9,017 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
Normal Mode Determination of Perovskite Crystal Structures with Octahedral Rotations: Theory and Applications
Nuclear site analysis methods are used to enumerate the normal modes of
perovskite polymorphs with octahedral rotations. We provide the modes
of the fourteen subgroups of the cubic aristotype describing the Glazer
octahedral tilt patterns, which are obtained from rotations of the
octahedra with different sense and amplitude about high symmetry axes. We
tabulate all normal modes of each tilt system and specify the contribution of
each atomic species to the mode displacement pattern, elucidating the physical
meaning of the symmetry unique modes. We have systematically generated 705
schematic atomic displacement patterns for the normal modes of all 15 (14
rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative
examples how to use these tables to identify the octahedral rotations,
symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing
distortions of the octahedra, and the associated Raman selection
rules. We anticipate that these tables and schematics will be useful in
understanding the lattice dynamics of bulk perovskites and would serve as
reference point in elucidating the atomic origin of a wide range of physical
properties in synthetic perovskite thin films and superlattices.Comment: 17 pages, 3 figures, 17 tables. Supporting information accessed
through link specified within manuscrip
Transform of Riccati equation of constant coefficients through fractional procedure
We use a particular fractional generalization of the ordinary differential
equations that we apply to the Riccati equation of constant coefficients. By
this means the latter is transformed into a modified Riccati equation with the
free term expressed as a power of the independent variable which is of the same
order as the order of the applied fractional derivative. We provide the
solutions of the modified equation and employ the results for the case of the
cosmological Riccati equation of FRW barotropic cosmologies that has been
recently introduced by FaraoniComment: 7 pages, 2 figure
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
Integrability and action operators in quantum Hamiltonian systems
For a (classically) integrable quantum mechanical system with two degrees of
freedom, the functional dependence of the
Hamiltonian operator on the action operators is analyzed and compared with the
corresponding functional relationship in
the classical limit of that system. The former is shown to converge toward the
latter in some asymptotic regime associated with the classical limit, but the
convergence is, in general, non-uniform. The existence of the function
in the integrable regime of a parametric
quantum system explains empirical results for the dimensionality of manifolds
in parameter space on which at least two levels are degenerate. The comparative
analysis is carried out for an integrable one-parameter two-spin model.
Additional results presented for the (integrable) circular billiard model
illuminate the same conclusions from a different angle.Comment: 9 page
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
Direct instantons, topological charge screening and QCD glueball sum rules
Nonperturbative Wilson coefficients of the operator product expansion (OPE)
for the spin-0 glueball correlators are derived and analyzed. A systematic
treatment of the direct instanton contributions is given, based on realistic
instanton size distributions and renormalization at the operator scale. In the
pseudoscalar channel, topological charge screening is identified as an
additional source of (semi-) hard nonperturbative physics. The screening
contributions are shown to be vital for consistency with the anomalous axial
Ward identity, and previously encountered pathologies (positivity violations
and the disappearance of the 0^{-+} glueball signal) are traced to their
neglect. On the basis of the extended OPE, a comprehensive quantitative
analysis of eight Borel-moment sum rules in both spin-0 glueball channels is
then performed. The nonperturbative OPE coefficients turn out to be
indispensable for consistent sum rules and for their reconciliation with the
underlying low-energy theorems. The topological short-distance physics strongly
affects the sum rule results and reveals a rather diverse pattern of glueball
properties. New predictions for the spin-0 glueball masses and decay constants
and an estimate of the scalar glueball width are given, and several
implications for glueball structure and experimental glueball searches are
discussed.Comment: 49 pages, 8 figure
A Hybrid (Monte-Carlo/Deterministic) Approach for Multi-Dimensional Radiation Transport
A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with
solar illumination, scattering and absorbing 2D atmosphere, a textured
reflecting mountain, and a small detector located in the sky (mounted on a
satellite or a airplane). It uses a deterministic approximation of an adjoint
transport solution to reduce variance, computed quickly by ignoring atmospheric
interactions. This allows significant variance and computational cost
reductions when the atmospheric scattering and absorption coefficient are
small. When combined with an atmospheric photon-redirection scheme, significant
variance reduction (equivalently acceleration) is achieved in the presence of
atmospheric interactions
Residence time and collision statistics for exponential flights: the rod problem revisited
Many random transport phenomena, such as radiation propagation,
chemical/biological species migration, or electron motion, can be described in
terms of particles performing {\em exponential flights}. For such processes, we
sketch a general approach (based on the Feynman-Kac formalism) that is amenable
to explicit expressions for the moments of the number of collisions and the
residence time that the walker spends in a given volume as a function of the
particle equilibrium distribution. We then illustrate the proposed method in
the case of the so-called {\em rod problem} (a 1d system), and discuss the
relevance of the obtained results in the context of Monte Carlo estimators.Comment: 9 pages, 8 figure
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