14,471 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
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
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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