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Theoretical continuous equation derived from the microscopic dynamics for growing interfaces in quenched media
1Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina.
Summary
We derived a continuous equation for the Tang and Leschhorn model, revealing a nonlinear term and multiplicative noise. Numerical results match the directed percolation depinning model
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Mathematical Modeling
Background:
- The Tang and Leschhorn model describes interface growth.
- Existing models often lack analytical continuous equations derived from microscopic rules.
- Understanding the dynamics of disordered systems is crucial.
Purpose of the Study:
- To derive an analytical continuous equation for the Tang and Leschhorn model.
- To investigate the emergence of nonlinear terms from microscopic dynamics.
- To compare the derived equation with existing models like the Kardar-Parisi-Zhang equation.
Main Methods:
- A regularization procedure was applied to the microscopic rules of the Tang and Leschhorn model.
- An analytical continuous equation was derived.
- Numerical integration of the derived equation was performed.
Main Results:
- A continuous equation was successfully derived from the Tang and Leschhorn model's microscopic rules.
- A nonlinear term, (nablah)(2), naturally emerged from the microscopic dynamics.
- The derived equation incorporates multiplicative quenched and thermal noise, differing from the standard QKPZ equation.
- Numerical simulations reproduced the scaling exponents of the directed percolation depinning model.
Conclusions:
- The derived analytical equation provides a continuous description of the Tang and Leschhorn model.
- The study highlights the natural emergence of nonlinearities and specific noise types from microscopic rules.
- The findings validate the derived equation by reproducing known scaling exponents in related physical systems.
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