Numerical Solutions of Matrix Differential Models using Cubic Matrix Splines II

This paper presents the non-linear generalization of a previous work on matrix differential models. It focusses on the construction of approximate solutions of first-order matrix differential equations Y'(x)=f(x,Y(x)) using matrix-cubic splines. An estimation of the approximation error, an algorithm for its implementation and illustrative examples for Sylvester and Riccati matrix differential equations are given.Comment: 14 pages; submitted to Math. Comp. Modellin

Classical Boundary-value Problem in Riemannian Quantum Gravity and Self-dual Taub-NUT-(anti)de Sitter Geometries

The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact ($S^{3}$) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii $(a,b).$ For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii $(a,b),$ we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a ``cusp catastrophe'' structure with a non-self-intersecting ``catastrophe manifold'' implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between $a$ and $b$ holds. The action of this solution is proportional to $-a^{3}$ for large $a (\sim b)$ and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a ``bolt'' is investigated in a forthcoming paper.Comment: 20 pages, 11 figures; Latex; Revised version with important new results on real infilling solutions and corrections. To appear in Nuclear Physics B, issue 648 (1,2), pp. 397-41

Pioneering a novel synthetic heart valve

Introduction Cardiac valve disease results in a disruption to haemodynamics, with frequent progression to end stage heart failure if left untreated. Valve replacement restores function to the heart and thus represents a lifesaving procedure [1]. Synthetic heart valves combine the durability of mechanical valves with the haemocompatibility of bioprosthetic valves. However, challenges including calcification, leaflet tearing and poor surface morphology mean that they have yet to reach clinical translation. The design of the Wheatley Heart Valve (WHV, Figure 1a) differs considerably from existing polymeric heart valves as it can be mathematically defined through a series of contiguous circles [2]. This permits changes to the design to be parametrically investigated (by changing the radius of the free edge and leaflet height) and facilitates a sinus washout through helical flow as blood exists the aorta. Computational mathematical modelling, in vitro testing and advanced surface characterisation technologies are investigated to advance the WHV closer towards clinical translation. Methods The leaflets were fabricated from solvent cast films of CarbothaneTM, an aliphatic polyurethane elastomer, which are then laser cut into leaflets. Sintered titanium stents were produced through additive manufacturing and the leaflets attached at the base and commissures via mechanical fixtures to form a tri-leaflet valve having both a concave and convex free edge. Flow performance through the valve was investigated through both steady (Ansys Fluent) and time-dependent (LS-Dyna) computational fluid modelling. Experimental tests were conducted through use of an in-house built pulse duplicator, based on a 3-element Windkessel model and a durability tester (ViVitro HiCycle). Pressure readings were taken using a Biopac MP36 System. Results & Discussion Our steady state computational analysis confirmed that that the unique curvature of the WHV facilitates helical blood flow downstream of the valve (Figure 1(b)). Work is ongoing to optimise the leaflet properties of the WHV by conducting an iterative process between our mathematical models and our in vitro bench tests. Investigations are also underway to enhancing the surface properties with Diamond Like Carbon (DLC) coatings using an ECR (electron cyclotron resonance) ion beam deposition facility. DLC are a class of amorphous carbons having similar properties to diamond, containing a mixture of both sp2 and sp3 carbon-carbon interatomic bonds. They have gained interest in medical applications due to their chemical inertness, and similar platelet absorption to LTI carbon (currently used as coatings in mechanical valves). Early investigations have demonstrated good adhesion of DLC films having a thickness of approximately 100 nm on our polymer leaflets. Further work will explore their biocompatibility and mechanical characteristics to enhance the performance of the WHV. Conclusion The WHV is a novel synthetic heart valve with the potential to facilitate a washout of blood flow as the leaflets close. Testing is ongoing in accordance with ISO 5840-1 and -2 to advance the WHV towards clinical translation

Metabolic maturation in the first 2 years of life in resource-constrained settings and its association with postnatal growths

Funding Information: The Etiology, Risk Factors, and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project (MAL-ED) is carried out as a collaborative project supported by the Bill & Melinda Gates Foundation (BMGF 47075), the Foundation for the National Institutes of Health, and the National Institutes of Health, Fogarty International Center, while additional support was obtained from BMGF for the examination of host innate factors on enteric disease risk and enteropathy (grants OPP1066146 and OPP1152146 to M.N.K.). Additional funding was obtained from the Sherrilyn and Ken Fisher Center for Environmental Infectious Diseases of the Johns Hopkins School of Medicine (to M.N.K.). Publisher Copyright: Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).Peer reviewedPublisher PD

The Two-Nucleon Potential from Chiral Lagrangians

Chiral symmetry is consistently implemented in the two-nucleon problem at low-energy through the general effective chiral lagrangian. The potential is obtained up to a certain order in chiral perturbation theory both in momentum and coordinate space. Results of a fit to scattering phase shifts and bound state data are presented, where satisfactory agreement is found for laboratory energies up to about 100 Mev.Comment: Postscript file; figures available by reques

The implications of Brexit for environmental law in Scotland

This report maps the possible implications of Brexit for environmental protection in Scotland, identifying core questions as well as solutions that may be adopted, with the objective of initiating a conversation about this complex subject matter. The report has been prepared as a joint endeavour by a group of environmental law experts based at Scottish Universities. Each section was drafted by a lead author, with inputs from the rest of the group. The paper is meant for a broad audience and intentionally uses a non-technical writing style. The paper is divided in two sections. The first section addresses cross-cutting questions affecting environmental governance after Brexit, focusing on the main Brexit scenarios and their trade, competition, and law enforcement implications. This analysis identifies a series of common challenges for nvironmental law in Scotland after Brexit, which relate to: •Loss of scrutiny and enforcement powers associated with the operation of EU law and institutions; •Loss of long-term policy horizon and of the stable regulatory framework provided by EU law; •Repositioning of the UK and Scotland in international and regional environmental governance cooperation; and •Restriction/loss of access to EU funds and programmes. The second section analyses specific questions likely to emerge in elected areas of environmental law, distinguishing between different types of EU environmental legislation and the related allocation of competences within the UK. The transposition of EU environmental law into domestic law takes place in different ways. Some pieces of EU environmental law have been transposed into UK/Scottish law and configure distinctively UK/Scottish solutions. After Brexit, retaining these pieces of legislation is going to be relatively straightforward. Other pieces of EU environmental law, conversely, heavily rely upon EU processes and institutions and will no longer be applicable in their present form after Brexit. On these matters, EU powers and competences will be repatriated, raising fundamental questions concerning the allocation of powers between the UK’s central and evolved administrations. Finally, EU membership has important implications concerning the UK’s implementation of international obligations in areas such as climate change law or air pollution. In these areas, EU law is often more ambitious than the underlying international obligations. Brexit will therefore confront the UK and devolved administrations with fundamental choices regarding how to continue to comply with international obligations, and maintain and enhance their current level of commitment and ambition over time

Mechanical Dissipation in Silicon Flexures

The thermo-mechanical properties of silicon make it of significant interest as a possible material for mirror substrates and suspension elements for future long-baseline gravitational wave detectors. The mechanical dissipation in 92um thick single-crystal silicon cantilevers has been observed over the temperature range 85 K to 300 K, with dissipation approaching levels down to phi = 4.4E-7.Comment: 7 pages. Accepted by Phys Lett A, submitted for publication on 28 October 200

Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency

In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser and a strong classical coupling laser, which form a three-level Lambda-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency (EIT) with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and inter-atomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.Comment: 9 pages, 1 figur