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res:granular_glass_transition [2013/04/29 14:00] – granular_glass_transition renamed to res:granular_glass_transition root | res:granular_glass_transition [2019/10/05 19:01] (current) – till | ||
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* Kranz, W. T., M. Sperl and A. Zippelius, [[http:// | * Kranz, W. T., M. Sperl and A. Zippelius, [[http:// | ||
- | Studying an air-fluidized, | + | Studying an air-fluidized, |
found that upon increasing the packing fraction $\varphi$, the mean squared displacement | found that upon increasing the packing fraction $\varphi$, the mean squared displacement | ||
$\delta r^2(t) = \langle[r(t+\tau)-r(\tau)]^2\rangle$ develops a plateau for intermediate times. | $\delta r^2(t) = \langle[r(t+\tau)-r(\tau)]^2\rangle$ develops a plateau for intermediate times. | ||
Such a behavior has been observed before in colloidal suspensions and is attributed to a | Such a behavior has been observed before in colloidal suspensions and is attributed to a | ||
- | structural glass transition. | + | structural glass transition |
- | <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 | ||
- | (colloidal) glass transition. In our work we found that MCT can be generalized to the far from | + | (colloidal) glass transition.((Götze, //Complex dynamics of glass-forming liquids: A mode-coupling theory//, OUP Oxford, 2009)) |
equilibrium stationary state of a model system for fluidized granular particles. We modeled the | equilibrium stationary state of a model system for fluidized granular particles. We modeled the | ||
granular particles as monodisperse smooth spheres with a constant coefficient of restitution | granular particles as monodisperse smooth spheres with a constant coefficient of restitution | ||
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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 |