Emergent Non-Singular Chromatin Dynamics: Environmental Regularization and Active Gel Hydrodynamics in Nuclear Mechanics

nside the eukaryotic cell nucleus, spatial genome orga-
nization spans multiple spatial and temporal scales, bal-
ancing structural stability with active enzymatic regula-
tion. Continuous hydrodynamics and active-gel field the-
ories serve as powerful tools for capturing these macro-
scale mechanics. However, standard continuum models
encounter critical short-range breakdowns: when active
molecular motors or boundary constraints are modeled
as localized point-like forces, the mathematical contin-
uum equations yield non-physical infinite stress concen-
trations.
To resolve these short-range anomalies without re-
sorting to artificial spatial cutoffs or non-local regular-
izations, we present a background-regularized field the-
ory of nuclear mechanics. By coupling the chromatin
compaction order parameter field Φ(r, t) to an ambi-
ent background energy density ρbg, our formulation na-
tively introduces an intrinsic physical screening length
rcore = pκΦ0/ρbg. This regularizes field growth at small
scales (r → 0), guarantees a square-integrable active
Cauchy stress tensor, and yields analytical domain wall
dynamics across interface boundaries.