Mathematical Modelling of flow in Schlemm's canal and its influence on primary open angle glaucoma

POAG (Primary Open Angle Glaucoma) is a major cause of blindness. This normally occurs when the IOP (intraocular pressure) increases. High pressure can be caused by an imbalance in the production and drainage of fluid (aqueous humour, AH) in the eye. AH is continually being produced but sometimes cannot be drained because of improperly functioning drainage channels (trabecular meshwork, TM). A mathematical model is presented for the flow of AH through the TM and into the SC (canal of Schlemm) and to couple this flow in order to predict changes in IOP. The governing equations have been developed by using the lubrication theory limit of the Navier-Stokes equations. To close the model, Friedenwald’s law has been used to predict changes of IOP. Several different cases have been examined in the model, relating AH flow to changes in IOP for various submodels: (i) the permeability, k in Darcy’s law may be either constant or not constant; (ii) the TM may be deformable so that the general theory of a beam under axial load is applicable - a number of different subcases where either ? or ?, may be either large or small have been considered. However only the subcase ? is small has been discussed in this study by assuming the permeability, k is constant and the TM is deformable. This subcase has been solved by using the regular perturbation method. The results show that the IOP rises continually when ? is small and may cause blindness

Gas Concentration Measurements in Underground Waste Storage Tanks

Currently over 100 underground tanks at the Hanford facility in eastern Washington state are being used to store high-level radioactive waste. With plans for a long-term nuclear-waste repository in Nevada in place (though not yet approved), one promising use for these underground storage tanks is as a temporary waystation for waste destined for the Nevada repository. However, without a reasonable understanding of the chemical reactions going on within the tanks, transporting waste in and out of the tanks has been deemed to be unsafe. One hazard associated with such storage mechanisms is explosion of flammable gases produced within the tank. Within many of the storage tanks is a sludge layer. This layer, which is a mixture of liquid and solids, contains most of the radioactive material. Radioactive decay and its associated heat can produce several flammable materials within this layer. Two components of particular concern are hydrogen (H2) and nitrous oxide (N2O), since they are highly volatile in the gaseous phase. Though the tanks have either forced or natural convection systems to vent these gases, the possibility of an explosion still exists. Measurements of these gases are taken in several ways. Continuous measurements are taken in the headspace, which is the layer between the tank ceiling and the liquid (supernatant) or sludge layer below. In tanks where a supernatant layer sits atop the sludge layer, there are often rollovers or gas release events (GREs), where a large chunk of sludge, after attaining a certain void fraction, becomes buoyant, rising through the supernatant and releasing its associated gas composition to the headspace. Such changes trigger a sensor, and thus measurements are also taken at that time. Lastly, a retained gas sample (RGS) can be taken from either the supernatant or sludge layer. Such a core sample is quite expensive, but can yield crucial data about the way gases are being produced in the sludge and convected through the supernatant. Unfortunately, the measurements from these three populations do not seem to match. In particular, the ratio r = [N2O]/[H2] varies from population to population. r also varies from tank to tank, but this can more readily be explained in terms of the waste composition of each tank. Since H2 is more volatile than N2O (and since there are more sources of oxygen in the headspace), lower values of r correspond to more hazardous situations. This variance in r is troubling, since we need to be able to explain why certain values of r are lower (and hence more dangerous) in certain areas of the tank. In this report we examine the data from three tanks. We first verify that the differences in r among populations is significant. We then postulate several mechanisms which could explain such a difference

Need a Lift? An Elevator Queueing Problem

Various aspects of the behavior and dispatching of elevators (lifts) were studied. Monte Carlo simulation was used to study the statistics of the several models for the peak demand at uppeak times. Analytical models problems were used to prove or disprove whether schemes were optimal. A mostly integer programming problem was formulated but not studied further

Spot-on: Safe Fuel/Air Compression

The emission of fuel vapors into the atmosphere from underground storage tanks at filling stations is a common occurrence in many parts the world. The conditions of the vapor in the tanks vary significantly over a 24 hour period such that evaporation and excess air ingestion during the refueling process can cause tank over pressurization and subsequent emissions. At other times during a 24 hour cycle, pressures can fall below atmospheric pressure. The state of California has recognized this emissions problem and has enacted regulations to address it. Due to these low-emission environmental requirements in California, solutions must be implemented that do not entail release of these vapors into the atmosphere. One solution requires that the vapors fill a balloon during the appropriate times. However, the size of the balloon at typical inflation rates requires a significant amount of physical space (approximately 1000-2000 liters), which may not necessarily be available at filling stations in urban areas. Veeder-Root has a patent pending for a system to compress the vapors that are released to a 10:1 ratio, store this compressed vapor in a small storage tank, and then return the vapors to the original underground fuel tank when the conditions are thermodynamically appropriate (see Figure 1 for the schematic representation of this system). The limitation of the compressor, however, is that the compression phase must take place below the ignition temperature of the vapor. For a 10:1 compression ratio, however, the adiabatic temperature rise of a vapor would be above the ignition temperature. Mathematical modeling is necessary here to estimate the performance of the compressor, and to suggest paths in design for improvement. This report starts with a mathematical formulation of an ideal compressor, and uses the anticipated geometry of the compressor to state a simplified set of partial differential equations. The adiabatic case is then considered, assuming that the temporary storage tank is kept at a constant temperature. Next, the heat transfer from the compression chamber through the compressor walls is incorporated into the model. Finally, we consider the case near the valve wall, which is subject to the maximum temperature rise over the estimated 10,000 cycles that will be necessary for the process to occur. We find that for adiabatic conditions, there is a hot spot close to the wall where the vapor temperature can exceed the wall temperature. Lastly, we discuss the implications of our analysis, and its limitations

Aqueous humour dynamics in anterior chamber under influence of cornea indentation

The existing temperature different between the cornea and the pupil induces the aqueous humour (AH) to circulate in the anterior chamber (AC). The buoyancy forces produced by the temperature gradient has driven the AH to flow. Previous studies have shown that cornea indentation changes the structure of the AC. This imply that the cornea indentation may change the fluid flow behaviour in the AC. A mathematical model of AH flow has been developed in order to analyse the fluid mechanics concerning the indentation of the cornea. Naiver-Stokes equations is used to describe the flow of AH in the AC. The governing equations have been solved numerically using finite element method. The results show that the cornea indentation has slow down the circulation the AH in the AC

Aqueous Humour Dynamics in Anterior Chamber with the Descemet's Membrane Detachment

Descemet membrane detachment (DMD) develops in the human eye once the aqueous humour (AH) enters the Descemet membrane (DM) space through a break and causes the membrane to separate from the stroma (the main layer of the cornea which is responsible in giving the cornea its strength). A mathematical model of AH flow through the DMD has been developed. The mathematical model is set up to analyze the fluid mechanics concerning the progression of DMD. This model is based on the Naiver-Stokes equations that govern the flow of AH in the anterior chamber (AC). Specifically, fluid flow in the AC is described as a flow driven by buoyancy effects due to the existing temperature different between the cornea and the pupil. A thin flap (DMD) which is kept in contact with a dome shape (cornea) is considered in the flow in order to show how the type of the DMD affect the fluid flow behave in the AC. The relevant fluid flow equations have been solved numerically using finite element method with the aiding of COMSOL Multiphysics. The results have shown that the different type of DMD do affect the characteristics of the fluid flow in the AC

Simulation of AH flows and deformation of DMD in a 3D AC

This paper presents the interaction between the aqueous humour (AH) flows and the deformation of Descemet membrane detachment (DMD) in a 3D anterior chamber (AC). Arbitrary Lagrangian Eulerian (ALE) method is used to model the problem. Finite element method using COMSOL Multiphysics software is adopted to solve the governing equations for the AH flows and the deformation of DMD. The fluid flow behaviour and the deformation of the detached Descemet membrane are analysed in order to comprehend the progression of the DMD in the AC due to the AH flows and vice versa. The re-attachment or re-detachment of the DMD is significantly affected by the AH flows. Advance treatment for the DMD can be developed based on a better understanding of the interaction between the AH flows and the DMD

Markowitz portfolio theory for soccer spread betting

Soccer spread betting is analysed using standard probabilistic methods assuming that goals are scored in a match according to Poisson distributions with constant means. A number of different possible forms of ‘edge’ (betting advantage) is identified. It is shown how the centre spreads of the more common bets in the ‘bet universe’ may be calculated. A more general question is then addressed, namely, how a punter should invest if they take a view that the online bookmakers have fixed the goal means incorrectly or some other edge is in their favour. It is shown that a Markowitz portfolio theory framework may be set up in such cases. This leads to the definitions of an ‘efficient betting frontier’ and an ‘optimal bet portfolio’. Examples are used throughout to illustrate the theory that is developed

Open Access and Research Data Management Roadshow

Set of powerpoint slides presented to Oxford Brookes academics at REF Roadshows, October – December 2014. The presentation covers the 11 surprises of the recent Hefce report - Policy for open access in the post-2014 Research Excellence Framework . One of the key requirements for the REF is that academics deposit their accepted version of their journal articles or conference papers at the point of acceptance. To encourage this Alistair Fitt, Pro-Vice Chancellor for Research demonstates, as part of the presentation, the ease of logging into the Current Research Information System (CRIS) and uploading outputs . Rowena Rouse, Scholarly Communications Manager then demonstates how the Scholarly Communications Team wil support this process and the checks that they will make