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7.2: Ентропна еластичність
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\[\begin{align} \langle R^2 \rangle & = \langle \vec{R}_n^2 \rangle \\ & = \langle \vec{R}_n \cdot \vec{R}_n \rangle \\ & = \left\langle \left( \sum_{i=1}^n \vec{r}_i \right) \cdot \left( \sum_{j=1}^n... $\begin{align} \langle R^2 \rangle & = \langle \vec{R}_n^2 \rangle \\ & = \langle \vec{R}_n \cdot \vec{R}_n \rangle \\ & = \left\langle \left( \sum_{i=1}^n \vec{r}_i \right) \cdot \left( \sum_{j=1}^n \vec{r}_j \right) \right\rangle \\ & = \sum_{i=1}^n \sum_{j=1}^n \langle \vec{r}_i \cdot \vec{r}_j \rangle \ .\end{align}$
7.1: Сегментні моделі
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\[\begin{array} {rcl} {\langle \vec{R}^2 \rangle } & = & {n \ell^2 + \sum_{j \ne i} \langle \vec{\ell_i} \cdot \vec{\ell_j} \rangle} \\ {} & = & {n \ell^2 + \ell^2 \sum_{j \ne i} \langle \cos \theta_{... $\begin{array} {rcl} {\langle \vec{R}^2 \rangle } & = & {n \ell^2 + \sum_{j \ne i} \langle \vec{\ell_i} \cdot \vec{\ell_j} \rangle} \\ {} & = & {n \ell^2 + \ell^2 \sum_{j \ne i} \langle \cos \theta_{ij} \rangle} \end{array} \label{eq7.1.1}$ $\begin{array} {rcl} {\langle \vec{\ell_i} \cdot \vec{\ell_{i + 2}} \rangle} & = & {\langle \cos (\theta_i) \cos (\theta_{i + 1}) - \sin (\theta_i) \sin (\theta_{i + 1}) \cos (\phi_{i + 1}) \rangle} \\ {} & = & {\ell^2 \cos^2 \theta} \end{array}\nonumber$