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Updated: Jun 6, 2026
11:54
Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
Published on: June 25, 2018
Recent developments on the Kardar-Parisi-Zhang surface-growth equation.
Horacio S Wio1, Carlos Escudero, Jorge A Revelli
1Instituto de Física de Cantabria (UC and CSIC), Avda. de los Castros, s/n, 39005 Santander, Spain. wio@ifca.unican.es
Summary
This study introduces a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation, challenging established beliefs about non-equilibrium growth dynamics and scaling relations. It explores new approaches to understanding surface and interface growth processes.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- The Kardar-Parisi-Zhang (KPZ) equation is a standard model for surface and interface growth.
- Established beliefs include that non-equilibrium processes are non-variational and scaling relies on Galilean symmetry.
- Equivalence of planar and radial interface profiles is commonly assumed.
Purpose of the Study:
- Introduce a variational formulation for the KPZ equation.
- Challenge mainstream views on Galilean symmetry and fluctuation-dissipation theorems in scaling.
- Investigate KPZ equation on growing domains for radial growth.
Main Methods:
- Development of a variational formulation for the KPZ equation.
- Analysis of discretization consistency.
- Derivation of the KPZ equation on a growing domain.
Main Results:
- A novel variational approach to the KPZ equation is presented.
- The necessity of Galilean symmetry and 1D fluctuation-dissipation theorem for scaling is questioned.
- The KPZ equation is derived as an approximation for radial growth on a growing domain.
Conclusions:
- The study offers a new perspective on the theoretical underpinnings of the KPZ equation.
- It suggests that current assumptions about non-equilibrium growth and scaling may need re-evaluation.
- New insights into radial growth dynamics are provided.
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