Second order additive invariants in elementary cellular automata
Second order additive invariants in elementary cellular automata
复制标题
初等元胞自动机中的二阶加性不变量
DOI：
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发表时间：
2005
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通讯作者：
H. Fuks
中科院分区：
文献类型：
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作者：
H. Fuks
研究了初等元胞自动机规则中的二阶加性不变量。具有加性不变量的规则的基本图要么是线性的，要么表现出与一阶不变量规则的奇异性相似的奇异性。只有恰好有一个不变量的规则才表现出奇点。在奇点处，电流以幂律形式衰减到平衡值$t^{\alpha}$，数值模拟得到的指数$\alpha$的值非常接近于-1/2。这与先前报道的数字守恒规则的值一致，并导致一个猜想，即无论不变式的顺序如何，指数$\alpha$似乎具有1/2的普遍值。
We investigate second order additive invariants in elementary cellular automata rules. Fundamental diagrams of rules which possess additive invariants are either linear or exhibit singularities similar to singularities of rules with first-order invariant. Only rules which have exactly one invariants exhibit singularities. At the singularity, the current decays to its equilibrium value as a power law $t^{\alpha}$, and the value of the exponent $\alpha$ obtained from numerical simulations is very close to -1/2. This is in agreements with values previously reported for number-conserving rules, and leads to a conjecture that regardless of the order of the invariant, exponent $\alpha$ seems to have a universal value of 1/2.