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Glassy behavior is observed not only in 'chemical' glasses, but also in granular materials and colloidal suspensions. These systems are characterized by having a glass transition temperature. That is, a temperature in which a mixed order out of equilibrium phase transition occurs and the relaxation times of the system diverge.
This critical slowing down in dynamics is one among many reasons as to why studying glassy behavior is challenging both experimentally and theoretically. Kinetically constrained models have been successful in this as they are simple enough to easily simulate large systems and are sometimes analytically solvable.
We have studied a three dimensional  extension of the 2D Spiral Model . The 2D model undergoes jamming at a critical density in which a fraction of the particles in the system cannot move anymore and form 1D clusters of frozen sites. The particles that can still move become rattlers - they are confined to some local area of the system and cannot diffuse far away.
In 3D however, that is not the case; a fraction of the particles in the system become frozen and creates a 1D frozen cluster, however mobile particles can diffuse over long distances. The reason is geometric - in 2D one-dimensional frozen clusters of particles act as effective walls, and particles are unable to cross these walls and travel to the other side. In 3D particles use the third dimension to travel around these clusters. We investigated the existence of a second critical density, one in which frozen clusters become 2D and particles become confined in local cages in the system.
Using a fast and efficient culling algorithm, we bypass running the dynamics of the system and find the underlying structural property of the system determining the diffusivity of particles.
We indeed find a second critical density. Its critical exponents value agree with those of random percolation.
In 2D a system undergoing jamming will cause particles to be confined in local cages. In 3D however that does not have to be the case - frozen clusters of particles appear at a density in which particles may still diffuse across the system. Only at a higher density particles become caged. The reason is geometrical. We use a fast algorithm bypassing the need to run the dynamics of the system to uncover the underlying structure of the system ...
I am an engineering grad student in Tel Aviv University, currently working on my PhD under the supervision of Yair Shokef.
My research focus is on glassy dynamics, jamming, active frustrated materials and active living matter, mostly using computational tools to tackle these subjects.
I have a multidisciplinary background; undergrad in Chemistry, Master thesis on jamming and caging in glassy systems, and my current work is on the subject of active frustrated materials.
Cells have been shown to share similarities with glasses. Amorphous structure and dynamical heterogeneities are among several such examples. The N3 model is known to have some glassy properties such as critical slowing down. Relying and both this biological motivation and statistical physics motivation we propose an active N3 model which shows a rich variety of dynamics, most notably aggregation of particles due to activity ...
Cells, in some instances  , have been known to behave in a glass like manner. Some cell tissues do not crystallize and interesting dynamical properties show on experiments. The N3 lattice model  is defined on a square lattice such that particles exclude one an other up to 3rd order nearest neighbors, meaning that the closest particles can get to one an other is 4th order neighbors. These rules virtually results in 'plus' shaped particles which cannot penetrate on an d other. These particles are geometrically frustrated and has shown interesting glassy properties such as a glass transition at some critical density in which dynamics critically slow down.
We propose an active variant of the N3 model, in which particles have a preferred direction to which they are more likely to move. Particles can also attempt to rotate, thus, changing their preferred direction. However, a particle may not rotate if it has even one closest neighbor (4th order, see figure to the right).
We simulate the model and find that adding activity results in aggregates; particles band together to form compact structures. The more active the system is, the less free particles are found in the system. This behavior seems consistent through a wide range of densities and amounts of activity. As more particles band together, more moves become forbidden, thus resulting in slower dynamics. To avoid wasting computational resources we run a rejection free simulation in which only allowed moves are considered. We calculate the actual MC time out of the number of rejected moves.
The systems starts from an initial random configuration. Every time step a move is selected at random and if that move is possible then it is performed. The entire dynamics is governed by the density and the two ratios between the rates of motion: the ratio between the active rate and the thermal rate, and the ratio between the rotational rate and thermal rate.
Future work will include a more quantitative analysis of the different phases of the system, as well as an analysis of cluster distribution as a function of various parameters.
Also, we would like to attempt to analytically solve the problem of an active tracer particle in an inactive (thermal) system. In this case we will consider a thermal system with a single active particle. The environment's equilibrium properties will be taken from the regular N3 model while we will have only a single active particle.
WORK IN PROGRESS