22,949 research outputs found
Limit cycles for a class of eleventh equivariant systems without infinite critical points
We analyze the complex dynamics dynamics of a family of
equivariant planar systems, by using their reduction to an
Abel equation. We derive conditions in the parameter space that allow
uniqueness and hyperbolicity of a limit cycle surrounding either or
equilibria.Comment: 12 pages, 1 figur
Application of K-integrals to radiative transfer in layered media
Simple yet accurate results for radiative transfer in layered media with
discontinuous refractive index are obtained by the method of K-integrals,
originally developed for neutron transport analysis. These are certain weighted
integrals applied to the angular intensity distribution at the refracting
boundaries. The radiative intensity is expressed as the sum of the asymptotic
angular intensity distribution valid in the depth of the scattering medium and
a transient term valid near the boundary. Integral boundary conditions are
obtained from the vanishing of the K-integrals of the boundary transient,
yielding simple linear equations for the intensity coefficients (two for a
halfspace, four for a slab or an interface), enabling the angular emission
intensity and the diffuse reflectance (albedo) and transmittance of the
scattering layer to be calculated. The K-integral method is orders of magnitude
more accurate than diffusion theory and can be applied to scattering media with
a wide range of scattering albedoes. For example, near five figure accuracy is
obtained for the diffuse reflectance of scattering layers of refractive index n
= 1.5 with single scattering albedo in the range 0.3 to 1Comment: 38 pages, 8 tables, 14 figure
The Energetics of Particle Acceleration Using High Intensity Lasers
We point out that even the most intense laser beams available today can
provide only a very small fraction of the beam energy required to reach the
design luminosity for a future e+e- linear collider. This fact seems to have
been overlooked in the extensive literature on laser acceleration of charged
particles
The Cyclic Hopf H mod K Theorem
The theorem gives all possible periodic solutions in a
equivariant dynamical system, based on the group-theoretical aspects.
In addition, it classifies the spatio temporal symmetries that are possible. By
the contrary, the equivariant Hopf theorem guarantees the existence of families
of small-amplitude periodic solutions bifurcating from the origin for each
axial subgroup of In this paper we
identify which periodic solution types, whose existence is guaranteed by the
theorem, are obtainable by Hopf bifurcation, when the group
is finite cyclic.Comment: 6 pages in Mathematical Reports (2015
Oscillation patterns in tori of modified FHN neurons
We analyze the dynamics of a network of electrically coupled, modified
FitzHugh-Nagumo (FHN) oscillators. The network building-block architecture is a
bidimensional squared array shaped as a torus, with unidirectional nearest
neighbor coupling in both directions. Linear approximation about the origin of
a single torus, reveals that the array is able to oscillate via a Hopf
bifurcation, controlled by the interneuronal coupling constants. Group
theoretic analysis of the dynamics of one torus leads to discrete rotating
waves moving diagonally in the squared array under the influence of the direct
product group
Then, we
studied the existence multifrequency patterns of oscillations, in networks
formed by two coupled tori. We showed that when acting on the traveling waves,
this group leaves them unchanged, while when it acts on the in-phase
oscillations, they are shifted in time by We therefore proved the
possibility of a pattern of oscillations in which one torus produces traveling
waves of constant phase shift, while the second torus shows synchronous
in-phase oscillations, at times the frequency shown by the traveling
waves.Comment: 23, 5 figure
Use of Slow Light to test the Isotropy of Space
It is suggested that slow light could be used to test for relative motion
with respect to an absolute reference frame at a sensitivity v ~ 10^{-3} m/s
Search for Higher Dimensions through their Gravitational Effects in High Energy Collisions
We consider the use of a microwave parametric converter for the direct
detection of gravitational effects at the LHC. Because of the extra dimensions
the strength of the gravitational interaction in the bulk grows at high
energies. This leads to possibly detectable signals
Saturable absorption and 'slow light'
Quantitative evaluation of some recent 'slow light' experiments based on
coherent population oscillations (CPO) shows that they can be more simply
interpreted as saturable absorption phenomena. Therefore they do not provide an
unambiguous demonstration of 'slow light'. Indeed a limiting condition on the
spectral bandwidth is not generally satisfied, such that the requirements for
burning a narrow spectral hole in the homogeneously broadened absorption line
are not met. Some definitive tests of 'slow light' phenomena are suggested,
derived from analysis of phase shift and pulse delay for a saturable absorberComment: 11 pages 4 figures (data analysis of bacteriorhodopsin 'slow light'
experiment by Wu and Rao: Phys Rev Letters 95 253601 (2005) added
The refractive index of the vacuum and the dark sector
We discuss a recent result about the refractive index of the vacuum and
compare it with existing limits. We consider a possible connection with the
dark sector.Comment: 4 page
Path Integral Quantization of Volume
A hyperlink is a finite set of non-intersecting simple closed curves in
. Let be a compact set inside
. The dynamical variables in General Relativity are the vierbein
and a -valued connection .
Together with Minkowski metric, will define a metric on the manifold.
Denote as the volume of , for a given choice of .
The Einstein-Hilbert action is defined on and . We
will quantize the volume of by integrating against a holonomy
operator of a hyperlink , disjoint from , and the exponential of the
Einstein-Hilbert action, over the space of vierbein and
-valued connection . Using our
earlier work done on Chern-Simons path integrals in , we will
write this infinite dimensional path integral as the limit of a sequence of
Chern-Simons integrals. Our main result shows that the volume operator can be
computed by counting the number of half-twists in the projected hyperlink,
which lie inside . By assigning an irreducible representation of
to each component of , the volume
operator gives the total kinetic energy, which comes from translational and
angular momentum
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