Particle-based methods for flow applications and biochemical networks

基于粒子的方法是一种流行的模拟工具，它提供了一种更精细的系统动力学，能够捕获和探索不能用微分方程建模的系统动力学。最近的技术进步使基于粒子的方法能够应用于一系列广泛的问题，包括基于粒子的流动模型和生化网络。应用基于粒子的方法模拟局部收缩流动的最新结果表明，基于粒子的方法具有可压缩的性质。在模拟不可压缩或弱可压缩流体(如血液)的流动时，必须注意控制并将这种影响降至最低。血液流动的真实流动区域，如通过狭窄动脉的流动，或通过分支血管的流动，自然会产生需要量化和控制的可压缩性效应。另一方面，内置的可压缩性是探索包括微流体在内的一系列可压缩流动问题的理想选择。此外，将反应结合到基于颗粒的方法中，允许研究反应或多相流应用，以及模拟空间分布的生化网络，例如大肠杆菌细胞的趋化反应。 这项研究计划将开展以下新颖的工作：开发用于量化复杂流动几何形状中的可压缩性和滑移性的数值和分析技术；开发多颗粒碰撞动力学(MPCD)流动的数值技术；开发反应性MPCD对反应性或多相流和生化网络的模拟；开发可压缩流动问题的分析和数值技术。 最近，当使用基于粒子的方法模拟局部收缩流动时，观察到了可压缩性效应，以及非平衡效应。利用MPCD流动中固有的可压缩性，将进行大量的数值和理论研究，以便根据需要对可压缩性进行量化和控制。该研究计划将在以下方面做出重要贡献：低浓度化学物种存在的化学反应介质的流动，可压缩流动，改进非平衡条件下MPCD流动中粘度表达式的数值/理论估计，MPCD流动在复杂流区中的应用，以及生物相关生化网络的数值模拟。根据该计划培训的HQP将获得非常可取的数学建模技能、编程经验、传播经验和可参考的期刊出版物，这些都是工业界和学术界非常可取的技能/里程碑。

Particle-based methods are a popular simulation tool that provide a more refined system dynamics with the ability to capture and explore system dynamics that cannot be modeled by differential equations. Recent technological advances have allowed for applications of particle-based methods to a wide array of problems including particle-based flow models and biochemical networks. Recent results in applying particle-based methods to simulate flow through a local constriction have shown the compressible nature of the particle-based method. Care must be taken to control and to minimize this effect when simulating flows for incompressible, or weakly compressible, fluids such as blood. Realistic flow domains for blood flow, such as flow through a constricted artery, or flow through a branched vessel naturally give rise to compressibility effects that need to be quantified and controlled for this particular application. On the other hand, the built-in compressibility is ideal for exploring a range of compressible flow problems including microfluidics. Additionally, incorporation of reactions into the particle-based method allows for the study of reactive or multiphase flow applications, as well as for simulating spatially distributed biochemical networks such as the chemotactic response of an E. coli cell for example. The following novel work will be carried out in this research program: Development of numerical and analytical techniques to quantify compressibility and slip in complex flow geometries; development of numerical techniques for multiparticle collision dynamics (MPCD) flow through domains with porous walls; development of reactive MPCD simulations of reactive or multiphase flow and biochemical networks; development of analytical and numerical techniques for compressible flow problems. Compressibility effects have recently been observed when using particle-based methods to simulate flow through a local constriction, as well as non-equilibrium effects. Making use of the built-in compressibility in MPCD flow, a number of numerical and theoretical investigations will be carried out in order to quantify and control the compressibility if desired. The research program will lead to important contributions in: flows of chemically reactive media for which low concentration chemical species exist, compressible flows, improved numerical/theoretical estimates for viscosity expressions in MPCD flow in non-equilibrium conditions, MPCD flow through complex flow domains with applications to blood flow and microfluidics, and numerical simulations of biologically relevant biochemical networks. The HQP trained under this program will obtain highly desirable mathematical modeling skills, programming experience, dissemination experience, and refereed journal publications, which are highly desirable skills/milestones for industry and academia alike.