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Analysis of the inverse problem for determining nematic liquid crystal director profiles from optical measurements using singular value decomposition.
Get PDFWe use the problem of determining nematic liquid crystal director profiles from optical measurements as an example to illustrate that what is often treated purely as a data fitting problem is really an inverse problem and that useful insights an be obtained by treating it in this way. Specifically we illustrate the analysis of he sufficiency of data and the sensitivity of a solution to measurement errors. We assume a stratified medium where the Berreman method can be used for the optical forward problem and we consider the inverse problem to be the determination of an
anisotropic dielectric permittivity tensor from optical data. A numerical Singular Value Decomposition (SVD) analysis reveals that although this inverse problem is severely ill-conditioned it is possible to determine depth-dependent information provided the
medium is sufficiently birefringent and that, as one might expect, a larger range of incident angles gives greater information. Analytical solutions of the Berreman equations for general perturbations of an orthorhombic crystal con¯rm uniqueness of solution for the linearized problem and give further insights into the severely ill-posed nature of the inverse problem
A band factorization technique for transition matrix element asymptotics
No full textA new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate and fast numerical treatment of transition matrix elements in the quasi-classical limit. Examples include the matrix elements of xp in the harmonic oscillator basis, and connections with the Wigner 3j symbols
Advanced quadrature methods to value multi-asset and complex path dependent options
No full textThis paper studies the effect of financial crises on trade credit for a sample of 890 firms in six emerging economies. Although the provision of trade credit increases right after a crisis, it contracts in the following months and years. Firms that are financially more vulnerable to crises extend less trade credit to their customers. We argue that the decline in aggregate trade credit ratios is driven by the reduction in the supply of trade credit that follows a bank credit crunch, consistent with the “redistribution view” of trade credit provision, whereby bank credit is redistributed via trade credit from financially stronger firms to weaker firms
Viscous-inviscid interaction in transonic Prandtl-Meyer flow
No full textThis paper presents a theoretical analysis of perfect gas flow over a convex corner of a rigid-body contour. It is assumed that the flow is subsonic before the corner. It accelerates around the corner to become supersonic, and then undergoes an additional acceleration in the expansion Prandtl–Meyer fan that forms in the supersonic part of the flow behind the corner. The entire process is described by a self-similar solution of the Kármán–Guderley equation. The latter shows that the boundary layer approaching the apex of the corner is exposed to a singular pressure gradient, , where denotes the coordinate measured along the body surface from the corner apex. Under these conditions, the solution for the boundary layer also develops a singularity. In particular, the longitudinal velocity near the body surface behaves as . Here is the normal coordinate scaled with the boundary-layer thickness ; being the Reynolds number, assumed large in this theory.
As usual, the boundary layer splits up into two parts, a viscous near-wall sublayer and a locally inviscid main part of the boundary layer. The analysis of the displacement effect of the boundary layer shows that neither the viscous sublayer nor the main part determines the displacement thickness. Instead, the overlapping region situated between them proves to be responsible for the shape of the streamlines at the outer edge of the boundary layer. This leads to a significant simplification of the analysis of the flow behaviour in the viscous–inviscid interaction region that forms in a small vicinity of the corner. In order to describe the flow behaviour in this region, one has to solve the Kármán–Guderley equation for the inviscid part of the flow outside the boundary layer. The influence of the boundary layer is expressed through a boundary condition, that relates the streamline deflection angle at the outer edge of the boundary layer to the pressure gradient acting upon the boundary layer. The boundary-layer analysis leads to an analytical formula that relates and (unlike in previous studies of the viscous–inviscid interaction). The interaction problem was solved numerically to confirm that the solution develops a finite-distance singularity
Nonlocal flow effects in bushfire spread rates
Get PDFThe entrainment of air into the bouyant flame and plume above any part of a fireline
must affect the air flow at all other parts of the fireline. Thus the local wind actually felt at any
one part of the fire is not necessarily the ambient wind; it is influenced, nonlocally, by all other
parts of the fireline. By modelling this effect of bouyancy on the ambient air as a line of suction
above the fireline, with a height and strength that varies with intensity of burning along the
fireline, the changes in air flow can be calculated for any given shape and size of fireline. To
illustrate the nature of the model, a fixed elliptical shape of fireline is examined within a steady
ambient wind, as measured far from the fire. A reduction in head fire spread rate is predicted for
finite widths of the fireline and, if the scale of the fireline increases, the spread rate approaches the
limiting value of the potential spread rate. The model is therefore in qualitative agreement with
the basic experimental findings of Cheney and Gould (1995)
Including suppression effectiveness in fireline growth models
Get PDFThe inclusion of suppression effectiveness in fire line growth models is formulated as a system of differential
equations. The model draws on earlier ideas using ellipses to model fire growth, particularly the head fire
and flank fire rates of spread, combines this with recent studies of the effect of fire line on spread rate and
appends a single equation for the increase of suppressed fire line with time. Representative parameter values
are used to illustrate this way of describing the effect of fire suppression activities on the fire line and to
develop criteria for the likely outcome of containment activities
A direct tracking method for a grounded conductor inside a pipeline from capacitance measurements
No full textWe present a new non-iterative method for tracking conductive water in a pipeline using a single excitation pattern from an interleaved ECT system. The problem arises, for example, in the oil industry where brine is often mixed with oil in a pipeline. If the size of the body of brine is very large compared with the size of electrodes attached to the pipeline, the corresponding electric potential in the region of brine is close to zero. This model leads to the inverse problem of identifying the dynamic change of the cross section of a grounded conducting region in a pipeline. Unfortunately, standard iterative reconstruction algorithms in ECT associated with the sensitivity matrix do not work in this case. Furthermore, due to the unavailability of Neumann data at the drive electrodes, the previously published layer potential methods for capturing the inhomogeneity are not applicable to this system. In this work, we derive a formula providing a concrete relation between the capacitance change in each receive electrode and the dynamical change in a grounded conducting region inside the pipeline. The proposed method successfully reconstructs feature information such as location and rough shape of the cross section of the water region. We demonstrate the performance of our method in numerical simulations and actual experiment
Model reduction of time-varying systems.
Get PDFThis paper presents new recursive projection techniques to compute reduced order models of time-varying linear systems. The methods produce a low rank approximation of the Gramians or of the Hankel map of the system and are mainly based on matrix operations that can exploit sparsity of the model. We show the practical relevance of our results with a few benchmark examples
Recursive estimation and order determination of space-time autoregressive processes
Get PDFSpace-time autoregressive moving average models may be used for time series measured at
the same times in a number of locations. In this paper we propose a recursive algorithm
for estimating space-time autoregressive (AR) models. We also propose an information
criterion for estimating the model order, and prove its strong consistency. The methods are
illustrated using both simulated and real data. The real data corresponds to hourly carbon
monoxide (CO) concentrations recorded in September 1995 at four different locations in
Venice
Statistical Analysis and Time Series Models for Minimum/Maximum Temperatures in the Antarctic Peninsula
Get PDFOur object in this paper is to study the temperature variations in the Antarctic
Peninsula using multiple regression models with correlated errors admitting ARMA
models with nonGaussian innovations. We found that the Øtted models adequately
describe the variations. The data we consider are minimum/maximum monthly
temperatures recorded at the Faraday station by the British Antarctic Survey for
the period from January 1951 to December 1995. The time series models considered
here are novel in the sense that the linear ARMA models have innovations which
have extreme value distributions, and the maximum likelihood estimation described
here can be widely used in many disciplines.
The time series models we Øtted indicate that the mean of the minimum temperatures
is likely to increase over the next 50 years and the temperatures will
be above 0oC during the summer months which means that the melting season
will increase, creating more climatic and ecological problems. Although the mean
temperature is reported to have increased by 2.5oC we believe that the maximum
temperatures have remained unchanged over the past 45 years. This has led to a
decrease in the diurnal temperature range which has also been observed in many
other parts of the globe.
The in°uence of human activity on climate is still unknown but our ability
to perturb the ozone layer is an established fact. We established a relationship
between minimum monthly temperatures and ozone levels and found they are highly
negatively correlated (at a lag of one month) implying that the higher levels of
ozone in the air keep temperatures low. This resulted in a new time series model
relating the minimum temperatures to ozone levels. After appropriate statistical
tests, we have come to the conclusion that the observed increase in the minimum
temperatures is a consequence of human activity rather than natural causes and
so a reduction in the production of \greenhouse gases" could lead to a decrease in
minimum temperatures, thereby reducing the adverse eÆect of global warming in
the Antarctic Peninsula