2,046 research outputs found
Phenomenology of -CDM model: a possibility of accelerating Universe with positive pressure
Among various phenomenological models, a time-dependent model is selected here to investigate the -CDM cosmology.
Using this model the expressions for the time-dependent equation of state
parameter and other physical parameters are derived. It is shown that
in model accelerated expansion of the Universe takes place at negative
energy density, but with a positive pressure. It has also been possible to
obtain the change of sign of the deceleration parameter during cosmic
evolution.Comment: 16 Latex pages, 11 figures, Considerable modifications in the text;
Accepted in IJT
Speeding up Tidal Analyses With PCs
A technique is suggested to effect the tidal analysis with PCs by using the Fast Fourier Transform applied to tidal heights obtained through a second order interpolation of the original data. If a turbo PC XT with mathematical coprocessor is available then it is possible to analyse a 369 days classical span (8856 hourly heights) and separate 170 constituents (up to the twelfth diurnal) in 13 minutes, without jeopardizing the accuracy of the results. If the same data are weighted with a cosine taper (hanning in the time domain), then a more accurate analysis of the same data can be worked out in about 3 minutes. The analyses of non tapered and tapered data will be called normal and refined, respectively
Time scale separation and dynamic heterogeneity in the low temperature East model
We consider the non-equilibrium dynamics of the East model, a linear chain of
0-1 spins evolving under a simple Glauber dynamics in the presence of a kinetic
constraint which forbids flips of those spins whose left neighbor is 1. We
focus on the glassy effects caused by the kinetic constraint as , where is the equilibrium density of the 0's. In the physical literature
this limit is equivalent to the zero temperature limit. We first prove that,
for any given , the divergence as of three basic
characteristic time scales of the East process of length is the same. Then
we examine the problem of dynamic heterogeneity, i.e. non-trivial
spatio-temporal fluctuations of the local relaxation to equilibrium, one of the
central aspects of glassy dynamics. For any mesoscopic length scale
, , we show that the characteristic time scale of
two East processes of length and respectively are indeed
separated by a factor , , provided that
is large enough (independent of , for ). In
particular, the evolution of mesoscopic domains, i.e. maximal blocks of the
form , occurs on a time scale which depends sharply on the size of the
domain, a clear signature of dynamic heterogeneity. A key result for this part
is a very precise computation of the relaxation time of the chain as a function
of , well beyond the current knowledge, which uses induction on length
scales on one hand and a novel algorithmic lower bound on the other. Finally we
show that no form of time scale separation occurs for , i.e. at the
equilibrium scale , contrary to what was assumed in the physical
literature based on numerical simulations.Comment: 40 pages, 4 figures; minor typographical corrections and improvement
Maximal Sharing in the Lambda Calculus with letrec
Increasing sharing in programs is desirable to compactify the code, and to
avoid duplication of reduction work at run-time, thereby speeding up execution.
We show how a maximal degree of sharing can be obtained for programs expressed
as terms in the lambda calculus with letrec. We introduce a notion of `maximal
compactness' for lambda-letrec-terms among all terms with the same infinite
unfolding. Instead of defined purely syntactically, this notion is based on a
graph semantics. lambda-letrec-terms are interpreted as first-order term graphs
so that unfolding equivalence between terms is preserved and reflected through
bisimilarity of the term graph interpretations. Compactness of the term graphs
can then be compared via functional bisimulation.
We describe practical and efficient methods for the following two problems:
transforming a lambda-letrec-term into a maximally compact form; and deciding
whether two lambda-letrec-terms are unfolding-equivalent. The transformation of
a lambda-letrec-term into maximally compact form proceeds in three
steps:
(i) translate L into its term graph ; (ii) compute the maximally
shared form of as its bisimulation collapse ; (iii) read back a
lambda-letrec-term from the term graph with the property . This guarantees that and have the same unfolding, and that
exhibits maximal sharing.
The procedure for deciding whether two given lambda-letrec-terms and
are unfolding-equivalent computes their term graph interpretations and , and checks whether these term graphs are bisimilar.
For illustration, we also provide a readily usable implementation.Comment: 18 pages, plus 19 pages appendi
Northern Lambda Nord Communique, Vol.3, No.10 (December 1982)
https://digitalcommons.usm.maine.edu/nln_communique/1098/thumbnail.jp
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