Collimated beam manifold with the number of output beams variable at a given output angle

An optical manifold is described which transforms a collimated beam, such as a laser beam, into a plurality of parallel beams having uniform intensity or having a desired intensity ratio. The manifold comprises an optical substrate coated on its rear surface with a fully reflective layer and on its front surface with a partially reflecting layer having a reflectivity gradient. An input collimated beam entering the rear surface and impinging on the front surface is reflected, multiply between the front and rear surfaces producing a plurality of parallel beams that emerge from the front surface. The intensities of the emerging beams have a relationship that depends on the reflectivity of the front surface at the points where the beams emerge. By properly selecting the reflectivity gradient, the emerging beams have uniform intensity or a desired intensity ratio

The latent process decomposition of cDNA microarray data sets

We present a new computational technique (a software implementation, data sets, and supplementary information are available at http://www.enm.bris.ac.uk/lpd/) which enables the probabilistic analysis of cDNA microarray data and we demonstrate its effectiveness in identifying features of biomedical importance. A hierarchical Bayesian model, called latent process decomposition (LPD), is introduced in which each sample in the data set is represented as a combinatorial mixture over a finite set of latent processes, which are expected to correspond to biological processes. Parameters in the model are estimated using efficient variational methods. This type of probabilistic model is most appropriate for the interpretation of measurement data generated by cDNA microarray technology. For determining informative substructure in such data sets, the proposed model has several important advantages over the standard use of dendrograms. First, the ability to objectively assess the optimal number of sample clusters. Second, the ability to represent samples and gene expression levels using a common set of latent variables (dendrograms cluster samples and gene expression values separately which amounts to two distinct reduced space representations). Third, in contrast to standard cluster models, observations are not assigned to a single cluster and, thus, for example, gene expression levels are modeled via combinations of the latent processes identified by the algorithm. We show this new method compares favorably with alternative cluster analysis methods. To illustrate its potential, we apply the proposed technique to several microarray data sets for cancer. For these data sets it successfully decomposes the data into known subtypes and indicates possible further taxonomic subdivision in addition to highlighting, in a wholly unsupervised manner, the importance of certain genes which are known to be medically significant. To illustrate its wider applicability, we also illustrate its performance on a microarray data set for yeast

Revisiting the 1954 Suspension Experiments of R. A.Bagnold

In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t=4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained

Investigating the relationship between predictability and imbalance in minimisation : a simulation study

Peer reviewedPublisher PD

Self-recording portable soil penetrometer

A lightweight portable penetrometer for testing soil characteristics is described. The penetrometer is composed of a handle, data recording, and probe components detachably joined together. The data recording component has an easily removed recording drum which rotates according to the downward force applied on the handle, and a stylus means for marking the drum along its height according to the penetration depth of probe into the soil

Computer and photogrammetric general land use study of central north Alabama

The object of this report is to acquaint potential users with two computer programs, developed at NASA, Marshall Space Flight Center. They were used in producing a land use survey and maps of central north Alabama from Earth Resources Technology Satellite (ERTS) digital data. The report describes in detail the thought processes and analysis procedures used from the initiation of the land use study to its completion, as well as a photogrammetric study that was used in conjunction with the computer analysis to produce similar land use maps. The results of the land use demonstration indicate that, with respect to computer time and cost, such a study may be economically and realistically feasible on a statewide basis

Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method

We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated spin-lattice models of interest in quantum magnetism, including their quantum phase transitions. The method itself is described, and it is shown how it may be implemented in practice to high orders in a systematically improvable hierarchy of (so-called LSUB$m$) approximations, by the use of computer-algebraic techniques. The method works from the outset in the thermodynamic limit of an infinite lattice at all levels of approximation, and it is shown both how the "raw" LSUB$m$ results are themselves generally excellent in the sense that they converge rapidly, and how they may accurately be extrapolated to the exact limit, $m \rightarrow \infty$, of the truncation index $m$, which denotes the {\it only} approximation made. All of this is illustrated via a specific application to a two-dimensional, frustrated, spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on a honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$, respectively, where both interactions are of the same anisotropic $XXZ$ type. We show how the method can be used to determine the entire zero-temperature ground-state phase diagram of the model in the range $0 \leq \kappa \leq 1$ of the frustration parameter and $0 \leq \Delta \leq 1$ of the spin-space anisotropy parameter. In particular, we identify a candidate quantum spin-liquid region in the phase space