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

Contribution of neutral processes to the assembly of gut microbial communities in the zebrafish over host development

Despite their importance to host health and development, the communities of microorganisms associated with humans and other animals are characterized by a large degree of unexplained variation across individual hosts. The processes that drive such inter-individual variation are not well understood. To address this, we surveyed the microbial communities associated with the intestine of the zebrafish, Danio rerio, over developmental time. We compared our observations of community composition and distribution across hosts with that predicted by a neutral assembly model, which assumes that community assembly is driven solely by chance and dispersal. We found that as hosts develop from larvae to adults, the fit of the model to observed microbial distributions decreases, suggesting that the relative importance of non-neutral processes, such as microbe-microbe interactions, active dispersal, or selection by the host, increases as hosts mature. We also observed that taxa which depart in their distributions from the neutral prediction form ecologically distinct sub-groups, which are phylogenetically clustered with respect to the full metacommunity. These results demonstrate that neutral processes are sufficient to generate substantial variation in microbiota composition across individual hosts, and suggest that potentially unique or important taxa may be identified by their divergence from neutral distributions