orthogonal Killing vector field Deser, Jackiw and Templeton's vacuum field
equations of topologically massive gravity allow only the trivial flat
space-time solution. Thus spin is necessary to support topological mass.Comment: published in Classical and Quantum Gravity 13 (1996) L2
A symmetric nodal conservative finite element method for the Darcy equation
This work introduces and analyzes novel stable Petrov-Galerkin EnrichedMethods (PGEM) for the Darcy problem based on the simplest but unstable continuous P1/P0 pair. Stability is recovered inside a Petrov-Galerkin framework where element-wise dependent residual functions, named multi-scale functions, enrich both velocity and pressure trial spaces. Unlike the velocity test space that is augmented with bubble-like functions, multi-scale functions correct edge residuals as well. The multi-scale functions turn out to be the well-known lowest order Raviart-Thomas basis functions for the velocity and discontinuous quadratics polynomial functions for the pressure. The enrichment strategy suggests the way to recover the local mass conservation property for nodal-based interpolation spaces. We prove that the method and its symmetric version are well-posed and achieve optimal error estimates in natural norms. Numerical validations confirm claimed theoretical results
Micro-Brillouin spectroscopy mapping of the residual density field induced by Vickers indentation in a soda-lime silicate glass
High-resolution Brillouin scattering is used to achieve 3-dimensional maps of
the longitudinal acoustic mode frequency shift in soda-lime silicate glasses
subject to Vickers indentations. Assuming that residual stress-induced effects
are simply proportional to density changes, residual densification fields are
obtained. The density gradient is nearly isotropic, confirming earlier optical
observations made on a similar glass. The results show that Brillouin
micro-spectroscopy opens the way to a fully quantitative comparison of
experimental data with predictions of mechanical models for the identification
of a constitutive law.Comment: 4 pages, 3 figures, revised version, to appear in Appl. Phys. Let
Black hole mass and angular momentum in 2+1 gravity
We propose a new definition for the mass and angular momentum of neutral or
electrically charged black holes in 2+1 gravity with two Killing vectors. These
finite conserved quantities, associated with the SL(2,R) invariance of the
reduced mechanical system, are shown to be identical to the quasilocal
conserved quantities for an improved gravitational action corresponding to
mixed boundary conditions. They obey a general Smarr-like formula and, in all
cases investigated, are consistent with the first law of black hole
thermodynamics. Our framework is applied to the computation of the mass and
angular momentum of black hole solutions to several field-theoretical models.Comment: 23 pages, 3 references added, to be published in Physical Review
Density modulations in an elongated Bose-Einstein condensate released from a disordered potential
We observe large density modulations in time-of-flight images of elongated
Bose-Einstein condensates, initially confined in a harmonic trap and in the
presence of weak disorder. The development of these modulations during the
time-of-flight and their dependence with the disorder are investigated. We
render an account of this effect using numerical and analytical calculations.
We conclude that the observed large density modulations originate from the weak
initial density modulations induced by the disorder, and not from initial phase
fluctuations (thermal or quantum).Comment: Published version; 4+ pages; 4 figure
Gravitating Chern-Simons vortices
The construction of self-dual vortex solutions to the Chern-Simons-Higgs
model (with a suitable eighth-order potential) coupled to Einstein gravity in
(2 + 1) dimensions is reconsidered. We show that the self-duality condition may
be derived from the sole assumption . Next, we derive a family of
exact, doubly self-dual vortex solutions, which interpolate between the
symmetrical and asymmetrical vacua. The corresponding spacetimes have two
regions at spatial infinity. The eighth-order Higgs potential is positive
definite, and closed timelike curves are absent, if the gravitational constant
is chosen to be negative.Comment: 11 pages, LaTe
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