Activity induced glass transition or active glass formers are one of the promising examples of non-equilibrium system and have drawn attention recently in the soft matter community due to their diverse features encompassing from biological systems to complex fluids. This active glass formers possess features that merge with both the dense active matter and the glass transition. For example, one of the features such as dynamical heterogeneity (DH) is still a central part of investigtion for understanding sluggishness exhibited by glassy system. Lot of research has been done in the context of passive glass formers, mostly focused on length scale and time scale analysis associated with DH, but the same is limited in the context of active glass formers. Recently, some observations are available also for active Brownian particle model (ABP) and active Ornstein-Uhlenbeck (AOUP) model glass formers only concerning the effect of activity towards the
glass transition. However, the exploration of various grwoing length scales, timescale associated with DH and the morphology analysis of DH are severely limited for Ornstein-Uhlenbeck model, precisely when it is athermal. The speciality about this athermal AOUP model is that it correctly describes the dynamics of
microswimmers where diffusion due to the thermal noise is negligible compared to that due to self-propulsion.
Here in this thesis, we use one such model, namely the athermal Ornstein-Uhlenbeck model (OU), to understand the following studies:
(i) A study on the growing length scales from the ‘four-point structure factor’ and one of the static length scales, namely ‘hexatic length scale’ for a quasi-two-dimensional (2D) system. The relationship between these two length scales concerning the propulsion time and effective temperatures. The concept of chemical potential, its relationship with the size of growing length scales, and its impact on the formation of clusters of different sizes. Observation for the variation of chemical potential for the persistent time solely when the former is scaled with the effective temperatures.
(ii) A study on the concept and formation of cluster substructures for an athermal active glass former by a density-based spatial clustering algorithm with the application of noise. We use this to observe the morphology of cooperatively rearranging regions (CRRs) formed by fast and slow-moving particles, often called subsets. The need for the radius of gyration to understand the substructures, notion of fractal dimensions, and their relationship to get direct and complete knowledge about the morphology of CRRs. An observation on the change of fractal dimensions leads to the understanding of relaxation dynamics of CRRs via the concept of the roughness of fractal objects and surface tension of such objects.

References:[1] Connecting relaxation time to a dynamical length scale in athermal active glass
formers; Dipanwita Ghoshal and Ashwin Joy, Phys. Rev. E 102, 062605 (2020);
[2] http://arxiv.org/abs/2112.08039