Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

Improved image quality for x-ray CT imaging of gel dosimeters

Purpose: This study provides a simple method for improving precision of x-ray computed tomography (CT) scans of irradiated polymer gel dosimetry. The noise affecting CT scans of irradiated gels has been an impediment to the use of clinical CT scanners for gel dosimetry studies. Method: In this study, it is shown that multiple scans of a single PAGAT gel dosimeter can be used to extrapolate a ‘zero-scan’ image which displays a similar level of precision to an image obtained by averaging multiple CT images, without the compromised dose measurement resulting from the exposure of the gel to radiation from the CT scanner. Results: When extrapolating the zero-scan image, it is shown that exponential and simple linear fits to the relationship between Hounsfield unit and scan number, for each pixel in the image, provides an accurate indication of gel density. Conclusions: It is expected that this work will be utilised in the analysis of three-dimensional gel volumes irradiated using complex radiotherapy treatments.

Application of electrical resistivity method to detect deep cracks in unsaturated residual soil slope

Crack is a significant influential factor in soil slope that could leads to rainfall-induced slope instability. Existence of cracks at soil surface will decrease the shear strength and increase the hydraulic conductivity of soil slope. Although previous research has shown the effect of surface-cracks in soil stability, the influence of deep-cracks on soil stability is still unknown. The limited availability of deep crack data due to the difficulty of effective investigate methods could be one of the obstacles. Current technology in electrical resistivity can be used to detect deep-cracks in soil. This paper discusses deep cracks in unsaturated residual soil slopes in Indonesia using electrical resistivity method. The field investigation such as bore hole and SPT tests was carried out at multiple locations in the area where the electrical resistivity testing have been conducted. Subsequently, the results from bore-hole and SPT test were used to verify the results of the electrical resistivity test. This study demonstrates the benefits and limitations of the electrical resistivity in detecting deep-cracks in a residual soil slopes.

Natural convection adjacent to an inclined flat plate and in an attic space under various thermal forcing conditions

The effect of viscous dissipation on natural convection from a vertical plate placed in a thermally stratified environment has been investigated numerically. The reduced equations are integrated by employing the implicit finite difference scheme or Ke1ler-box method and obtained the effect of heat due to viscous dissipation on the local skin-friction and loca1 Nusselt number at various stratification levels, for fluids having Prandtl number equals 10, 50, and 100. Solutions are also obtained using the perturbation technique for small values of viscous dissipation parameters and compared with the Finite Difference solutions. Effect of the heat transfer due to viscous dissipation and the temperature stratification are also shown on the velocity and temperature distributions in the boundary layer region. A numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium is also considered for this study. Solutions are obtained using the implicit Finite Difference method and compared with the local non-similarity method. The velocity and temperature distributions for different values of stratification parameter are shown graphically. The results show many interesting aspects of complex interaction of the two buoyant mechanisms.

Inexact uniformization method for computing transient distributions of Markov chains

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.