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

Endoscopy is of low yield in the identification of gastrointestinal neoplasia in patients with dermatomyositis: A cross-sectional study.

AimTo determine the prevalence of gastrointestinal neoplasia among dermatomyositis patients who underwent an esophagogastroduodenoscopy and/or colonoscopy.MethodsA cross-sectional study examining the results of upper endoscopy and colonoscopy in adults with dermatomyositis at an urban, university hospital over a ten year period was performed. Chart review was performed to confirm the diagnosis of dermatomyositis. Findings on endoscopy were collected and statistical analyses stratified by age and presence of symptoms were performed.ResultsAmong 373 adult patients identified through a code based search strategy, only 163 patients had dermatomyositis confirmed by chart review. Of the 47 patients who underwent upper endoscopy, two cases of Barrett's esophagus without dysplasia were identified and there were no cases of malignancy. Of the 67 patients who underwent colonoscopy, no cases of malignancy were identified and an adenoma was identified in 15% of cases. No significant differences were identified in the yield of endoscopy when stratified by age or presence of symptoms.ConclusionThe yield of endoscopy is low in patients with dermatomyositis and is likely similar to the general population; we identified no cases of malignancy. A code based search strategy is inaccurate for the diagnosis of dermatomyositis, calling into question the results of prior population-based studies. Larger studies with rigorously validated search strategies are necessary to understand the risk of gastrointestinal malignancy in patients with dermatomyositis

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

The parameter space of graphene chemical vapor deposition on polycrystalline Cu

A systematic study on the parameter space of graphene CVD on polycrystalline Cu foils is presented, aiming at a more fundamental process rationale in particular regarding the choice of carbon precursor and mitigation of Cu sublimation. CH4 as precursor requires H2 dilution and temperatures ≥1000°C to keep the Cu surface reduced and yield a high quality, complete monolayer graphene coverage. The H2 atmosphere etches as-grown graphene, hence maintaining a balanced CH4/H2 ratio is critical. Such balance is more easily achieved at low pressure conditions, at which however Cu sublimation reaches deleterious levels. In contrast, C6H6 as precursor requires no reactive diluent and consistently gives similar graphene quality at 100-150°C lower temperatures. The lower process temperature and more robust processing conditions allow the problem of Cu sublimation to be effectively addressed. Graphene formation is not inherently self-limited to a monolayer for any of the precursors. Rather, the higher the supplied carbon chemical potential the higher the likelihood of film inhomogeneity and primary and secondary multilayer graphene nucleation. For the latter, domain boundaries of the inherently polycrystalline CVD graphene offer pathways for a continued carbon supply to the catalyst. Graphene formation is significantly affected by the Cu crystallography, i.e. the evolution of microstructure and texture of the catalyst template form an integral part of the CVD process.S.H. acknowledges funding from ERC grant InsituNANO (n°279342) and from EPSRC (Grant Nr. EP/H047565/1). P.R.K. acknowledges funding from the Cambridge Commonwealth Trust and C.D. acknowledges funding from Royal Society.This is the accepted manuscript. The final version is available from ACS at http://pubs.acs.org/doi/abs/10.1021/jp303597m

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

Scalable Production of Glioblastoma Tumor-initiating Cells in 3 Dimension Thermoreversible Hydrogels

There is growing interest in developing drugs that specifically target glioblastoma tumor-initiating cells (TICs). Current cell culture methods, however, cannot cost-effectively produce the large numbers of glioblastoma TICs required for drug discovery and development. In this paper we report a new method that encapsulates patient-derived primary glioblastoma TICs and grows them in 3 dimension thermoreversible hydrogels. Our method allows long-term culture (~50 days, 10 passages tested, accumulative ~\u3e1010-fold expansion) with both high growth rate (~20-fold expansion/7 days) and high volumetric yield (~2.0 × 107 cells/ml) without the loss of stemness. The scalable method can be used to produce sufficient, affordable glioblastoma TICs for drug discovery