Asymptotic modelling of a dynamic response of multiscale systems

多尺度系统动态响应的渐近建模

• 批准号: 2599756
• 金额: --
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2599756
• 关键词: Asymptotic; modelling; dynamic; response; multiscale

We consider the asymptotic analysis of singularly perturbed problems for partial differential equations and its applications in propagation of waves, heat conduction and mathematical elasticity. We also study the asymptotic analysis of fields in multi-structures and the asymptotic behaviour of solutions to boundary value problems. For networks of fluids in thin channels, asymptotic approximations will be constructed with the focus on the analysis of junctions of the network, and both slow flows and dynamic regimes will be addressed. Furthermore, the formulations, which take into account the fluid-solid interaction, will include the wave phenomena. Such waves are dispersive, and their dynamics in multi-scale networks is a challenge. Analytical models will be accompanied by numerical simulations. Applications are envisaged in the analysis of vascular systems in biological systems as well as rock dynamics in the studies of earthquake phenomena.

我们考虑对部分微分方程的奇异性问题的渐近分析及其在传播波，热传导和数学弹性中的应用。我们还研究了多结构中田间的渐近分析以及解决边界价值问题的解决方案的渐近行为。对于薄通道中的流体网络，将构建渐近近似值，重点是对网络连接的分析，并将解决慢速流量和动态方案。此外，考虑到流体固定相互作用的制剂将包括波浪现象。这样的波是分散的，它们在多尺度网络中的动态是一个挑战。分析模型将伴随数值模拟。在生物系统中的血管系统以及地震现象研究中的岩石动力学分析中设想了应用。