Survival analysis with internal covariates modelled using a longitudinal dispersion model and flexible links

Poster presented at the From Basic Sciences to Clinical Research: 1st International Congress of CiiEM. Egas Moniz, Caparica, Portugal, 27-28 November 2015

Longitudinal dispersion in spiral wound RO modules and its effect on the performance of batch mode RO operations

Operation of reverse osmosis (RO) in cyclic batch mode can in principle provide both high energy efficiency and high recovery. However, one factor that causes the performance to be less than ideal is longitudinal dispersion in the RO module. At the end of the batch pressurisation phase it is necessary to purge and then refill the module. During the purge and refill phases, dispersion causes undesirable mixing of concentrated brine with less concentrated feed water, therefore increasing the salt concentration and energy usage in the subsequent pressurisation phase of the cycle. In this study, we quantify the significance of dispersion through theory and experiment. We provide an analysis that relates the energy efficiency of the batch operation to the amount of dispersion. With the help of a model based on the analysis by Taylor, dispersion is quantified according to flow rate. The model is confirmed by experiments with two types of proprietary spiral wound RO modules, using sodium chloride (NaCl) solutions of concentration 1000 to 20,000 ppm. In practice the typical energy usage increases by 4% to 5.5% compared to the ideal case of zero dispersion.

Joint dispersion model with a flexible link

Poster presented at the Workshop on Flexible Models for Longitudinal and Survival Data with Applications in Biostatistics. University of Warwick, Coventry, UK, 27-29 July 2015

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Ancient DNA from Hunter-Gatherer and Farmer Groups from Northern Spain Supports a Random Dispersion Model for the Neolithic Expansion into Europe

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Longitudinal dispersion in laboratory and natural streams

This study concerns the longitudinal dispersion of fluid particles which are initially distributed uninformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream.

Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required.

Large values of the dimensionless dispersion coefficient D/rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio.

A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments.

Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington.

Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factory of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.

The conceptual development of a simple scale-adaptive reactive pollutant dispersion model

The paper develops the basis for a self-consistent, operationally useful, reactive pollutant dispersion model, for application in urban environments. The model addresses the multi-scale nature of the physical and chemical processes and the interaction between the different scales. The methodology builds on existing techniques of source apportionment in pollutant dispersion and on reduction techniques of detailed chemical mechanisms. © 2005 Published by Elsevier Ltd.