Mathematical Sciences: Infinite Particle Systems and RelatedModels

这个项目将研究无限粒子系统。这些系统被用作许多不同领域的模型，如统计物理、化学、计算机科学和群体遗传学。这个模型给数学家提出了许多具有挑战性的问题。该研究提出了一个简单而丰富的模型，展示了许多有趣的新特性。一个特定的模型由于亚稳态而陷入悖论。一个物理系统是亚稳态的，如果它稳定到一个表面的平衡状态，在那里停留很长一段时间，然后最终突然过渡到它真正的不变状态。为了研究这些复杂的系统，需要进行大量的计算机图形学工作。计算机图形学也将被用来向更广泛的观众解释这部作品。

This project will study infinite particle systems. These systems are used as models in many diverse fields such as statistical physics, chemistry, computer science and population genetics. The model offers many challenging problems to a mathematician. The research proposes a simple but rich model exhibiting many new interesting properties. A specific such models runs in to a paradox due to metastability. A physical system is metastable if it settles down to an apparent equilibrium, stays there for a very long time, and then eventually makes a sudden transition to its true invariant state. Extensive computer graphics work will be done to study these complex systems. Coputer graphics will also be used to explain the work to wider audiences.