Numerical simulation of a fractional mathematical model for 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 numerical simulation of fractional model 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 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 the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

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.

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 simulation of anomalous diffusion with application to medical imaging

The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

Numerical simulation of downburst winds

The wind field of an intense idealised downburst wind storm has been studied using an axisymmetric, dry, non-hydrostatic numerical sub-cloud model. The downburst driving processes of evaporation and melting have been paramaterized by an imposed cooling source that triggers and sustains a downdraft. The simulated downburst exhibits many characteristics of observed full-scale downburst events, in particular the presence of a primary and counter rotating secondary ring vortex at the leading edge of the diverging front. The counter-rotating vortex is shown to significantly influence the development and structure of the outflow. Numerical forcing and environmental characteristics have been systematically varied to determine the influence on the outflow wind field. Normalised wind structure at the time of peak outflow intensity was generally shown to remain constant for all simulations. Enveloped velocity profiles considering the velocity structure throughout the entire storm event show much more scatter. Assessing the available kinetic energy within each simulated storm event, it is shown that the simulated downburst wind events had significantly less energy available for loading isolated structures when compared with atmospheric boundary layer winds. The discrepancy is shown to be particularly prevalent when wind speeds were integrated over heights representative of tall buildings. A similar analysis for available full scale measurements led to similar findings.

Numerical simulation of idealised three-dimensional downburst wind fields

Convective downburst wind storms generate the peak annual gust wind speed for many parts of the non-cyclonic world at return periods of importance for ultimate limit state design. Despite this there is little clear understanding of how to appropriately design for these wind events given their significant dissimilarities to boundary layer winds upon which most design is based. To enhance the understanding of wind fields associated with these storms a three-dimensional numerical model was developed to simulate a multitude of idealised downburst scenarios and to investigate their near-ground wind characteristics. Stationary and translating downdraft wind events in still and sheared environments were simulated with baseline results showing good agreement with previous numerical work and full-scale observational data. Significant differences are shown in the normalised peak wind speed velocity profiles depending on the environmental wind conditions in the vicinity of the simulated event. When integrated over the height of mid- to high rise structures, all simulated profiles are shown to produce wind loads smaller than an equivalent 10 m height matched open terrain boundary layer profile. This suggests that for these structures the current design approach is conservative from an ultimate loading standpoint. Investigating the influence of topography on the structure of the simulated near-ground downburst wind fields, it is shown that these features amplify wind speeds in a manner similar to that expected for boundary layer winds, but the extent of amplification is reduced. The level of reduction is shown to be dependent on the depth of the simulated downburst outflow.

Nanosphere monolayer-templated, ion-assisted nanofeature etching in dielectric materials : a numerical simulation of nanoscale ion flux topography

The results of numerical simulations of nanometer precision distributions of microscopic ion fluxes in ion-assisted etching of nanoscale features on the surfaces of dielectric materials using a self-assembled monolayer of spherical nanoparticles as a mask are presented. It is shown that the ion fluxes to the substrate and nanosphere surfaces can be effectively controlled by the plasma parameters and the external bias applied to the substrate. By proper adjustment of these parameters, the ion flux can be focused onto the areas uncovered by the nanospheres. Under certain conditions, the ion flux distributions feature sophisticated hexagonal patterns, which may lead to very different nanofeature etching profiles. The results presented are generic and suggest viable ways to overcome some of the limitations of the existing plasma-assisted nanolithography.

Multi-scale hybrid numerical simulation of the growth of high-aspect-ratio nanostructures

Recently, a variety high-aspect-ratio nanostructures have been grown and profiled for various applications ranging from field emission transistors to gene/drug delivery devices. However, fabricating and processing arrays of these structures and determining how changing certain physical parameters affects the final outcome is quite challenging. We have developed several modules that can be used to simulate the processes of various physical vapour deposition systems from precursor interaction in the gas phase to gas-surface interactions and surface processes. In this paper, multi-scale hybrid numerical simulations are used to study how low-temperature non-equilibrium plasmas can be employed in the processing of high-aspect-ratio structures such that the resulting nanostructures have properties suitable for their eventual device application. We show that whilst using plasma techniques is beneficial in many nanofabrication processes, it is especially useful in making dense arrays of high-aspect-ratio nanostructures.

Numerical simulation of self-organized nano-islands in plasma-based assembly of quantum dot arrays

This work presents the details of the numerical model used in simulation of self-organization of nano-islands on solid surfaces in plasma-assisted assembly of quantum dot structures. The model includes the near-substrate non-neutral layer (plasma sheath) and a nanostructured solid deposition surface and accounts for the incoming flux of and energy of ions from the plasma, surface temperature-controlled adatom migration about the surface, adatom collisions with other adatoms and nano-islands, adatom inflow to the growing nano-islands from the plasma and from the two-dimensional vapour on the surface, and particle evaporation to the ambient space and the two-dimensional vapour. The differences in surface concentrations of adatoms in different areas within the quantum dot pattern significantly affect the self-organization of the nano-islands. The model allows one to formulate the conditions when certain islands grow, and certain ones shrink or even dissolve and relate them to the process control parameters. Surface coverage by selforganized quantum dots obtained from numerical simulation appears to be in reasonable agreement with the available experimental results.

Numerical simulation of nanoparticle-generating electronegative plasmas in the PECVD of nanostructured silicon film

The results of numerical simulation of the equilibrium parameters of a low pressure nanopowder-generating discharge in silane for the plasma enhanced chemical vapor deposition (PECVD) of nanostructured silicon-based films are presented. It is shown that a low electron temperature and a low density of negative SiH3 - ions are favorable for the PECVD process. This opens a possibility to predict the main parameters of the reactive plasma and plasma-nucleated nanoparticles, and hence, to control the quality of silicon nanofilms.

A novel approach for numerical simulation of plant tissue shrinkage during drying

Drying is a key processing techniques used in food engineering which demands continual developments on advanced analysis techniques in order to optimize the product and the process. In this regard, plant based materials are a frequent subject of interest where microstructural studies can provide a clearer understanding on the fundamental physical mechanisms involved. In this context, considering numerous challenges of using conventional numerical grid-based modelling techniques, a meshfree particle based model was developed to simulate extreme deformations of plant microstructure during drying. The proposed technique is based on a particle based meshfree method: Smoothed Particle Hydrodynamics (SPH) and a Discrete Element Method (DEM). A tissue model was developed by aggrading individual cells modelled with SPH-DEM coupled approach by initializing the cells as hexagons and aggregating them to form a tissue. The model also involves a middle lamella resembling real tissues. Using the model, different dried tissue states were simulated with different moisture content, the turgor pressure, and cell wall contraction effects. Compared to the state of the art grid-based microscale plant tissue drying models, the proposed model is capable of simulating plant tissues at lower moisture contents which results in excessive shrinkage and cell wall wrinkling. Model predictions were compared with experimental findings and a fairly good agreement was observed both qualitatively and quantitatively.

Numerical simulation of micro-scale morphological changes of plant food materials during drying - a meshfree approach

This thesis developed a high preforming alternative numerical technique to investigate microscale morphological changes of plant food materials during drying. The technique is based on a novel meshfree method, and is more capable of modeling large deformations of multiphase problem domains, when compared with conventional grid-based numerical modeling techniques. The developed cellular model can effectively replicate dried tissue morphological changes such as shrinkage and cell wall wrinkling, as influenced by moisture reduction and turgor loss.