Granular Continuum-Transition Regime

颗粒材料在工业和农业中是普遍存在的、自然的和核心的。拟议的项目将侧重于它们的流化阶段，即“颗粒气体”。强有力的运动论方法已被用来对颗粒气体进行非常成功的流体力学描述。流体力学受限于低克努森数（平均自由程与相关宏观尺度的比值），因此；不适用于例如，冲击或稀薄（颗粒）气体的内部。当克努森数远远大于单位时，适用玻尔兹曼方程的无碰撞极限，然而，当它是单位数量级时，就需要对动力学进行详细的研究。这定义了“连续过渡制度”，它与分子冲击和涉及稀薄气体的系统类似，例如在高空飞行和芯片生产反应堆中遇到的系统。拟议项目的目标是产生颗粒连续过渡状态的连续描述，并将其应用于特定系统，范例是垂直振动颗粒气体。计划通过利用最近开发的强大的计算机辅助分析工具来研究相关的玻尔兹曼方程（使用Grad矩展开作为方法之一），并结合有效的数值模拟来实现这一目标。

Granular materials are ubiquitous and Nature and central in industry and agriculture. The proposed project will focus on their fluidized phase, known as the "granular gas". Powerful methods of kinetic theory have been employed to produce highly successful hydrodynamic descriptions of granular gases. Hydrodynamics is restricted to low Knudsen numbers (ratio of the mean free path to the pertinent macroscopic scales), and it therefore does; not apply to e.g., the interior of shocks or rarefied (granular) gases. When the Knudsen number is much larger than unity the collisionless limit of the Boltzmann equation applies, however, when is it of the order of unity a detailed study of the kinetics is called for. This defines the "continuum transition regime", which has parallels in e.g., molecular shocks and systems that involve rarefied gases as encountered e.g., in high altitude flights and chip-producing reactors. The goal of the proposed project is to produce continuum descriptions of the granular continuum transition regime and apply these to specific systems, the paradigm being vertically vibrated granular gases. This is planned to be achieved by harnessing recently developed powerful computer-aided analytic tools for the study of the pertinent Boltzmann equation (using the Grad moment expansion as one of the methods) in conjunction with efficient numerical simulations.