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 modifying 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>β</a:mi><a:mo>=</a:mo><a:mn>5</a:mn><a:mo>/</a:mo><a:mn>4</a:mn></a:mrow></a:math>, the roughening exponent <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>α</b:mi><b:mo>=</b:mo><b:mn>2</b:mn></b:mrow></b:math>, and the new (size) exponent <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>γ</c:mi><c:mo>=</c:mo><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math>. The model requires modifying the Family-Vicsek scaling, resulting in the dynamical exponent <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>z</d:mi><d:mo>=</d:mo><d:mfrac><d:mrow><d:mi>α</d:mi><d:mo>+</d:mo><d:mi>γ</d:mi></d:mrow><d:mi>β</d:mi></d:mfrac><d:mo>=</d:mo><d:mn>2</d:mn></d:mrow></d:math>. This modified scaling collapses the surface width vs time curves for various lattice sizes. This previously unobserved universality class of surface growth could describe the surface properties of a wide range of natural systems.