Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Measurements of Flow Patterns and Velocities of Gas -Water Two -Phase Flows Using Electrical Resistance Imaging

This paper presents a measurement of flow patterns and flow velocities of gas-water two-phase flows based on the technique of electrical resistance tomography (ERT) in a 40m horizontal flow loop. A single-plane and dual-plane ERT sensor on conductive ring technique were used to gather sufficient information for the implementation of flow characteristics particularly flow pattern recognition and air cavity velocity measurement. A fast data collection strategy was applied to the dual-plane ERT sensor and an iterative algorithm was used for image reconstruction. Results, in respect to flow patterns and velocity maps, are reported.

Least Squares Estimation Principle and its Geometrical Interpretation

pdf contains 14 pages)

Visualization of molecule interaction between antigen and antibody - One of ellipsometric imaging applications

It is to investigate molecule interactions between antigen and antibody with ellipsometric imaging technique and demonstrate some features and possibilities offered by applications of the technique. Molecule interaction is an important interest for molecule biologist and immunologist. They have used some established methods such as immufluorcence, radioimmunoassay and surface plasma resonance, etc, to study the molecule interaction. At the same time, experimentalists hope to use some updated technique with more direct visual results. Ellipsometric imaging is non-destructive and exhibits a high sensitivity to phase transitions with thin layers. It is capable of imaging local variations in the optical properties such as thickness due to the presence of different surface concentration of molecule or different deposited molecules. If a molecular mono-layer (such as antigen) with bio-activity were deposited on a surface to form a sensing surface and then incubated in a solution with other molecules (such as antibody), a variation of the layer thickness when the molecules on the sensing surface reacted with the others in the solution could be observed with ellipsometric imaging. Every point on the surface was measured at the same time with a high sensitivity to distinguish the variation between mono-layer and molecular complexes. Ellipsometric imaging is based on conventional ellipsometry with charge coupled device (CCD) as detector and images are caught with computer with image processing technique. It has advantages of high sensitivity to thickness variation (resolution in the order of angstrom), big field of view (in square centimeter), high sampling speed (a picture taken within one second), and high lateral resolution (in the order of micrometer). Here it has just shown one application in study of antigen-antibody interaction, and it is possible to observe molecule interaction process with an in-situ technique.

An auto-focusing method for imaging ellipsometry system

An auto-focusing method based on the image brightness gradient sharpness function is presented for imaging ellipsometry system, in which the image plane of the thin-film specimen is not perpendicular to the optical axis. The clear image of a specimen with large area is obtained by moving the imaging sensor in optical axis direction and around its sensitive surface centre successively. The experimental results demonstrate its feasibility.

An automatic imaging spectroscopic ellipsometer for characterization of nano-film pattern on solid substrate

In order to characterize the physical and spatial properties of nano-film pattern on solid substrates, an automatic imaging spectroscopic ellipsometer (ISE) based on a polarizer - compensator - specimen - analyzer configuration in the visible region is presented. It can provide the spectroscopic ellipsometric parameters psi (x, y, lambda) and Delta (x, y, lambda) of a large area specimen with a lateral resolution in the order of some microns. A SiO2 stepped layers pattern is used to demonstrate the function of the ISE which shows potential application in thin film devices' such as high-throughput bio-chips.

Digital ‘lens’ on the UK PSF: supporting the digital capabilities of teaching staff in UK HE

This resource can also be used by professional staff who are seeking accreditation via the UK PSF for relevant aspects of their role, e.g. staff who support the use of technologies for learning and/or support the development of digital literacies.

Biologically-inspired data decorrelation for hyper-spectral imaging

Hyper-spectral data allows the construction of more robust statistical models to sample the material properties than the standard tri-chromatic color representation. However, because of the large dimensionality and complexity of the hyper-spectral data, the extraction of robust features (image descriptors) is not a trivial issue. Thus, to facilitate efficient feature extraction, decorrelation techniques are commonly applied to reduce the dimensionality of the hyper-spectral data with the aim of generating compact and highly discriminative image descriptors. Current methodologies for data decorrelation such as principal component analysis (PCA), linear discriminant analysis (LDA), wavelet decomposition (WD), or band selection methods require complex and subjective training procedures and in addition the compressed spectral information is not directly related to the physical (spectral) characteristics associated with the analyzed materials. The major objective of this article is to introduce and evaluate a new data decorrelation methodology using an approach that closely emulates the human vision. The proposed data decorrelation scheme has been employed to optimally minimize the amount of redundant information contained in the highly correlated hyper-spectral bands and has been comprehensively evaluated in the context of non-ferrous material classification