Mathematical Modelling of Spatial Spread in Anisotropic Landscapes

各向异性景观空间扩散的数学建模

• 批准号: 250302-2012
• 负责人: Hillen, Thomas
• 金额: $ 2.19万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=594435
• 关键词: Mathematical; Modelling; Spatial; Spread; Anisotropic

The primary goal of my research is to investigate mathematical models for spread in anisotropic landscapes and their applications. Anisotropy refers to directional information in the environment, for example white matter fiber tracks in the brain, seismic lines and roads in forest habitats, or wind and slope directions in landscapes. I will focus on two types of models, transport equations on networks and anisotropic diffusion equations. Anisotropic diffusion models are characterized by a diffusion tensor, which describes the mobility of particles in different directions. The project will focus on a detailed qualitative analysis of these models and applications. The application to glioma growth will help us to obtain more accurate tumor growth predictions, which can then be used for treatment planning. The application to forest fires is part of a new generation of forest fire prediction tools. And finally, an application to wolf movement in habitats with seismic lines will enable us to inform policy makers of strategies to reduce the impact of these seismic lines on the wolf hunting behavior.

我的研究的主要目的是研究在各向异性景观及其应用中传播的数学模型。各向异性是指环境中的方向信息，例如大脑中的白质纤维轨道，森林栖息地中的地震线和道路，或景观中的风和斜率方向。我将专注于两种类型的模型，网络上的传输方程和各向异性扩散方程。各向异性扩散模型的特征是扩散张量，该扩散张量描述了粒子在不同方向上的迁移率。该项目将重点介绍对这些模型和应用的详细定性分析。胶质瘤生长的应用将有助于我们获得更准确的肿瘤生长预测，然后将其用于治疗计划。森林火灾的应用是新一代森林火灾预测工具的一部分。最后，在具有地震线条的栖息地中，对狼运动的应用将使我们能够将这些地震线对狼狩猎行为的影响的战略告知决策者。