12,722 research outputs found
Comparative Monte Carlo Efficiency by Monte Carlo Analysis
We propose a modified power method for computing the subdominant eigenvalue
of a matrix or continuous operator. Here we focus on defining
simple Monte Carlo methods for its application. The methods presented use
random walkers of mixed signs to represent the subdominant eigenfuction.
Accordingly, the methods must cancel these signs properly in order to sample
this eigenfunction faithfully. We present a simple procedure to solve this sign
problem and then test our Monte Carlo methods by computing the of
various Markov chain transition matrices. We first computed for
several one and two dimensional Ising models, which have a discrete phase
space, and compared the relative efficiencies of the Metropolis and heat-bath
algorithms as a function of temperature and applied magnetic field. Next, we
computed for a model of an interacting gas trapped by a harmonic
potential, which has a mutidimensional continuous phase space, and studied the
efficiency of the Metropolis algorithm as a function of temperature and the
maximum allowable step size . Based on the criterion, we
found for the Ising models that small lattices appear to give an adequate
picture of comparative efficiency and that the heat-bath algorithm is more
efficient than the Metropolis algorithm only at low temperatures where both
algorithms are inefficient. For the harmonic trap problem, we found that the
traditional rule-of-thumb of adjusting so the Metropolis acceptance
rate is around 50% range is often sub-optimal. In general, as a function of
temperature or , for this model displayed trends defining
optimal efficiency that the acceptance ratio does not. The cases studied also
suggested that Monte Carlo simulations for a continuum model are likely more
efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure
Horizon energy and angular momentum from a Hamiltonian perspective
Classical black holes and event horizons are highly non-local objects,
defined in terms of the causal past of future null infinity. Alternative,
(quasi)local definitions are often used in mathematical, quantum, and numerical
relativity. These include apparent, trapping, isolated, and dynamical horizons,
all of which are closely associated to two-surfaces of zero outward null
expansion. In this paper we show that three-surfaces which can be foliated with
such two-surfaces are suitable boundaries in both a quasilocal action and a
phase space formulation of general relativity. The resulting formalism provides
expressions for the quasilocal energy and angular momentum associated with the
horizon. The values of the energy and angular momentum are in agreement with
those derived from the isolated and dynamical horizon frameworks.Comment: 39 pages, 3 figures, Final Version : content essentially unchanged
but many small improvements made in response to referees, a few references
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Black brane entropy and hydrodynamics: the boost-invariant case
The framework of slowly evolving horizons is generalized to the case of black
branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The
results are used to analyze the behavior of both event and apparent horizons in
the gravity dual to boost-invariant flow. These considerations are motivated by
the fact that at second order in the gradient expansion the hydrodynamic
entropy current in the dual Yang-Mills theory appears to contain an ambiguity.
This ambiguity, in the case of boost-invariant flow, is linked with a similar
freedom on the gravity side. This leads to a phenomenological definition of the
entropy of black branes. Some insights on fluid/gravity duality and the
definition of entropy in a time-dependent setting are elucidated.Comment: RevTeX, 42 pages, 4 figure
The strong coupling constant from lattice QCD with N_f=2 dynamical quarks
We compute for two flavors of light dynamical quarks
using non-perturbatively improved Wilson fermions. We improve on a
recent calculation by employing Pad\'e-improved two-loop and three-loop
perturbation theory to convert the lattice numbers to the scheme.Comment: Contribution to Lattice 2001 (matrix elements), typo correcte
A return to strong radio flaring by Circinus X-1 observed with the Karoo Array Telescope test array KAT-7
Circinus X-1 is a bright and highly variable X-ray binary which displays
strong and rapid evolution in all wavebands. Radio flaring, associated with the
production of a relativistic jet, occurs periodically on a ~17-day timescale. A
longer-term envelope modulates the peak radio fluxes in flares, ranging from
peaks in excess of a Jansky in the 1970s to an historic low of milliJanskys
during the years 1994 to 2007. Here we report first observations of this source
with the MeerKAT test array, KAT-7, part of the pathfinder development for the
African dish component of the Square Kilometre Array (SKA), demonstrating
successful scientific operation for variable and transient sources with the
test array. The KAT-7 observations at 1.9 GHz during the period 13 December
2011 to 16 January 2012 reveal in temporal detail the return to the
Jansky-level events observed in the 1970s. We compare these data to
contemporaneous single-dish measurements at 4.8 and 8.5 GHz with the HartRAO
26-m telescope and X-ray monitoring from MAXI. We discuss whether the overall
modulation and recent dramatic brightening is likely to be due to an increase
in the power of the jet due to changes in accretion rate or changing Doppler
boosting associated with a varying angle to the line of sight.Comment: 7 pages, 5 figures, accepted for publication in MNRAS 14 May 201
Monte Carlo Determination of Multiple Extremal Eigenpairs
We present a Monte Carlo algorithm that allows the simultaneous determination
of a few extremal eigenpairs of a very large matrix without the need to compute
the inner product of two vectors or store all the components of any one vector.
The new algorithm, a Monte Carlo implementation of a deterministic one we
recently benchmarked, is an extension of the power method. In the
implementation presented, we used a basic Monte Carlo splitting and termination
method called the comb, incorporated the weight cancellation method of Arnow
{\it et al.}, and exploited a new sampling method, the sewing method, that does
a large state space sampling as a succession of small state space samplings. We
illustrate the effectiveness of the algorithm by its determination of the two
largest eigenvalues of the transfer matrices for variously-sized
two-dimensional, zero field Ising models. While very likely useful for other
transfer matrix problems, the algorithm is however quite general and should
find application to a larger variety of problems requiring a few dominant
eigenvalues of a matrix.Comment: 22 pages, no figure
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