57,645 research outputs found
The Universe of Approximations
AbstractThe idea of approximate entailment has been in [13] as a way of modeling the reasoning of an agent with limited resources. They proposed a system in which a family of logics, parameterized by a set of propositional letters, approximates classical logic as the size of the set increases.In this paper, we take the idea further, extending two of their systems to deal with full propositional logic, giving them semantics and sound and complete proof methods based on tableaux. We then present a more general system of which the two previous systems are particular cases and show how it can be used to formalize heuristics used in theorem proving
Beyond Zel'dovich-Type Approximations in Gravitational Instability Theory --- Pad\'e Prescription in Spheroidal Collapse ---
Among several analytic approximations for the growth of density fluctuations
in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate
scheme is known to be unusually accurate even in mildly non-linear regime. This
approximation is very similar to the Pad\'e approximation in appearance. We
first establish, however, that these two are actually different and independent
approximations with each other by using a model of spheroidal mass collapse.
Then we propose Pad\'e-prescribed Zel'dovich-type approximations and
demonstrate, within this model, that they are much accurate than any other
known nonlinear approximations.Comment: 4 pages, latex, 3 figures include
Archipelagian Cosmology: Dynamics and Observables in a Universe with Discretized Matter Content
We consider a model of the Universe in which the matter content is in the
form of discrete islands, rather than a continuous fluid. In the appropriate
limits the resulting large-scale dynamics approach those of a
Friedmann-Robertson-Walker (FRW) universe. The optical properties of such a
space-time, however, do not. This illustrates the fact that the optical and
`average' dynamical properties of a relativistic universe are not equivalent,
and do not specify each other uniquely. We find the angular diameter distance,
luminosity distance and redshifts that would be measured by observers in these
space-times, using both analytic approximations and numerical simulations.
While different from their counterparts in FRW, the effects found do not look
like promising candidates to explain the observations usually attributed to the
existence of Dark Energy. This incongruity with standard FRW cosmology is not
due to the existence of any unexpectedly large structures or voids in the
Universe, but only to the fact that the matter content of the Universe is not a
continuous fluid.Comment: 49 pages, 15 figures. Corrections made to description of lattice
constructio
Constraints on the topology of the universe from the 2-yr COBE data
The cosmic microwave background (CMB) is a unique probe of cosmological
parameters and conditions. There is a connection between anisotropy in the CMB
and the topology of the Universe. Adopting a universe with the topology of a
3-Torus, or a universe where only harmonics of the fundamental mode are
allowed, and using 2-years of COBE/DMR data, we obtain constraints on the
topology of the Universe. Previous work constrained the topology using the
slope information and the correlation function of the CMB. We obtain more
accurate results by using all multipole moments, avoiding approximations by
computing their full covariance matrix. We obtain the best fit for a cubic
toroidal universe of scale 7200h^{-1} Mpc for n=1. The data set a lower limit
on the cell size of 4320h^{-1} Mpc at 95% confidence and 5880h^{-1} Mpc at 68%
confidence. These results show that the most probable cell size would be around
1.2 times larger than the horizon scale, implying that the 3-Torus topology is
no longer an interesting cosmological model.Comment: Minor revisions to match published version. 14 pages, with 4 figures
included. Color figures and links at
http://www.sns.ias.edu/~angelica/topology.htm
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