Approximating multi-dimensional Hamiltonian flows by billiards

Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the original billiard, and provide asymptotic expansion of the smooth Hamiltonian solution in terms of these billiard approximations. The asymptotic expansion includes error estimates in the $C^{r}$ norm and an iteration scheme for improving this approximation. Applying this theory to smooth potentials which limit to the multi-dimensional close to ellipsoidal billiards, we predict when the separatrix splitting persists for various types of potentials

Billiards with polynomial mixing rates

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.Comment: 39pages, 11 figue

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction

Growth and dislocation studies of β-HMX

Background: The defect structure of organic materials is important as it plays a major role in their crystal growth properties. It also can play a subcritical role in “hot-spot” detonation processes of energetics and one such energetic is cyclotetramethylene-tetranitramine, in the commonly used beta form (β-HMX). Results: The as-grown crystals grown by evaporation from acetone show prismatic, tabular and columnar habits, all with {011}, {110}, (010) and (101) faces. Etching on (010) surfaces revealed three different types of etch pits, two of which could be identified with either pure screw or pure edge dislocations, the third is shown to be an artifact of the twinning process that this material undergoes. Examination of the {011} and {110} surfaces show only one type of etch pit on each surface; however their natural asymmetry precludes the easy identification of their Burgers vector or dislocation type. Etching of cleaved {011} surfaces demonstrates that the etch pits can be associated with line dislocations. All dislocations appear randomly on the crystal surfaces and do not form alignments characteristic of mechanical deformation by dislocation slip. Conclusions: Crystals of β-HMX grown from acetone show good morphological agreement with that predicted by modelling, with three distinct crystal habits observed depending upon the supersaturation of the growth solution. Prismatic habit was favoured at low supersaturation, while tabular and columnar crystals were predominant at higher super saturations. The twin plane in β-HMX was identified as a (101) reflection plane. The low plasticity of β-HMX is shown by the lack of etch pit alignments corresponding to mechanically induced dislocation arrays. On untwinned {010} faces, two types of dislocations exist, pure edge dislocations with b = [010] and pure screw dislocations with b = [010]. On twinned (010) faces, a third dislocation type exists and it is proposed that these pits are associated with pure screw dislocations with b = [010]

How metal films de-wet substrates - identifying the kinetic pathways and energetic driving forces

We study how single-crystal chromium films of uniform thickness on W(110) substrates are converted to arrays of three-dimensional (3D) Cr islands during annealing. We use low-energy electron microscopy (LEEM) to directly observe a kinetic pathway that produces trenches that expose the wetting layer. Adjacent film steps move simultaneously uphill and downhill relative to the staircase of atomic steps on the substrate. This step motion thickens the film regions where steps advance. Where film steps retract, the film thins, eventually exposing the stable wetting layer. Since our analysis shows that thick Cr films have a lattice constant close to bulk Cr, we propose that surface and interface stress provide a possible driving force for the observed morphological instability. Atomistic simulations and analytic elastic models show that surface and interface stress can cause a dependence of film energy on thickness that leads to an instability to simultaneous thinning and thickening. We observe that de-wetting is also initiated at bunches of substrate steps in two other systems, Ag/W(110) and Ag/Ru(0001). We additionally describe how Cr films are converted into patterns of unidirectional stripes as the trenches that expose the wetting layer lengthen along the W[001] direction. Finally, we observe how 3D Cr islands form directly during film growth at elevated temperature. The Cr mesas (wedges) form as Cr film steps advance down the staircase of substrate steps, another example of the critical role that substrate steps play in 3D island formation

In vitro production of bovine embryos derived from individual donors in the Corral® dish

Background: Since the identity of the embryo is of outmost importance during commercial in vitro embryo production, bovine oocytes and embryos have to be cultured strictly per donor. Due to the rather low yield of oocytes collected after ovum pick-up (OPU) per individual cow, oocyte maturation and embryo culture take place in small groups, which is often associated with inferior embryo development. The objective of this study was to improve embryonic development in small donor groups by using the Corral (R) dish. This commercial dish is designed for human embryo production. It contains two central wells that are divided into quadrants by a semi-permeable wall. In human embryo culture, one embryo is placed per quadrant, allowing individual follow-up while embryos are exposed to a common medium. In our study, small groups of oocytes and subsequently embryos of different bovine donors were placed in the Corral (R) dish, each donor group in a separate quadrant. Results: In two experiments, the Corral (R) dish was evaluated during in vitro maturation (IVM) and/or in vitro culture (IVC) by grouping oocytes and embryos of individual bovine donors per quadrant. At day 7, a significantly higher blastocyst rate was noted in the Corral (R) dish used during IVM and IVC than when only used during IVM (12.9% +/- 2.10 versus 22.8% +/- 2.67) (P < 0.05). However, no significant differences in blastocyst yield were observed anymore between treatment groups at day 8 post insemination. Conclusions: In the present study, the Corral (R) dish was used for in vitro embryo production (IVP) in cattle; allowing to allocate oocytes and/or embryos per donor. As fresh embryo transfers on day 7 have higher pregnancy outcomes, the Corral (R) dish offers an added value for commercial OPU/IVP, since a higher blastocyst development at day 7 is obtained when the Corral (R) dish is used during IVM and IVC

Pseudo-Label Assisted nnU-Net enables automatic segmentation of 7T MRI from a single acquisition

IntroductionAutomatic whole brain and lesion segmentation at 7T presents challenges, primarily from bias fields, susceptibility artifacts including distortions, and registration errors. Here, we sought to use deep learning algorithms (D/L) to do both skull stripping and whole brain segmentation on multiple imaging contrasts generated in a single Magnetization Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE) acquisition on participants clinically diagnosed with multiple sclerosis (MS), bypassing registration errors.MethodsBrain scans Segmentation from 3T and 7T scanners were analyzed with software packages such as FreeSurfer, Classification using Derivative-based Features (C-DEF), nnU-net, and a novel 3T-to-7T transfer learning method, Pseudo-Label Assisted nnU-Net (PLAn). 3T and 7T MRIs acquired within 9 months from 25 study participants with MS (Cohort 1) were used for training and optimizing. Eight MS patients (Cohort 2) scanned only at 7T, but with expert annotated lesion segmentation, was used to further validate the algorithm on a completely unseen dataset. Segmentation results were rated visually by experts in a blinded fashion and quantitatively using Dice Similarity Coefficient (DSC).ResultsOf the methods explored here, nnU-Net and PLAn produced the best tissue segmentation at 7T for all tissue classes. In both quantitative and qualitative analysis, PLAn significantly outperformed nnU-Net (and other methods) in lesion detection in both cohorts. PLAn's lesion DSC improved by 16% compared to nnU-Net.DiscussionLimited availability of labeled data makes transfer learning an attractive option, and pre-training a nnUNet model using readily obtained 3T pseudo-labels was shown to boost lesion detection capabilities at 7T

Highly efficient separation of actinides from lanthanides by a phenanthroline-derived bis-triazine ligand

The synthesis, lanthanide complexation, and solvent ex- traction of actinide(III) and lanthanide(III) radiotracers from nitric acid solutions by a phenanthroline-derived quadridentate bis-triazine ligand are described. The ligand separates Am(III) and Cm(III) from the lanthanides with remarkably high efficiency, high selectivity, and fast extraction kinetics compared to its 2,2'-bipyridine counterpart. Structures of the 1:2 bis-complexes of the ligand with Eu(III) and Yb(III) were elucidated by X-ray crystallography and force field calculations, respec-tively. The Eu(III) bis-complex is the first 1:2 bis-complex of a quadridentate bis-triazine ligand to be characterized by crystallography. The faster rates of extraction were verified by kinetics measurements using the rotating membrane cell technique in several diluents. The improved kinetics of metal ion extraction are related to the higher surface activity of the ligand at the phase interface. The improvement in the ligand's properties on replacing the bipyridine unit with a phenanthroline unit far exceeds what was anticipated based on ligand design alone

Obstetric fistula in Burundi: a comprehensive approach to managing women with this neglected disease.

BACKGROUND: In Burundi, the annual incidence of obstetric fistula is estimated to be 0.2-0.5% of all deliveries, with 1000-2000 new cases per year. Despite this relatively high incidence, national capacity for identifying and managing obstetric fistula is very limited. Thus, in July 2010, Medecins Sans Frontieres (MSF) set up a specialised Obstetric Fistula Centre in Gitega (Gitega Fistula Centre, GFC), the only permanent referral centre for obstetric fistula in Burundi. A comprehensive model of care is offered including psychosocial support, conservative and surgical management, post-operative care and follow-up. We describe this model of care, patient outcomes and the operational challenges. METHODS: Descriptive study using routine programme data. RESULTS: Between July 2010 and December 2011, 470 women with obstetric fistula presented for the first time at GFC, of whom 458 (98%) received treatment. Early urinary catheterization (conservative management) was successful in four out of 35 (11%) women. Of 454 (99%) women requiring surgical management, 394 (87%) were discharged with a closed fistula, of whom 301 (76%) were continent of urine and/or faeces, while 93 (24%) remained incontinent of urine and/or faeces. In 59 (13%) cases, the fistula was complex and could not be closed. Outcome status was unknown for one woman. Median duration of stay at GFC was 39 days (Interquartile range IQR, 31-51 days). CONCLUSION: In a rural African setting, it is feasible to implement a comprehensive package of fistula care using a dedicated fistula facility, and satisfactory surgical repair outcomes can be achieved. Several operational challenges are discussed