Deformation of an elastic cell in a uniform stream and in a circulatory flow

The deformation of a circular, inextensible elastic cell is examined when the cell is placed into two different background potential flows: a uniform stream and a circulatory flow induced by a point vortex located inside the cell. In a circulatory flow a cell may deform into a mode m shape with m-fold rotational symmetry. In a uniform stream, shapes with two-fold rotational symmetry tend to be selected. In a weak stream a cell deforms linearly into an ellipse with either its major or its minor axis aligned with the oncoming flow. This marks an interesting difference with a bubble with constant surface tension in a uniform stream, which can only deform into a mode 2 shape with its major axis perpendicular to the stream (Vanden-Broeck & Keller, 1980b). In general, as the strength of the uniform stream is increased from zero, solutions emerge continuously from the cell configurations in quiescent fluid found by Flaherty et al. (1972). A richly populated solution space is described with multiple solution branches which either terminate when a cell reaches a state with a point of self-contact or loop round to continuously connect cell states which exist under identical conditions in the absence of flow

Solitary waves on a ferrofluid jet

The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully-nonlinear travelling solitary waves and predictions of elevation waves and depression waves by Rannacher & Engel (2006) using a weakly-nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp

On the transition to dripping of an inverted liquid film

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the LCM and FCM, respectively), and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased. For any fixed volume the LCM reaches the horizontal state where it attains a cosine-shaped profile. For sufficiently small volume, the FCM and Stokes solutions attain a weak Young-Laplace equilibrium profile, the approach to which is described by an asymptotic analysis generalising that of Kalliadasis & Chang (1994) for the LCM. For large volumes, the bifurcation curves for the FCM and Stokes model have a turning point so that the fully inverted state is never reached. For fixed flow rate the LCM blows up at a critical angle that is well predicted by asymptotic analysis. The bifurcation curve for the FCM either has a turning point or else reaches a point at which the surface profile has an infinite slope singularity, indicating the onset of multi-valuedness. The latter is confirmed by the Stokes model which can be continued to obtain overturning surface profiles. Overall the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle

On the critical free-surface flow over localised topography

Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far-field, and their stability. Using the forced Korteweg-de Vries (fKdV) equation the weakly-nonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Non-uniqueness is established and a seemingly infinite set of steady solutions is uncovered. Non-uniqueness is also demonstrated for the fully nonlinear problem via boundary-integral calculations. It is shown analytically that critical flow solutions have algebraic decay in the far-field both for the fKdV equation and for the fully nonlinear problem and, moreover, that the leading-order form of the decay is the same in both cases. The linear stability of the steady fKdV solutions is examined via eigenvalue computations and by a numerical study of the initial value fKdV problem. It is shown that there exists a linearly stable steady solution in which the deflection from the otherwise uniform surface level is everywhere negative

Flow in a slowly-tapering channel with oscillating walls

The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou \cite{HP}. A careful study of the governing partial differential system for the first order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry-breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window stability is again lost to exponentially growing solutions as the Reynolds number is increased

A Cone Jet-Finding Algorithm for Heavy-Ion Collisions at LHC Energies

Standard jet finding techniques used in elementary particle collisions have not been successful in the high track density of heavy-ion collisions. This paper describes a modified cone-type jet finding algorithm developed for the complex environment of heavy-ion collisions. The primary modification to the algorithm is the evaluation and subtraction of the large background energy, arising from uncorrelated soft hadrons, in each collision. A detailed analysis of the background energy and its event-by-event fluctuations has been performed on simulated data, and a method developed to estimate the background energy inside the jet cone from the measured energy outside the cone on an event-by-event basis. The algorithm has been tested using Monte-Carlo simulations of Pb+Pb collisions at $\sqrt{s}=5.5$ TeV for the ALICE detector at the LHC. The algorithm can reconstruct jets with a transverse energy of 50 GeV and above with an energy resolution of $\sim30$.Comment: 13 pages, 7 figure

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

A simple model for global H i profiles of galaxies

Context. Current and future blind surveys for H i generate large catalogs of spectral lines for which automated characterisation would be convenient

Towards a Full Census of the Obscure(d) Vela Supercluster using MeerKAT

Recent spectroscopic observations of a few thousand partially obscured galaxies in the Vela constellation revealed a massive overdensity on supercluster scales straddling the Galactic Equator (l $\sim$ 272.5deg) at $cz \sim 18000$km/s. It remained unrecognised because it is located just beyond the boundaries and volumes of systematic whole-sky redshift and peculiar velocity surveys - and is obscured by the Milky Way. The structure lies close to the apex where residual bulkflows suggest considerable mass excess. The uncovered Vela Supercluster (VSCL) conforms of a confluence of merging walls, but its core remains uncharted. At the thickest foreground dust column densities (|b| < 6 deg) galaxies are not visible and optical spectroscopy is not effective. This precludes a reliable estimate of the mass of VSCL, hence its effect on the cosmic flow field and the peculiar velocity of the Local Group. Only systematic HI-surveys can bridge that gap. We have run simulations and will present early-science observing scenarios with MeerKAT 32 (M32) to complete the census of this dynamically and cosmologically relevant supercluster. M32 has been put forward because this pilot project will also serve as precursor project for HI MeerKAT Large Survey Projects, like Fornax and Laduma. Our calculations have shown that a survey area of the fully obscured part of the supercluster, where the two walls cross and the potential core of the supercluster resides, can be achieved on reasonable time-scales (200 hrs) with M32.Comment: 10 pages, 3 figures, accepted for publication, Proceedings of Science, workshop on "MeerKAT Science: On the Pathway to the SKA", held in Stellenbosch 25-27 May 201

Predicting lung cancer recurrence from circulating tumour DNA. Commentary on 'Phylogenetic ctDNA analysis depicts early-stage lung cancer evolution'

No abstract available