13,636 research outputs found
Computability of entropy and information in classical Hamiltonian systems
We consider the computability of entropy and information in classical
Hamiltonian systems. We define the information part and total information
capacity part of entropy in classical Hamiltonian systems using relative
information under a computable discrete partition.
Using a recursively enumerable nonrecursive set it is shown that even though
the initial probability distribution, entropy, Hamiltonian and its partial
derivatives are computable under a computable partition, the time evolution of
its information capacity under the original partition can grow faster than any
recursive function. This implies that even though the probability measure and
information are conserved in classical Hamiltonian time evolution we might not
actually compute the information with respect to the original computable
partition
Two Body Relaxation in Simulated Cosmological Haloes
This paper aims at quantifying discreetness effects, born of finite particle
number, on the dynamics of dark matter haloes forming in the context of
cosmological simulations. By generalising the standard calculation of two body
relaxation to the case when the size and mass distribution are variable, and
parametrising the time evolution using established empirical relations, we find
that the dynamics of a million particle halo is noise-dominated within the
inner percent of the final virial radius. Far larger particle numbers (~ 10^8)
are required for the RMS perturbations to the velocity to drop to the 10 %
level there. The radial scaling of the relaxation time is simple and strong:
t_relax ~ r^2, implying that numbers >> 10^8 are required to faithfully model
the very inner regions; artificial relaxation may thus constitute an important
factor, contributing to the contradictory claims concerning the persistence of
a power law density cusp to the very centre. The cores of substructure haloes
can be many relaxation times old. Since relaxation first causes their expansion
before recontraction occurs, it may render them either more difficult or easier
to disrupt, depending on their orbital parameters. It may thus modify the
characteristics of the subhalo distribution and effects of interactions with
the parent. We derive simple closed form formulas for the characteristic
relaxation times, as well as for the weak N-scaling reported by Diemand et al.
when the main contribution comes from relaxing subhaloes (abridged).Comment: 11 Pages, 7 figs, Monthly Notices styl
Does the Fornax dwarf spheroidal have a central cusp or core?
The dark matter dominated Fornax dwarf spheroidal has five globular clusters
orbiting at ~1 kpc from its centre. In a cuspy CDM halo the globulars would
sink to the centre from their current positions within a few Gyrs, presenting a
puzzle as to why they survive undigested at the present epoch. We show that a
solution to this timing problem is to adopt a cored dark matter halo. We use
numerical simulations and analytic calculations to show that, under these
conditions, the sinking time becomes many Hubble times; the globulars
effectively stall at the dark matter core radius. We conclude that the Fornax
dwarf spheroidal has a shallow inner density profile with a core radius
constrained by the observed positions of its globular clusters. If the phase
space density of the core is primordial then it implies a warm dark matter
particle and gives an upper limit to its mass of ~0.5 keV, consistent with that
required to significantly alleviate the substructure problem.Comment: 6 pages, 5 figures, accepted for publication in MNRAS, high
resolution simulations include
Quantification of the performance of iterative and non-iterative computational methods of locating partial discharges using RF measurement techniques
Partial discharge (PD) is an electrical discharge phenomenon that occurs when the insulation materialof high voltage equipment is subjected to high electric field stress. Its occurrence can be an indication ofincipient failure within power equipment such as power transformers, underground transmission cableor switchgear. Radio frequency measurement methods can be used to detect and locate discharge sourcesby measuring the propagated electromagnetic wave arising as a result of ionic charge acceleration. Anarray of at least four receiving antennas may be employed to detect any radiated discharge signals, thenthe three dimensional position of the discharge source can be calculated using different algorithms. These algorithms fall into two categories; iterative or non-iterative. This paper evaluates, through simulation, the location performance of an iterative method (the standardleast squares method) and a non-iterative method (the Bancroft algorithm). Simulations were carried outusing (i) a "Y" shaped antenna array and (ii) a square shaped antenna array, each consisting of a four-antennas. The results show that PD location accuracy is influenced by the algorithm's error bound, thenumber of iterations and the initial values for the iterative algorithms, as well as the antenna arrangement for both the non-iterative and iterative algorithms. Furthermore, this research proposes a novel approachfor selecting adequate error bounds and number of iterations using results of the non-iterative method, thus solving some of the iterative method dependencies
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