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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. Inspired by these biological systems and 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 such as dynamical heterogeneities have been shown 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 co-penetrate one an other. The system is geometrically frustrated and exhibit fascinating glassy properties such as a non-thermal glass transition at 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.
WORK IN PROGRESS
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.
We plot the mean squared displacement (MSD) of particles in the system as a function of time for different rates of rotation. At low densities the system exhibits short time ballistic behavior and long time diffusive behavior, with the crossover time scaling as the inverse of the rate of rotation. This is the expected result for a collection of active particles.
When density is increased the motion of particles is governed more by the formation of vacancies and less by the active nature of particles. As a result the observed MSD is more similar to diffusive then ballistic.
Generate a phase diagram of the system as a function of activity, rotation, and density.
Give a more quantitative analysis to the phenomena observed in our system.
The motion of a charged tracer particle moving through a system of diffusing particles had been studied widely both theoretically and experimentally. Here we study the motion of an active particle tracer through a thermal geometrically frustrated glassy system. This simple model allows us to better understand the motion of the particle analytically and gain deeper insight on the diffusivity of active particles ...
WORK IN PROGRESS
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 co-penetrate one an other. The system is geometrically frustrated and exhibit fascinating glassy properties such as a non-thermal glass transition at which dynamics critically slow down. Cells, in some instances  , have been known to behave in a glass like manner. To further understand the motion of active agents within a glassy regime we simulate a single active particle within a bath of thermal N3 particles and develope analytical expression for the diffusivity of the particle. The active tracer may move thermally, but moreover has a preferred direction to which motion is biased. It may attempt to move towards that preferred direction (active move) or may attempt to change its preferred direction (rotation move).
We start from a simple case of a non-rotating active tracer, set with an initial condition where its preferred direction is set towards the x+ direction.
The active particle attempts to move at a thermal rate RT, and an active rate RA. For the move to be successful, the five sites in front of the particle must be unoccupied (see illustration). From these simple considerations we can write a simple probabilistic equation for the position of the particle as a function of time. By averaging over it, taking the third neighbors exclusion principle and deriving it with respect to time we obtain the expression for the drift velocity of the particle.
The analytical prediction is in excellent agreement with the numerical calculation.
Developing an analytical expression that depends only on the equilibrium properties of the system.
Expand this result for the rotating case (Levy walk).