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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=547583
• 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.

我研究的主要目标是研究在各向异性景观中传播的数学模型及其应用。各向异性指的是环境中的方向性信息，例如大脑中的白质纤维轨迹，森林生境中的地震线和道路，或者景观中的风向和坡向。我将集中讨论两种类型的模型，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，它描述了粒子在不同方向上的迁移率。该项目将侧重于对这些模型和应用进行详细的定性分析。对胶质瘤生长的应用将帮助我们获得更准确的肿瘤生长预测，然后用于治疗计划。对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，应用于有地震线的栖息地中的狼的运动将使我们能够向政策制定者提供减少这些地震线对狼狩猎行为的影响的策略。