Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Decoherence in ion traps due to laser intensity and phase fluctuations

We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with recent experiments and predict that the decoherence rate will depend on vibrational quantum number in different ways depending on which vibrational excitation sideband is used.

Overflow characteristics of circular weirs: Effects of inflow conditions

The most common types of weirs are the broad-crested weir, the sharp-crested weir, the circular-crested weir, and nowadays, the ogee crest weir, Advantages of the cylindrical weir shape include the stable overflow pattern, the ease to pass floating debris, the simplicity of design compared to ogee crest design, and the associated lower costs. in this study, the writers describe new experiments of circular weir overflows, with eight cylinder sizes, for several weir heights and for five types of inflow conditions: partially developed inflow, fully developed inflow, upstream ramp, upstream undular hydraulic jump, and upstream (breaking) hydraulic jump. Within the range of the experiments, the cylinder size, the weir height DIR and the presence of an upstream ramp had no effect on the discharge coefficient, flow depth at crest, and energy dissipation. But the inflow conditions had substantial effects on the discharge characteristics and flow properties at the crest. Practically, the results indicate that discharge measurements with circular weirs are significantly affected by the upstream flow conditions.

Simultaneous detection of multiple antigens with triple immunolabeling

Immunolabeling is commonly used to localize antigens within frozen or paraffin tissue sections. We modified existing immunolabeling techniques to allow the detection of three antigens simultaneously within the one tissue section. The approach relies on the use of three monoclonal antibodies in sequential immunoperoxidase staining steps, each with colored substrates, resulting in the deposition of black, brown, and rose stains. The method is rapid and does not require novel techniques or materials. In this report, we demonstrate the colocalization of mast cell tryptase, neurofilament protein, and CD31 (platelet-endothelial cell adhesion molecule) or laminin in normal human skin and normal buccal mucosa, as an illustration of the power and simplicity of the multiple antigen localization technique.

Modeling the optical constants of AlxGa1-xAs alloys

The extension of Adachi's model with a Gaussian-like broadening function, in place of Lorentzian, is used to model the optical dielectric function of the alloy AlxGa1-xAs. Gaussian-like broadening is accomplished by replacing the damping constant in the Lorentzian line shape with a frequency dependent expression. In this way, the comparative simplicity of the analytic formulas of the model is preserved, while the accuracy becomes comparable to that of more intricate models, and/or models with significantly more parameters. The employed model accurately describes the optical dielectric function in the spectral range from 1.5 to 6.0 eV within the entire alloy composition range. The relative rms error obtained for the refractive index is below 2.2% for all compositions. (C) 1999 American Institute of Physics. [S0021-8979(99)00512-5].

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

A note on the decomposition of the health concentration index

In recent work, the concentration index has been widely used as a measure of income-related health inequality. The purpose of this note is to illustrate two different methods for decomposing the overall health concentration index using data collected from a Short Form (SF-36) survey of the general Australian population conducted in 1995. For simplicity, we focus on the physical functioning scale of the SF-36. Firstly we examine decomposition 'by component' by separating the concentration index for the physical functioning scale into the ten items on which it is based. The results show that the items contribute differently to the overall inequality measure, i.e. two of the items contributed 13% and 5%, respectively, to the overall measure. Second, to illustrate the 'by subgroup' method we decompose the concentration index by employment status. This involves separating the population into two groups: individuals currently in employment; and individuals not currently employed. We find that the inequality between these groups is about five times greater than the inequality within each group. These methods provide insights into the nature of inequality that can be used to inform policy design to reduce income related health inequalities. Copyright (C) 2002 John Wiley Sons, Ltd.

Formal methods within a totally functional approach to programming

Taking functional programming to its extremities in search of simplicity still requires integration with other development (e.g. formal) methods. Induction is the key to deriving and verifying functional programs, but can be simplified through packaging proofs with functions, particularly folds, on data (structures). Totally Functional Programming avoids the complexities of interpretation by directly representing data (structures) as platonic combinators - the functions characteristic to the data. The link between the two simplifications is that platonic combinators are a kind of partially-applied fold, which means that platonic combinators inherit fold-theoretic properties, but with some apparent simplifications due to the platonic combinator representation. However, despite observable behaviour within functional programming that suggests that TFP is widely-applicable, significant work remains before TFP as such could be widely adopted.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

A simple solution of the laminar dam break wave

The sudden release of a mass of fluid in a channel generates a highly unsteady flow motion, called dam break wave. While industrial fluids exhibit sometimes non-Newtonian behaviours, the viscous fluid flow assumption remains a useful approximation for simplified analyses. In this study, new solutions of laminar dam break wave are proposed for a semi-infinite reservoir based upon the method of characteristics. The solutions yield simple explicit expressions of the wave front location, wave front celerity and instantaneous free-surface profiles that compare favourably with experimental observations. Both horizontal and sloping channel configurations are treated. The simplicity of the equations may allow future extension to more complicated fluid flows.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.