Speaker: Dr. Debjyoti Majumdar
Department of Solar Energy and Environmental Physics,
Jacob Blaustein Institutes for Desert Research
Ben-Gurion University, Israel
Title: "Non-equilibrium dynamics of fractal networks with
active forces."
Day and Date: Wednesday, February 18, 2026
Time: 11.00 am.
Venue: Room no. 350, Chemistry Department
Second floor, Annex
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Hosted by Prof. Rajarshi Chakrabarti
Abstract We investigate, using Langevin dynamics simulations, the Rouse-type
dynamics of active fractal bead-spring networks constructed using the
critical bond percolation cluster of the square lattice. Two types of
active stochastic
forces, modelled as random telegraph process with finite decorrelation
time, are considered: force monopoles, acting on individual nodes in random
directions, and force dipoles, where extensile or contractile forces act
between pairs of connected nodes. For force monopoles, a dynamical steady
state is reached where the network is dynamically swollen and the mean
square displacement (MSD) shows sub-diffusive behavior determined solely
by the spectral dimension of the underlying fractal network, in accord
with a previously proposed general analytic theory [Singh and Granek,
Chaos, 34(113107), 2024]. In contrast, dipolar forces require diverging
times to reach the steady state and lead to network shrinkage. We find a
continuous crossover to a collapsed state for the non-diluted square
lattice, resulting from its marginal stability. The MSD is found to
saturate at the same temporal regime, followed by ballistic-like and/or
diffusive behaviors. We further extend our study of dipolar forces to
diluted regimes above the “rigidity percolation”
threshold for triangular lattices [D. Majumdar et al., J.Chem. Phys.,
163(114902), 2025]. Here, weak dipolar forces do not shrink the network in
the steady state. Moreover, for the triangular lattice, an incipient
discontinuous collapse transition occurs above a critical force amplitude.
Importantly, we find that the inclusion of active force dipoles rigidify
the triangular network even below the regular rigidity percolation point,
which can be exactly identified by including the extra constraints from
the active dipole links in the Maxwell constraint counting method.
Finally, we will show how spatial correlation in these active dipoles
affect the dynamics of the active network.