31,046 research outputs found
Multifractal Properties of Aperiodic Ising Model: role of geometric fluctuations
The role of the geometric fluctuations on the multifractal properties of the
local magnetization of aperiodic ferromagnetic Ising models on hierachical
lattices is investigated. The geometric fluctuations are introduced by
generalized Fibonacci sequences. The local magnetization is evaluated via an
exact recurrent procedure encompassing a real space renormalization group
decimation. The symmetries of the local magnetization patterns induced by the
aperiodic couplings is found to be strongly (weakly) different, with respect to
the ones of the corresponding homogeneous systems, when the geometric
fluctuations are relevant (irrelevant) to change the critical properties of the
system. At the criticality, the measure defined by the local magnetization is
found to exhibit a non-trivial F(alpha) spectra being shifted to higher values
of alpha when relevant geometric fluctuations are considered. The critical
exponents are found to be related with some special points of the F(alpha)
function and agree with previous results obtained by the quite distinct
transfer matrix approach.Comment: 10 pages, 7 figures, 3 Tables, 17 reference
Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
Though loop quantization of several spacetimes has exhibited existence of a
bounce via an explicit evolution of states using numerical simulations, the
question about the way central singularity is resolved in the black hole
interior has remained open. The quantum Hamiltonian constraint in loop
quantization turns out to be a finite difference equation whose stability is
important to understand to gain insights on the viability of the underlying
quantization and resulting physical implications. We take first steps towards
addressing these issues for a loop quantization of the Schwarzschild interior
recently given by Corichi and Singh. Von-Neumann stability analysis is
performed using separability of solutions as well as a full two dimensional
quantum difference equation. This results in a stability condition for black
holes which have a very large mass compared to the Planck mass. For black holes
of smaller masses evidence of numerical instability is found. In addition,
stability analysis for macroscopic black holes leads to a constraint on the
choice of the allowed states in numerical evolution. With the caveat of using
kinematical norm, sharply peaked Gaussian states are evolved using the quantum
difference equation and singularity resolution is obtained. A bounce is found
for one of the triad variables, but for the other triad variable singularity
resolution amounts to a non-singular passage through the zero volume. States
are found to be peaked at the classical trajectory for a long time before and
after the singularity resolution, and retain their semi-classical character
across the zero volume. Our main result is that quantum bounce occurs in loop
quantized Schwarzschild interior at least for macroscopic black holes.Comment: 10 pages, 10 figures; Discussion of results expanded. To appear in
CQ
Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics
The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool
for aeroacoustic computations. However, the LBM has been shown to present
accuracy and stability issues in the medium-low Mach number range, that is of
interest for aeroacoustic applications. Several solutions have been proposed
but often are too computationally expensive, do not retain the simplicity and
the advantages typical of the LBM, or are not described well enough to be
usable by the community due to proprietary software policies. We propose to use
an original regularized collision operator, based on the expansion in Hermite
polynomials, that greatly improves the accuracy and stability of the LBM
without altering significantly its algorithm. The regularized LBM can be easily
coupled with both non-reflective boundary conditions and a multi-level grid
strategy, essential ingredients for aeroacoustic simulations. Excellent
agreement was found between our approach and both experimental and numerical
data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder
and the 3D turbulent jet. Finally, most of the aeroacoustic computations with
LBM have been done with commercial softwares, while here the entire theoretical
framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of
America (in press
An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials
A fully parallel version of the contact dynamics (CD) method is presented in
this paper. For large enough systems, 100% efficiency has been demonstrated for
up to 256 processors using a hierarchical domain decomposition with dynamic
load balancing. The iterative scheme to calculate the contact forces is left
domain-wise sequential, with data exchange after each iteration step, which
ensures its stability. The number of additional iterations required for
convergence by the partially parallel updates at the domain boundaries becomes
negligible with increasing number of particles, which allows for an effective
parallelization. Compared to the sequential implementation, we found no
influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics
(2011
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