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DISPERSAL OF HYDROGEN IN THE RETINA—A THREE-LAYER MODEL 氢在视网膜中的分散——一个三层模型
The ANZIAM journal Pub Date : 2022-01-01 DOI: 10.1017/S1446181122000050
W. Mansoor, G. Hocking, D. Farrow
{"title":"DISPERSAL OF HYDROGEN IN THE RETINA—A THREE-LAYER MODEL","authors":"W. Mansoor, G. Hocking, D. Farrow","doi":"10.1017/S1446181122000050","DOIUrl":"https://doi.org/10.1017/S1446181122000050","url":null,"abstract":"Abstract Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"32 1","pages":"1 - 22"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88153309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ANZ VOLUME 64 ISSUE 1 COVER AND BACK MATTER 澳新银行64卷第1期封面和封底
The ANZIAM journal Pub Date : 2022-01-01 DOI: 10.1017/s1446181121000407
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引用次数: 0
EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ode的显式nordsieck二阶导数一般线性方法
The ANZIAM journal Pub Date : 2022-01-01 DOI: 10.1017/S1446181122000049
P. Ramazani, A. Abdi, G. Hojjati, A. Moradi
{"title":"EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES","authors":"P. Ramazani, A. Abdi, G. Hojjati, A. Moradi","doi":"10.1017/S1446181122000049","DOIUrl":"https://doi.org/10.1017/S1446181122000049","url":null,"abstract":"Abstract The paper deals with the construction of explicit Nordsieck second derivative general linear methods with s stages of order p with \u0000$p=s$\u0000 and high stage order \u0000$q=p$\u0000 with inherent Runge–Kutta or quadratic stability properties. Satisfying the order and stage order conditions together with inherent stability conditions leads to methods with some free parameters, which will be used to obtain methods with a large region of absolute stability. Examples of methods with r external stages and \u0000$p=q=s=r-1$\u0000 up to order five are given, and numerical experiments in a fixed stepsize environment are presented.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"39 1","pages":"69 - 88"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80356680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
ANZ VOLUME 64 ISSUE 1 COVER AND FRONT MATTER 澳新银行64卷第1期封面和封面
The ANZIAM journal Pub Date : 2022-01-01 DOI: 10.1017/s1446181121000390
{"title":"ANZ VOLUME 64 ISSUE 1 COVER AND FRONT MATTER","authors":"","doi":"10.1017/s1446181121000390","DOIUrl":"https://doi.org/10.1017/s1446181121000390","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"22 1","pages":"f1 - f2"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88551641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
HOPF BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER HOLLING–TANNER PREDATOR-PREY MODEL WITH TIME DELAY 具有时滞的分数阶holling-tanner捕食者-猎物模型的Hopf分岔分析
The ANZIAM journal Pub Date : 2022-01-01 DOI: 10.1017/S1446181122000025
C. Çelik, K. Degerli̇
{"title":"HOPF BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER HOLLING–TANNER PREDATOR-PREY MODEL WITH TIME DELAY","authors":"C. Çelik, K. Degerli̇","doi":"10.1017/S1446181122000025","DOIUrl":"https://doi.org/10.1017/S1446181122000025","url":null,"abstract":"Abstract We study a fractional-order delayed predator-prey model with Holling–Tanner-type functional response. Mainly, by choosing the delay time \u0000$tau $\u0000 as the bifurcation parameter, we show that Hopf bifurcation can occur as the delay time \u0000$tau $\u0000 passes some critical values. The local stability of a positive equilibrium and the existence of the Hopf bifurcations are established, and numerical simulations for justifying the theoretical analysis are also presented.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"46 1","pages":"23 - 39"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77181784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
THREE-DIMENSIONAL ANALYTICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION FOR AIR POLLUTION DISPERSION 空气污染扩散的平流-扩散方程的三维解析解
The ANZIAM journal Pub Date : 2022-01-01 DOI: 10.1017/S1446181122000037
M. Farhane, Omar Alehyane, O. Souhar
{"title":"THREE-DIMENSIONAL ANALYTICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION FOR AIR POLLUTION DISPERSION","authors":"M. Farhane, Omar Alehyane, O. Souhar","doi":"10.1017/S1446181122000037","DOIUrl":"https://doi.org/10.1017/S1446181122000037","url":null,"abstract":"Abstract We develop a new analytical solution of a three-dimensional atmospheric pollutant dispersion. The main idea is to subdivide vertically the planetary boundary layer into sub-layers, where the wind speed and eddy diffusivity assume average values for each sub-layer. Basically, the model is assessed and validated using data obtained from the Copenhagen diffusion and Prairie Grass experiments. Our findings show that there is a good agreement between the predicted and observed crosswind-integrated concentrations. Moreover, the calculated statistical indices are within the range of acceptable model performance.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"68 1","pages":"40 - 53"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73415197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
NUMERICAL SOLUTIONS TO A FRACTIONAL DIFFUSION EQUATION USED IN MODELLING DYE-SENSITIZED SOLAR CELLS 用于染料敏化太阳能电池建模的分数扩散方程的数值解
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/S1446181121000353
B. Maldon, B. Lamichhane, N. Thamwattana
{"title":"NUMERICAL SOLUTIONS TO A FRACTIONAL DIFFUSION EQUATION USED IN MODELLING DYE-SENSITIZED SOLAR CELLS","authors":"B. Maldon, B. Lamichhane, N. Thamwattana","doi":"10.1017/S1446181121000353","DOIUrl":"https://doi.org/10.1017/S1446181121000353","url":null,"abstract":"Abstract Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"152 1","pages":"420 - 433"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77705555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ANZ VOLUME 63 ISSUE 4 COVER AND BACK MATTER 澳新银行第63卷第4期封面和封底
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/s1446181121000201
{"title":"ANZ VOLUME 63 ISSUE 4 COVER AND BACK MATTER","authors":"","doi":"10.1017/s1446181121000201","DOIUrl":"https://doi.org/10.1017/s1446181121000201","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"9 1","pages":"b1 - b6"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85923272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
DO POOR ENVIRONMENTAL CONDITIONS DRIVE TRACHOMA TRANSMISSION IN BURUNDI? A MATHEMATICAL MODELLING STUDY 在布隆迪，恶劣的环境条件导致沙眼传播吗?数学模型研究
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/S1446181121000389
D. Ndisabiye, E. Waters, R. Gore, H. Sidhu
{"title":"DO POOR ENVIRONMENTAL CONDITIONS DRIVE TRACHOMA TRANSMISSION IN BURUNDI? A MATHEMATICAL MODELLING STUDY","authors":"D. Ndisabiye, E. Waters, R. Gore, H. Sidhu","doi":"10.1017/S1446181121000389","DOIUrl":"https://doi.org/10.1017/S1446181121000389","url":null,"abstract":"Abstract Trachoma is an infectious disease and it is the leading cause of preventable blindness worldwide. To achieve its elimination, the World Health Organization set a goal of reducing the prevalence in endemic areas to less than \u0000$5$\u0000 % by 2020, utilizing the SAFE (surgery, antibiotics, facial cleanliness, environmental improvement) strategy. However, in Burundi, trachoma prevalences of greater than \u0000$5$\u0000 % are still reported in 11 districts and it is hypothesized that this is due to the poor implementation of the environmental improvement factor of the SAFE strategy. In this paper, a model based on an ordinary differential equation, which includes an environmental transmission component, is developed and analysed. The model is calibrated to recent field data and is used to estimate the reductions in trachoma that would have occurred if adequate environmental improvements were implemented in Burundi. Given the assumptions in the model, it is clear that environmental improvement should be considered as a key component of the SAFE strategy and, hence, it is crucial for eliminating trachoma in Burundi.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"51 1","pages":"434 - 447"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90321247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ANZ VOLUME 63 ISSUE 4 COVER AND FRONT MATTER 澳新银行第63卷第4期封面和封面
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/s1446181121000195
{"title":"ANZ VOLUME 63 ISSUE 4 COVER AND FRONT MATTER","authors":"","doi":"10.1017/s1446181121000195","DOIUrl":"https://doi.org/10.1017/s1446181121000195","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"6 1","pages":"f1 - f2"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72916908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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