Discontinuous shear modulus determines the glass transition temperature

A solid - amorphous or crystalline - is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long wavelength limit of the dispersion relation we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behaviour of the elastic moduli at the glass transition. This not only determines the transition temperature T_G of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behaviour.Comment: 8 pages, 6 figure

A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems

Retrospective Analysis of Wood Anatomical Traits Reveals a Recent Extension in Tree Cambial Activity in Two High-Elevation Conifers

The study of xylogenesis or wood formation is a powerful, yet labor intensive monitoring approach to investigate intra-annual tree growth responses to environmental factors. However, it seldom covers more than a few growing seasons, so is in contrast to the much longer lifespan of woody plants and the time scale of many environmental processes. Here we applied a novel retrospective approach to test the long-term (1926–2012) consistency in the timing of onset and ending of cambial activity, and in the maximum cambial cell division rate in two conifer species, European larch and Norway spruce at high-elevation in the Alps. We correlated daily temperature with time series of cell number and lumen area partitioned into intra-annual sectors. For both species, we found a good correspondence (1–10 days offset) between the periods when anatomical traits had significant correlations with temperature in recent decades (1969–2012) and available xylogenesis data (1996–2005), previously collected at the same site. Yet, results for the 1926–1968 period indicate a later onset and earlier ending of the cambial activity by 6–30 days. Conversely, the peak in the correlation between annual cell number and temperature, which should correspond to the peak in secondary growth rate, was quite stable over time, with just a minor advance of 4–5 days in the recent decades. Our analyses on time series of wood anatomical traits proved useful to infer on past long-term changes in xylogenetic phases. Combined with intensive continuous monitoring, our approach will improve the understanding of tree responses to climate variability in both the short- and long-term context

Lepton asymmetry and primordial nucleosynthesis in the era of precision cosmology

We calculate and display the primordial light-element abundances as a function of a neutrino degeneracy parameter \xi common to all flavors. It is the only unknown parameter characterizing the thermal medium at the primordial nucleosynthesis epoch. The observed primordial helium abundance Y_p is the most sensitive cosmic ``leptometer.'' Adopting the conservative Y_p error analysis of Olive and Skillman implies -0.04 \alt \xi \alt 0.07 whereas the errors stated by Izotov and Thuan imply \xi=0.0245+-0.0092 (1 sigma). Improved determinations of the baryon abundance have no significant impact on this situation. A determination of Y_p that reliably distinguishes between a vanishing or nonvanishing \xi is a crucial test of the cosmological standard assumption that sphaleron effects equilibrate the cosmic lepton and baryon asymmetries.Comment: 5 pages, 2 figures; minor changes, references added, replaced to match the published version in PRD (Brief Reports

A simple minimax estimator for quantum states

Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting the gathered data into an estimate of the state works very well. For smaller data sets, however, it often suffers from problems of rank deficiency in the estimated state. For many systems of relevance for quantum information processing, the preparation of a very large number of copies of the same quantum state is still a technological challenge, which motivates us to look for estimation strategies that perform well even when there is not much data. In this article, we review the concept of minimax state estimation, and use minimax ideas to construct a simple estimator for quantum states. We demonstrate that, for the case of tomography of a single qubit, our estimator significantly outperforms the ML estimator for small number of copies of the state measured. Our estimator is always full-rank, and furthermore, has a natural dependence on the number of copies measured, which is missing in the ML estimator.Comment: 26 pages, 3 figures. v2 contains minor improvements to the text, and an additional appendix on symmetric measurement

Quantum control of electron--phonon scatterings in artificial atoms

The phonon-induced dephasing dynamics in optically excited semiconductor quantum dots is studied within the frameworks of the independent Boson model and optimal control. We show that appropriate tailoring of laser pulses allows a complete control of the optical excitation despite the phonon dephasing, a finding in marked contrast to other environment couplings.Comment: to appear in Phys. Rev. Let

Studying carbonisation with raman spectroscopy

Raman spectroscopy can provide fast and non-destructive analysis of carbonaceous materials. As it is able to detect nanometre-sized structural features, Raman spectroscopy is widely used in the study of carbon nanotubes, fullerenes, graphenes, and many other carbon-rich materials. Raman analysis has previously shown potential for estimating the heat treatment temperatures (HTT) employed in the preparation of Japanese cedar charcoals which suggested future usefulness in quality control . In the current work, Raman spectroscopy was used to investigate the nanostructural development which had occurred within various chars prepared and carbonised at a range of heat treatment temperatures between ≈ 340°C and 1000°C. Chars were produced from sucrose sugar as standard precursor of high purity and two sources of biomass common in New Zealand (Radiata pine wood and Harakeke leaf fibres). In chars produced at lower HTTs, signals could be detected which were interpreted as representing hydrogen-rich amorphous carbon structures. In contrast, the Raman spectra of well-carbonised chars produced at higher HTTs featured signals consistent with graphene-like structures with coherent domains limited in size to below a few nanometres across. Measurement of such signals provides the ability to evaluate the extent of nanostructural development, identify char samples which are ‘undercooked’ when compared to other char samples, and estimate effective HTTs used in the production of a given char sample. More detailed Raman analysis of Radiata-derived chars was carried out, including analysis of chars produced from carbonising pyrolysis tars. Results of Raman analysis were correlated to H/C atom ratios obtained through elemental analysis for these chars produced from Radiata pine