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Ballistic deposition with memory: a new universality class of surface growth with a new scaling law

Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its neighbors. By studying the statistics of surfaces in this model, we obtain three independent critical exponents: the growth exponent $β=5/4$, the roughening exponent $α= 2$, and the new (size) exponent $γ= 1/2$. The model requires a modification to the Family-Vicsek scaling, resulting in the dynamical exponent $z = \frac{α+γ}β = 2$. This modified scaling collapses the surface width vs time curves for various lattice sizes. This is a previously unobserved universality class of surface growth that could describe surface properties of a wide range of natural systems.