Workload reduction of a generalized Brownian network

We consider a dynamic control problem associated with a generalized Brownian network, the objective being to minimize expected discounted cost over an infinite planning horizon. In this Brownian control problem (BCP), both the system manager's control and the associated cumulative cost process may be locally of unbounded variation. Due to this aspect of the cost process, both the precise statement of the problem and its analysis involve delicate technical issues. We show that the BCP is equivalent, in a certain sense, to a reduced Brownian control problem (RBCP) of lower dimension. The RBCP is a singular stochastic control problem, in which both the controls and the cumulative cost process are locally of bounded variation.Comment: Published at http://dx.doi.org/10.1214/105051605000000458 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Finite pseudo orbit expansions for spectral quantities of quantum graphs

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the number of bonds of the graph appear, analogous to a cut off at half the Heisenberg time. The calculation simplifies previous approaches to pseudo orbit expansions on graphs. We formulate coefficients of the characteristic polynomial and derive a secular equation in terms of the irreducible pseudo orbits. From the secular equation, whose roots provide the graph spectrum, the zeta function is derived using the argument principle. The spectral zeta function enables quantities, such as the spectral determinant and vacuum energy, to be obtained directly as finite expansions over the set of short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy calculation expande

Effects on Amorphous Silicon Photovoltaic Performance from High-temperature Annealing Pulses in Photovoltaic Thermal Hybrid Devices

There is a renewed interest in photovoltaic solar thermal (PVT) hybrid systems, which harvest solar energy for heat and electricity. Typically, a main focus of a PVT system is to cool the photovoltaic (PV) cells to improve the electrical performance, however, this causes the thermal component to under-perform compared to a solar thermal collector. The low temperature coefficients of amorphous silicon (a-Si:H) allow for the PV cells to be operated at higher temperatures and are a potential candidate for a more symbiotic PVT system. The fundamental challenge of a-Si:H PV is light-induced degradation known as the Staebler-Wronski effect (SWE). Fortunately, SWE is reversible and the a-Si:H PV efficiency can be returned to its initial state if the cell is annealed. Thus an opportunity exists to deposit a-Si:H directly on the solar thermal absorber plate where the cells could reach the high temperatures required for annealing. In this study, this opportunity is explored experimentally. First a-Si:H PV cells were annealed for 1 hour at 100\degreeC on a 12 hour cycle and for the remaining time the cells were degraded at 50\degreeC in order to simulate stagnation of a PVT system for 1 hour once a day. It was found that, when comparing the cells after stabilization at normal 50\degreeC degradation, this annealing sequence resulted in a 10.6% energy gain when compared to a cell that was only degraded at 50\degreeC

Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions

We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics in a classically chaotic system with multiple scales corresponding to the lengths of the bonds. For graph Laplacians we briefly report results for the spectral determinant, vacuum energy and heat kernel asymptotics of general graphs in terms of the vertex matching conditions.Comment: 5 pages, submitted to proceedings of QFEXT09, minor corrections made

UK regional scale modelling of natural geohazards and climate change

For over 10 years, the British Geological Survey (BGS) has been investigating geotechnical and mineralogical factors controlling volume change behaviour of UK clay soils and mudrocks. A strong understanding of the relationship between these parameters and the clays' shrink-swell properties has been developed. More recently, partly resulting from concerns of users of this knowledge, a study of the relationships between climate change and shrink-swell behaviour over the last 30 years has been carried out. Information on subsidence insurance claims has been provided by the Association of British Insurers (ABI) and the UK Meteorological Office (UKMO) historical climate station data has also been utilised. This is being combined with the BGS's GeoSure national geohazard data, to build a preliminary GIS model to provide an understanding of the susceptibility of the Tertiary London Clay to climate change. This paper summarises the data analysis and identifies future work for model construction and refinement

Positive recurrence of reflecting Brownian motion in three dimensions

Consider a semimartingale reflecting Brownian motion (SRBM) $Z$ whose state space is the $d$-dimensional nonnegative orthant. The data for such a process are a drift vector $\theta$, a nonsingular $d\times d$ covariance matrix $\Sigma$, and a $d\times d$ reflection matrix $R$ that specifies the boundary behavior of $Z$. We say that $Z$ is positive recurrent, or stable, if the expected time to hit an arbitrary open neighborhood of the origin is finite for every starting state. In dimension $d=2$, necessary and sufficient conditions for stability are known, but fundamentally new phenomena arise in higher dimensions. Building on prior work by El Kharroubi, Ben Tahar and Yaacoubi [Stochastics Stochastics Rep. 68 (2000) 229--253, Math. Methods Oper. Res. 56 (2002) 243--258], we provide necessary and sufficient conditions for stability of SRBMs in three dimensions; to verify or refute these conditions is a simple computational task. As a byproduct, we find that the fluid-based criterion of Dupuis and Williams [Ann. Probab. 22 (1994) 680--702] is not only sufficient but also necessary for stability of SRBMs in three dimensions. That is, an SRBM in three dimensions is positive recurrent if and only if every path of the associated fluid model is attracted to the origin. The problem of recurrence classification for SRBMs in four and higher dimensions remains open.Comment: Published in at http://dx.doi.org/10.1214/09-AAP631 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org