Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

Topographic mappings and feed-forward neural networks

This thesis is a study of the generation of topographic mappings - dimension reducing transformations of data that preserve some element of geometric structure - with feed-forward neural networks. As an alternative to established methods, a transformational variant of Sammon's method is proposed, where the projection is effected by a radial basis function neural network. This approach is related to the statistical field of multidimensional scaling, and from that the concept of a 'subjective metric' is defined, which permits the exploitation of additional prior knowledge concerning the data in the mapping process. This then enables the generation of more appropriate feature spaces for the purposes of enhanced visualisation or subsequent classification. A comparison with established methods for feature extraction is given for data taken from the 1992 Research Assessment Exercise for higher educational institutions in the United Kingdom. This is a difficult high-dimensional dataset, and illustrates well the benefit of the new topographic technique. A generalisation of the proposed model is considered for implementation of the classical multidimensional scaling (¸mds}) routine. This is related to Oja's principal subspace neural network, whose learning rule is shown to descend the error surface of the proposed ¸mds model. Some of the technical issues concerning the design and training of topographic neural networks are investigated. It is shown that neural network models can be less sensitive to entrapment in the sub-optimal global minima that badly affect the standard Sammon algorithm, and tend to exhibit good generalisation as a result of implicit weight decay in the training process. It is further argued that for ideal structure retention, the network transformation should be perfectly smooth for all inter-data directions in input space. Finally, there is a critique of optimisation techniques for topographic mappings, and a new training algorithm is proposed. A convergence proof is given, and the method is shown to produce lower-error mappings more rapidly than previous algorithms.

Humans assume a mixture of diffuse and point-source lighting when viewing sinusoidal shading patterns

Observers perceive sinusoidal shading patterns as being due to sinusoidally corrugated surfaces, and perceive surface peaks to be offset from luminance maxima by between zero and 1/4 wavelength. This offset varies with grating orientation. Physically, the shading profile of a sinusoidal surface will be approximately sinusoidal, with the same spatial frequency as the surface, only when: (A) it is lit suitably obliquely by a point source, or (B) the light source is diffuse and hemispherical--the 'dark is deep' rule applies. For A, surface peaks will be offset by 1/4 wavelength from the luminance maxima; for B, this offset will be zero. As the sum of two same-frequency sinusoids with different phases is a sinusoid of intermediate phase, our results suggest that observers assume a mixture of two light sources whose relative strength varies with grating orientation. The perceived surface offsets imply that gratings close to horizontal are taken to be lit by a point source; those close to vertical by a diffuse source. [Supported by EPSRC grants to AJS and MAG].

Strain distributionand electronic property modifications in Si/Ge axial nanowires hetrostructures

Molecular dynamics simulations were carried out for Si/Ge axial nanowire heterostructures using modified effective atom method (MEAM) potentials. A Si–Ge MEAM interatomic cross potential was developed based on available experimental data and was used for these studies. The atomic distortions and strain distributions near the Si/Ge interfaces are predicted for nanowires with their axes oriented along the [111] direction. The cases of 10 and 25 nm diameter Si/Ge biwires and of 25 nm diameter Si/Ge/Si axial heterostructures with the Ge disk 1 nm thick were studied. Substantial distortions in the height of the atoms adjacent to the interface were found for the biwires but not for the Ge disks. Strains as high as 3.5% were found for the Ge disk and values of 2%–2.5% were found at the Si and Ge interfacial layers in the biwires. Deformation potential theory was used to estimate the influence of the strains on the band gap, and reductions in band gap to as small as 40% of bulk values are predicted for the Ge disks. The localized regions of increased strain and resulting energy minima were also found within the Si/Ge biwire interfaces with the larger effects on the Ge side of the interface. The regions of strain maxima near and within the interfaces are anticipated to be useful for tailoring band gaps and producing quantum confinement of carriers. These results suggest that nanowire heterostructures provide greater design flexibility in band structure modification than is possible with planar layer growth.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

Stand-alone groundwater desalination system using reverse osmosis combined with a cooled greenhouse for use in arid and semi-arid zones of India

In many areas of northern India, salinity renders groundwater unsuitable for drinking and even for irrigation. Though membrane treatment can be used to remove the salt, there are some drawbacks to this approach e.g. (1) depletion of the groundwater due to over-abstraction, (2) saline contamination of surface water and soil caused by concentrate disposal and (3) high electricity usage. To address these issues, a system is proposed in which a photovoltaic-powered reverse osmosis (RO) system is used to irrigate a greenhouse (GH) in a stand-alone arrangement. The concentrate from the RO is supplied to an evaporative cooling system, thus reducing the volume of the concentrate so that finally it can be evaporated in a pond to solid for safe disposal. Based on typical meteorological data for Delhi, calculations based on mass and energy balance are presented to assess the sizing and cost of the system. It is shown that solar radiation, freshwater output and evapotranspiration demand are readily matched due to the approximately linear relation among these variables. The demand for concentrate varies independently, however, thus favouring the use of a variable recovery arrangement. Though enough water may be harvested from the GH roof to provide year-round irrigation, this would require considerable storage. Some practical options for storage tanks are discussed. An alternative use of rainwater is in misting to reduce peak temperatures in the summer. An example optimised design provides internal temperatures below 30EC (monthly average daily maxima) for 8 months of the year and costs about €36,000 for the whole system with GH floor area of 1000 m2 . Further work is needed to assess technical risks relating to scale-deposition in the membrane and evaporative pads, and to develop a business model that will allow such a project to succeed in the Indian rural context.

Waveform type evaluation in congenital nystagmus

Congenital nystagmus is an ocular-motor disorder characterised by involuntary, conjugated and bilateral to and fro ocular oscillations. In this study a method to recognise automatically jerk waveform inside a congenital nystagmus recording and to compute foveation time and foveation position variability is presented. The recordings were performed with subjects looking at visual targets, presented in nine eye gaze positions; data were segmented into blocks corresponding to each gaze position. The nystagmus cycles were identified searching for local minima and maxima (SpEp sequence) in intervals centred on each slope change of the eye position signal (position criterion). The SpEp sequence was then refined using an adaptive threshold applied to the eye velocity signal; the outcome is a robust detection of each slow phase start point, fundamental to accurately compute some nystagmus parameters. A total of 1206 slow phases was used to compute the specificity in waveform recognition applying only the position criterion or adding the adaptive threshold; results showed an increase in negative predictive value of 25.1% using both features. The duration of each foveation window was measured on raw data or using an interpolating function of the congenital nystagmus slow phases; foveation time estimation less sensitive to noise was obtained in the second case. © 2010.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

FITC-lectin avidity of Cryptococcus neoformans cell wall and capsular components

Flow cytometry and confocal microscopy were used to quantify and visualize FITC-lectin binding to cell-surface carbohydrate ligands of log and stationary phase acapsular and capsular Cryptococcus neoformans strains. Cell populations demonstrated marked avidity for terminal a-linked mannose and glucose specific FITC-Con A, mannose specific FITC-GNL, as well as N-acetylglucosamine specific FITC-WGA. Exposure to other FITC-lectins specific for mannose, fucose and N-acetylgalactosamine resulted in little cell-surface fluorescence. The nature of cell-surface carbohydrates was investigated further by measurement of the fluorescence from surfaces of log and stationary phase cell populations after exposing them to increasing concentrations of FITC-Con A and FITC-WGA. Cell fluorescence increased significantly with small increases in FITC-Con A and FITC-WGA concentrations attaining reproducible maxima. Measurements of this nature supported calculation of the lectin binding determinants EC 50, Hn, Fmax and relative Bmax values. EC50 values indicated that the yeast-cell surfaces had greatest affinity for FITC-WGA, however, relative Bmax values indicated that greater numbers of Con A binding sites were present on these same cell surfaces. Hn values suggested a co-operative lectin-carbohydrate ligand interaction. Imaging of FITC-Con A and FITC-WGA cell-surface fluorescence by confocal microscopy demonstrated marked localization of both lectins to cell surfaces associated with cell division and maturation, indicative of dynamic carbohydrate ligand exposure and masking. Some fluorescence was associated with entrapment of FITC-Con A by capsular components, but FITC-Con A and FITC-WGA readily penetrated the capsule matrix to bind to the same cell surfaces labelled in acapsular cells.