  In certain supergravity backgrounds, D0 branes may polarize into higher
dimensional Dp branes. We study this phenomenon in some generality from the
perspective of a local inertial observer and explore polarization effects
resulting from tidal-like forces. We find D2 brane droplets made of D0 branes
at an extremum of the Born-Infeld action even in scenarios where the RR fields
may be zero. These solutions lead us to a local formulation of the UV-IR
correspondence. A holographic Planck scale bound on the number of D0 branes
plays an important role in the analysis. We focus on the impact of higher order
moments of background fields and work out extensions of the non-commutative
algebra beyond the Lie and Heisenberg structures. In this context, it appears
that q-deformed algebras come into play.
