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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://dx.doi.org/10.1103/PhysRevE.58.6073|PRE]] **58**, 6073 (1998) )).
-<WRAP box 260px right>{{:phic2d3d.png?250}}</WRAP>
+<WRAP box 260px right>{{:phic2d3d.png?250}} The critical packing fraction $\varphi_c$ as a function of the coefficient of restitution $\varepsilon$ in both two and three dimensions</WRAP>
 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
 $$
-m(q,t)\approx \int d^Dq\mathcal V_{\vec q\vec k}\mathcal W_{\vec q\vec k}\phi(q,t)\phi(|\vec q-\vec k|, t).
+m(q,t)\approx \int d^Dk\mathcal V_{\vec q\vec k}\mathcal W_{\vec q\vec k}\phi(q,t)\phi(|\vec q-\vec k|, t).
 $$
-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.
 This difference reflects the loss of detailed balance in the nonequilibrium granular fluid. The
 inelastic collisions make the direction of time obvious.
-<WRAP box 310px left>{{:coh_eps.png?300}}</WRAP>
+<WRAP box 310px left>{{:coh_eps.png?300}} The coherent scattering function $\phi(q,t)$ as a function of time for wave number $qd = 4.2$, coefficient of restitution $\varepsilon=0.7$ and several packing fractions $\varphi$ close to the glass transition.</WRAP>
 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