Critical gap estimation by numerical and statistical highest likelihood search

Many traffic situations require drivers to cross or merge into a stream having higher priority. Gap acceptance theory enables us to model such processes to analyse traffic operation. This discussion demonstrated that numerical search fine tuned by statistical analysis can be used to determine the most likely critical gap for a sample of drivers, based on their largest rejected gap and accepted gap. This method shares some common features with the Maximum Likelihood Estimation technique (Troutbeck 1992) but lends itself well to contemporary analysis tools such as spreadsheet and is particularly analytically transparent. This method is considered not to bias estimation of critical gap due to very small rejected gaps or very large rejected gaps. However, it requires a sufficiently large sample that there is reasonable representation of largest rejected gap/accepted gap pairs within a fairly narrow highest likelihood search band.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Radiation effect on free convection laminar flow along a vertical flat plate with streamwise sinusoidal surface temperature

The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical flat plate with streamwise sinusoidal surface temperature has been investigated in this study. Using the appropriate variables; the basic governing equations are transformed to convenient form and then solved numerically employing two efficient methods, namely, Implicit finite difference method (IFD) together with Keller box scheme and Straight forward finite difference (SFFD) method. Effects of the variation of the physical parameters, for example, conduction-radiation parameter (Planck number), surface temperature parameter, and the amplitude of the surface temperature, are shown on the skin friction and heat transfer rate quantitatively are shown numerically. Velocity and temperature profiles as well as streamlines and isotherms are also presented and discussed for the variation of conduction-radiation parameter. It is found that both skin-friction and rate of heat transfer are enhanced considerably by increasing the values of conduction radiation parameter, Rd.

A review of natural convection and heat transfer in attic-shaped space

This paper presents a review of studies on natural convection heat transfer in the triangular enclosure namely, in attic-shaped space. Much research activity has been devoted to this topic over the last three decades with a view to providing thermal comfort to the occupants in attic-shaped buildings and to minimising the energy costs associated with heating and air-conditioning. Two basic thermal boundary conditions of attic are considered to represent hot and cold climates or day and night time. This paper also reports on a significant number of studies which have been performed recently on other topics related to the attic space, for example, attics subject to localized heating and attics filled with porous media.

Advanced numerical study of impact forces on railway sleepers under wheel flat

Wheel-rail interaction is one of the most important research topics in railway engineering. It includes track vibration, track impact response and safety of the track. Track structure failures caused by impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. The wheel-rail impact forces occur because of imperfections on the wheels or rails such as wheel flats, irregular wheel profile, rail corrugation and differences in the height of rails connected at a welded joint. In this paper, a finite element model for the wheel flat study is developed by use of the FEA software package ANSYS. The effect of the wheel flat to impact force on sleepers is investigated. It has found that the wheel flat significantly increases impact forces and maximum Von Mises stress, and also delays the peak position of dynamic variation for impact forces on both rail and sleeper.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.