res:granular_glass_transition

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
res:granular_glass_transition [2013/04/29 14:00] – granular_glass_transition renamed to res:granular_glass_transition rootres:granular_glass_transition [2019/10/05 19:01] (current) – till
Line 5: Line 5:
   * Kranz, W. T., M. Sperl and A. Zippelius, [[http://dx.doi.org/10.1103/PhysRevE.87.022207|PRE]] **87**, 022207 (2013)   * Kranz, W. T., M. Sperl and A. Zippelius, [[http://dx.doi.org/10.1103/PhysRevE.87.022207|PRE]] **87**, 022207 (2013)
  
-Studying an air-fluidized,quasi two dimensional assembly of steel balls, Abate & Durian +Studying an air-fluidized,quasi two dimensional assembly of steel balls, Abate & Durian ((Abate & Durian, [[http://dx.doi.org/10.1103/PhysRevE.74.031308|PRE]] **74**, 031308 (2006) ))
 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 ((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  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)) In our work we found that MCT can be generalized to the far from
 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
Line 26: Line 26:
 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,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. 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>{{: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  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
  • Last modified: 2013/04/29 14:00
  • by root