An investigation of the Eigenvalue Calibration Method (ECM) using GASP for non-imaging and imaging detectors

Polarised light from astronomical targets can yield a wealth of information about their source radiation mechanisms, and about the geometry of the scattered light regions. Optical observations, of both the linear and circular polarisation components, have been impeded due to non-optimised instrumentation. The need for suitable observing conditions and the availability of luminous targets are also limiting factors. GASP uses division of amplitude polarimeter (DOAP) (Compain and Drevillon) to measure the four components of the Stokes vector simultaneously, which eliminates the constraints placed upon the need for moving parts during observation, and offers a real-time complete measurement of polarisation. Results from the GASP calibration are presented in this work for both a 1D detector system, and a pixel-by-pixel analysis on a 2D detector system. Following Compain et al. we use the Eigenvalue Calibration Method (ECM) to measure the polarimetric limitations of the instrument for each of the two systems. Consequently, the ECM is able to compensate for systematic errors introduced by the calibration optics, and it also accounts for all optical elements of the polarimeter in the output. Initial laboratory results of the ECM are presented, using APD detectors, where errors of 0.2% and 0.1{\deg} were measured for the degree of linear polarisation and polarisation angle respectively. Channel-to-channel image registration is an important aspect of 2-D polarimetry. We present our calibration results of the measured Mueller matrix of each sample, used by the ECM. A set of Zenith flat-field images were recorded during an observing campaign at the Palomar 200 inch telescope in November 2012. From these we show the polarimetric errors from the spatial polarimetry indicating both the stability and absolute accuracy of GASP.Comment: Accepted for publication in Experimental Astronom

Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure

The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains. In this paper, we take advantage of the overlapping asymptotic regime that applies to both the NLS and Whitham modulation descriptions in order to develop a universal analytical description of dispersive shock waves (DSWs) generated in Riemann problems for a broad class of integrable and non-integrable nonlinear dispersive equations. The proposed method extends DSW fitting theory that prescribes the motion of a DSW's edges into the DSW's interior, i.e., this work reveals the DSW structure. Our approach also provides a natural framework in which to analyze DSW stability. We consider several representative, physically relevant examples that illustrate the efficacy of the developed general theory. Comparisons with direct numerical simulations show that inclusion of higher order terms in the NLS equation enables a remarkably accurate description of the DSW structure in a broad region that extends from the harmonic, small amplitude edge

Shear-driven size segregation of granular materials: modeling and experiment

Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then re-segregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we locally map the measured height of the experimental sample (which indicates the degree of segregation) to the local packing density. We observe that the model successfully captures the presence of a fast mixing process and relatively slower re-segregation process, but the model predicts a finite re-segregation time, while in the experiment re-segregation occurs only exponentially in time

A Wannier-function-based ab initio Hartree-Fock study of polyethylene

In the present letter, we report the extension of our Wannier-function-based ab initio Hartree-Fock approach---meant originally for three-dimensional crystalline insulators---to deal with quasi-one-dimensional periodic systems such as polymers. The system studied is all-transoid polyethylene, and results on optimized lattice parameters, cohesive energy and the band structure utilizing 6-31G** basis sets are presented. Our results are also shown to be in excellent agreement with those obtained with traditional Bloch-orbital-based approaches.Comment: 15 Pages, RevTex, inludes four figures, Chem. Phys. Letts., in press (1998

The Natural History and Management of Patients With Pancreatic Pseudocysts as a Complication of Acute Pancreatitis

In this thesis I have studied the natural course, outcome and management of patients who developed a pancreatic pseudocyst following an episode of acute pancreatitis. The clinical information for this work originated in 2 studies involving a total of 129 patients with a pseudocyst. This represents one of the largest reports of such patients in medical literature. One study was of 100 patients with a pseudocyst presenting to Glasgow Royal Infirmary, over a period of 23 years (1962 - 1984 ) (Chapter 3 ) (Imrie et al 1988 . Appendix 1). The second study was of 29 similar patients (Chapter 4) documented during a prospective trial of therapeutic peritoneal lavage in patients with severe acute pancreatitis recorded in Leeds, Bristol and Glasgow (1982 - 1984) (Corfield et al 1985, Mayer et al 1985. Appendix 1). Using the information derived from these studies, I have formulated an assessment system for predicting the likelihood of spontaneous resolution of a pseudocyst (Chapter 8). With the addition of results obtained from an analysis of percutaneous needle aspiration (Chapter 6) and analysis of acute phase reactant proteins within pseudocyst fluid (Chapter 7) I propose a new plan of management for patients with acute pancreatic pseudocysts. The important findings of this thesis are summarised as follows:- 1. The "waiting time" for conservative management of a pancreatic pseudocyst could safely be extended to 12 weeks. Bradley et al (1979) have suggested that a period of 6 weeks from the time of pseudocyst formation should be regarded as both the maximum time to wait for spontaneous resolution of a pseudocyst and the optimum time to consider some form of drainage procedure. A pseudocyst was drained surgically in 78 (%) of the 100 patients from Glasgow Royal Infirmary and resolved spontaneously in the other 22 (%). The median time from diagnosis to drainage by cystogastrostomy was 12 weeks (range 2 - 69 weeks). The median time to complete spontaneous resolution was also 12 weeks (range 2 - 104 weeks). Of the 29 patients from Leeds, Bristol and Glasgow surgical drainage was performed in 11 (38%) at a median time of 7 weeks (range 3-38 weeks) and spontaneous resolution occurred in 15 (52%) at a median time of 7 weeks (range 2-20 weeks). Bradley et al (1979) also found an increasing proportion of patients developed complications the greater the time a pseudocyst was left untreated. Only 6 (5%) of all 129 patients studied suffered complications as a result of an undrained pseudocyst. Based on the above results I suggest that 6 weeks is too short a period and 12 weeks is a more appropriate time to wait for spontaneous resolution to occur provided the is repeatedly assessed by clinical examination and ultrasound scanning to confirm that the diameter of the pseudocyst is not increasing and that the clinical state of the clinical state of the patient is not deteriorating. 2. No single factor causing acute pancreatitis predisposes to pseudocyst formation. Of the 100 patients from Glasgow Royal Infirmary alcohol was the cause of acute pancreatitis in 59%, gallstones in 27% and the aetiology was idiopathic in 9%. In contrast, of the 29 patients from Leeds, Bristol and Glasgow alcohol was the aetiological factor in 23%, gallstones in 48% and it was idiopathic in 23 %. This distribution was very similar to that of a total of 418 patients with acute pancreatitis studied in the three cities (Chapter 4)(gallstones 54%: alcohol 20%: idiopathic 21%). This suggests that no single aetiological factor of acute pancreatitis is more likely to cause pseudocyst formation. 3. The aetiology of the preceding acute pancreatitis is an important factor in determining the outcome of patients with a pseudocyst. The mortality amongst patients from Glasgow Royal Infirmary with gallstone induced pancreatitis and pseudocyst formation was 22% significantly greater than that of patiens with alcohol induced disease (5% mortality. The majority of patients who died as a result of gallstone induced disease did so because of sepsis and/or haemorrhage. The implication from this is that, if possible, in order to decrease the possibility of infection, the biliary tract should be cleared of stones at the time of definitive pseudocyst surgery. 4. Spontaneous resolution of a pseudocyst can be predicted using a multi-factor assessment system. A pseudocyst resolved spontaneously in 22 (%) of the 100 Glasgow Royal Infirmary patients and 15 (52%) of those from Leeds, Bristol and Glasgow. Differences in clinical, laboratory and radiological findings in these patients were compared with those of patients whose pseudocyst needed drainage. The proportion of patients with a palpable abdominal mass was significantly greater in those who required surgery in both groups of patients. The results for the patients from Leeds, Bristol and Glasgow also showed a significantly higher proportion with abdominal distension and a leukocytosis (>10 x 10e9 cells/1) amongst those who underwent surgery. (Abstract shortened by ProQuest.)

Are megaquakes clustered?

We study statistical properties of the number of large earthquakes over the past century. We analyze the cumulative distribution of the number of earthquakes with magnitude larger than threshold M in time interval T, and quantify the statistical significance of these results by simulating a large number of synthetic random catalogs. We find that in general, the earthquake record cannot be distinguished from a process that is random in time. This conclusion holds whether aftershocks are removed or not, except at magnitudes below M = 7.3. At long time intervals (T = 2-5 years), we find that statistically significant clustering is present in the catalog for lower magnitude thresholds (M = 7-7.2). However, this clustering is due to a large number of earthquakes on record in the early part of the 20th century, when magnitudes are less certain.Comment: 5 pages, 5 figure

Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is non-standard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case