We derive a microscopic criterion for the stability of hard sphere configurations and we show empirically that this criterion is marginally satisfied in the glass. This observation supports a geometric interpretation for the initial rapid rise in viscosity with packing fraction or previtrification. It also implies that barely stable soft modes characterize the glass structure, whose spatial extension is estimated. We show that both the short-term dynamics and activation processes occur mostly along those soft modes and we study some implications of these observations. This article synthesizes new and previous results [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006); C. Brito and M. Wyart, J. Stat. Mech.: Theory Exp. 2007, L08003] in a unified view.
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机译：我们得出了硬球构型稳定性的微观标准，并从经验上表明该标准在玻璃中得到了一定程度的满足。该观察结果支持了几何学解释，即随着填料分数或预玻璃化作用，粘度开始迅速上升。这也意味着勉强稳定的软模式是玻璃结构的特征，其空间扩展是估计的。我们表明短期动力学和激活过程都主要沿着这些软模式发生，并且我们研究了这些观察结果的一些含义。本文综合了新的和以前的结果[C. Brito和M.Wyart，Europhys。来吧76，149（2006）; C. Brito和M. Wyart，J. Stat。机械：理论经验。 2007，L08003]的统一视图。
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