A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Is diurnal temperature range a risk factor for childhood diarrhea?

Background Previous studies have found that high and cold temperatures increase the risk of childhood diarrhea. However, little is known about whether the within-day variation of temperature has any effect on childhood diarrhea. Methods A Poisson generalized linear regression model combined with a distributed lag non-linear model was used to examine the relationship between diurnal temperature range and emergency department admissions for diarrhea among children under five years in Brisbane, from 1st January 2003 to 31st December 2009. Results There was a statistically significant relationship between diurnal temperature range and childhood diarrhea. The effect of diurnal temperature range on childhood diarrhea was the greatest at one day lag, with a 3% (95% confidence interval: 2%–5%) increase of emergency department admissions per 1°C increment of diurnal temperature range. Conclusion Within-day variation of temperature appeared to be a risk factor for childhood diarrhea. The incidence of childhood diarrhea may increase if climate variability increases as predicted.

Experimental study on mechanical properties of pumpkin tissue

Purpose: The purpose of this study was to calculate mechanical properties of tough skinned vegetables as a part of Finite Element Modelling (FEM) and simulation of tissue damage during mechanical peeling of tough skinned vegetables. Design/methodology: There are some previous studies on mechanical properties of fruits and vegetables however, behaviour of tissue under different processing operations will be different. In this study indentation test was performed on Peel, Flesh and Unpeeled samples of pumpkin as a tough skinned vegetable. Additionally, the test performed in three different loading rates for peel: 1.25, 10, 20 mm/min and 20 mm/min for flesh and unpeeled samples respectively. The spherical end indenter with 8mm diameter used for the experimental tests. Samples prepare from defect free and ripped pumpkin purchased from local shops in Brisbane, Australia. Humidity and temperature were 20-55% and 20-250C respectively. Findings: Consequently, force deformation and stress and strain of samples were calculated and shown in presented figures. Relative contribution (%) of skin to different mechanical properties is computed and compared with data available from literature. According the results, peel samples had the highest value of rupture force (291N) and as well as highest value of firmness (1411Nm-1). Research limitations/implications: The proposed study focused on one type of tough skinned vegetables and one variety of pumpkin however, more tests will give better understandings of behaviours of tissue. Additionally, the behaviours of peel, unpeeled and flesh samples in different speed of loading will provide more details of tissue damages during mechanical loading. Originality/value: Mechanical properties of pumpkin tissue calculated using the results of indentation test, specifically the behaviours of peel, flesh and unpeeled samples were explored which is a new approach in Finite Element Modelling (FEM) of food processes. Keywords: Finite Element Modelling (FEM), relative contribution, firmness, toughness and rupture force.

Ergodic capacity of the slotted amplify and forward relay channel with finite relays

Abstract—In this paper we investigate the capacity of a general class of the slotted amplify and forward (SAF) relaying protocol where multiple, though a finite number of relays may transmit in a given cooperative slot and the relay terminals being half-duplex have a finite slot memory capacity. We derive an expression for the capacity per channel use of this generalized SAF channel assuming all source to relay, relay to destination and source to destination channel gains are independent and modeled as complex Gaussian. We show through the analysis of eigenvalue distributions that the increase in limiting capacity per channel use is marginal with the increase of relay terminals.

Muscle, skin and core temperature after −110°C cold air and 8°C water treatment

The aim of this investigation was to elucidate the reductions in muscle, skin and core temperature following exposure to −110°C whole body cryotherapy (WBC), and compare these to 8°C cold water immersion (CWI). Twenty active male subjects were randomly assigned to a 4-min exposure of WBC or CWI. A minimum of 7 days later subjects were exposed to the other treatment. Muscle temperature in the right vastus lateralis (n = 10); thigh skin (average, maximum and minimum) and rectal temperature (n = 10) were recorded before and 60 min after treatment. The greatest reduction (P<0.05) in muscle (mean ± SD; 1 cm: WBC, 1.6±1.2°C; CWI, 2.0±1.0°C; 2 cm: WBC, 1.2±0.7°C; CWI, 1.7±0.9°C; 3 cm: WBC, 1.6±0.6°C; CWI, 1.7±0.5°C) and rectal temperature (WBC, 0.3±0.2°C; CWI, 0.4±0.2°C) were observed 60 min after treatment. The largest reductions in average (WBC, 12.1±1.0°C; CWI, 8.4±0.7°C), minimum (WBC, 13.2±1.4°C; CWI, 8.7±0.7°C) and maximum (WBC, 8.8±2.0°C; CWI, 7.2±1.9°C) skin temperature occurred immediately after both CWI and WBC (P<0.05). Skin temperature was significantly lower (P<0.05) immediately after WBC compared to CWI. The present study demonstrates that a single WBC exposure decreases muscle and core temperature to a similar level of those experienced after CWI. Although both treatments significantly reduced skin temperature, WBC elicited a greater decrease compared to CWI. These data may provide information to clinicians and researchers attempting to optimise WBC and CWI protocols in a clinical or sporting setting.

Behaviour and design of cold-formed steel beams subject to lateral-torsional buckling at elevated temperatures

Cold-formed steel beams are increasingly used as floor joists and bearers in buildings and often their behaviour and moment capacities are influenced by lateral-torsional buckling. With increasing usage of cold-formed steel beams their fire safety design has become an important issue. Fire design rules are commonly based on past research on hot-rolled steel beams. Hence a detailed parametric study was undertaken using validated finite element models to investigate the lateral-torsional buckling behaviour of simply supported cold-formed steel lipped channel beams subjected to uniform bending at uniform elevated temperatures. The moment capacity results were compared with the predictions from the available ambient temperature and fire design rules and suitable recommendations were made. European fire design rules were found to be over-conservative while the ambient temperature design rules could not be used based on single buckling curve. Hence a new design method was proposed that includes the important non-linear stress-strain characteristics observed for cold-formed steels at elevated temperatures. Comparison with numerical moment capacities demonstrated the accuracy of the new design method. This paper presents the details of the parametric study, comparisons with current design rules and the new design rules proposed in this research for lateral-torsional buckling of cold-formed steel lipped channel beams at elevated temperatures.

A dynamic wheel-rail impact analysis of railway track under wheel flat by Finite Element Analysis

Wheel–rail interaction is one of the most important research topics in railway engineering. It involves track impact response, track vibration and track safety. Track structure failures caused by wheel–rail impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. Wheel–rail impact forces occur because of imperfections in the wheels or rails such as wheel flats, irregular wheel profiles, rail corrugations and differences in the heights of rails connected at a welded joint. A wheel flat can cause a large dynamic impact force as well as a forced vibration with a high frequency, which can cause damage to the track structure. In the present work, a three-dimensional (3-D) finite element (FE) model for the impact analysis induced by the wheel flat is developed by use of the finite element analysis (FEA) software package ANSYS and validated by another validated simulation. The effect of wheel flats on impact forces is thoroughly investigated. It is found that the presence of a wheel flat will significantly increase the dynamic impact force on both rail and sleeper. The impact force will monotonically increase with the size of wheel flats. The relationships between the impact force and the wheel flat size are explored from this finite element analysis and they are important for track engineers to improve their understanding of the design and maintenance of the track system.

How to design extended finite state machine test models in Java

This chapter is a tutorial that teaches you how to design extended finite state machine (EFSM) test models for a system that you want to test. EFSM models are more powerful and expressive than simple finite state machine (FSM) models, and are one of the most commonly used styles of models for model-based testing, especially for embedded systems. There are many languages and notations in use for writing EFSM models, but in this tutorial we write our EFSM models in the familiar Java programming language. To generate tests from these EFSM models we use ModelJUnit, which is an open-source tool that supports several stochastic test generation algorithms, and we also show how to write your own model-based testing tool. We show how EFSM models can be used for unit testing and system testing of embedded systems, and for offline testing as well as online testing.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Finite volume approach of natural convection in a triangular enclosure with localized heating from below

In this study, natural convection heat transfer and buoyancy driven flows have been investigated in a right angled triangular enclosure. The heater located on the bottom wall while the inclined wall is colder and the remaining walls are maintained as adiabatic. Governing equations of natural convection are solved through the finite volume approach, in which buoyancy is modeled via the Boussinesq approximation. Effects of different parameters such as Rayleigh number, aspect ratio, prantdl number and heater location are considered. Results show that heat transfer increases when the heater is moved toward the right corner of the enclosure. It is also revealed that increasing the Rayleigh number, increases the strength of free convection regime and consequently increases the value of heat transfer rate. Moreover, larger aspect ratio enclosure has larger Nusselt number value. In order to have better insight, streamline and isotherms are shown.

Natural convection flow in a strong cross magnetic field with radiation

The problem of MHD natural convection boundary layer flow of an electrically conducting and optically dense gray viscous fluid along a heated vertical plate is analyzed in the presence of strong cross magnetic field with radiative heat transfer. In the analysis radiative heat flux is considered by adopting optically thick radiation limit. Attempt is made to obtain the solutions valid for liquid metals by taking Pr≪1. Boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation (SFF) and primitive variable formulation (PVF). Non-similar equations obtained from SFF are then simulated by implicit finite difference (Keller-box) method whereas parabolic partial differential equations obtained from PVF are integrated numerically by hiring direct finite difference method over the entire range of local Hartmann parameter, $xi$ . Further, asymptotic solutions are also obtained for large and small values of local Hartmann parameter $xi$ . A favorable agreement is found between the results for small, large and all values of $xi$ . Numerical results are also demonstrated graphically by showing the effect of various physical parameters on shear stress, rate of heat transfer, velocity and temperature.

Natural convection flow with surface radiation along a vertical wavy surface

In this study, natural convection boundary layer flow of thermally radiating fluid along a heated vertical wavy surface is analyzed. Here, the radiative component of heat flux emulates the surface temperature. Governing equations are reduced to dimensionless form, subject to the appropriate transformation. Resulting dimensionless equations are transformed to a set of parabolic partial differential equations by using primitive variable formulation, which are then integrated numerically via iterative finite difference scheme. Emphasis has been given to low Prandtl number fluid. The numerical results obtained for the physical parameters, such as, surface radiation parameter, R, and radiative length parameter, ξ, are discussed in terms of local skin friction and Nusselt number coefficients. Comprehensive interpretation of velocity distribution is also given in the form of streamlines.

Microanalysis of clays at low temperature

Accurate thin-film energy dispersive spectroscopic (EDS) analyses of clays with low-atomic-number (low Z) elements (e.g. Na, Al, Si), presents a challenge to the microscopist not only because of the spatial resolution required, but also because of their susceptibility to electron beam-induced radiation damange and very low X-ray count rates. Most common clays, such as kaolinite, smectite and illite occur as submicrometer crystallites with varying degrees of structural disorder in at least two directions and may have dimensions as small as one or two unit cells along the basal direction. Thus, even clays with relatively large a-b dimenstions (e.g., 100 x 100 nm) may be <5nm in the c-axis direction. For typical conditions in an analytical electron microscope (AEM), this sample thickness gives rise to very poor count rates (<200cps) and necessitates long counting times (>300s) in order to obtain satisfactory statistical precision. Unfortunately, beam damage rates for the common clays are very rapid (<10s in imaging mode) between 100kV and 200kV. With a focussed probe for elemental analyses, the damage rate is exacerbated by a high current density and may result in loss of low-Z elements during data collection and consequent loss of analytical accuracy.