Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Tooth fracture risk analysis based on a new finite element dental structure models using micro-CT data

The finite element (FE) analysis is an effective method to study the strength and predict the fracture risk of endodontically-treated teeth. This paper presents a rapid method developed to generate a comprehensive tooth FE model using data retrieved from micro-computed tomography (μCT). With this method, the inhomogeneity of material properties of teeth was included into the model without dividing the tooth model into different regions. The material properties of the tooth were assumed to be related to the mineral density. The fracture risk at different tooth portions was assessed for root canal treatments. The micro-CT images of a tooth were processed by a Matlab software programme and the CT numbers were retrieved. The tooth contours were obtained with thresholding segmentation using Amira. The inner and outer surfaces of the tooth were imported into Solidworks and a three-dimensional (3D) tooth model was constructed. An assembly of the tooth model with the periodontal ligament (PDL) layer and surrounding bone was imported into ABAQUS. The material properties of the tooth were calculated from the retrieved CT numbers via ABAQUS user's subroutines. Three root canal geometries (original and two enlargements) were investigated. The proposed method in this study can generate detailed 3D finite element models of a tooth with different root canal enlargements and filling materials, and would be very useful for the assessment of the fracture risk at different tooth portions after root canal treatments.

Finite element analyses of lipped channel beams with Web openings in shear

Cold-formed steel members are increasingly used as primary structural elements in buildings due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. Shear behaviour of LCBs with web openings is more complicated and their shear capacities are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs with web openings. Finite element models of simply supported LCBs with aspect ratios of 1.0 and 1.5 were considered under a mid-span load. They were then validated by comparing their results with test results and used in a detailed parametric study. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs with web openings. Improved design equations were therefore proposed for the shear strength of LCBs with web openings. This paper presents the details of this numerical study of LCBs with web openings, and the results.

Numerical and experimental studies of cold-formed steel floor systems under standard fire conditions

Light gauge cold-formed steel frame (LSF) structures are increasingly used in industrial, commercial and residential buildings because of their non-combustibility, dimensional stability, and ease of installation. A floor-ceiling system is an example of its applications. LSF floor-ceiling systems must be designed to serve as fire compartment boundaries and provide adequate fire resistance. Fire rated floor-ceiling assemblies formed with new materials and construction methodologies have been increasingly used in buildings. However, limited research has been undertaken in the past and hence a thorough understanding of their fire resistance behaviour is not available. Recently a new composite panel in which an external insulation layer is used between two plasterboards has been developed at QUT to provide a higher fire rating to LSF floors under standard fire conditions. But its increased fire rating could not be determined using the currently available design methods. Research on LSF floor systems under fire conditions is relatively recent and the behaviour of floor joists and other components in the systems is not fully understood. The present design methods thus require the use of expensive fire protection materials to protect them from excessive heat increase during a fire. This leads to uneconomical and conservative designs. Fire rating of these floor systems is provided simply by adding more plasterboard sheets to the steel joists and such an approach is totally inefficient. Hence a detailed fire research study was undertaken into the structural and thermal performance of LSF floor systems including those protected by the new composite panel system using full scale fire tests and extensive numerical studies. Experimental study included both the conventional and the new steel floor-ceiling systems under structural and fire loads using a gas furnace designed to deliver heat in accordance with the standard time- temperature curve in AS 1530.4 (SA, 2005). Fire tests included the behavioural and deflection characteristics of LSF floor joists until failure as well as related time-temperature measurements across the section and along the length of all the specimens. Full scale fire tests have shown that the structural and thermal performance of externally insulated LSF floor system was superior than traditional LSF floors with or without cavity insulation. Therefore this research recommends the use of the new composite panel system for cold-formed LSF floor-ceiling systems. The numerical analyses of LSF floor joists were undertaken using the finite element program ABAQUS based on the measured time-temperature profiles obtained from fire tests under both steady state and transient state conditions. Mechanical properties at elevated temperatures were considered based on the equations proposed by Dolamune Kankanamge and Mahendran (2011). Finite element models were calibrated using the full scale test results and used to further provide a detailed understanding of the structural fire behaviour of the LSF floor-ceiling systems. The models also confirmed the superior performance of the new composite panel system. The validated model was then used in a detailed parametric study. Fire tests and the numerical studies showed that plasterboards provided sufficient lateral restraint to LSF floor joists until their failure. Hence only the section moment capacity of LSF floor joists subjected to local buckling effects was considered in this research. To predict the section moment capacity at elevated temperatures, the effective section modulus of joists at ambient temperature is generally considered adequate. However, this research has shown that it leads to considerable over- estimation of the local buckling capacity of joist subject to non-uniform temperature distributions under fire conditions. Therefore new simplified fire design rules were proposed for LSF floor joist to determine the section moment capacity at elevated temperature based on AS/NZS 4600 (SA, 2005), NAS (AISI, 2007) and Eurocode 3 Part 1.3 (ECS, 2006). The accuracy of the proposed fire design rules was verified with finite element analysis results. A spread sheet based design tool was also developed based on these design rules to predict the failure load ratio versus time, moment capacity versus time and temperature for various LSF floor configurations. Idealised time-temperature profiles of LSF floor joists were developed based on fire test measurements. They were used in the detailed parametric study to fully understand the structural and fire behaviour of LSF floor panels. Simple design rules were also proposed to predict both critical average joist temperatures and failure times (fire rating) of LSF floor systems with various floor configurations and structural parameters under any given load ratio. Findings from this research have led to a comprehensive understanding of the structural and fire behaviour of LSF floor systems including those protected by the new composite panel, and simple design methods. These design rules were proposed within the guidelines of the Australian/New Zealand, American and European cold- formed steel structures standard codes of practice. These may also lead to further improvements to fire resistance through suitable modifications to the current composite panel system.

Finite element modelling of load bearing steel stud walls under real building fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. Conventionally the fire rating of load bearing wall systems made of Light gauge Steel Frames (LSF) is determined using fire tests based on the standard time-temperature curve given in ISO 834 (ISO, 1999). The standard time-temperature curve given in ISO 834 (ISO, 1999) originated from the application of wood burning furnaces in the early 1900s. However, modern commercial and residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the performance of LSF walls was undertaken using the developed real fire curves based on Eurocode parametric curves (ECS, 2002) and Barnett’s BFD curves (Barnett, 2002) using both full scale fire tests and numerical studies. It included LSF walls without any insulation, and the recently developed externally insulated composite panel system. This paper presents the details of the numerical studies and the results. It also includes brief details of the development of real building fire curves and experimental studies.

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.

Effects of extreme temperatures on years of life lost for cardiovascular deaths : a time series study in Brisbane, Australia

Background: Extreme temperatures are associated with cardiovascular disease (CVD) deaths. Previous studies have investigated the relative CVD mortality risk of temperature, but this risk is heavily influenced by deaths in frail elderly persons. To better estimate the burden of extreme temperatures we estimated their effects on years of life lost due to CVD. Methods and Results: The data were daily observations on weather and CVD mortality for Brisbane, Australia between 1996 and 2004. We estimated the association between daily mean temperature and years of life lost due to CVD, after adjusting for trend, season, day of the week, and humidity. To examine the non-linear and delayed effects of temperature, a distributed lag non-linear model was used. The model’s residuals were examined to investigate if there were any added effects due to cold spells and heat waves. The exposure-response curve between temperature and years of life lost was U-shaped, with the lowest years of life lost at 24 °C. The curve had a sharper rise at extremes of heat than of cold. The effect of cold peaked two days after exposure, whereas the greatest effect of heat occurred on the day of exposure. There were significantly added effects of heat waves on years of life lost. Conclusions: Increased years of life lost due to CVD are associated with both cold and hot temperatures. Research on specific interventions is needed to reduce temperature-related years of life lost from CVD deaths.

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.

High temperatures-related elderly mortality varied greatly from year to year : important information for heat-warning systems

We examined the variation in association between high temperatures and elderly mortality (age ≥ 75 years) from year to year in 83 US cities between 1987 and 2000. We used a Poisson regression model and decomposed the mortality risk for high temperatures into: a “main effect” due to high temperatures using lagged non-linear function, and an “added effect” due to consecutive high temperature days. We pooled yearly effects across both regional and national levels. The high temperature effects (both main and added effects) on elderly mortality varied greatly from year to year. In every city there was at least one year where higher temperatures were associated with lower mortality. Years with relatively high heat-related mortality were often followed by years with relatively low mortality. These year to year changes have important consequences for heat-warning systems and for predictions of heat-related mortality due to climate change.

Flexural-torsional buckling tests of cold-formed steel compression members at elevated temperatures

Current design standards do not provide adequate guidelines for the fire design of cold-formed steel compression members subject to flexural-torsional buckling. Eurocode 3 Part 1.2 (2005) recommends the same fire design guidelines for both hot-rolled and cold-formed steel compression members subject to flexural-torsional buckling although considerable behavioural differences exist between cold-formed and hot-rolled steel members. Past research has recommended the use of ambient temperature cold-formed steel design rules for the fire design of cold-formed steel compression members provided appropriately reduced mechanical properties are used at elevated temperatures. To assess the accuracy of flexural-torsional buckling design rules in both ambient temperature cold-formed steel design and fire design standards, an experimental study of slender cold-formed steel compression members was undertaken at both ambient and elevated temperatures. This paper presents the details of this experimental study, its results, and their comparison with the predictions from the current design rules. It was found that the current ambient temperature design rules are conservative while the fire design rules are overly conservative. Suitable recommendations have been made in relation to the currently available design rules for flexural-torsional buckling including methods of improvement. Most importantly, this paper has addressed the lack of experimental results for slender cold-formed steel columns 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.