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.

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.

Numerical solutions of stochastic differential equations – implementation and stability issues

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Porohyperelastic analysis to explore mechanical properties of chondrocytes using numerical modeling and experiments : a finite element study

There are many continuum mechanical models have been developed such as liquid drop models, solid models, and so on for single living cell biomechanics studies. However, these models do not give a fully approach to exhibit a clear understanding of the behaviour of single living cells such as swelling behaviour, drag effect, etc. Hence, the porohyperelastic (PHE) model which can capture those aspects would be a good candidature to study cells behaviour (e.g. chondrocytes in this study). In this research, an FEM model of single chondrocyte cell will be developed by using this PHE model to simulate Atomic Force Microscopy (AFM) experimental results with the variation of strain rate. This material model will be compared with viscoelastic model to demonstrate the advantages of PHE model. The results have shown that the maximum value of force applied of PHE model is lower at lower strain rates. This is because the mobile fluid does not have enough time to exude in case of very high strain rate and also due to the lower permeability of the membrane than that of the protoplasm of chondrocyte. This behavior is barely observed in viscoelastic model. Thus, PHE model is the better model for cell biomechanics studies.

Thermal performance of composite panels under fire conditions using numerical studies : plasterboards, rockwool, glass fibre and cellulose insulations

In recent times, light gauge steel frame (LSF) wall systems are increasingly used in the building industry. They are usually made of cold-formed and thin-walled steel studs that are fire-protected by two layers of plasterboard on both sides. A composite LSF wall panel system was developed recently, where an insulation layer was used externally between the two plasterboards to improve the fire performance of LSF wall panels. In this research, finite element thermal models of the new composite panels were developed using a finite element program, SAFIR, to simulate their thermal performance under both standard and Eurocode design fire curves. Suitable apparent thermal properties of both the gypsum plasterboard and insulation materials were proposed and used in the numerical models. The developed models were then validated by comparing their results with available standard fire test results of composite panels. This paper presents the details of the finite element models of composite panels, the thermal analysis results in the form of time-temperature profiles under standard and Eurocode design fire curves and their comparisons with fire test results. Effects of using rockwool, glass fibre and cellulose fibre insulations with varying thickness and density were also investigated, and the results are presented in this paper. The results show that the use of composite panels in LSF wall systems will improve their fire rating, and that Eurocode design fires are likely to cause severe damage to LSF walls than standard fires.

Multi-scale numerical simulations of thermal expansion properties of CNT-reinforced nanocomposites

In this work, the thermal expansion properties of carbon nanotube (CNT)-reinforced nanocomposites with CNT content ranging from 1 to 15 wt% were evaluated using a multi-scale numerical approach, in which the effects of two parameters, i.e., temperature and CNT content, were investigated extensively. For all CNT contents, the obtained results clearly revealed that within a wide low-temperature range (30°C ~ 62°C), thermal contraction is observed, while thermal expansion occurs in a high-temperature range (62°C ~ 120°C). It was found that at any specified CNT content, the thermal expansion properties vary with temperature - as temperature increases, the thermal expansion rate increases linearly. However, at a specified temperature, the absolute value of the thermal expansion rate decreases nonlinearly as the CNT content increases. Moreover, the results provided by the present multi-scale numerical model were in good agreement with those obtained from the corresponding theoretical analyses and experimental measurements in this work, which indicates that this multi-scale numerical approach provides a powerful tool to evaluate the thermal expansion properties of any type of CNT/polymer nanocomposites and therefore promotes the understanding on the thermal behaviors of CNT/polymer nanocomposites for their applications in temperature sensors, nanoelectronics devices, etc.

Numerical Modelling of Mechanical Behaviour of Graphene

Graphene, one of the allotropes (diamond, carbon nanotube, and fullerene) of element carbon, is a monolayer of honeycomb lattice of carbon atoms, which was discovered in 2004. The Nobel Prize in Physics 2010 was awarded to Andre Geim and Konstantin Novoselov for their ground breaking work on the two-dimensional (2D) graphene [1]. Since its discovery, the research communities have shown a lot of interest in this novel material owing to its intriguing electrical, mechanical and thermal properties. It has been confirmed that grapheme possesses very peculiar electrical properties such as anomalous quantum hall effect, and high electron mobility at room temperature (250000 cm2/Vs). Graphene also has exceptional mechanical properties. It is one of the stiffest (modulus ~1 TPa) and strongest (strength ~100 GPa) materials. In addition, it has exceptional thermal conductivity (5000 Wm-1K-1). Due to these exceptional properties, graphene has demonstrated its potential for broad applications in micro and nano devices, various sensors, electrodes, solar cells and energy storage devices and nanocomposites. In particular, the excellent mechanical properties of graphene make it more attractive for development next generation nanocomposites and hybrid materials...

Shear strengths of lipped channel beams with stiffened web openings using numerical studies

This paper presents the details of numerical studies on the shear behaviour and strength of lipped channel beams (LCBs) with stiffened web openings. Over the last couple of decades, cold-formed steel beams have been used extensively in residential, industrial and commercial buildings as primary load bearing structural components. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Our research has shown that shear strengths of LCBs were reduced by up to 70% due to the inclusion of web openings. Hence there is a need to improve the shear strengths of LCBs with web openings. A cost effective way to improve the detrimental effects of a large web opening is to attach appropriate stiffeners around the web openings in order to restore the original shear strength and stiffness of LCBs. Hence numerical studies were undertaken to investigate the shear strengths of LCBs with stiffened web openings. In this research, finite element models of LCBs with stiffened web openings in shear were developed to simulate the shear behaviour and strength of LCBs. Various stiffening methods using plate and LCB stud stiffeners attached to LCBs using screw-fastening were attempted. The developed models were then validated by comparing their results with experimental results and used in parametric studies. Both finite element analysis and experimental results showed that the stiffening arrangements recommended by past re-search for cold-formed steel channel beams are not adequate to restore the shear strengths of LCBs with web openings. Therefore new stiffener arrangements were proposed for LCBs with web openings based on experimental and finite element analysis results. This paper presents the details of finite element models and analyses used in this research and the results including the recommended stiffener arrangements.

Numerical studies of load bearing LSF walls under realistic design fire conditions

Fire safety of light gauge steel frame (LSF) stud walls is important in the design of buildings. Currently LSF walls are increasingly used in the building industry, and are usually made of cold-formed and thin-walled steel studs that are fire-protected by two layers of plasterboard on both sides. Many experimental and numerical studies have been undertaken to investigate the fire performance of load bearing LSF walls under standard fire conditions. However, the standard time-temperature curve does not represent the fire load present in typical residential and commercial buildings that include considerable amount of thermoplastic materials. Real building fires are unlikely to follow a standard time-temperature curve. However, only limited research has been undertaken to investigate the fire performance of load bearing LSF walls under realistic design fire conditions. Therefore in this research, finite element thermal models of the traditional LSF wall panels without cavity insulation and the new LSF composite wall panels were developed to simulate their fire performance under recently developed realistic design fire curves. Suitable thermal properties were proposed for plasterboards and insulations based on laboratory tests and literature review. The developed models were then validated by comparing their thermal performance results with available results from realistic design fire tests, and were later used in parametric studies. This paper presents the details of the developed finite element thermal models of load bearing LSF wall panels under realistic design fire time-temperature curves and the re-sults. It shows that finite element thermal models can be used to predict the fire performance of load bearing LSF walls with varying configurations of insulations and plasterboards under realistic design fires. Failure times of load bearing LSF walls were also predicted based on the results from finite element thermal analyses.

Numerical analysis of shape transition in graphene nanoribbons

Graphene nanoribbon (GNR) with free edges can exhibit non-flat morphologies due to pre-existing edge stress. Using molecular dynamics (MD) simulations, we investigate the free-edge effect on the shape transition in GNRs with different edge types, including regular (armchair and zigzag), armchair terminated with hydrogen and reconstructed armchair. The results show that initial edge stress and energy are dependent on the edge configurations. It is confirmed that pre-strain on the free edges is a possible way to limit the random shape transition of GNRs. In addition, the influence of surface attachment on the shape transition is also investigated in this work. It is found that surface attachment can lead to periodic ripples in GNRs, dependent on the initial edge configurations.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.