A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Towards a single crystal Raman spectrum of kaolinite at 77 K

The Raman spectra at 77 K of the hydroxyl stretching of kaolinite were obtained along the three axes perpendicular to the crystal faces. Raman bands were observed at 3616, 3658 and 3677 cm−1 together with a distinct band observed at 3691 cm−1 and a broad profile between 3695 and 3715 cm−1. The band at 3616 cm−1 is assigned to the inner hydroxyl. The bands at 3658 and 3677 cm−1 are attributed to the out-of-phase vibrations of the inner surface hydroxyls. The Raman spectra of the in-phase vibrations of the inner-surface hydroxyl-stretching region are described in terms of transverse and longitudinal optic splitting. The band at 3691 cm−1 is assigned to the transverse optic and the broad profile to the longitudinal optic mode. This splitting remained even at liquid nitrogen temperature. The transverse optic vibration may be curve resolved into two or three bands, which are attributed to different types of hydroxyl groups in the kaolinite.

An infrared spectroscopic study of the some Autunite minerals

A series of selected autunites with phosphate as the anion have been studied using infrared spectroscopy. Each autunite mineral has its own characteristic spectrum. The spectra for different autunites with the same composition are different. It is proposed that this difference is due to the structure of water and hydrated cations in the interlayer region between the uranyl phosphate sheets. This structure is different for different autunites. The position of the water hydroxyl stretching bands is related to the strength of the hydrogen bonds as determined by hydrogen bond distance. The highly ordered structure of water is also observed in the water HOH bending modes where a high wavenumber bands are observed. The phosphate and uranyl stretching vibrations overlap and are obtained by curve resolution.

Deniable Authenticated Key Establishment for Internet Protocols

We propose two public-key schemes to achieve “deniable authentication” for the Internet Key Exchange (IKE). Our protocols can be implemented using different concrete mechanisms and we discuss different options; in particular we suggest solutions based on elliptic curve pairings. The protocol designs use the modular construction method of Canetti and Krawczyk which provides the basis for a proof of security. Our schemes can, in some situations, be more efficient than existing IKE protocols as well as having stronger deniability properties.

Response and damage evaluation of reinforced concrete frames subjected to blast loading

Bomb attacks carried out by terrorists, targeting high occupancy buildings, have become increasingly common in recent times. Large numbers of casualties and property damage result from overpressure of the blast followed by failing of structural elements. Understanding the blast response of multi-storey buildings and evaluating their remaining life have therefore become important. Response and damage analysis of single structural components, such as columns or slabs, to explosive loads have been examined in the literature, but the studies on blast response and damage analysis of structural frames in multi-storey buildings is limited and this is necessary for assessing the vulnerability of them. This paper investigates the blast response and damage evaluation of reinforced concrete (RC) frames, designed for normal gravity loads, in order to evaluate their remaining life. Numerical modelling and analysis were carried out using the explicit finite element software, LS DYNA. The modelling and analysis takes into consideration reinforcement details together and material performance under higher strain rates. Damage indices for columns are calculated based on their residual and original capacities. Numerical results generated in the can be used to identify relationships between the blast load parameters and the column damage. Damage index curve will provide a simple means for assessing the damage to a typical multi-storey building RC frame under an external bomb circumstance.

Characterization of commercial double-walled carbon nanotube material : composition, structure, and heat capacity

A purified commercial double-walled carbon nanotube (DWCNT) sample was investigated by transmission electron microscopy (TEM), thermogravimetry (TG), and Raman spectroscopy. Moreover, the heat capacity of the DWCNT sample was determined by temperature-modulated differential scanning calorimetry in the range of temperature between -50 and 290 °C. The main thermo-oxidation characterized by TG occurred at 474 °C with the loss of 90 wt% of the sample. Thermo-oxidation of the sample was also investigated by high-resolution TG, which indicated that a fraction rich in carbon nanotube represents more than 80 wt% of the material. Other carbonaceous fractions rich in amorphous coating and graphitic particles were identified by the deconvolution procedure applied to the derivative of TG curve. Complementary structural data were provided by TEM and Raman studies. The information obtained allows the optimization of composites based on this nanomaterial with reliable characteristics.

Radiographic outcomes over time after endoscopic anterior scoliosis correction

A prospective, consecutive series of 106 patients receiving endoscopic anterior scoliosis correction. The aim was to analyse changes in radiographic parameters and rib hump in the two years following surgery. Endoscopic anterior scoliosis correction is a level sparing approach, therefore it is important to assess the amount of decompensation which occurs after surgery. All patients received a single anterior rod and vertebral body screws using a standard compression technique. Cleared disc spaces were packed with either mulched femoral head allograft or rib head/iliac crest autograft. Radiographic parameters (major, instrumented, minor Cobb, T5-T12 kyphosis) and rib hump were measured at 2,6,12 and 24 months after surgery. Paired t-tests and Wilcoxon signed ranks tests were used to assess the statistical significant of changes between adjacent time intervals.----- Results: Mean loss of major curve correction from 2 to 24 months after surgery was 4 degrees. Mean loss of rib hump correction was 1.4 degrees. Mean sagittal kyphosis increased from 27 degrees at 2 months to 30.6 degrees at 24 months. Rod fractures and screw-related complications resulted in several degrees less correction than patients without complications, but overall there was no clinically significant decompensation following complications. The study concluded that there are small changes in deformity measures after endoscopic anterior scoliosis surgery, which are statistically significant but not clinically significant.

i-Cobb - An innovative technique in spinal radiographic measurement

The measurement of Cobb angles from radiographs is routine practice in spinal clinics. The technique relies on the use and availability of specialist equipment such as a goniometer, cobbometer or protractor. The aim of this study was to validate the use of i-Phone (Apple Inc) combined with Tilt Meter Pro software as compared to a protractor in the measurement of Cobb angles. Between November 2008 and December 2008 20 patients were selected at random from the Paediatric Spine Research Groups Database. A power calculation was performed which indicated if n=240 measurements the study had a 96% chance of detecting a 5 degree difference between groups. All patients had idiopathic scoliosis with a range of curve types and severities. The study found the i-Phone combined with Tilt Meter Pro software offers a faster alternative to the traditional method of Cobb angle measurement. The use of i-Phone offers a more convenient way of measuring Cobb angles in the outpatient setting. The intra-observer repeatability of the iPhone is equivalent to the protractor in the measurement of Cobb angles.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how AIS affects bone density distribution within the vertebrae. Existing pre-operative CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. This study demonstrated that AIS patients have a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. To the best of our knowledge, the only previous studies of bone density distribution in AIS are those of Périé et al [1,2], who reported a coronal plane ‘mechanical migration’ of 0.54mm toward the concavity of the scoliotic curve in the lumbar apical vertebrae of 11 scoliosis patients. This is comparable to the value of 0.8mm (4%) in our study, especially since our patients had more severe scoliotic curves. From a bone adaptation perspective, these results suggest that the axial loading on the scoliotic spine is strongly asymmetric.

Computed tomography evaluation of axial vertebral derotation in endoscopic anterior instrumentation for adolescent idiopathic scoliosis

Thoracoscopic instrumented anterior spinal fusion for adolescent idiopathic scoliosis (AIS) has clinical benefits that include reduced pulmonary morbidity, postoperative pain, and improved cosmesis. However, quantitative data on radiological improvement of vertebral rotation using this method is lacking. This study’s objectives were to measure preoperative and postoperative axial vertebral rotational deformity at the curve apex in endoscopically-treated anterior-instrumented scoliosis patients using CT, and assess the relevance of these findings to clinically measured chest wall rib hump deformity correction. This is the first quantitative CT study to confirm that endoscopic anterior instrumented fusion for AIS substantially improves axial vertebral body rotational deformity at the apex of the curve. The margin of correction of 43% compares favourably with historically published figures of 24% for patients with posterior all-hook-rod constructs. CT measurements correlated significantly to the clinical outcome of rib hump deformity correction.

Neurolinguistic contributions to understanding the bilingual mental lexicon

Introduction Many bilinguals will have had the experience of unintentionally reading something in a language other than the intended one (e.g. MUG to mean mosquito in Dutch rather than a receptacle for a hot drink, as one of the possible intended English meanings), of finding themselves blocked on a word for which many alternatives suggest themselves (but, somewhat annoyingly, not in the right language), of their accent changing when stressed or tired and, occasionally, of starting to speak in a language that is not understood by those around them. These instances where lexical access appears compromised and control over language behavior is reduced hint at the intricate structure of the bilingual lexical architecture and the complexity of the processes by which knowledge is accessed and retrieved. While bilinguals might tend to blame word finding and other language problems on their bilinguality, these difficulties per se are not unique to the bilingual population. However, what is unique, and yet far more common than is appreciated by monolinguals, is the cognitive architecture that subserves bilingual language processing. With bilingualism (and multilingualism) the rule rather than the exception (Grosjean, 1982), this architecture may well be the default structure of the language processing system. As such, it is critical that we understand more fully not only how the processing of more than one language is subserved by the brain, but also how this understanding furthers our knowledge of the cognitive architecture that encapsulates the bilingual mental lexicon. The neurolinguistic approach to bilingualism focuses on determining the manner in which the two (or more) languages are stored in the brain and how they are differentially (or similarly) processed. The underlying assumption is that the acquisition of more than one language requires at the very least a change to or expansion of the existing lexicon, if not the formation of language-specific components, and this is likely to manifest in some way at the physiological level. There are many sources of information, ranging from data on bilingual aphasic patients (Paradis, 1977, 1985, 1997) to lateralization (Vaid, 1983; see Hull & Vaid, 2006, for a review), recordings of event-related potentials (ERPs) (e.g. Ardal et al., 1990; Phillips et al., 2006), and positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) studies of neurologically intact bilinguals (see Indefrey, 2006; Vaid & Hull, 2002, for reviews). Following the consideration of methodological issues and interpretative limitations that characterize these approaches, the chapter focuses on how the application of these approaches has furthered our understanding of (1) selectivity of bilingual lexical access, (2) distinctions between word types in the bilingual lexicon and (3) control processes that enable language selection.