Mathematical Modelling of Spatial Spread in Anisotropic Landscapes

我的研究的主要目标是研究数学模型在各向异性景观及其应用。各向异性是指环境中的方向信息，例如大脑中的白色物质纤维轨迹，森林栖息地中的地震线和道路，或景观中的风向和坡度方向。我将集中在两种类型的模型，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在于扩散张量，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。应用于胶质瘤生长将有助于我们获得更准确的肿瘤生长预测，然后可以用于治疗计划。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，应用于狼在具有地震线的栖息地中的运动将使我们能够告知政策制定者减少这些地震线对狼狩猎行为的影响的策略。

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.