Conical defects in growing sheets

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle $se$ at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if $se <= 0$, the disc can fold into one of a discrete infinite number of states if $se$ is positive. We construct these states in the regime where bending dominates, determine their energies and how stress is distributed in them. For each state a critical value of $se$ is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has two-fold symmetry.Comment: 4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to the one published in PR

Experimentally induced incomplete burst fractures - a novel technique for calf and human specimens

Background: Fracture morphology is crucial for the clinical decision-making process preceding spinal fracture treatment. The presented experimental approach was designed in order to ensure reproducibility of induced fracture morphology. Results: The presented method resulted in fracture morphology, found in clinical classification systems like the Magerl classification. In the calf spine samples, 70% displayed incomplete burst fractures corresponding to type A3.1 and A3.2 fractures. In all human samples, superior incomplete burst fractures (Magerl A3.1) were identified by an independent radiologist and spine surgeon. Conclusions: The presented set up enables the first experimental means to reliably model and study distinct incomplete burst fracture patterns in an in vitro setting. Thus, we envisage this protocol to facilitate further studies on spine fracture treatment of incomplete burst fractures

De Branges spaces and Krein's theory of entire operators

This work presents a contemporary treatment of Krein's entire operators with deficiency indices $(1,1)$ and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected and the interplay between them has had an impact in both spectral theory and the theory of functions. This work exhibits the interrelation between Krein's and de Branges' theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors were corrected. The bibliography style was change

Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

Inflationary Perturbations: the Cosmological Schwinger Effect

This pedagogical review aims at presenting the fundamental aspects of the theory of inflationary cosmological perturbations of quantum-mechanical origin. The analogy with the well-known Schwinger effect is discussed in detail and a systematic comparison of the two physical phenomena is carried out. In particular, it is demonstrated that the two underlying formalisms differ only up to an irrelevant canonical transformation. Hence, the basic physical mechanisms at play are similar in both cases and can be reduced to the quantization of a parametric oscillator leading to particle creation due to the interaction with a classical source: pair production in vacuum is therefore equivalent to the appearance of a growing mode for the cosmological fluctuations. The only difference lies in the nature of the source: an electric field in the case of the Schwinger effect and the gravitational field in the case of inflationary perturbations. Although, in the laboratory, it is notoriously difficult to produce an electric field such that pairs extracted from the vacuum can be detected, the gravitational field in the early universe can be strong enough to lead to observable effects that ultimately reveal themselves as temperature fluctuations in the Cosmic Microwave Background. Finally, the question of how quantum cosmological perturbations can be considered as classical is discussed at the end of the article.Comment: 49 pages, 6 figures, to appear in a LNP volume "Inflationary Cosmology

Predicted gamma-ray line emission from the Cygnus complex

The Cygnus region harbours a huge complex of massive stars at a distance of 1.0-2.0kpc from us. About 170 O stars are distributed over several OB associations, among which the Cyg OB2 cluster is by far the most important with about 100-120 O stars. These massive stars inject large quantities of radioactive nuclei into the interstellar medium, such as 26Al and 60Fe, and their gamma-ray line decay signals can provide insight into the physics of massive stars and core-collapse supernovae. Past studies of the nucleosynthesis activity of Cygnus have concluded that the level of 26Al decay emission as deduced from CGRO/COMPTEL observations was a factor 2-3 above the predictions based on the theoretical yields available at that time and on the observed stellar content of the Cygnus region. We reevaluate the situation from new measurements of the gamma-ray decay fluxes with INTEGRAL/SPI and new predictions based on recently improved stellar models including some of the effects of stellar rotation for the higher mass stars and a coherent estimate of the contribution from SNIb/c. We developed a population synthesis code to predict the nucleosynthesis activity and corresponding decay fluxes of a given stellar population of massive stars. The observed decay fluxes from the Cygnus complex are found to be consistent with the values predicted by population synthesis at solar metallicity. The observed extent of the 1809keV emission from Cygnus is found to be consistent with the result of a numerical simulation of the diffusion of 26Al inside the superbubble blown by Cyg OB2. Our work indicates that the past dilemma regarding the gamma-ray line emission from Cygnus resulted from an overestimate of the 1809keV flux of the Cygnus complex, combined with an underestimate of the nucleosynthesis yields.Comment: 13 pages, 9 figures, accepted for publication in A&

Bohr-Sommerfeld quantization and meson spectroscopy

We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulae for the energy spectra which closely approximate numerical exact calculations performed with the Schrodinger or the spinless Salpeter equations. The Bohr-Sommerfeld quantization procedure can also be used to calculate other observables such as r.m.s. radius or wave function at the origin. Asymptotic dependence of these observables on quantum numbers are also obtained in the case of potentials which behave asymptotically as a power-law. We discuss the constraints imposed by these formulae on the dynamics of the quark-antiquark interaction.Comment: 13 page

New observations on test architecture and construction of Jullienella foetida Schlumberger, 1890, the largest shallow-water agglutinated foraminifer in modern oceans

We present new observations on Jullienella foetida Schlumberger, 1890, a giant agglutinated foraminifer with a leaf- or fan-like test reaching a maximum dimension of 14 cm, that is common on some parts of the west African continental shelf. The test wall comprises a smooth, outer veneer of small (7.0 g wet weight m−2 for the seafloor biomass of J. foetida in areas where it is particularly abundant. The relatively restricted distribution of this species off the north-west African coast at depths above 100 m is probably related to the elevated, upwelling-related surface productivity along this margin, which provides enough food to sustain this high biomass. This remarkable species appears to play an important, perhaps keystone, role in benthic ecosystems where it is abundant, providing the only common hard substrate on which sessile organisms can settle

Sharp interface limits of phase-field models

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface limit'' from phase field models which have interfaces that are diffuse on a length scale $\xi$. In particular,phase-field equations are mapped onto sharp interface equations in the limits $\xi \kappa \ll 1$ and $\xi v/D \ll 1$, where $\kappa$ and $v$ are respectively the interface curvature and velocity and $D$ is the diffusion constant in the bulk. The calculations provide one general set of sharp interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation and the Kardar-Parisi-Zhang equation.Comment: 17 pages, 9 figure