60,074 research outputs found

### 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

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