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 $d \times d$ 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 $d \times d$ 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 $2 \times 2$ 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 $\mathsf{A}_{\alpha_*}$ does not satisfy the finiteness property.Comment: 27 pages, 2 figure