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

Benjamin-Ono Kadomtsev-Petviashvili’s models in interfacial electro-hydrodynamics

Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3

Trapped waves on interfacial hydraulic falls over bottom obstacles

Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated

Markers for tumor margin assessment through raman spectroscopy in comparative oncology

The occurrence of tumour diseases in both animals and humans is continuously increasing. Research in nanosciences and molecular biology has put lately an intense effort to identify the aetiology factors and seek for new ways of diagnostic and targeted therapies aimed at reducing mortality and increasing chances to healing. Extensive development of cancer tumours is frequently counteracted through surgery. Assessment of a clean surgical margin is vital and a precise and rapid diagnostic down to molecule level represents a technical challenge with important clinical implications. We present a new way of using surgery instruments and surface enhanced Raman spectroscopy for direct ex vivo (no freezing, no staining) and in vivo diagnostic of clean margins in mammary tumour surgery of pets (dogs and cats).Raman spectroscopy extracts chemical information with reported 100%sensitivity, 100% specificity and overall accuracy of 93% in identifying carcinomas. Our main result stays in identification of a set of molecular markers (carotenoids, lipids and intramolecular water) for Raman diagnostic in cat and dog mammary tumour surgery. Those markers have already been confirmed for human patients

Nonlinear three-dimensional gravity–capillary solitary waves

Steady three-dimensional fully nonlinear gravity–capillary solitary waves are calculated numerically in infinite depth. These waves have decaying oscillations in the direction of propagation and monotone decay perpendicular to the direction of propagation. They travel at a velocity U smaller than the minimum velocity cmin of linear gravity–capillary waves. It is shown that the structure of the solutions in three dimensions is similar to that found by Vanden-Broeck & Dias (J. Fluid Mech. vol. 240, 1992, pp. 549–557) for the corresponding two-dimensional problem