Three-dimensional compressible stability-transition calculations using the spatial theory

The e(exp n)-method is employed with the spatial amplification theory to compute the onset of transition on a swept wing tested in transonic cryogenic flow conditions. Two separate eigenvalue formulations are used. One uses the saddle-point method and the other assumes that the amplification vector is normal to the leading edge. Comparisons of calculated results with experimental data show that both formulations give similar results and indicate that the wall temperature has a rather strong effect on the value of the n factor

Tubular Surface Evolution for Segmentation of the Cingulum Bundle From DW-MRI

Presented at the 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical and Statistical Methods for Biological Shape Variability Modeling, September 6th, 2008, Kimmel Center, New York, USA.This work provides a framework for modeling and extracting the Cingulum Bundle (CB) from Diffusion-Weighted Imagery (DW-MRI) of the brain. The CB is a tube-like structure in the brain that is of potentially of tremendous importance to clinicians since it may be helpful in diagnosing Schizophrenia. This structure consists of a collection of fibers in the brain that have locally similar diffusion patterns, but vary globally. Standard region-based segmentation techniques adapted to DW-MRI are not suitable here because the diffusion pattern of the CB cannot be described by a global set of simple statistics. Active surface models extended to DW-MRI are not suitable since they allow for arbitrary deformations that give rise to unlikely shapes, which do not respect the tubular geometry of the CB. In this work, we explicitly model the CB as a tube-like surface and construct a general class of energies defined on tube-like surfaces. An example energy of our framework is optimized by a tube that encloses a region that has locally similar diffusion patterns, which differ from the diffusion patterns immediately outside. Modeling the CB as a tube-like surface is a natural shape prior. Since a tube is characterized by a center-line and a radius function, the method is reduced to a 4D (center-line plus radius) curve evolution that is computationally much less costly than an arbitrary surface evolution. The method also provides the center-line of CB, which is potentially of clinical significance

Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels

The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions for continuous kernels $K$ that are homogeneous of degree $\gamma \in [0,1)$ and satisfy $K(x,y) \leq C (x^{\gamma} + y^{\gamma})$. More precisely, for any $\rho \in (\gamma,1)$ we establish the existence of a continuous weak self-similar profile with decay $x^{-(1{+}\rho)}$ as $x \to \infty$

The Incidence and Clinical Relevance of Graft Hypertrophy After Matrix-Based Autologous Chondrocyte Implantation

Background: Graft hypertrophy is the most common complication of periosteal autologous chondrocyte implantation (p-ACI). Purpose: The aim of this prospective study was to analyze the development, the incidence rate, and the persistence of graft hypertrophy after matrix-based autologous chondrocyte implantation (mb-ACI) in the knee joint within a 2-year postoperative course. Study Design: Case series; Level of evidence, 4. Methods: Between 2004 and 2007, a total of 41 patients with 44 isolated cartilage defects of the knee were treated with the mb-ACI technique. The mean age of the patients was 35.8 years (standard deviation [SD], 11.3 years), and the mean body mass index was 25.9 (SD, 4.2; range, 19-35.3). The cartilage defects were arthroscopically classified as Outerbridge grades III and IV. The mean area of the cartilage defect measured 6.14 cm2 (SD, 2.3 cm2). Postoperative clinical and magnetic resonance imaging (MRI) examinations were conducted at 3, 6, 12, and 24 months to analyze the incidence and course of the graft. Results: Graft hypertrophy developed in 25% of the patients treated with mb-ACI within a postoperative course of 1 year; 16% of the patients developed hypertrophy grade 2, and 9% developed hypertrophy grade 1. Graft hypertrophy occurred primarily in the first 12 months and regressed in most cases within 2 years. The International Knee Documentation Committee (IKDC) and visual analog scale (VAS) scores improved during the postoperative follow-up time of 2 years. There was no difference between the clinical results regarding the IKDC and VAS pain scores and the presence of graft hypertrophy. Conclusion: The mb-ACI technique does not lead to graft hypertrophy requiring treatment as opposed to classic p-ACI. The frequency of occurrence of graft hypertrophy after p-ACI and mb-ACI is comparable. Graft hypertrophy can be considered as a temporary excessive growth of regenerative cartilage tissue rather than a true graft hypertrophy. It is therefore usually not a persistent or systematic complication in the treatment of circumscribed cartilage defects with mb-ACI

Regression uncertainty on the Grassmannian

Trends in longitudinal or cross-sectional studies over time are often captured through regression models. In their simplest manifestation, these regression models are formulated in ℝn. However, in the context of imaging studies, the objects of interest which are to be regressed are frequently best modeled as elements of a Riemannian manifold. Regression on such spaces can be accomplished through geodesic regression. This paper develops an approach to compute confidence intervals for geodesic regression models. The approach is general, but illustrated and specifically developed for the Grassmann manifold, which allows us, e.g., to regress shapes or linear dynamical systems. Extensions to other manifolds can be obtained in a similar manner. We demonstrate our approach for regression with 2D/3D shapes using synthetic and real data

On thermodynamically consistent Stefan problems with variable surface energy

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv admin note: substantial text overlap with arXiv:1101.376

Reproductive Biology of the Green Turtle (Chelonia mydas) at Tern Island, French Frigate Shoals, Hawai'i

We monitored nesting of the green turtle (Chelonia mydas Linnaeus) on Tern Island, French Frigate Shoals, in the Northwestern Hawaiian Islands from 1986 through 1991. Egg oviposition occurred between 26 April and 20 October. Nesting peaked between mid-June and early August. Hatchlings emerged between 8 July and 27 December. Hatchling emergence peaked between mid-August and early October. Mean incubation period was 66.0 (range 53-97) days. Mean clutch size was 92.4 (range 33-150) eggs. Mean hatching success was 78.6% when averaged over success of individual nests and 81.1% when calculated as percentage of total number of eggs. Natural hatchling emergence was 71.1 %, based on percentage of total number of eggs. Live and dead hatchlings were found when nests were excavated and accounted for 10.0% of the eggs. Incubation periods tended to be longer in early and late portions of the season than in midseason, and incubation periods tended to decrease the farther inland the nest was situated from the high tide line. Maximum hatching success occurred at an incubation length of 66.7 days. Other trends indicated that nesting peaked near 5 July when conditions produced a near optimal incubation period for yielding maximum hatching success

Quantum properties of dichroic silicon vacancies in silicon carbide

The controlled generation and manipulation of atom-like defects in solids has a wide range of applications in quantum technology. Although various defect centres have displayed promise as either quantum sensors, single photon emitters or light-matter interfaces, the search for an ideal defect with multi-functional ability remains open. In this spirit, we investigate here the optical and spin properties of the V1 defect centre, one of the silicon vacancy defects in the 4H polytype of silicon carbide (SiC). The V1 centre in 4H-SiC features two well-distinguishable sharp optical transitions and a unique S=3/2 electronic spin, which holds promise to implement a robust spin-photon interface. Here, we investigate the V1 defect at low temperatures using optical excitation and magnetic resonance techniques. The measurements, which are performed on ensemble, as well as on single centres, prove that this centre combines coherent optical emission, with up to 40% of the radiation emitted into the zero-phonon line (ZPL), a strong optical spin signal and long spin coherence time. These results single out the V1 defect in SiC as a promising system for spin-based quantum technologies