43,104 research outputs found
Results on the Dimension Spectra of Planar Lines
In this paper we investigate the (effective) dimension spectra of lines in the Euclidean plane. The dimension spectrum of a line L_{a,b}, sp(L), with slope a and intercept b is the set of all effective dimensions of the points (x, ax + b) on L. It has been recently shown that, for every a and b with effective dimension less than 1, the dimension spectrum of L_{a,b} contains an interval. Our first main theorem shows that this holds for every line. Moreover, when the effective dimension of a and b is at least 1, sp(L) contains a unit interval.
Our second main theorem gives lower bounds on the dimension spectra of lines. In particular, we show that for every alpha in [0,1], with the exception of a set of Hausdorff dimension at most alpha, the effective dimension of (x, ax + b) is at least alpha + dim(a,b)/2. As a consequence of this theorem, using a recent characterization of Hausdorff dimension using effective dimension, we give a new proof of a result by Molter and Rela on the Hausdorff dimension of Furstenberg sets
Transient and steady-state shear banding in a lamellar phase as studied by Rheo-NMR
Flow fields and shear-induced structures in the lamellar (L-alpha) phase of the system triethylene glycol mono n-decyl ether (C10E3)/water were investigated by NMR velocimetry, diffusometry, and H-2 NMR spectroscopy. The transformation from multilamellar vesicles (MLVs) to aligned planar lamellae is accompanied by a transient gradient shear banding. A high-shear-rate band of aligned lamellae forms next to the moving inner wall of the cylindrical Couette shear cell while a low-shear-rate band of the initial MLV structure remains close to the outer stationary wall. The band of layers grows at the expense of the band of MLVs until the transformation is completed. This process scales with the applied strain. Wall slip is a characteristic of the MLV state, while aligned layers show no deviation from Newtonian flow. The homogeneous nature of the opposite transformation from well aligned layers to MLVs via an intermediate structure resembling undulated multilamellar cylinders is confirmed. The strain dependence of this transformation appears to be independent of temperature. The shear diagram, which represents the shear-induced structures as a function of temperature and shear rate, contains a transition region between stable layers and stable MLVs. The steady-state structures in the transition region show a continuous change from layer-like at high temperature to MLV-like at lower temperature. These structures are homogeneous on a length scale above a few micrometers
Semiclassical trace formulae for systems with spin-orbit interactions: successes and limitations of present approaches
We discuss the semiclassical approaches for describing systems with
spin-orbit interactions by Littlejohn and Flynn (1991, 1992), Frisk and Guhr
(1993), and by Bolte and Keppeler (1998, 1999). We use these methods to derive
trace formulae for several two- and three-dimensional model systems, and
exhibit their successes and limitations. We discuss, in particular, also the
mode conversion problem that arises in the strong-coupling limit.Comment: LaTeX2e, 25 pages incl. 9 figures, version 3: final version in print
for J. Phys.
Driving Rydberg-Rydberg transitions from a co-planar microwave waveguide
The coherent interaction between ensembles of helium Rydberg atoms and
microwave fields in the vicinity of a solid-state co-planar waveguide is
reported. Rydberg-Rydberg transitions, at frequencies between 25 GHz and 38
GHz, have been studied for states with principal quantum numbers in the range
30 - 35 by selective electric-field ionization. An experimental apparatus
cooled to 100 K was used to reduce effects of blackbody radiation.
Inhomogeneous, stray electric fields emanating from the surface of the
waveguide have been characterized in frequency- and time-resolved measurements
and coherence times of the Rydberg atoms on the order of 250 ns have been
determined.Comment: 5 pages, 5 figure
Multivariate Approaches to Classification in Extragalactic Astronomy
Clustering objects into synthetic groups is a natural activity of any
science. Astrophysics is not an exception and is now facing a deluge of data.
For galaxies, the one-century old Hubble classification and the Hubble tuning
fork are still largely in use, together with numerous mono-or bivariate
classifications most often made by eye. However, a classification must be
driven by the data, and sophisticated multivariate statistical tools are used
more and more often. In this paper we review these different approaches in
order to situate them in the general context of unsupervised and supervised
learning. We insist on the astrophysical outcomes of these studies to show that
multivariate analyses provide an obvious path toward a renewal of our
classification of galaxies and are invaluable tools to investigate the physics
and evolution of galaxies.Comment: Open Access paper.
http://www.frontiersin.org/milky\_way\_and\_galaxies/10.3389/fspas.2015.00003/abstract\>.
\<10.3389/fspas.2015.00003 \&g
Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart
We have subjected the planar pendulum eigenproblem to a symmetry analysis
with the goal of explaining the relationship between its conditional
quasi-exact solvability (C-QES) and the topology of its eigenenergy surfaces,
established in our earlier work [Frontiers in Physical Chemistry and Chemical
Physics 2, 1-16, (2014)]. The present analysis revealed that this relationship
can be traced to the structure of the tridiagonal matrices representing the
symmetry-adapted pendular Hamiltonian, as well as enabled us to identify many
more -- forty in total to be exact -- analytic solutions. Furthermore, an
analogous analysis of the hyperbolic counterpart of the planar pendulum, the
Razavy problem, which was shown to be also C-QES [American Journal of Physics
48, 285 (1980)], confirmed that it is anti-isospectral with the pendular
eigenproblem. Of key importance for both eigenproblems proved to be the
topological index , as it determines the loci of the intersections
(genuine and avoided) of the eigenenergy surfaces spanned by the dimensionless
interaction parameters and . It also encapsulates the conditions
under which analytic solutions to the two eigenproblems obtain and provides the
number of analytic solutions. At a given , the anti-isospectrality
occurs for single states only (i.e., not for doublets), like C-QES holds solely
for integer values of , and only occurs for the lowest eigenvalues of
the pendular and Razavy Hamiltonians, with the order of the eigenvalues
reversed for the latter. For all other states, the pendular and Razavy spectra
become in fact qualitatively different, as higher pendular states appear as
doublets whereas all higher Razavy states are singlets
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