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Two continuous models for the dynamics of sandpile surfaces
1Department of Solar Energy and Environmental Physics, Blaustein Institute for Desert Research, Ben Gurion University of the Negev, Sede Boqer Campus, 84990 Israel. leonid@bgumail.bgu.ac.il
Summary
This study simplifies pile surface dynamics using a modified Bouchaud-Cates-Ravi Prakash-Edwards model. In the long-scale limit, it converges to a quasistationary pile growth model described by an evolutionary variational inequality.
Area of Science:
- Physics
- Materials Science
- Mathematical Modeling
Background:
- The Bouchaud-Cates-Ravi Prakash-Edwards model describes complex granular material dynamics.
- Understanding pile surface evolution is crucial for various applications.
Purpose of the Study:
- To analyze a modified Bouchaud-Cates-Ravi Prakash-Edwards model for pile surface dynamics.
- To investigate the long-scale limit behavior of this modified model.
Main Methods:
- Modification of the Bouchaud-Cates-Ravi Prakash-Edwards model.
- Analysis of the model in the long-scale limit.
Main Results:
- The modified model converges to a quasistationary state.
- The long-scale limit is characterized by an evolutionary variational inequality.
Conclusions:
- The study provides a simplified, yet accurate, model for quasistationary pile growth.
- This work offers a new mathematical framework for understanding granular pile dynamics.