381 research outputs found
Semilocal Generic Formal Fibers
Let T be a complete local ring and C a finite set of incomparable prime
ideals of T. We find necessary and sufficient conditions for T to be the
completion of an integral domain whose generic formal fiber is semilocal with
maximal ideals the elements of C. In addition, if char T = 0, we give necessary
and sufficient conditions for T to be the completion of an excellent integral
domain whose generic formal fiber is semilocal with maximal ideals the elements
of C.Comment: 15 page
Scalar field phase dynamics in preheating
We study the model of a massive inflaton field coupled to another
scalar filed with interaction term for the first stage
of preheating. We obtain the the behavior of the phase in terms of the
iteration of a simple family of circle maps. When expansion of the universe is
taken into account the qualitative behavior of the phase and growth number
evolution is reminiscent of the behavior found in the case without expansion.Comment: 4 pages, 4 figures, LaTeX; submitted to the Proceedings of Eleventh
Marcel Grossmann Meetin
Report on "Scheduling in a factory"
In order to carry out their orders of shoe soles, this company has a number of tasks T_1, ..., T_n of different lengths to be assigned to groups of machines.
Each group is operated by one worker (two in one case), and an operation cycle corresponds to injection, cooling, and removal of the sole. The time taken at each step varies from one order to another, and when starting a new task a machine needs to be tuned, which takes some extra time. Machines are working in parallel. At the moment the assignment is carried out empirically, and the problem proposed is to optimize the procedure
Self-interacting scalar field cosmologies: unified exact solutions and symmetries
We investigate a mechanism that generates the exact solutions of scalar field
cosmologies in a unified way. The procedure investigated here permits to
recover allmost all known solutions, and allows one to derive new solutions as
well. In particular, we derive and discuss one novel solution defined in terms
of the Lambert function. The solutions are organized in a classification which
depends on the choice of a generating function which we have denoted by
that reflects the underlying thermodynamics of the model. We also
analyse and discuss the existence of form invariances and dualities between
solutions. A general way of defining the latter in an appropriate fashion for
scalar fields is put forward.Comment: 6 figures, 30 page
Reheating induced by competing decay modes
We address the problem of studying the decay of the inflaton field to
another scalar field through parametric resonance in the case of a
coupling that involves several decay modes. This amounts to the presence of
extra harmonic terms in the perturbation of the field dynamics. For the
case of two frequencies we compute the geometry of the resonance regions, which
is significantly altered due to the presence of non-cuspidal resonance regions
associated to higher harmonics and to the emergence of instability `pockets'.
We discuss the effect of this change in the efficiency of the energy transfer
process for the simplest case of a coupling given by a combination of the two
interaction terms of homogeneous degree usually considered in the literature.
We find that the presence of higher harmonics has limited cosmological
implications.Comment: 14 pages, 4 figures Added references. Corrected typo
Form invariance symmetry generates a large set of FRW cosmologies
We show that Einstein's field equations for spatially flat
Friedmann-Robertson-Walker (FRW) space times have a form invariance symmetry
(FIS) realized by the form invariance transformations (FIT) which are indeed
generated by an invertible function of the source energy density. These
transformations act on the Hubble expansion rate, the energy density, and
pressure of the cosmic fluid; likewise such transformations are endowed with a
Lie group structure. Each representation of this group is associated with a
particular fluid and consequently a determined cosmology, so that, the FIS
defines a set of equivalent cosmological models. We focus our seek in the FIT
generated by a linear function because it provides a natural framework to
express the duality and also produces a large sets of cosmologies, starting
from a seed one, in several contexts as for instance in the cases of a perfect
fluid source and a scalar field driven by a potential depending linearly on the
scalar field kinetic energy density.Comment: 11 pages, 3 figures. Accepted for publication in Modern Physics
Letters A (2012
Subacute combined degeneration of the cord secondary to nitrous oxide misuse:No laughing matter
Nitrous oxide (N(2)O) has several traditional uses as a surgical and dental anaesthetic, as well as in aerosol spray propellants. It is the combination of analgesic and euphoric qualities coupled with accessibility as an over-the-counter household item that lends N(2)O to recreational use. Despite increasing evidence that prolonged use of N(2)O both medically and as a drug of abuse can cause disabling neurological side-effects, it remains widely used. We present the case of an 18-year-old male who was diagnosed with subacute combined degeneration of the cord (SCDC) secondary to acute, heavy recreational use of N(2)O. The patient presented with progressive paraesthesia affecting his hands and feet associated with distal weakness. MRI of the cervical spine revealed symmetric bilateral high T2 signal within the dorsal columns extending from the level of C2 to T2 with the inverted âVâ sign on axial T(2)-weighted slices indicative of SCDC. Although vitamin B12 levels were within normal range, marked elevation of methylmalonic acid and homocysteine support the diagnosis of B12 inactivation and functional B12 deficiency, which fully resolved with treatment
Stability analysis of cosmological models through Liapunov's method
We investigate the general asymptotic behaviour of Friedman-Robertson-Walker
(FRW) models with an inflaton field, scalar-tensor FRW cosmological models and
diagonal Bianchi-IX models by means of Liapunov's method. This method provides
information not only about the asymptotic stability of a given equilibrium
point but also about its basin of attraction. This cannot be obtained by the
usual methods found in the literature, such as linear stability analysis or
first order perturbation techniques. Moreover, Liapunov's method is also
applicable to non-autonomous systems. We use this advantadge to investigate the
mechanism of reheating for the inflaton field in FRW models.Comment: Latex file, 8 pages, no figures, accepted for publication in Class. &
Quant. Gra
On the potentials yielding cosmological scaling solutions
In the present work we perform a phase-plane analysis of the complete
dynamical system corresponding to a flat FRW cosmological models with a perfect
fluid and a self-interacting scalar field and show that every positive and
monotonous potential which is asymptotically exponential yields a scaling
solution as a global attractor.Comment: RevTeX, 10 pages, no figure
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