AI 中文总结
研究布朗城堡界面生长模型，通过数值验证其界面宽度呈现修正的家族-维塞克标度性质，得出生长指数和粗糙度指数，发现短时间标度修正，还揭示了高度概率分布与简单高斯行为的偏差及高度变化概率分布的形式。
AI 中文摘要
布朗城堡是一种新的界面生长模型，是著名弹道沉积模型的变体，导致全新的普适类。我们给出数值验证，表明布朗城堡界面的界面宽度在有限尺寸修正范围内呈现修正的家族-维塞克标度性质。具体而言，我们发现生长指数β = 0.470 ± 0.012，粗糙度指数α = 1.01 ± 0.018。在短时间内标度被修正，具有描述界面宽度早期长度依赖性的尺寸标度指数。布朗城堡界面高度的概率分布与简单高斯行为有显著偏差，高度变化的概率分布呈现与涉及相对大跳跃过程预期一致的柯西-洛伦兹形式。
英文摘要
The Brownian Castle is a new interface growth model that is a variation on the well-known ballistic deposition model that results in an entirely new universality class. We present numerical verification that the interface width for BC interfaces displays modified Family-Vicsek scaling properties up to finite size corrections. Specifically, we find a growth exponent of $β=0.470 \pm 0.012$ and a roughness exponent of $α=1.01 \pm 0.018$. The scaling is modified at short times with a size scaling exponent that described the early time dependence of interface width on length. The probability distribution of heights for the BC interface shows significant deviations from simple Gaussian behavior and the probability distribution of height changes shows a Cauchy-Lorentz form consistent with expectations for a process involving relatively large jumps.
