11,523 research outputs found
When are projections also embeddings?
We study an autonomous four-dimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents that satisfy , so the Lyapunov dimension is in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from to . In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other
A Comparison of Tests for Embeddings
It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions
CP violation conditions in N-Higgs-doublet potentials
Conditions for CP violation in the scalar potential sector of general
N-Higgs-doublet models (NHDMs) are analyzed from a group theoretical
perspective. For the simplest two-Higgs-doublet model (2HDM) potential, a
minimum set of conditions for explicit and spontaneous CP violation is
presented. The conditions can be given a clear geometrical interpretation in
terms of quantities in the adjoint representation of the basis transformation
group for the two doublets. Such conditions depend on CP-odd pseudoscalar
invariants. When the potential is CP invariant, the explicit procedure to reach
the real CP-basis and the explicit CP transformation can also be obtained. The
procedure to find the real basis and the conditions for CP violation are then
extended to general NHDM potentials. The analysis becomes more involved and
only a formal procedure to reach the real basis is found. Necessary conditions
for CP invariance can still be formulated in terms of group invariants: the
CP-odd generalized pseudoscalars. The problem can be completely solved for
three Higgs-doublets.Comment: RevTeX4 used. Minor modifications, in particular, the parameter
counting of . v3: Eqs.(28)-(31) correcte
Extragalactic Background Light and Gamma-Ray Attenuation
Data from (non-) attenuation of gamma rays from active galactic nuclei (AGN)
and gamma ray bursts (GRBs) give upper limits on the extragalactic background
light (EBL) from the UV to the mid-IR that are only a little above the lower
limits from observed galaxies. These upper limits now rule out some EBL models
and purported observations, with improved data likely to provide even stronger
constraints. We present EBL calculations both based on multiwavelength
observations of thousands of galaxies and also based on semi-analytic models,
and show that they are consistent with these lower limits from observed
galaxies and with the gamma-ray upper limit constraints. Such comparisons
"close the loop" on cosmological galaxy formation models, since they account
for all the light, including that from galaxies too faint to see. We compare
our results with those of other recent works, and discuss the implications of
these new EBL calculations for gamma ray attenuation. Catching a few GRBs with
groundbased atmospheric Cherenkov Telescope (ACT) arrays or water Cherenkov
detectors could provide important new constraints on the high-redshift star
formation history of the universe.Comment: 12 pages, 8 multi-panel figures, Invited talk at the 25th Texas
Symposium on Relativistic Astrophysics, Heidelberg December 6-10, 201
Preferential attachment during the evolution of a potential energy landscape
It has previously been shown that the network of connected minima on a
potential energy landscape is scale-free, and that this reflects a power-law
distribution for the areas of the basins of attraction surrounding the minima.
Here, we set out to understand more about the physical origins of these
puzzling properties by examining how the potential energy landscape of a
13-atom cluster evolves with the range of the potential. In particular, on
decreasing the range of the potential the number of stationary points increases
and thus the landscape becomes rougher and the network gets larger. Thus, we
are able to follow the evolution of the potential energy landscape from one
with just a single minimum to a complex landscape with many minima and a
scale-free pattern of connections. We find that during this growth process, new
edges in the network of connected minima preferentially attach to more
highly-connected minima, thus leading to the scale-free character. Furthermore,
minima that appear when the range of the potential is shorter and the network
is larger have smaller basins of attraction. As there are many of these smaller
basins because the network grows exponentially, the observed growth process
thus also gives rise to a power-law distribution for the hyperareas of the
basins.Comment: 10 pages, 10 figure
Catching GRBs with atmospheric Cherenkov telescopes
Fermi has shown GRBs to be a source of >10 GeV photons. We present an
estimate of the detection rate of GRBs with a next generation Cherenkov
telescope. Our predictions are based on the observed properties of GRBs
detected by Fermi, combined with the spectral properties and redshift
determinations for the bursts population by instruments operating at lower
energies. While detection of VHE emission from GRBs has eluded ground-based
instruments thus far, our results suggest that ground-based detection may be
within reach of the proposed Cherenkov Telescope Array (CTA), albeit with a low
rate, 0.25 - 0.5/yr. Such a detection would help constrain the emission
mechanism of gamma-ray emission from GRBs. Photons at these energies from
distant GRBs are affected by the UV-optical background light, and a
ground-based detection could also provide a valuable probe of the Extragalactic
Background Light (EBL) in place at high redshift.Comment: 4 pages, 3 figures, to appear in the Proceedings of "Gamma Ray Bursts
2010", held Nov. 1-4, 2010 in Annapolis, M
Constraining the Distribution of L- & T-Dwarfs in the Galaxy
We estimate the thin disk scale height of the Galactic population of L- &
T-dwarfs based on star counts from 15 deep parallel fields from the Hubble
Space Telescope. From these observations, we have identified 28 candidate L- &
T- dwarfs based on their (i'-z') color and morphology. By comparing these star
counts to a simple Galactic model, we estimate the scale height to be 350+-50
pc that is consistent with the increase in vertical scale with decreasing
stellar mass and is independent of reddening, color-magnitude limits, and other
Galactic parameters. With this refined measure, we predict that less than 10^9
M_{sol} of the Milky Way can be in the form L- & T- dwarfs, and confirm that
high-latitude, z~6 galaxy surveys which use the i'-band dropout technique are
97-100% free of L- & T- dwarf interlopers.Comment: 4 pages, 4 figures, accepted to ApJ
Generalized coherent states are unique Bell states of quantum systems with Lie group symmetries
We consider quantum systems, whose dynamical symmetry groups are semisimple
Lie groups, which can be split or decay into two subsystems of the same
symmetry. We prove that the only states of such a system that factorize upon
splitting are the generalized coherent states. Since Bell's inequality is never
violated by the direct product state, when the system prepared in the
generalized coherent state is split, no quantum correlations are created.
Therefore, the generalized coherent states are the unique Bell states, i.e.,
the pure quantum states preserving the fundamental classical property of
satisfying Bell's inequality upon splitting.Comment: 4 pages, REVTeX, amssymb style. More information on
http://www.technion.ac.il/~brif/science.htm
Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics
We undertake a systematic exploration of recurrent patterns in a
1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather
turbulent system, the long-time dynamics takes place on a low-dimensional
invariant manifold. A set of equilibria offers a coarse geometrical partition
of this manifold. A variational method enables us to determine numerically a
large number of unstable spatiotemporally periodic solutions. The attracting
set appears surprisingly thin - its backbone are several Smale horseshoe
repellers, well approximated by intrinsic local 1-dimensional return maps, each
with an approximate symbolic dynamics. The dynamics appears decomposable into
chaotic dynamics within such local repellers, interspersed by rapid jumps
between them.Comment: 11 pages, 11 figure
- âŠ