Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Analysis and clustering of residential customers energy behavioral demand using smart meter data

Clustering methods are increasingly being applied to residential smart meter data, providing a number of important opportunities for distribution network operators (DNOs) to manage and plan the low voltage networks. Clustering has a number of potential advantages for DNOs including, identifying suitable candidates for demand response and improving energy profile modelling. However, due to the high stochasticity and irregularity of household level demand, detailed analytics are required to define appropriate attributes to cluster. In this paper we present in-depth analysis of customer smart meter data to better understand peak demand and major sources of variability in their behaviour. We find four key time periods in which the data should be analysed and use this to form relevant attributes for our clustering. We present a finite mixture model based clustering where we discover 10 distinct behaviour groups describing customers based on their demand and their variability. Finally, using an existing bootstrapping technique we show that the clustering is reliable. To the authors knowledge this is the first time in the power systems literature that the sample robustness of the clustering has been tested.

Kinetics analysis and automated online screening of aminocarbonylation of aryl halides in flow

Temperature, pressure, gas stoichiometry, and residence time were varied to control the yield and product distribution of the palladium-catalyzed aminocarbonylation of aromatic bromides in both a silicon microreactor and a packed-bed tubular reactor. Automation of the system set points and product sampling enabled facile and repeatable reaction analysis with minimal operator supervision. It was observed that the reaction was divided into two temperature regimes. An automated system was used to screen steady-state conditions for offline analysis by gas chromatography to fit a reaction rate model. Additionally, a transient temperature ramp method utilizing online infrared analysis was used, leading to more rapid determination of the reaction activation energy of the lower temperature regimes. The entire reaction spanning both regimes was modeled in good agreement with the experimental data.