A two-dimensional bidisperse granular fluid is shown to exhibit pronounced
long-ranged dynamical heterogeneities as dynamical arrest is approached. Here
we focus on the most direct approach to study these heterogeneities: we
identify clusters of slow particles and determine their size, Ncβ, and their
radius of gyration, RGβ. We show that NcββRGdfββ, providing
direct evidence that the most immobile particles arrange in fractal objects
with a fractal dimension, dfβ, that is observed to increase with packing
fraction Ο. The cluster size distribution obeys scaling, approaching an
algebraic decay in the limit of structural arrest, i.e., ΟβΟcβ.
Alternatively, dynamical heterogeneities are analyzed via the four-point
structure factor S4β(q,t) and the dynamical susceptibility Ο4β(t).
S4β(q,t) is shown to obey scaling in the full range of packing fractions,
0.6β€Οβ€0.805, and to become increasingly long-ranged as
ΟβΟcβ. Finite size scaling of Ο4β(t) provides a consistency
check for the previously analyzed divergences of Ο4β(t)β(ΟβΟcβ)βΞ³Οβ and the correlation length ΞΎβ(ΟβΟcβ)βΞ³ΞΎβ. We check the robustness of our results with
respect to our definition of mobility. The divergences and the scaling for
ΟβΟcβ suggest a non-equilibrium glass transition which seems
qualitatively independent of the coefficient of restitution.Comment: 14 pages, 25 figure