89,671 research outputs found
On initial conditions and global existence for accelerating cosmologies from string theory
We construct a solution satisfying initial conditions for accelerating
cosmologies from string/M-theory. Gowdy symmetric spacetimes with a positive
potential are considered. Also, a global existence theorem for the spacetimes
is shown.Comment: To appear in Annales Henri Poincar
Runtime verification for biochemical programs
The biochemical paradigm is well-suited for modelling autonomous systems and new programming languages are emerging from this approach. However, in order to validate such programs, we need to define precisely their semantics and to provide verification techniques. In this paper, we consider a higher-order biochemical calculus that models the structure of system states and its dynamics thanks to rewriting abstractions, namely rules and strategies. We extend this calculus with a runtime verification technique in order to perform automatic discovery of property satisfaction failure. The property specification language is a subclass of LTL safety and liveness properties
Cosmological fluctuation growth in bimetric MOND
I look at the growth of weak density inhomogeneities of nonrelativistic
matter, in bimetric-MOND (BIMOND) cosmology. I concentrate on
matter-twin-matter-symmetric versions of BIMOND, and assume that, on average,
the universe is symmetrically populated in the two sectors. MOND effects are
absent in an exactly symmetric universe, apart from the appearance of a
cosmological constant, Lambda~(a0/c)^2. MOND effects-local and cosmological-do
enter when density inhomogeneities that differ in the two sectors appear and
develop. MOND later takes its standard form in systems that are islands
dominated by pure matter. I derive the nonrelativistic equations governing
small-scale fluctuation growth. The equations split into two uncoupled systems,
one for the sum, the other for the difference, of the fluctuations in the two
sectors. The former is governed strictly by Newtonian dynamics. The latter is
governed by MOND dynamics, which entails stronger gravity, and nonlinearity
even for the smallest of perturbations. These cause the difference to grow
faster than the sum, conducing to matter-twin-matter segregation. The
nonlinearity also causes interaction between nested perturbations on different
scales. Because matter and twin matter (TM) repel each other in the MOND
regime, matter inhomogeneities grow not only by their own self gravity, but
also through shepherding by flanking TM overdensitie. The relative importance
of gravity and pressure in the MOND system depends also on the strength of the
perturbation. The development of structure in the universe, in either sector,
thus depends crucially on two initial fluctuation spectra: that of matter alone
and that of the matter-TM difference. I also discuss the back reaction on
cosmology of BIMOND effects that appear as "phantom matter" resulting from
inhomogeneity differences between the two sectors.Comment: 14 pages. Some clarifications added. Version published in Phys. Rev.
High order recombination and an application to cubature on Wiener space
Particle methods are widely used because they can provide accurate
descriptions of evolving measures. Recently it has become clear that by
stepping outside the Monte Carlo paradigm these methods can be of higher order
with effective and transparent error bounds. A weakness of particle methods
(particularly in the higher order case) is the tendency for the number of
particles to explode if the process is iterated and accuracy preserved. In this
paper we identify a new approach that allows dynamic recombination in such
methods and retains the high order accuracy by simplifying the support of the
intermediate measures used in the iteration. We describe an algorithm that can
be used to simplify the support of a discrete measure and give an application
to the cubature on Wiener space method developed by Lyons and Victoir [Proc. R.
Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198].Comment: Published in at http://dx.doi.org/10.1214/11-AAP786 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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