Surface concentration of transmission eigenfunctions

The transmission eigenvalue problem is a type of non-elliptic and non-selfadjoint spectral problem that arises in the wave scattering theory when invisibility/transparency occurs. The transmission eigenfunctions are the interior resonant modes inside the scattering medium. We are concerned with the geometric rigidity of the transmission eigenfunctions and show that they concentrate on the boundary surface of the underlying domain in two senses. This substantiates the recent numerical discovery in [10] on such an intriguing spectral phenomenon of the transmission resonance. Our argument is based on generalized Weyl's law and certain novel ergodic properties of the coupled boundary layer-potential operators which are employed to analyze the generalized transmission eigenfunctions.Comment: 25 pages and comments are welcom

Simple models of the chemical field around swimming plankton

International audienceThe chemical field around swimming plankton depends on the swimming style and speed of the organism and the processes affecting uptake or exudation of chemicals by the organism. Here we present a simple model for the flow field around a neutrally buoyant self-propelled organism at low Reynolds number, and numerically calculate the chemical field around the organism. We show how the concentration field close to the organism and the mass transfer rates vary with swimming speed and style for Dirichlet (diffusion limited transport) boundary conditions. We calculate how the length of the chemical wake, defined as being the distance at which the chemical field drops to 10% of the surface concentration of the organism when stationary, varies with swimming speed and style for both Dirichlet and Neumann (production limited) boundary conditions. For Dirichlet boundary conditions, the length of the chemical wake increases with increasing swimming speed, and the self-propelled organism displays a significantly longer wake than the towed-body model. For the Neumann boundary conditions the converse is true; because swimming enhances the transport of the chemical away from the organism, the surface concentration of chemical is reduced and thus the wake length is reduced

Low Phosphorus Concentrations in Si by Diffusion from Doped Oxide Layers

The diffusion of phosphorus into silicon from doped oxide layers, deposited at low temperatures, has been studied in order to achieve reproducible impurity distributions with surface concentrations varying from 5 × 1015 to 1018 atoms/cm3. Special attention has been given to the differences arising from indiffusion in an N2 or in an O2 ambient. The dependence on the temperature of the diffusion coefficients of phosphorus in silicon and in silicon dioxide is determined at a surface concentration of 5 × 1016 atoms/cm3

Studies of a weak polyampholyte at the air-buffer interface: The effect of varying pH and ionic strength

We have carried out experiments to probe the static and dynamic interfacial properties of $\beta$--casein monolayers spread at the air-buffer interface, and analysed these results in the context of models of weak polyampholytes. Measurements have been made systematically over a wide range of ionic strength and pH. In the semi-dilute regime of surface concentration a scaling exponent, which can be linked to the degree of chain swelling, is found. This shows that at pH close to the isoelectric point, the protein is compact. At pH away from the isoelectric pH the protein is extended. The transition between compact and extended states is continuous. As a function of increasing ionic strength, we observe swelling of the protein at the isoelectric pH but contraction of the protein at pH values away from it. These behaviours are typical of a those predicted theoretically for a weak polyampholyte. Dilational moduli measurements, made as a function of surface concentration exhibit maxima that are linked to the collapse of hydrophilic regions of the protein into the subphase. Based on this data we present a configuration map of the protein configuration in the monolayer. These findings are supported by strain (surface pressure) relaxation measurements and surface quasi-elastic light scattering (SQELS) measurements which suggest the existence of loops and tails in the subphase at higher surface concentrations.Comment: Submitted to J. Chem. Phy

Studies of a weak polyampholyte at the air-buffer interface: The effect of varying pH and ionic strength

We have carried out experiments to probe the static and dynamic interfacial properties of $\beta$--casein monolayers spread at the air-buffer interface, and analysed these results in the context of models of weak polyampholytes. Measurements have been made systematically over a wide range of ionic strength and pH. In the semi-dilute regime of surface concentration a scaling exponent, which can be linked to the degree of chain swelling, is found. This shows that at pH close to the isoelectric point, the protein is compact. At pH away from the isoelectric pH the protein is extended. The transition between compact and extended states is continuous. As a function of increasing ionic strength, we observe swelling of the protein at the isoelectric pH but contraction of the protein at pH values away from it. These behaviours are typical of a those predicted theoretically for a weak polyampholyte. Dilational moduli measurements, made as a function of surface concentration exhibit maxima that are linked to the collapse of hydrophilic regions of the protein into the subphase. Based on this data we present a configuration map of the protein configuration in the monolayer. These findings are supported by strain (surface pressure) relaxation measurements and surface quasi-elastic light scattering (SQELS) measurements which suggest the existence of loops and tails in the subphase at higher surface concentrations.Comment: Submitted to J. Chem. Phy

Reversible Tuning of the Wettability of Carbon Nanotube Arrays: The Effect of Ultraviolet/Ozone and Vacuum Pyrolysis Treatments

Among diverse types of synthetic materials, arrays of vertically aligned carbon nanotubes have attracted the most attention, mainly because of their exceptional mechanical, electrical, optical, and thermal properties. However, their wetting properties are yet to be understood. In this present study, oxygenated surface functional groups have been identified as a vital factor in controlling the wetting properties of carbon nanotube arrays. The results presented herein indeed show that a combination of ultraviolet/ozone and vacuum pyrolysis treatments can be used to vary the surface concentration of these functional groups such that the carbon nanotube array can be repeatedly switched between hydrophilic and hydrophobic