17,199 research outputs found
Global geometry of T2 symmetric spacetimes with weak regularity
We define the class of weakly regular spacetimes with T2 symmetry, and
investigate their global geometry structure. We formulate the initial value
problem for the Einstein vacuum equations with weak regularity, and establish
the existence of a global foliation by the level sets of the area R of the
orbits of symmetry, so that each leaf can be regarded as an initial
hypersurface. Except for the flat Kasner spacetimes which are known explicitly,
R takes all positive values. Our weak regularity assumptions only require that
the gradient of R is continuous while the metric coefficients belong to the
Sobolev space H1 (or have even less regularity).Comment: 5 page
_Limusaurus_ and bird digit identity
_Limusaurus_ is a remarkable herbivorous ceratosaur unique among theropods in having digits II, III and IV, with only a small metacarpal vestige of digit I. This raises interesting questions regarding the controversial identity of avian wing digits. The early tetanuran ancestors of birds had tridactyl hands with digital morphologies corresponding to digits I, II & III of other dinosaurs. In bird embryos, however, the pattern of cartilage formation indicates that their digits develop from positions that become digits II, III, & IV in other amniotes. _Limusaurus_ has been argued to provide evidence that the digits of tetanurans, currently considered to be I, II and III, may actually be digits II, III, & IV, thus explaining the embryological position of bird wing digits. However, morphology and gene expression of the anterior bird wing digit specifically resemble digit I, not II, of other amniotes. We argue that digit I loss in _Limusaurus_ is derived and thus irrelevant to understanding the development of the bird wing
Compost and digestate: sustainability, benefits, impacts for the environment and for plant production
This proceedings volume contains the papers presented at the CODIS 2008 congress held on 27 - 29 February 2008 in Solothurn (Switzerland).The composting and digestion of biogenic waste materials and the subsequent application of compost and digestate to soil contributes to nutrient recycling and renewable energy production. Moreover, compost and digestate can improve soil fertility and suppress plant diseases. On the other hand, compost and digestate may also contain a variety of pollutants hazardous to soil, such as heavy metals and organic contaminants.Compost and digestate have been thoroughly investigated in the framework of two associated projects entitled Organic Pollutants in Compost and Digestate in Switzerland and Effects of Composts and Digestate on the Environment, Soil Fertility and Plant Health. These projects yielded new insights into the properties of compost and digestate, mainly with regard to biological parameters and the occurrence of both classic and emerging organic pollutants.The CODIS 2008 congress was the final event of these two projects
Measurement of thermal conductance of silicon nanowires at low temperature
We have performed thermal conductance measurements on individual single
crystalline silicon suspended nanowires. The nanowires (130 nm thick and 200 nm
wide) are fabricated by e-beam lithography and suspended between two separated
pads on Silicon On Insulator (SOI) substrate. We measure the thermal
conductance of the phonon wave guide by the 3 method. The cross-section
of the nanowire approaches the dominant phonon wavelength in silicon which is
of the order of 100 nm at 1K. Above 1.3K the conductance behaves as T3, but a
deviation is measured at the lowest temperature which can be attributed to the
reduced geometry
Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantized
We analyze Niels Bohr's proposed two-slit interference experiment with highly
charged particles that argues that the consistency of elementary quantum
mechanics requires that the electromagnetic field must be quantized. In the
experiment a particle's path through the slits is determined by measuring the
Coulomb field that it produces at large distances; under these conditions the
interference pattern must be suppressed. The key is that as the particle's
trajectory is bent in diffraction by the slits it must radiate and the
radiation must carry away phase information. Thus the radiation field must be a
quantized dynamical degree of freedom. On the other hand, if one similarly
tries to determine the path of a massive particle through an inferometer by
measuring the Newtonian gravitational potential the particle produces, the
interference pattern would have to be finer than the Planck length and thus
undiscernable. Unlike for the electromagnetic field, Bohr's argument does not
imply that the gravitational field must be quantized.Comment: 8 pages, 4 figures. To appear in Proc. Natl. Acad. Sc
An explicit counterexample to the Lagarias-Wang finiteness conjecture
The joint spectral radius of a finite set of real matrices is
defined to be the maximum possible exponential rate of growth of long products
of matrices drawn from that set. A set of matrices is said to have the
\emph{finiteness property} if there exists a periodic product which achieves
this maximal rate of growth. J.C. Lagarias and Y. Wang conjectured in 1995 that
every finite set of real matrices satisfies the finiteness
property. However, T. Bousch and J. Mairesse proved in 2002 that
counterexamples to the finiteness conjecture exist, showing in particular that
there exists a family of pairs of matrices which contains a
counterexample. Similar results were subsequently given by V.D. Blondel, J.
Theys and A.A. Vladimirov and by V.S. Kozyakin, but no explicit counterexample
to the finiteness conjecture has so far been given. The purpose of this paper
is to resolve this issue by giving the first completely explicit description of
a counterexample to the Lagarias-Wang finiteness conjecture. Namely, for the
set \mathsf{A}_{\alpha_*}:= \{({cc}1&1\\0&1), \alpha_*({cc}1&0\\1&1)\} we
give an explicit value of \alpha_* \simeq
0.749326546330367557943961948091344672091327370236064317358024...] such that
does not satisfy the finiteness property.Comment: 27 pages, 2 figure
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