Dynamical self-affinity of damage spreading in surface growth models

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Surface growth models are crucial for understanding phenomena from thin-film deposition to biological pattern formation.
• Dynamical anisotropic scaling properties describe how surfaces evolve over time and space, often exhibiting complex behaviors.
• Existing methods for analyzing these properties can be computationally intensive or limited in scope.

Purpose of the Study:

• To re-examine the dynamical anisotropic scaling properties of surface growth models.
• To introduce and utilize the concept of damage spreading for analyzing surface growth.
• To establish a new method for determining critical properties and dynamical self-affinity in surface growth.

Main Methods:

• Introduction of vertical damage spreading distance (d⊥) and lateral damage spreading distance (d∥).
• Development of scaling Ansatzes for d⊥(d∥,t), D∥ ≡ , and D⊥ ≡ .
• Simulation of various surface growth models with substrate dimension d=1 to test the proposed scaling relations.
• Analysis of the probability distribution P(d∥,t) for survived damages.

Main Results:

• The study successfully introduced novel damage spreading metrics (d⊥ and d∥) for surface growth analysis.
• Proposed scaling relations for damage spreading distances and their averages were formulated.
• Simulations confirmed the validity of the suggested scaling relations for d=1 substrate dimension.
• The probability distribution of survived damages was found to exhibit critical properties.

Conclusions:

• Damage spreading provides a powerful and effective tool for investigating the critical properties of surface growth models.
• Dynamical self-affinity in surface growth can be reliably determined by analyzing damage spreading phenomena.
• This approach offers a complementary and potentially more efficient method for characterizing complex surface dynamics.