Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

The topographic distribution of the magnetic P100M to full- and half-field stimulation

Visual evoked magnetic responses were recorded to full-field and left and right half-field stimulation with three check sizes (70′, 34′ and 22′) in five normal subjects. Recordings were made sequentially on a 20-position grid (4 × 5) based on the inion, by means of a single-channel direct current-Superconducting Quantum Interference Device second-order gradiometer. The topographic maps were consistent on the same subjects recorded 2 months apart. The half-field responses produced the strongest signals in the contralateral hemisphere and were consistent with the cruciform model of the calcarine fissure. Right half fields produced upper-left-quadrant outgoing fields and lower-left-quadrant ingoing fields, while the left half field produced the opposite response. The topographic maps also varied with check size, with the larger checks producing positive or negative maximum position more anteriorly than small checks. In addition, with large checks the full-field responses could be explained as the summation of the two half fields, whereas full-field responses to smaller checks were more unpredictable and may be due to sources located at the occipital pole or lateral surface. In addition, dipole sources were located as appropriate with the use of inverse problem solutions. Topographic data will be vital to the clinical use of the visual evoked field but, in addition, provides complementary information to visual evoked potentials, allowing detailed studies of the visual cortex. © 1992 Kluwer Academic Publishers.

Size frequency distribution of prion protein (PrP) aggregates in variant Creutzfeldt-Jakob disease (vCJD)

The frequency distribution of aggregate size of the diffuse and florid-type prion protein (PrP) plaques was studied in various brain regions in cases of variant Creutzfeldt-Jakob disease (vCJD). The size distributions were unimodal and positively skewed and resembled those of β-amyloid (Aβ) deposits in Alzheimer's disease (AD) and Down's syndrome (DS). The frequency distributions of the PrP aggregates were log-normal in shape, but there were deviations from the expected number of plaques in specific size classes. More diffuse plaques were observed in the modal size class and fewer in the larger size classes than expected and more florid plaques were present in the larger size classes compared with the log-normal model. It was concluded that the growth of the PrP aggregates in vCJD does not strictly follow a log-normal model, diffuse plaques growing to within a more restricted size range and florid plaques to larger sizes than predicted. © Springer-Verlag 2005.

Size frequency distribution of beta-amyloid (Abeta) deposits in dementia with Lewy bodies

In Alzheimer's disease (AD) and Down's syndrome (DS), the size frequency distribution of the beta-amyloid (Abeta) deposits can be described by a log-normal model and may indictae the growth of the deposits. This study determined the size frequency distribution of the Abeta deposits in the temporal lobe in 8 casaes of dementia with Lewy bodies (DLB) with associated AD pathology (DLB/AD. The size distributions of Abeta deposits were unimodal and positively skewed; the mean size of deposi and the degree of skew varying with deposit type and brain region. Size distributions of the primitive deposits had lower means and were less skewed compared with the diffuse and classic deposits. In addition, size distributions in the hippocampus and parahippocampal gyrus (PHG) had larger means and a greater degree of skew compared with other cortical gyri. All size distributions deviated significantly from a log-normal model. There were more Abeta deposits than expected in the smaller size classes and fewer than expected near the mean and in the larger size classes. The data suggest thatthe pattern of growth of the Abeta deposits in DLB/AD depends both on deposit morphology and brain area. In addition, Abeta deposits in DLB appear to grow to within a more restricted size range than predicted and hence, to have less potential for growth compared with cases of 'pure' AD and DS.

Statnote 1: is the data normal?

Testing whether an observed distribution of observations deviates from normality is a common type of statistical test available in statistics software. Most software offer two ways of judging whether there are significant deviations of the observed from the expected distributions, viz., chi-square and the KS test. These tests have different sensitivities and problems and often give conflicting results. The results of these tests together with observations of the shape of the observed distribution should be used to judge normality.

Statnote 4: what if the data are not normal?

When testing the difference between two groups, if previous data indicate non-normality, then either transform the data if they comprise percentages, integers or scores or use a non-parametric test. If there is uncertainty whether the data are normally distributed, then deviations from normality are likely to be small if the data are measurements to three significant figures. Unless there is clear evidence that the distribution is non-normal, it is more efficient to use the conventional t-tests. It is poor statistical practice to carry out both the parametric and non-parametric tests on a set of data and then choose the result that is most convenient to the investigator!

Further studies on flow distribution on distillation sieve trays

The thesis describes experimental work on the possibility of using deflection baffles in conventional distillation trays as flow straightening devices, with the view of enhancing tray efficiency. The mode of operation is based on deflecting part of the liquid momentum from the centre of the tray to the segment regions in order to drive stagnating liquid at the edges forward. The first part of the work was a detailed investigation into the two-phase flow patterns produced on a conventional sieve tray having 1 mm hole size perforations. The data provide a check on some earlier work and extend the range of the existing databank, particularly to conditions more typical of industrial operation. A critical survey of data collected on trays with different hole sizes (Hine, 1990; Chambers, 1993; Fenwick, 1996; this work) showed that the hole diameter has a significant influence on the flow regime, the size of the stagnant regions and the hydraulic and mass transfer performance. Five modified tray topologies were created with different configurations of baffles and tested extensively in the 2.44 m diameter air-water pilot distillation simulator for their efficacy in achieving uniform flow across the tray and for their impact on tray loading capacity and mass transfer efficiency. Special attention was given to the calibration of the over 100 temperature probes used in measuring the water temperature across the tray on which the heat and mass transfer analogy is based. In addition to normal tray capacity experiments, higher weir load experiments were conducted using a 'half-tray' mode in order to extend the range of data to conditions more typical of industrial operation. The modified trays show superior flow characteristics compared to the conventional tray in terms of the ability to replenish the zones of exceptionally low temperatures and high residence times at the edges of the tray, to lower the bulk liquid gradient and to achieve a more uniform flow across the tray. These superior flow abilities, however, tend to diminish with increasing weir load because of the increasing tendency for the liquid to jump over the barriers instead of flowing over them. The modified tray topologies showed no tendency to cause undue limitation to tray loading capacity. Although the improvement in the efficiency of a single tray over that of the conventional tray was moderate and in some cases marginal, the multiplier effect in a multiple tray column situation would be significant (Porter et al., 1972). These results are in good agreement with an associated CFD studies (Fischer, 1999) carried out by partners in the Advanced Studies in Distillation consortium. It is concluded that deflection baffles can be used in a conventional distillation sieve tray to achieve better liquid flow distribution and obtain enhanced mass transfer efficiency, without undermining the tray loading capacity. Unlike any other controlled-flow tray whose mechanical complexity impose stringent manufacturing and installation tolerances, the baffled-tray models are simple to design, manufacture and install and thus provide an economic method of retrofitting badly performing sieve trays both in terms of downtime and fabrication. NOTE APPENDICES 2-5 ARE ON A SEPARATE FLOPPY DISK ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY WITH PRIOR ARRANGEMENT

β-amyloid (Aβ) deposition in cognitively normal brain, dementia with Lewy bodies, and Alzheimer's disease:a study using principal components analysis

The densities of diffuse, primitive, and classic ß-amyloid (Aß) deposits were studied in the temporal lobe in cognitively normal brain, dementia with Lewy bodies (DLB), familial Alzheimer’s disease (FAD), and sporadic AD (SAD). Principal components analysis (PCA) was used to determine whether there were distinct differences between groups or whether Aß pathology was more continuously distributed from group to group. Three principal components (PC) were extracted from the data accounting for 56% of the total variance. Plots of cases in relation to the PC did not result in distinct groups but suggested overlap in Aß deposition between the groups. In addition, there were linear correlations between the densities of Aß deposits and the distribution of the cases along the PC in specific brain regions suggesting continuous variation from group to group. PC1 was associated with the degree of maturation of Aß deposits, PC2 with differences between FAD and SAD, and PC3 with the degree of spread of Aß pathology into the hippocampus. Apolipoprotein E (APOE) genotype was not associated with variation in Aß deposition between cases. PCA may be a useful method of studying the pathological interface between closely related neurodegenerative disorders.

Corneal pachymetry in normal and keratoconic eyes:Orbscan II versus ultrasound

Purpose: To compare corneal thickness measurements using Orbscan II (OII) and ultrasonic (US) pachymetry in normal and in keratoconic eyes. Setting: Eye Department, Heartlands and Solihull NHS Trust, Birmingham, United Kingdom. Methods: Central corneal thickness (CCT) was measured by means of OII and US pachymetry in 1 eye of 72 normal subjects and 36 keratoconus patients. The apical corneal thickness (ACT) in keratoconus patients was also evaluated using each method. The mean of the difference, standard deviation (SD), and 95% limits of agreement (LoA = mean ± 2 SD), with and without applying the default linear correction factor (LCF), were determined for each sample. The Student t test was used to identify significant differences between methods, and the correlation between methods was determined using the Pearson bivariate correlation. Bland-Altman analysis was performed to confirm that the results of the 2 instruments were clinically comparable. Results: In normal eyes, the mean difference (± 95% LoA) in CCT was 1.04 μm ± 68.52 (SD) (P>.05; r = 0.71) when the LCF was used and 46.73 ± 75.40 μm (P = .0001; r = 0.71) without the LCF. In keratoconus patients, the mean difference (± 95% LoA) in CCT between methods was 42.46 ± 66.56 μm (P<.0001: r = 0.85) with the LCF, and 2.51 ± 73.00 μm (P>.05: r = 0.85) without the LCF. The mean difference (± 95% LoA) in ACT for this group was 49.24 ± 60.88 μm (P<.0001: r = 0.89) with the LCF and 12.71 ± 68.14 μm (P = .0077; r = 0.89) when the LCF was not used. Conclusions: This study suggests that OII and US pachymetry provide similar readings for CCT in normal subjects when an LCF is used. In keratoconus patients, OII provides a valid clinical tool for the noninvasive assessment of CCT when the LCF is not applied. © 2004 ASCRS and ESCRS.

Dynamic models of exchange rate dependence using option prices and historical returns

Models for the conditional joint distribution of the U.S. Dollar/Japanese Yen and Euro/Japanese Yen exchange rates, from November 2001 until June 2007, are evaluated and compared. The conditional dependency is allowed to vary across time, as a function of either historical returns or a combination of past return data and option-implied dependence estimates. Using prices of currency options that are available in the public domain, risk-neutral dependency expectations are extracted through a copula repre- sentation of the bivariate risk-neutral density. For this purpose, we employ either the one-parameter \Normal" or a two-parameter \Gumbel Mixture" specification. The latter provides forward-looking information regarding the overall degree of covariation, as well as, the level and direction of asymmetric dependence. Specifications that include option-based measures in their information set are found to outperform, in-sample and out-of-sample, models that rely solely on historical returns.

Properties of the Bellman Gamma Distribution

2000 Mathematics Subject Classification: 62H10.

The effects of yoked prisms on body posture and egocentric perception in a normal population

The principal theme of this thesis is the effect of yoked prisms on body posture and egocentric perception. Yoked prisms have been clinically used in the management of a variety of visual and neuro-motor dysfunctions. Most studies have been conducted in pathological populations by studying the effects of prismatic adaptation, without distinguishing short and long term effects. In this study, postural and perceptual prismatic effects have been studied by preventing prism adaptation. A healthy population was selected in order to investigate the immediate prismatic effects, when there is no obvious benefit from their use for the individual. Posturography was used to assess changes in weight distribution and shifts in centre of pressure (barycentre). In addition, photographic analyses were used to assess effects on posture on the x and z axis. Experiments with space board and visual midline shift were used for the evaluation of spatial perception and egocentric localisation. One pair of 8 Δ yoked prisms base left (BL) and one pair of 8 Δ yoked prisms base up (BU) were applied randomly and compared to a pair of plano lenses. Results suggest that immediate prismatic effects take place on a perceptual level and are reflected on an altered body posture respectively without significant changes in weight distribution. Yoked prisms BL showed a rightward rotational effect on spatial perception by expanding space on the z axis when viewing through the base of the prism and constricting space through the apex of the prism. Body posture responded respectively to what was visually perceived by altering posture. A rightward shift and tilt of the head was recorded along with the hips shift and shoulders tilt in the dame direction. Additionally, right shoulder shifted backwards and an angular midline shift to the right was recorded. The egocentric localisation was affected by shifting the midline perception to the left. Yoked prisms BU resulted on a head shift forward and a reduction of the head-neck angle by bringing the chin closer to the chest. The egocentric localisation was altered on the vertical axis providing subjects the perception that their eye level was higher during the experiment. In conclusion, yoked prisms seemed to induce changes in body posture, mainly in the upper body and head, without any significant changes in weight distribution. These changes are partially reflected in spatial perception tests and egocentric localisation before any prismatic adaptation takes place.

Study on Pore Distribution and Formation Rule of Sepiolite Mineral Nanomaterials

Theoretical research and specific surface area analysis of nitrogen adsorption indicated that a lot of structural micropores exist in sepiolite minerals fibers. However, the microporous size, existing form, and the distribution relationship between microporous structures were not proved yet. In this paper, the section TEM samples of nanofibers were prepared on the basis of the metal embedding and cutting technique, and the inner structure of sepiolite nanofibers was observed by TEM. The results showed that sepiolite fibers have multiplayer structure similar to concentric circles, and many micropores with the size of about 2–5 nm are normal and parallel to the -axis. The reason for the previously mentioned phenomenon was explained by using BET analysis and X-ray diffraction analysis results.

New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.