15,344 research outputs found
The Cotton, Simon-Mars and Cotton-York Tensors in Stationary Spacetimes
The Cotton-York and Simon-Mars tensors in stationary vacuum spacetimes are
studied in the language of the congruence approach pioneered by Hawking and
Ellis. Their relationships with the Papapetrou field defined by the stationary
Killing congruence and with a recent characterization of the Kerr spacetime in
terms of the alignment between of the principal null directions of the Weyl
tensor with those of the Papapetrou field are also investigated in this more
transparent language.Comment: 14 pages latex(2e) iopart style, no figure
Non-Lipschitz points and the SBV regularity of the minimum time function
This paper is devoted to the study of the Hausdorff dimension of the singular
set of the minimum time function under controllability conditions which do
not imply the Lipschitz continuity of . We consider first the case of normal
linear control systems with constant coefficients in . We
characterize points around which is not Lipschitz as those which can be
reached from the origin by an optimal trajectory (of the reversed dynamics)
with vanishing minimized Hamiltonian. Linearity permits an explicit
representation of such set, that we call . Furthermore, we show
that is -rectifiable with positive
-measure. Second, we consider a class of control-affine
\textit{planar} nonlinear systems satisfying a second order controllability
condition: we characterize the set in a neighborhood of the
origin in a similar way and prove the -rectifiability of
and that . In both cases, is
known to have epigraph with positive reach, hence to be a locally function
(see \cite{CMW,GK}). Since the Cantor part of must be concentrated in
, our analysis yields that is , i.e., the Cantor part of
vanishes. Our results imply also that is locally of class
outside a -rectifiable set. With small
changes, our results are valid also in the case of multiple control input.Comment: 23 page
Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning
We show that linear congruential pseudo-random-number generators can cause
systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm,
if the lattice size is a multiple of a very large power of 2 and one random
number is used per bond. These systematic errors arise from correlations within
a single bond-update half-sweep. The errors can be eliminated (or at least
radically reduced) by updating the bonds in a random order or in an aperiodic
manner. It also helps to use a generator of large modulus (e.g. 60 or more
bits).Comment: Revtex4, 4 page
Non Abelian gauge symmetries induced by the unobservability of extra-dimensions in a Kaluza-Klein approach
In this work we deal with the extension of the Kaluza-Klein approach to a
non-Abelian gauge theory; we show how we need to consider the link between the
n-dimensional model and a four-dimensional observer physics, in order to
reproduce fields equations and gauge transformations in the four-dimensional
picture. More precisely, in fields equations any dependence on
extra-coordinates is canceled out by an integration, as consequence of the
unobservability of extra-dimensions. Thus, by virtue of this extra-dimensions
unobservability, we are able to recast the multidimensional Einstein equations
into the four-dimensional Einstein-Yang-Mills ones, as well as all the right
gauge transformations of fields are induced. The same analysis is performed for
the Dirac equation describing the dynamics of the matter fields and, again, the
gauge coupling with Yang-Mills fields are inferred from the multidimensional
free fields theory, together with the proper spinors transformations.Comment: 5 pages, no figures, to appear in Mod. Phys. Lett.
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Longitudinal RNA-Seq analysis of acute and chronic neurogenic skeletal muscle atrophy.
Skeletal muscle is a highly adaptable tissue capable of changes in size, contractility, and metabolism according to functional demands. Atrophy is a decline in mass and strength caused by pathologic loss of myofibrillar proteins, and can result from disuse, aging, or denervation caused by injury or peripheral nerve disorders. We provide a high-quality longitudinal RNA-Seq dataset of skeletal muscle from a cohort of adult C57BL/6J male mice subjected to tibial nerve denervation for 0 (baseline), 1, 3, 7, 14, 30, or 90 days. Using an unbiased genomics approach to identify gene expression changes across the entire longitudinal course of muscle atrophy affords the opportunity to (1) establish acute responses to denervation, (2) detect pathways that mediate rapid loss of muscle mass within the first week after denervation, and (3) capture the molecular phenotype of chronically atrophied muscle at a stage when it is largely resistant to recovery
Low-energy sector of 8-dimensional General Relativity: Electro-Weak model and neutrino mass
In a Kaluza-Klein space-time , we demonstrate that the
dimensional reduction of spinors provides a 4-field, whose associated SU(2)
gauge connections are geometrized. However, additional and gauge-violating
terms arise, but they are highly suppressed by a factor , which fixes
the amount of the spinor dependence on extra-coordinates. The application of
this framework to the Electro-Weak model is performed, thus giving a lower
bound for from the request of the electric charge conservation.
Moreover, we emphasize that also the Higgs sector can be reproduced, but
neutrino masses are predicted and the fine-tuning on the Higgs parameters can
be explained, too.Comment: 14 pages, 1 figure, to appear on Int. J. Mod. Phys.
Towards Loop Quantum Gravity without the time gauge
The Hamiltonian formulation of the Holst action is reviewed and it is
provided a solution of second-class constraints corresponding to a generic
local Lorentz frame. Within this scheme the form of rotation constraints can be
reduced to a Gauss-like one by a proper generalization of
Ashtekar-Barbero-Immirzi connections. This result emphasizes that the Loop
Quantum Gravity quantization procedure can be applied when the time-gauge
condition does not stand.Comment: 5 pages, accepted for publication in Phys. Rev. Let
First results on the use of a EDXRF scanner for 3D imaging of paintings
A 3D map of chemical elements distribution from energy-dispersive X-ray fluorescence (EDXRF) analysis would be a perfect conclusion in a detailed study of any type of artifact. This map can be easily achieved by using synchrotron light as source of radiation, and microoptics both at the source and at the detector. In such a manner a micro-voxel is irradiated and detected, which can be at any depth with respect to the surface of the artifact. This method is effective but needs a high-intensity X-ray source; therefore, its use in archaeometry is limited. An alternative method is proposed in the present paper, which uses a portable EDXRF-device to measure the altered Kα/Kβ or Lα/Lβ-ratios, which allow to locate the chemical elements. Several examples are described
On the Properties of a Bundle of Flexible Actin Filaments in an Optical Trap
We establish the Statistical Mechanics framework for a bundle of Nf living
and uncrosslinked actin filaments in a supercritical solution of free monomers
pressing against a mobile wall. The filaments are anchored normally to a fixed
planar surface at one of their ends and, because of their limited flexibility,
they grow almost parallel to each other. Their growing ends hit a moving
obstacle, depicted as a second planar wall, parallel to the previous one and
subjected to a harmonic compressive force. The force constant is denoted as
trap strength while the distance between the two walls as trap length to make
contact with the experimental optical trap apparatus. For an ideal solution of
reactive filaments and free monomers at fixed free monomers chemical potential,
we obtain the general expression for the grand potential from which we derive
averages and distributions of relevant physical quantities, namely the obstacle
position, the bundle polymerization force and the number of filaments in direct
contact with the wall. The grafted living filaments are modeled as discrete
Wormlike chains, with Factin persistence length, subject to discrete contour
length variations to model single monomer (de)polymerization steps. Rigid
filaments, either isolated or in bundles, all provide average values of the
stalling force in agreement with Hill's predictions, independent of the average
trap length. Flexible filaments instead, for values of the trap strength
suitable to prevent their lateral escape, provide an average bundle force and
an average trap length slightly larger than the corresponding rigid cases (few
percents). Still the stalling force remains nearly independent on the average
trap length, but results from the product of two strongly L dependent
contributions: the fraction of touching filaments and the single filament
buckling force.Comment: 21 pages, 8 figure
Excitons in carbon nanotubes: an ab initio symmetry-based approach
The optical absorption spectrum of the carbon (4,2) nanotube is computed
using an ab-initio many-body approach which takes into account excitonic
effects. We develop a new method involving a local basis set which is symmetric
with respect to the screw symmetry of the tube. Such a method has the
advantages of scaling faster than plane-wave methods and allowing for a precise
determination of the symmetry character of the single particle states,
two-particle excitations, and selection rules. The binding energy of the
lowest, optically active states is approximately 0.8 eV. The corresponding
exciton wavefunctions are delocalized along the circumference of the tube and
localized in the direction of the tube axis.Comment: 4 pages, 1 LaTex file + 4 eps figure
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