Physics & AstronomyUniversity of PennsylvaniaPhysics of Complex System - PDF document

Physics & AstronomyUniversity of PennsylvaniaPhysics of Complex SystemsWeizmann Institute of Science Jamming Mechanisms & Density Dependence Liu, Nagel (1998)O’Hern, Silbert, Liu, Nagel (2002,2003) TemperatureDensity JJamming TransitionDurian (1995) Density, Scaling + Diverging relaxation time (Bubbles / Soft spheres Separation, rPotential, u(r) Shear + What are the mechanisms for jamming ?Is there universality in jamming along different paths ?Is non-equilibrium “shaking” equivalent to equilibrium “heating” ?How Do Systems Jam ? TemperatureDensity J Use kinetically-constrained models… Lattice gas (Ising) , No interactions All configurations equally probableDefine transitions rates that obey detailed-balance, but induce slow relaxation to equilibrium non-ergodic / jammed Jäckle-Krönig(1994) square lattice, on-site exclusion (n=0,1), no interactions (H=0), limited transitions:Toninelli, Biroli, Fisher (2007)particle can move to neighboring site if (NE or SW) and (NW or SE) empty before and after the move Non-ergodicity transition at 0Mixed naturediscontinuitydiverging time Solvable diverging relaxation time discontinuous -map to directed percolation-clusters of blocked particles Add Temperature & Driving to Spiral ModelHeatingDriving kinetic constrain = energy barrierprobability to overcomeoccasional strong kicksprobability to move along drive direction (irrespective of kinetic constraint) Both ergodic at any density TF J Jammed phase reduces to line Experimental definition of glass (long relaxation time) defines jamming surface Relaxation Times Diverge Along Different Paths to Jamming TF J Path 1 (T=0,F=0) 1 TF J 12 Relaxation Times Diverge Along Different Paths to Jamming scaling Path 2 ( Path 3 ( Relaxation Times Diverge Along Different Paths to Jamming 3 TF J Temperature Relaxation Times Diverge Along Different Paths to JammingDoes jamming occur due to the same mechanism along different paths ?Can we see that ? No static structure Look at dynamic heterogeneities… TF J 123 Dynamic Heterogeneities Motion of particle requires rearrangement of many othersDynamics are spatially correlated or heterogeneousCompare several subsystems / copies of the system: Look at variance between them: t -Numerical Simulations of Model Glasses -Granular Experiments -Kinetically Constrained Models Dauchot, Marty, Biroli(2005)Keys, Abate, Glotzer, Durian (2007)Glotzer(2000)Franz, Mulet, Parisi(2002)-Glass & Colloid Experiments Berthieret al. (2005) =Dynamic Heterogeneities 1 Path 1 (T=0,F=0) TF J TF J 123 T=0 , F=0=0.8 , T=0=0.8 , F=0 Dynamic Heterogeneities Depend on Path to Jammingcompare jamming mechanisms… TF J Different Jamming Mechanisms Along Different Paths Density (Path 1) Temperature (Path 2) Driving (Path 3) Indirect(environment changes)Collective (percolating clusters of blocked particles)Direct (“tunneling”) heterogeneous dynamicshomogeneous dynamicsweak heterogeneity Dynamic heterogeneities largest near point J (hardly seen when jamming at higher densities)Spiral model has mixed (1order) jamming transition at TF J Can we understand scaling behavior around jamming transition ?Can driving be described in terms of effective temperature ? Jamming Mechanisms & Density Dependencein Kinetically-Constrained ModelsYair Shokef & Andrea LiuWe added temperature & driving, explored jamming along