The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Collapse of three vortices on a sphere

The self-similar collapse of three point vortices moving on the surface of a sphere of radius R is analysed and compared with known results from the corresponding planar problem described in (AREF H., Motion of three vortices, Phys. Fluids, 22 (1979) 393-400; NOVIKOV E. A., Dynamics and statistics of a system of vortices, Sov. Phys. JETP, 41 (1975) 937-943; NOVIKOV E. A. and SEDOV Y., Vortex collapse, Sov. Phys. JETP, 50 (1979) 297-301; SYNGE J. L., On the motion of three vortices, Can. J. Math., 1 (1949) 257-270). An important conserved quantity is the center of vorticity vector c4(!i41 3 Gi xi )O!i41 3 Gi, which must have length R for collapse to occur. Collapse trajectories occur in pairs, called “partner states”, which have two distinct collapse times t2Et1. The collapse time that is achieved for a given configuration depends on the sign of the parallelpiped volume formed by the vortex position vectors, hence depends on whether the vortices (G1 , G2 , G3 ) are arranged in a right-handed or left-handed sense. From a given collapsing configuration, one can obtain the partner state by reversing the signs of the Gi’s, or, alternatively, by using a discrete symmetry associated with the initial configuration that leaves all relative distances unchanged, but reverses the sign of the parallelepiped volume. In the plane, there is only one collapse time associated with a given configuration—the partner state is one that expands self-similarly (AREF H., Motion of three vortices, Phys. Fluids, 22 (1979) 393-400). Formulas for the collapsing trajectories are derived and compared with the planar formulas. The collapse trajectories are then projected onto the stereographic plane where a new Hamiltonian system is derived governing the vortex motion. In this projected plane, the solutions are not self-similar. In the last section, the collapse process is studied using tri-linear coordinates, which reduces the system to a planar one

Graphene-based ultrathin flat lenses

Flat lenses when compared to curved surface lenses have the advantages of being aberration free and they offer a compact design necessary for a myriad of electro-optical applications. In this paper we present flat and ultra-thin lenses based on graphene, the world’s thinnest known material. Monolayers and low number multilayers of graphene were fabricated into Fresnel zones to produce Fresnel zone plates which utilize the reflection and transmission properties of graphene for their operation. The working of the lens and their performance in the visible and terahertz regimes was analyzed computationally. Experimental measurements were also performed to characterize the lens in the visible regime and a good agreement was obtained with the simulations. The work demonstrates the principle of atom thick graphene-based lenses, with perspectives for ultra-compact integration.HB would like to thank The Leverhulme Trust for the research funding. QD is supported by Bureau of International Cooperation, Chinese Academy of Sciences (121D11KYSB20130013).This is the accepted manuscript. The final version is available from ACS at http://pubs.acs.org/doi/abs/10.1021/ph500197j

Point vortices on the sphere: a case with opposite vorticities

We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilibria, and then study their stability with the ``Energy Momentum Method''. Most of the results obtained are nonlinear stability results. To end, some bifurcations are described.Comment: 35 pages, 9 figure

Mechanisms of titania nanoparticle mediated growth of turbostratic carbon nanotubes and nanofibers

Turbostratic carbon nanotubes (CNTs) and nanofibers (CNFs) are synthesized by chemical vapor deposition using titania nanoparticle catalysts, and a quantitative lift-off model is developed to explain CNT and CNF growth. Micron-scale long turbostratic CNTs and CNFs were observed when acetylene is utilized as a carbon feedstock, and an alumina substrate was incorporated to improve the homogeneity of catalyst distribution. Turbostratic CNTs/CNFs are always found attached to nanoparticle corners, in the absence of the graphitic cage that is typically observed with metal nanoparticle-mediated growth. The observed morphology in turbostratic CNTs/CNFs supports a model in which several layers of graphene lift off from high-curvature corners of the titania nanoparticle catalysts. This model explains a key feature, which differentiates the growth of turbostratic CNTs/CNFs via non-metallic nanoparticles from growth using standard metal nanoparticle catalysts. The observed CNT/CNF growth and the accompanying model can impact the assessment of other metal-oxide nanoparticle catalysts, with the findings here contributing to a metal-free synthesis of turbostratic CNTs/CNFs

A novel and practical screening tool for the detection of silent myocardial infarction in patients with type 2 diabetes

Silent myocardial infarction (MI) is a prevalent finding in patients with type 2 diabetes and is associated with significant mortality and morbidity. Late gadolinium enhancement (LGE) by cardiovascular magnetic resonance (CMR) is the most validated technique for detection of silent MI but is time consuming, costly and requires administration of intravenous contrast. We therefore planned to develop a simple and low cost population screening tool to identify those at highest risk of silent MI validated against the CMR reference standard.100 asymptomatic patients with type 2 diabetes underwent electrocardiogram (ECG), echocardiography, biomarker assessment and CMR at 3.0T including assessment of left ventricular ejection fraction and LGE. Global longitudinal strain (GLS) from 2 and 4 chamber cines was measured using feature tracking.17/100 patients with no history of cardiovascular disease had silent MI defined by LGE in an infarct pattern on CMR. Only 4 silent MI patients had Q waves on ECG. Patients with silent MI were older (65 vs 60, p=0.05), had lower E/A ratio (0.75 vs 0.89, p=0.004), lower GLS (-15.2% vs -17.7%, p=0.004) and higher NT-proBNP (106ng/L vs 52ng/L, p=0.003). A combined risk score derived from these 4 factors had an area under the receiver operating characteristic (ROC) curve of 0.823 (0.734-0.892), P<0.0001. A score of ?3/5 had 82% sensitivity and 72% specificity for silent MI.Using measures that can be derived in an outpatient clinic setting, we have developed a novel screening tool for the detection of silent MI in type 2 diabetes. The screening tool had significantly superior diagnostic accuracy than current ECG criteria for the detection of silent MI in asymptomatic patients

The role of left ventricular deformation in the assessment of microvascular obstruction and intramyocardial haemorrhage

In the setting of acute ST-elevation myocardial infarction (STEMI), it remains unclear which strain parameter most strongly correlates with microvascular obstruction (MVO) or intramyocardial haemorrhage (IMH). We aimed to investigate the association of MVO, IMH and convalescent left ventricular (LV) remodelling with strain parameters measured with cardiovascular magnetic resonance (CMR). Forty-three patients with reperfused STEMI and 10 age and gender matched healthy controls underwent CMR within 3-days and at 3-months following reperfused STEMI. Cine, T2-weighted, T2*-imaging and late gadolinium enhancement (LGE) imaging were performed. Infarct size, MVO and IMH were quantified. Peak global longitudinal strain (GLS), global radial strain (GRS), global circumferential strain (GCS) and their strain rates were derived by feature tracking analysis of LV short-axis, 4-chamber and 2-chamber cines. All 43 patients and ten controls completed the baseline scan and 34 patients completed 3-month scans. In multivariate regression, GLS demonstrated the strongest association with MVO or IMH (beta = 0.53, p 20%). Baseline GLS also demonstrated the strongest diagnostic performance in predicting adverse LV remodelling (AUC = 0.79; 95% CI 0.60–0.98; p = 0.03). Post-reperfused STEMI, baseline GLS was most closely associated with the presence of MVO or IMH. Baseline GLS was more strongly associated with adverse LV remodelling than other CMR parameters

Propofol induces MAPK/ERK cascade dependant expression of cFos and Egr-1 in rat hippocampal slices

Background: Propofol is a commonly used intravenous anesthetic agent, which produce rapid induction of and recovery from general anesthesia. Numerous clinical studies reported that propofol can potentially cause amnesia and memory loss in human subjects. The underlying mechanism for this memory loss is unclear but may potentially be related to the induction of memory-associated genes such as c-Fos and Egr-1 by propofol. This study explored the effects of propofol on c-Fos and Egr-1 expression in rat hippocampal slices. Findings: Hippocampal brain slices were exposed to varying concentrations of propofol at multiple time intervals. The transcription of the immediate early genes, c-Fos and Egr-1, was quantified using quantitative reverse transcriptase polymerase chain reaction (qRT-PCR). MAPK/ERK inhibitors were used to investigate the mechanism of action. We demonstrate that propofol induced the expression of c-Fos and Egr-1 within 30 and 60 min of exposure time. At 16.8 μM concentration, propofol induced a 110% increase in c-Fos transcription and 90% decrease in the transcription of Egr-1. However, at concentrations above 100 μM, propofol failed to induce expression of c-Fos but did completely inhibit the transcription of Egr-1. Propofol-induced c-Fos and Egr-1 transcription was abolished by inhibitors of RAS, RAF, MEK, ERK and p38-MAPK in the MAPK/ERK cascade. Conclusions: Our study shows that clinically relevant concentrations of propofol induce c-Fos and down regulated Egr-1 expression via an MAPK/ERK mediated pathway. We demonstrated that propofol induces a time and dose dependant transcription of IEGs c-Fos and Egr-1 in rat hippocampal slices. We further demonstrate for the first time that propofol induced IEG expression was mediated via a MAPK/ERK dependant pathway. These novel findings provide a new avenue to investigate transcription-dependant mechanisms and suggest a parallel pathway of action with an unclear role in the activity of general anesthetics

In Situ Observations during Chemical Vapor Deposition of Hexagonal Boron Nitride on Polycrystalline Copper.

Using a combination of complementary in situ X-ray photoelectron spectroscopy and X-ray diffraction, we study the fundamental mechanisms underlying the chemical vapor deposition (CVD) of hexagonal boron nitride (h-BN) on polycrystalline Cu. The nucleation and growth of h-BN layers is found to occur isothermally, i.e., at constant elevated temperature, on the Cu surface during exposure to borazine. A Cu lattice expansion during borazine exposure and B precipitation from Cu upon cooling highlight that B is incorporated into the Cu bulk, i.e., that growth is not just surface-mediated. On this basis we suggest that B is taken up in the Cu catalyst while N is not (by relative amounts), indicating element-specific feeding mechanisms including the bulk of the catalyst. We further show that oxygen intercalation readily occurs under as-grown h-BN during ambient air exposure, as is common in further processing, and that this negatively affects the stability of h-BN on the catalyst. For extended air exposure Cu oxidation is observed, and upon re-heating in vacuum an oxygen-mediated disintegration of the h-BN film via volatile boron oxides occurs. Importantly, this disintegration is catalyst mediated, i.e., occurs at the catalyst/h-BN interface and depends on the level of oxygen fed to this interface. In turn, however, deliberate feeding of oxygen during h-BN deposition can positively affect control over film morphology. We discuss the implications of these observations in the context of corrosion protection and relate them to challenges in process integration and heterostructure CVD.P.R.K. acknowledges funding from the Cambridge Commonwealth Trust and the Lindemann Trust Fellowship. R.S.W. acknowledges a research fellowship from St. John’s College, Cambridge. S.H. acknowledges funding from ERC grant InsituNANO (no. 279342), EPSRC under grant GRAPHTED (project reference EP/K016636/1), Grant EP/H047565/1 and EU FP7 Work Programme under grant GRAFOL (project reference 285275). The European Synchrotron Radiation Facility (ESRF) is acknowledged for provision of synchrotron radiation and assistance in using beamline BM20/ROBL. We acknowledge Helmholtz-Zentrum-Berlin Electron storage ring BESSY II for synchrotron radiation at the ISISS beamline and continuous support of our experiments.This is the final version. It was first published by ACS at http://pubs.acs.org/doi/abs/10.1021/cm502603