Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints.
Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints.
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驱动接口的缩放属性：对称性、守恒定律和约束的作用。
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发表时间：
1991
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影响因子：
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通讯作者：
Plischke
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文献类型：
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作者：
Rácz;Siegert;Liu;Plischke
通过分析和数值模拟研究表面动力学的一维模型。在所有情况下，形成沉积物的颗粒数量都是保守的。我们发现，最初平坦的表面通常会随着时间而变粗糙，并且可以通过宽度suremath{xi}来表征，对于线性尺寸为L的基板上的沉积物，宽度ensuremath{xi}遵循缩放形式ensuremath{xi}(L,t)=${mathit{L}}^{mathrm{ensuremath{chi}}}$f(t/${mathit{L}}^{mathit{z}}$)。 (RSOS) 型模型，其中微观动力学服从详细平衡，被证明处于“自由场”普适性类别，指数 z=4 且 Ensuremath{chi}=1/2。另一方面，如果详细的平衡被打破，则存在多个普遍性类别。随着RSOS模型中“最大高度差”约束的变化，人们可以观察到平坦相（z=2，ensuremath{chi}=0）和凹槽相之间的相变，凹槽相的特征是稳态指数ensuremath{chi}=1，但在松弛过程中没有缩放。在转变点，出现一个非常粗糙的表面，其指数（zensuremath{approxeq}3.67，ensuremath{chi}ensuremath{approxeq}0.33）接近守恒 Kardar-Parisi-Zhang 方程的指数。我们提出了一个可以解释这些观察结果的现象学模型。
One-dimensional models of surface dynamics are studied analytically and by numerical simulation. In all cases the number of particles that form the deposit is conserved. We find that an initially flat surface, in general, roughens as a function of time and can be characterized by a width ensuremath{xi} which obeys the scaling form ensuremath{xi}(L,t)=${mathit{L}}^{mathrm{ensuremath{chi}}}$f(t/${mathit{L}}^{mathit{z}}$) for a deposit on a substrate of linear dimension L. Restricted solid-on-solid (RSOS) -type models in which the microscopic dynamics obeys detailed balance are shown to be in the ``free-field' universality class with exponents z=4 and ensuremath{chi}=1/2. On the other hand, if detailed balance is broken, several universality classes exist. As the ``maximum-height-difference' constraint in a RSOS model is varied, one can observe a phase transition between a flat phase (z=2, ensuremath{chi}=0) and a grooved phase characterized by a steady-state exponent ensuremath{chi}=1 but with no scaling in the relaxation process. At the transition point, a nontrivially rough surface emerges with exponents (zensuremath{approxeq}3.67, ensuremath{chi}ensuremath{approxeq}0.33) close to those of the conserved Kardar-Parisi-Zhang equation. We propose a phenomenological model that may account for these observations.