粒子包封随机流形的膨胀
Swelling of particle-encapsulating random manifolds
摘要：
我们研究了一个封闭的随机流形的统计力学的固定面积和波动的体积，封装一个固定数量的非相互作用的粒子。标度分析产生一个统一的描述，这样的膨胀流形，根据该平均体积逐渐增加的粒子数，遵循一个单一的标度律。这与固定压差下的膨胀明显不同，在固定压差下，某些模型表现出临界性。因此，我们指出，当膨胀由于封装的颗粒是热力学不等同于所造成的固定压力。一般的预测支持的蒙特卡罗模拟的两个粒子封装模型系统-一个二维的自避免环和三维的自避免流体囊泡。在前者中，颗粒引起的溶胀与压力引起的溶胀在热力学上是等价的，而在后者中则不是。
英文摘要：
We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds, according to which the mean volume gradually increases with particle number, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We thereby indicate when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions are supported by Monte Carlo simulations of two particle-encapsulating model systems -- a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. In the former the particle-induced swelling is thermodynamically equivalent to the pressure-induced one whereas in the latter it is not.
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