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.

Numerical studies of gypsum plasterboard panels under standard fire conditions

Gypsum plasterboards are commonly used as a fire safety material in the building industry. Many research studies have been undertaken to investigate the thermal behaviour of plasterboards under standard fire conditions. However, there are many discrepancies in relation to the basic thermal properties of plasterboards while simple equations are not available to predict the ambient surface time–temperature profiles of gypsum plasterboard panels that can be used in simulating the behaviour and strength of steel studs or joists in load bearing LSF wall and floor systems. In this research, suitable thermal properties of plasterboards were proposed based on a series of tests and available results from past research. Finite element models of gypsum plasterboard panels were then developed to simulate their thermal behaviour under standard fire conditions. The accuracy of the proposed thermal properties and the finite element models was validated by comparing the numerical results with available fire test results of plasterboard panels. This paper presents the details of the finite element models of plasterboard panels, the thermal analysis results from finite element analyses under standard fire conditions and their comparisons with experimental results

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

“They’re My Two Favourites” versus “The Bigger Scheme of Things” : pro-Am historians remember Australian television

This chapter reports on eleven interviews with Pro-Am archivists of Australian television which aimed to find out how they decide what materials are important enough to archive. Interviewees mostly choose to collect materials in which they have a personal interest. But they are also aware of the relationship between their own favourites and wider accounts of Australian television history, and negotiate between these two positions. Most interviewees acknowledged Australian television’s links with British and American programming, but also felt that Australian television is distinctive. They argued that Australian television history is ignored in a way that isn’t true for the UK or the US. Several also argued that Australian television has had a ‘naïve’ nature that has allowed it to be more experimental.

Advanced numerical characterization of silicon with defect by nanoindentation

Nano silicon is widely used as the essential element of complementary metal–oxide–semiconductor (CMOS) and solar cells. It is recognized that today, large portion of world economy is built on electronics products and related services. Due to the accessible fossil fuel running out quickly, there are increasing numbers of researches on the nano silicon solar cells. The further improvement of higher performance nano silicon components requires characterizing the material properties of nano silicon. Specially, when the manufacturing process scales down to the nano level, the advanced components become more and more sensitive to the various defects induced by the manufacturing process. It is known that defects in mono-crystalline silicon have significant influence on its properties under nanoindentation. However, the cost involved in the practical nanoindentation as well as the complexity of preparing the specimen with controlled defects slow down the further research on mechanical characterization of defected silicon by experiment. Therefore, in current study, the molecular dynamics (MD) simulations are employed to investigate the mono-crystalline silicon properties with different pre-existing defects, especially cavities, under nanoindentation. Parametric studies including specimen size and loading rate, are firstly conducted to optimize computational efficiency. The optimized testing parameters are utilized for all simulation in defects study. Based on the validated model, different pre-existing defects are introduced to the silicon substrate, and then a group of nanoindentation simulations of these defected substrates are carried out. The simulation results are carefully investigated and compared with the perfect Silicon substrate which used as benchmark. It is found that pre-existing cavities in the silicon substrate obviously influence the mechanical properties. Furthermore, pre-existing cavities can absorb part of the strain energy during loading, and then release during unloading, which possibly causes less plastic deformation to the substrate. However, when the pre-existing cavities is close enough to the deformation zone or big enough to exceed the bearable stress of the crystal structure around the spherical cavity, the larger plastic deformation occurs which leads the collapse of the structure. Meanwhile, the influence exerted on the mechanical properties of silicon substrate depends on the location and size of the cavity. Substrate with larger cavity size or closer cavity position to the top surface, usually exhibits larger reduction on Young’s modulus and hardness.

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. The vehicle speed and static wheel load are important factors of the track design, because they are related to the impact forces under wheel-rail defects. In this paper, a 3-Dimensional finite element model for the study of wheel flat impact is developed by use of the FEA software package ANSYS. The effects of the wheel flat to impact force on sleepers with various speeds and static wheel loads under a critical wheel flat size are investigated. It has found that both wheel-rail impact force and impact force on sleeper induced by wheel flat are varying nonlinearly by increasing the vehicle speed; both impact forces are nonlinearly and monotonically increasing by increasing the static wheel load. The relationships between both of impact forces induced by wheel flat and vehicles speed or static load are important to the track engineers to improve the design and maintenance methods in railway industry.

Numerical simulation of red blood cells' deformation using SPH method

A numerical simulation method for the Red Blood Cells’ (RBC) deformation is presented in this study. The two-dimensional RBC membrane is modeled by the spring network, where the elastic stretch/compression energy and the bending energy are considered with the constraint of constant RBC surface area. Smoothed Particle Hydrodynamics (SPH) method is used to solve the Navier-Stokes equation coupled with the Plasma-RBC membrane and Cytoplasm- RBC membrane interaction. To verify the method, the motion of a single RBC is simulated in Poiseuille flow and compared with the results reported earlier. Typical motion and deformation mechanism of the RBC is observed.

Numerical simulation of red blood cells’ motion : a review

The micro-circulation of blood plays an important role in human body by providing oxygen and nutrients to the cells and removing carbon dioxide and wastes from the cells. This process is greatly affected by the rheological properties of the Red Blood Cells (RBCs). Changes in the rheological properties of the RBCs are caused by certain human diseases such as malaria and sickle cell diseases. Therefore it is important to understand the motion and deformation mechanism of RBCs in order to diagnose and treat this kind of diseases. Although, many methods have been developed to explore the behavior of the RBCs in micro-channels, they could not explain the deformation mechanism of the RBCs properly. Recently developed Particle Methods are employed to explain the RBCs’ behavior in micro-channels more comprehensively. The main objective of this study is to critically analyze the present methods, used to model the RBC behavior in micro-channels, in order to develop a computationally efficient particle based model to describe the complete behavior of the RBCs in micro-channels accurately and comprehensively

Simulation of phosphine flow in vertical grain storage : a preliminary numerical study

To fumigate grain stored in a silo, phosphine gas is distributed by a combination of diffusion and fan-forced advection. This initial study of the problem mainly focuses on the advection, numerically modelled as fluid flow in a porous medium. We find satisfactory agreement between the flow predictions of two Computational Fluid Dynamics packages, Comsol and Fluent. The flow predictions demonstrate that the highest velocity (>0.1 m/s) occurs less than 0.2m from the inlet and reduces drastically over one metre of silo height, with the flow elsewhere less than 0.002 m/s or 1% of the velocity injection. The flow predictions are examined to identify silo regions where phosphine dosage levels are likely to be too low for effective grain fumigation.

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.

Numerical modelling and full scale testing of load bearing steel walls under real fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. 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. However, modern residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the performance of load bearing LSF walls was undertaken using a series of realistic design fire curves developed based on Eurocode parametric curves and Barnett’s BFD curves. It included both full scale fire tests and numerical studies of LSF walls without any insulation, and the recently developed externally insulated composite panels. This paper presents the details of fire tests first, and then the numerical models of tested LSF wall studs. It shows that suitable finite element models can be developed to predict the fire rating of load bearing walls under real fire conditions. The paper also describes the structural and fire performances of externally insulated LSF walls in comparison to the non-insulated walls under real fires, and highlights the effects of standard and real fire curves on fire performance of LSF walls.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.