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res:granular_glass_transition [2013/04/30 16:58] – root | res:granular_glass_transition [2019/10/05 19:01] (current) – till | ||
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structural glass transition ((van Megen //et al.//, [[http:// | structural glass transition ((van Megen //et al.//, [[http:// | ||
- | <WRAP box 260px right> | + | <WRAP box 260px right> |
Mode coupling theory (MCT) turned out to be successful in describing many features of the | Mode coupling theory (MCT) turned out to be successful in describing many features of the | ||
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memory kernel $m(q,t)$ can be given in terms of a mode coupling approximation | memory kernel $m(q,t)$ can be given in terms of a mode coupling approximation | ||
$$ | $$ | ||
- | m(q, | + | m(q, |
$$ | $$ | ||
- | The two vertices or transition rates $\mathcal V_{\vec q\vec k}\ne\mathcal W_{\vec q\vec k}$ are | + | The two vertices or transition rates $\mathcal V_{\vec q\vec k}\ne\mathcal W_{\vec q\vec k}=\frac{1+\varepsilon}{2}\mathcal V_{\vec q\vec k}$ are |
unequal, different form the theory for colloidal suspensions which are in thermal equilibrium. | unequal, different form the theory for colloidal suspensions which are in thermal equilibrium. | ||
This difference reflects the loss of detailed balance in the nonequilibrium granular fluid. The | This difference reflects the loss of detailed balance in the nonequilibrium granular fluid. The | ||
inelastic collisions make the direction of time obvious. | inelastic collisions make the direction of time obvious. | ||
- | <WRAP box 310px left> | + | <WRAP box 310px left> |
As a result we find that there is a glass transition for our driven granular model fluid for all | As a result we find that there is a glass transition for our driven granular model fluid for all | ||
values of the coefficient of restitution and that the MSD indeed develops a plateau | values of the coefficient of restitution and that the MSD indeed develops a plateau |