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arXiv 1202.1272cond-mat.mtrl-sciphysics.comp-ph
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雪晶生长中小面斑图形成的数值计算

Numerical computations of facetted pattern formation in snow crystal growth

John W. Barrett, Harald Garcke, Robert Nürnberg

摘要:

雪晶的面状生长导致了丰富多样的形式,并表现出显着的六重对称性。雪晶结构是在各向异性表面能和各向异性附着动力学的存在下由扩散限制的晶体生长产生的。现在已经很好地理解,冰晶的形态稳定性强烈地依赖于过饱和度、晶体尺寸和温度。直到最近,对这种高度各向异性的晶体生长进行数值模拟还是非常困难的。特别地,获得与树枝状分支相结合的小面生长是一项具有挑战性的任务。我们提出了一种新的计算方法,在两个和三个空间维度的雪晶体生长的数值模拟。我们提出了定性和定量计算。特别地,观察到尖端速度和过饱和度之间的线性关系。计算还表明,表面能的影响,虽然很小,有一个更大的影响晶体生长比以前预期的。我们计算固体板,固体棱柱,空心柱,针,树枝状晶体,加盖柱和卷轴板。尽管所有这些形式都出现在自然界中,但其中大多数形式都是在连续体模型的数值模拟中首次计算的。

英文摘要:

Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and anisotropic attachment kinetics. It is by now well understood that the morphological stability of ice crystals strongly depends on supersaturation, crystal size and temperature. Until very recently it was very difficult to perform numerical simulations of this highly anisotropic crystal growth. In particular, obtaining facet growth in combination with dendritic branching is a challenging task. We present numerical simulations of snow crystal growth in two and three space dimensions using a new computational method recently introduced by the authors. We present both qualitative and quantitative computations. In particular, a linear relationship between tip velocity and supersaturation is observed. The computations also suggest that surface energy effects, although small, have a larger effect on crystal growth than previously expected. We compute solid plates, solid prisms, hollow columns, needles, dendrites, capped columns and scrolls on plates. Although all these forms appear in nature, most of these forms are computed here for the first time in numerical simulations for a continuum model.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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