9,146 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
Influence of Levantine Artificial Reefs on the fish assemblage of the surrounding seabed
Four Artificial Reef (AR) units were deployed at a 20m depth on a flat hard substrate 3 km west of Haifa, Israel and then surveyed for fish for 12 months. AR units supported 20 times the biomass of control quadrates and their enrichment impact was still significant at a radius of 13m away from units. The 13m values were also significantly higher than those of quadrates adjacent to units, suggesting the existence of a halo of relative depletion within the outer enrichment halo. The main species contributing to this pattern was the migrant herbivore Siganus rivulatus. A decrease in grazing resources is thus suggested as an explanation for creation of this halo. The most consistent AR residents were also Lessepsian migrants - Sargocentron rubrum, nocturnal predators which displayed high microhabitat fidelity and a steady increase in density. The 6 species of migrants recorded accounted for 65.3% of the commercially exploitable biomass and 25.2% of the specimens in the AR site. Other constant AR residents were the groupers Epinephelus costae and Epinephelus marginatus, which are rare and commercially important species. Site protection from fishing and storms were found to be of utmost importance, and design and deployment considerations are discussed
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
INTEGRAL observations of the blazar Mrk 421 in outburst (Results of a multi-wavelength campaign)
We report the results of a multi-wavelength campaign on the blazar Mrk 421
during outburst. We observed four strong flares at X-ray energies that were not
seen at other wavelengths (partially because of missing data). From the fastest
rise in the X-rays, an upper limit could be derived on the extension of the
emission region. A time lag between high-energy and low-energy X-rays was
observed, which allowed an estimation of the magnetic-field strength. The
spectral analysis of the X-rays revealed a slight spectral hardening of the
low-energy (3 - 43 keV) spectral index. The hardness-ratio analysis of the
Swift-XRT (0.2 - 10 keV) data indicated a small correlation with the intensity;
i. e., a hard-to-soft evolution was observed. At the energies of IBIS/ISGRI (20
- 150 keV), such correlations are less obvious. A multiwavelength spectrum was
composed and the X-ray and bolometric luminosities are calculated.Comment: 15 pages, 18 figures; accepted by Astronomy & Astrophysic
Relativistic central--field Green's functions for the RATIP package
From perturbation theory, Green's functions are known for providing a simple
and convenient access to the (complete) spectrum of atoms and ions. Having
these functions available, they may help carry out perturbation expansions to
any order beyond the first one. For most realistic potentials, however, the
Green's functions need to be calculated numerically since an analytic form is
known only for free electrons or for their motion in a pure Coulomb field.
Therefore, in order to facilitate the use of Green's functions also for atoms
and ions other than the hydrogen--like ions, here we provide an extension to
the Ratip program which supports the computation of relativistic
(one--electron) Green's functions in an -- arbitrarily given -- central--field
potential \rV(r). Different computational modes have been implemented to
define these effective potentials and to generate the radial Green's functions
for all bound--state energies . In addition, care has been taken to
provide a user--friendly component of the Ratip package by utilizing features
of the Fortran 90/95 standard such as data structures, allocatable arrays, or a
module--oriented design.Comment: 20 pages, 1 figur
-to-Glueball form factor and Glueball production in decays
We investigate transition form factors of meson decays into a scalar
glueball in the light-cone formalism. Compared with form factors of to
ordinary scalar mesons, the -to-glueball form factors have the same power in
the expansion of . Taking into account the leading twist light-cone
distribution amplitude, we find that they are numerically smaller than those
form factors of to ordinary scalar mesons. Semileptonic ,
and decays are subsequently investigated. We
also analyze the production rates of scalar mesons in semileptonic decays
in the presence of mixing between scalar and glueball states. The
glueball production in meson decays is also investigated and the LHCb
experiment may discover this channel. The sizable branching fraction in , or could be a clear signal for a scalar glueball
state.Comment: 17 pages, 3 figure, revtex
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
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
Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants
We continue the discussion of the fermion models on graphs that started in
the first paper of the series. Here we introduce a Graphical Gauge Model (GGM)
and show that : (a) it can be stated as an average/sum of a determinant defined
on the graph over (binary) gauge field; (b) it is equivalent
to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the
model allows an explicit expression in terms of a series over disjoint directed
cycles, where each term is a product of local contributions along the cycle and
the determinant of a matrix defined on the remainder of the graph (excluding
the cycle). We also establish a relation between the MD model on the graph and
the determinant series, discussed in the first paper, however, considered using
simple non-Belief-Propagation choice of the gauge. We conclude with a
discussion of possible analytic and algorithmic consequences of these results,
as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte
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
- …