8,762 research outputs found
Dequantisation of the Dirac Monopole
Using a sheaf-theoretic extension of conventional principal bundle theory,
the Dirac monopole is formulated as a spherically symmetric model free of
singularities outside the origin such that the charge may assume arbitrary real
values. For integral charges, the construction effectively coincides with the
usual model. Spin structures and Dirac operators are also generalised by the
same technique.Comment: 22 pages. Version to appear in Proc. R. Soc. London
Negative forms and path space forms
We present an account of negative differential forms within a natural
algebraic framework of differential graded algebras, and explain their
relationship with forms on path spaces.Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology
dropped in Proposition 3.2; material slightly reorganize
Gauge Group and Topology Change
The purpose of this study is to examine the effect of topology change in the
initial universe. In this study, the concept of -cobordism is introduced to
argue about the topology change of the manifold on which a transformation group
acts. This -manifold has a fiber bundle structure if the group action is
free and is related to the spacetime in Kaluza-Klein theory or
Einstein-Yang-Mills system. Our results revealed that fundamental processes of
compactification in -manifolds. In these processes, the initial high
symmetry and multidimensional universe changes to present universe by the
mechanism which lowers the dimensions and symmetries.Comment: 8 page
Enteral Nutrition and Acute Pancreatitis: A Review
Introduction. In patients with acute pancreatitis (AP), nutritional support is required if normal food cannot be tolerated within several days. Enteral nutrition is preferred over parenteral nutrition. We reviewed the literature about enteral nutrition in AP. Methods. A MEDLINE search of the English language literature between 1999–2009. Results. Nasogastric tube feeding appears to be safe and well tolerated in the majority of patients with severe AP, rendering the concept of pancreatic rest less probable. Enteral nutrition has a beneficial influence on the outcome of AP and should probably be initiated as early as possible (within 48 hours). Supplementation of enteral formulas with glutamine or prebiotics and probiotics cannot routinely be recommended. Conclusions. Nutrition therapy in patients with AP emerged from supportive adjunctive therapy to a proactive primary intervention. Large multicentre studies are needed to confirm the safety and effectiveness of nasogastric feeding and to investigate the role of early nutrition support
Improving the Lagrangian perturbative solution for cosmic fluid: Applying Shanks transformation
We study the behavior of Lagrangian perturbative solutions. For a spherical
void model, the higher order the Lagrangian perturbation we consider, the worse
the approximation becomes in late-time evolution. In particular, if we stop to
improve until an even order is reached, the perturbative solution describes the
contraction of the void. To solve this problem, we consider improving the
perturbative solution using Shanks transformation, which accelerates the
convergence of the sequence. After the transformation, we find that the
accuracy of higher-order perturbation is recovered and the perturbative
solution is refined well. Then we show that this improvement method can apply
for a CDM model and improved the power spectrum of the density field.Comment: 17 pages, 7 figures; accepted for publication in Phys.Rev.D; v2:
Evolution of power spectrum in LCDM model is added; v3: References are
correcte
Phase space measure concentration for an ideal gas
We point out that a special case of an ideal gas exhibits concentration of
the volume of its phase space, which is a sphere, around its equator in the
thermodynamic limit. The rate of approach to the thermodynamic limit is
determined. Our argument relies on the spherical isoperimetric inequality of
L\'{e}vy and Gromov.Comment: 15 pages, No figures, Accepted by Modern Physics Letters
Future asymptotic expansions of Bianchi VIII vacuum metrics
Bianchi VIII vacuum solutions to Einstein's equations are causally
geodesically complete to the future, given an appropriate time orientation, and
the objective of this article is to analyze the asymptotic behaviour of
solutions in this time direction. For the Bianchi class A spacetimes, there is
a formulation of the field equations that was presented in an article by
Wainwright and Hsu, and in a previous article we analyzed the asymptotic
behaviour of solutions in these variables. One objective of this paper is to
give an asymptotic expansion for the metric. Furthermore, we relate this
expansion to the topology of the compactified spatial hypersurfaces of
homogeneity. The compactified spatial hypersurfaces have the topology of
Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII
spacetimes, the length of a circle fibre converges to a positive constant but
that in the case of general Bianchi VIII solutions, the length tends to
infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces
correcte
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Convergence of Ginzburg-Landau functionals in 3-d superconductivity
In this paper we consider the asymptotic behavior of the Ginzburg- Landau
model for superconductivity in 3-d, in various energy regimes. We rigorously
derive, through an analysis via {\Gamma}-convergence, a reduced model for the
vortex density, and we deduce a curvature equation for the vortex lines. In a
companion paper, we describe further applications to superconductivity and
superfluidity, such as general expressions for the first critical magnetic
field H_{c1}, and the critical angular velocity of rotating Bose-Einstein
condensates.Comment: 45 page
Perturbed Three Vortex Dynamics
It is well known that the dynamics of three point vortices moving in an ideal
fluid in the plane can be expressed in Hamiltonian form, where the resulting
equations of motion are completely integrable in the sense of Liouville and
Arnold. The focus of this investigation is on the persistence of regular
behavior (especially periodic motion) associated to completely integrable
systems for certain (admissible) kinds of Hamiltonian perturbations of the
three vortex system in a plane. After a brief survey of the dynamics of the
integrable planar three vortex system, it is shown that the admissible class of
perturbed systems is broad enough to include three vortices in a half-plane,
three coaxial slender vortex rings in three-space, and `restricted' four vortex
dynamics in a plane. Included are two basic categories of results for
admissible perturbations: (i) general theorems for the persistence of invariant
tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff
type arguments; and (ii) more specific and quantitative conclusions of a
classical perturbation theory nature guaranteeing the existence of periodic
orbits of the perturbed system close to cycles of the unperturbed system, which
occur in abundance near centers. In addition, several numerical simulations are
provided to illustrate the validity of the theorems as well as indicating their
limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic
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