On the Jacobi Equation and Manifolds with Multiple Conjugate Points

We investigate the phenomenon of multiple conjugate points along a geodesic. In the first instance, we investigate conjugate points in the context of the Jacobi equation, a second order ordinary differential equation, which captures precisely the geometry of conjugate points on surfaces. We then construct geometric examples which exhibit similar properties in higher dimensions

On the Jacobi Equation and Manifolds with Multiple Conjugate Points

We investigate the phenomenon of multiple conjugate points along a geodesic. In the first instance, we investigate conjugate points in the context of the Jacobi equation, a second order ordinary differential equation, which captures precisely the geometry of conjugate points on surfaces. We then construct geometric examples which exhibit similar properties in higher dimensions

Active transverse mode control and optimisation of an all-solid-state laser using an intracavity adaptive-optic mirror

A 37 element adaptive optic mirror has been used intracavity to control the oscillation mode profile of a diode-laser pumped Nd:YVO4 laser. Mode and power optimisation are demonstrated by closed loop automatic optimisation of the deformable mirror

Active transverse mode control and optimisation of an all-solid-state laser using an intracavity adaptive-optic mirror

A 37 element adaptive optic mirror has been used intracavity to control the oscillation mode profile of a diode-laser pumped Nd:YVO4 laser. Mode and power optimisation are demonstrated by closed loop automatic optimisation of the deformable mirror

Study of fluid–structure interaction with undulating flow using channel driven cavity flow system

17 USC 105 interim-entered record; under review.The article of record as published may be found at https://doi.org/10.1007/s41939-021-00112-7Fluid–structure interaction (FSI) induced by undulated flows was investigated using a channel driven cavity flow (CDCF) system. The bottom of the cavity section has a flexible plate made of either an aluminum alloy or carbon fiber composite, which interacts with flows in the cavity. Undulating flows were generated by controlling a series of solenoid valves programmed to interrupt the flow at various different frequencies from 0.5 to 1.25 Hz. Mean flow velocity was also varied for each given undulation frequency. The dynamic motion of the flexible test panel, made of aluminum alloy or carbon fiber composite, was measured for transverse deflections using laser displacement sensors. The study showed that the structural response was very dependent on the input flow. The plate vibrational modes had three to five dominant frequencies ranging from the undulated flow frequencies to about 5.0 Hz. Those frequencies were either at or very close to the multiples of the flow frequencies. The most dominant frequency was not always the same as the flow frequency, but it varied depending on the applied flow frequency.Office of Naval ResearchIdentified in text as U.S. Government work

Rapid manufacturing – impact on supply chain methodologies and practice

This paper demonstrates the use of Rapid Manufacturing (RM) as the enabling technology for flexible manufacturing in a number of industrial sectors. The paper discusses the evolution of Rapid Prototyping (RP) to Rapid Manufacturing and the current issues that require further research for the successful integration of this technology within manufacturing companies. The use of RM will have particular impact on supply chain management paradigms such as lean and agile and has particular strategic fit with mass customisation. The effect RM will have on these paradigms is discussed and confirmed with example cases from automotive production, motor sport and medical devices industries. In conclusion RM has already been shown in the three cases to offer benefits, particularly where fast re-configuration of the manufacturing process is required and with the production of customised components

Semiconductor disk lasers: the future's bright; the colour's flexible

Presentation describing semiconductor disk lasers, their use and how they work

Probing Supersymmetry With Third-Generation Cascade Decays

The chiral structure of supersymmetric particle couplings involving third generation Standard Model fermions depends on left-right squark and slepton mixings as well as gaugino-higgsino mixings. The shapes and intercorrelations of invariant mass distributions of a first or second generation lepton with bottoms and taus arising from adjacent branches of SUSY cascade decays are shown to be a sensitive probe of this chiral structure. All possible cascade decays that can give rise to such correlations within the MSSM are considered. For bottom-lepton correlations the distinctive structure of the invariant mass distributions distinguishes between decays originating from stop or sbottom squarks through either an intermediate chargino or neutralino. For decay through a chargino the spins of the stop and chargino are established by the form of the distribution. When the bottom charge is signed through soft muon tagging, the structure of the same-sign and opposite-sign invariant mass distributions depends on a set function of left-right and gaugino-higgsino mixings, as well as establishes the spins of all the superpartners in the sequential two-body cascade decay. Tau-lepton and tau-tau invariant mass distributions arising from MSSM cascade decays are likewise systematically considered with particular attention to their dependence on tau polarization. All possible tau-lepton and tau-tau distributions are plotted using a semi-analytic model for hadronic one-prong taus. Algorithms for fitting tau-tau and tau-lepton distributions to data are suggested.Comment: 35 pages, 17 .eps figure

The composition of the zebrafish intestinal microbial community varies across development

The assembly of resident microbial communities is an important event in animal development; however, the extent to which this process mirrors the developmental programs of host tissues is unknown. Here we surveyed the intestinal bacteria at key developmental time points in a sibling group of 135 individuals of a model vertebrate, the zebrafish (Danio rerio). Our survey revealed stage-specific signatures in the intestinal microbiota and extensive interindividual variation, even within the same developmental stage. Microbial community shifts were apparent during periods of constant diet and environmental conditions, as well as in concert with dietary and environmental change. Interindividual variation in the intestinal microbiota increased with age, as did the difference between the intestinal microbiota and microbes in the surrounding environment. Our results indicate that zebrafish intestinal microbiota assemble into distinct communities throughout development, and that these communities are increasingly different from the surrounding environment and from one another