627 research outputs found
Level spacings and periodic orbits
Starting from a semiclassical quantization condition based on the trace
formula, we derive a periodic-orbit formula for the distribution of spacings of
eigenvalues with k intermediate levels. Numerical tests verify the validity of
this representation for the nearest-neighbor level spacing (k=0). In a second
part, we present an asymptotic evaluation for large spacings, where consistency
with random matrix theory is achieved for large k. We also discuss the relation
with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for
two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of
validity of asymptotic evaluation clarifie
How well-proportioned are lens and prism spaces?
The CMB anisotropies in spherical 3-spaces with a non-trivial topology are
analysed with a focus on lens and prism shaped fundamental cells. The
conjecture is tested that well proportioned spaces lead to a suppression of
large-scale anisotropies according to the observed cosmic microwave background
(CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly
proportioned. However, there are inhomogeneous lens spaces whose shape of the
Voronoi domain depends on the position of the observer within the manifold.
Such manifolds possess no fixed measure of well-proportioned and allow a
predestined test of the well-proportioned conjecture. Topologies having the
same Voronoi domain are shown to possess distinct CMB statistics which thus
provide a counter-example to the well-proportioned conjecture. The CMB
properties are analysed in terms of cyclic subgroups Z_p, and new point of view
for the superior behaviour of the Poincar\'e dodecahedron is found
MetaboTools: A comprehensive toolbox for analysis of genome-scale metabolic models
Metabolomic data sets provide a direct read-out of cellular phenotypes and
are increasingly generated to study biological questions. Our previous work
revealed the potential of analyzing extracellular metabolomic data in the
context of the metabolic model using constraint-based modeling. Through this
work, which consists of a protocol, a toolbox, and tutorials of two use cases,
we make our methods available to the broader scientific community. The protocol
describes, in a step-wise manner, the workflow of data integration and
computational analysis. The MetaboTools comprise the Matlab code required to
complete the workflow described in the protocol. Tutorials explain the
computational steps for integration of two different data sets and demonstrate
a comprehensive set of methods for the computational analysis of metabolic
models and stratification thereof into different phenotypes. The presented
workflow supports integrative analysis of multiple omics data sets.
Importantly, all analysis tools can be applied to metabolic models without
performing the entire workflow. Taken together, this protocol constitutes a
comprehensive guide to the intra-model analysis of extracellular metabolomic
data and a resource offering a broad set of computational analysis tools for a
wide biomedical and non-biomedical research community
On the Rate of Quantum Ergodicity on hyperbolic Surfaces and Billiards
The rate of quantum ergodicity is studied for three strongly chaotic (Anosov)
systems. The quantal eigenfunctions on a compact Riemannian surface of genus
g=2 and of two triangular billiards on a surface of constant negative curvature
are investigated. One of the triangular billiards belongs to the class of
arithmetic systems. There are no peculiarities observed in the arithmetic
system concerning the rate of quantum ergodicity. This contrasts to the
peculiar behaviour with respect to the statistical properties of the quantal
levels. It is demonstrated that the rate of quantum ergodicity in the three
considered systems fits well with the known upper and lower bounds.
Furthermore, Sarnak's conjecture about quantum unique ergodicity for hyperbolic
surfaces is confirmed numerically in these three systems.Comment: 19 pages, Latex, This file contains no figures. A postscript file
with all figures is available at http://www.physik.uni-ulm.de/theo/qc/ (Delay
is expected to 23.7.97 since our Web master is on vacation.
Hot pixel contamination in the CMB correlation function?
Recently, it was suggested that the map-making procedure, which is applied to
the time-ordered CMB data by the WMAP team, might be flawed by hot pixels. This
could lead to a bias in the pixels having an angular distance of about 141
degrees from hot pixels due to the differential measuring process of the
satellite WMAP. Here, the bias is confirmed, and the temperature two-point
correlation function C(theta) is reevaluated by excluding the affected pixels.
It is shown that the most significant effect occurs in C(theta) at the largest
angles near theta = 180 degrees. Furthermore, the corrected correlation
function C(theta) is applied to the cubic topology of the Universe, and it is
found that such a multi-connected universe matches the temperature correlation
better than the LCDM concordance model, provided the cubic length scale is
close to L=4 measured in units of the Hubble length
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
Nodal domains statistics - a criterion for quantum chaos
We consider the distribution of the (properly normalized) numbers of nodal
domains of wave functions in 2- quantum billiards. We show that these
distributions distinguish clearly between systems with integrable (separable)
or chaotic underlying classical dynamics, and for each case the limiting
distribution is universal (system independent). Thus, a new criterion for
quantum chaos is provided by the statistics of the wave functions, which
complements the well established criterion based on spectral statistics.Comment: 4 pages, 5 figures, revte
Supernovae observations and cosmic topology
Two fundamental questions regarding our description of the Universe concern
the geometry and topology of its 3-dimensional space. While geometry is a local
characteristic that gives the intrinsic curvature, topology is a global feature
that characterizes the shape and size of the 3-space. The geometry constrains,
but does not dictate the the spatial topology. We show that, besides
determining the spatial geometry, the knowledge of the spatial topology allows
to place tight constraints on the density parameters associated with dark
matter () and dark energy (). By using the
Poincar\'e dodecahedral space as the observable spatial topology, we reanalyze
the current type Ia supenovae (SNe Ia) constraints on the density parametric
space . From this SNe Ia plus cosmic topology
analysis, we found best fit values for the density parameters, which are in
agreement with a number of independent cosmological observations.Comment: 5 pages, 2 figures. Minor changes and a ref. added. To appear in A&A
(2006
Modeling deformations of the workpiece and removal of material when turning
During machining mechanical energy is dissipated into heat by frictional processes and plastic deformations of the workpiece material. Workpiece and tool are thereby subjected to thermal and mechanical loads that cause thermal expansions and mechanical deformations. These decrease the accuracy of machining. In order to reduce such deformations, enhanced cutting conditions need to be determined. Finite element (FE) simulations allow for such an optimization prior to actual machining. A validated 3D FE model to determine the temperature distribution and the deformations of the workpiece regarding the cutting condition and the actual tool position is outlined for turning. The continuous removal of material for arbitrary geometries when simulating the temperature distribution and the deformations is considered. This allows for the calculation of the actual workpiece diameter after turning
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