Patterns and Growth Far from Equilibrium

9420335桑德将研究远离平衡的统计物理理论中的一系列项目。随机粗糙表面的生长将被考虑；在分子束外延生长的描述中提出了新的工作。逆方法将应用于界面生长的一般理论，并将使用相同的技术研究火焰锋面的Kuramoto-Shivashinsky方程。与扩散限制凝聚模型相关的三个问题将被研究：空隙问题，由该模型产生的分形团簇的均匀性的统计分析，以及应用逆方法生成连续介质方程。最后，将在化学反应的模式和波动领域开展工作。在两个简单的统计模型的背景下，将尝试理解噪声和无序对化学模式形成的影响。%将在不平衡的系统上开展一系列项目。这些系统的例子包括：材料表面的生长、火焰的行为、颗粒聚集的模型、化学反应中发生的图案形成以及噪声对这些系统的影响。我们将研究描述这些不同现象的常见模型。

9420335 Sander A series of projects in the theory of statistical physics far from equilibrium will be studied. The growth of random rough surfaces will be considered; new work is proposed in the description of growth by molecular-beam epitaxy. An inverse method will be applied to the generic theory of interface growth, and the Kuramoto-Shivashinsky equation of flame fronts will be investigated using the same techniques. Three problems related to the diffusion-limited aggregation model will be studied: the question of lacunarity, a statistical analysis of the homogenieties of the fractal clusters produced by the model, and the inverse method will be applied to generate a continuum equation. Finally work will be done in the field of patterns and fluctuations in chemical reactions. In the context of two simple statistical models an attempt to understand the effects of noise and disorder on the formation of chemical patterns will be undertaken. %%% A series of projects will be undertaken on systems which are not in equilibrium. Examples of these systems include: the growth of surfaces in materials, the behavior of flames, models of aggregation of particles, pattern formation occuring in chemical reactions and the effects of noise on these systems. Common models which describe these various phenomena will be studied.