Physical Review Letters · 1986 · 5.4K citations · 20 references
Natural SciencesMathematicsDynamical SystemsInterface ScienceStochastic ProcessesInterface ModelingInterface PhysicsPolymer InterfacesPolymer PhysicsStochastic Differential EquationsDynamic ScalingInterface Evolution EquationsRelaxation TimesRenormalization GroupRenormalization Group TheoryScaling Laws In Polymer Physics
The authors propose a model for the evolution of a growing interface and predict its behavior in higher dimensions. The model is analyzed deterministically and stochastically, using dynamic renormalization‑group methods and mappings to Burgers’s equation and a random directed‑polymer problem. Exact solutions reveal nontrivial relaxation and dynamic scaling, with the one‑dimensional scaling form agreeing with numerical simulations.
A model is proposed for the evolution of the profile of a growing interface. The deterministic growth is solved exactly, and exhibits nontrivial relaxation patterns. The stochastic version is studied by dynamic renormalization-group techniques and by mappings to Burgers's equation and to a random directed-polymer problem. The exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations. Predictions are made for more dimensions.
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Instabilities and pattern formation in crystal growth
J. S. Langer · Reviews of Modern Physics · 1980 · 2.6K citations
Current Topics in Materials Science
E. Kaldis, E. Sirtl · Journal of The Electrochemical Society · 1980 · 2.3K citations
Natural Sciences, Materials Engineering, Materials Science +14