Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

Spatial and temporal characterisation of ground deformation recorded by geodetic techniques

A critical point in the analysis of ground displacements time series is the development of data driven methods that allow the different sources that generate the observed displacements to be discerned and characterised. A widely used multivariate statistical technique is the Principal Component Analysis (PCA), which allows reducing the dimensionality of the data space maintaining most of the variance of the dataset explained. Anyway, PCA does not perform well in finding the solution to the so-called Blind Source Separation (BSS) problem, i.e. in recovering and separating the original sources that generated the observed data. This is mainly due to the assumptions on which PCA relies: it looks for a new Euclidean space where the projected data are uncorrelated. The Independent Component Analysis (ICA) is a popular technique adopted to approach this problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, I use a variational bayesian ICA (vbICA) method, which models the probability density function (pdf) of each source signal using a mix of Gaussian distributions. This technique allows for more flexibility in the description of the pdf of the sources, giving a more reliable estimate of them. Here I present the application of the vbICA technique to GPS position time series. First, I use vbICA on synthetic data that simulate a seismic cycle (interseismic + coseismic + postseismic + seasonal + noise) and a volcanic source, and I study the ability of the algorithm to recover the original (known) sources of deformation. Secondly, I apply vbICA to different tectonically active scenarios, such as the 2009 L'Aquila (central Italy) earthquake, the 2012 Emilia (northern Italy) seismic sequence, and the 2006 Guerrero (Mexico) Slow Slip Event (SSE).

Characterisation of indoor air organic pollutants in Brisbane

The occurrence and levels of airborne polycyclic aromatic hydrocarbons and volatile organic compounds in selected non-industrial environments in Brisbane have been investigated as part of an integrated indoor air quality assessment program. The most abundant and most frequently encountered compounds include, nonanal, decanal, texanol, phenol, 2-ethyl-1-hexanol, ethanal, naphthalene, 2,6-tert-butyl-4-methyl-phenol (BHT), salicylaldehyde, toluene, hexanal, benzaldehyde, styrene, ethyl benzene, o-, m- and pxylenes, benzene, n-butanol, 1,2-propandiol, and n-butylacetate. Many of the 64 compounds usually included in the European Collaborative Action method of TVOC analysis were below detection limits in the samples analysed. In order to extract maximum amount of information from the data collected, multivariate data projection methods have been employed. The implications of the information extracted on source identification and exposure control are discussed.

A bridging transition technique for the combination of meshfree method with finite element method in 2D solids and structures

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the meshfree method is used in the sub-domain where the MM is required to obtain high accuracy, and the finite element method is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the meshfree method and FEM when overcome their shortcomings.

Synthesis and characterisation of cobalt hydroxide, cobalt oxyhydroxide and cobalt oxide nanodiscs

Cobalt hydroxide, cobalt oxyhydroxide and cobalt oxide nanomaterials were synthesized through simple soft chemistry. The cobalt hydroxide displays hexagonal morphology with clear edges 20 nm long. This morphology and nanosize is retained through to cobalt oxide Co3O4 through a topotactical relationship. Cobalt oxyhydroxide and cobalt oxide nanomaterials were synthesized through oxidation and low temperature calcination from the as-prepared cobalt hydroxide. Characterisation of these cobalt-based nanomaterials were fully developed, including X-ray diffraction, transmission electron microscopy combined with selected area electron diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy, Raman spectroscopy, and thermal gravimetric analysis. Bonding of the divalent cobalt hydroxide from the oxyhydroxide and oxides by studying their high resolution XPS spectra for Co 2p3/2 and O 1s. Raman spectroscopy of the as-prepared Co(OH)2, CoO(OH) and Co3O4 nanomaterials characterised each material. The thermal stability of the materials Co(OH)2 and CoO(OH) were established. This research has developed methodology for the synthesis of cobalt oxide and cobalt oxyhydroxide nanodiscs at low temperatures.