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Structural Evolution of Granular Systems: Theory
Soft Condensed Matter · Submitted 13 Apr 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that all the steady states are stable and that they satisfy detailed balance-like condition when the CO$\,\leq 6$.
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A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy detailed balance-like condition when the CO$\,\leq 6$. Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. | contribution 1.00 | 0.94 | 0.07 | asserted 1.00 |
| s1 | Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. | method 0.85 | 0.95 | 0.06 | asserted 1.00 |
| s2 | We find that all the steady states are stable and that they satisfy detailed balance-like condition when the CO$\,\leq 6$. | result 1.00 | 0.95 | 0.43 | asserted 1.00 |
| s3 | Illustrative numerical solutions of the evolution are shown. | contribution 0.41 | 0.91 | 0.03 | asserted 0.98 |
| s4 | Our theoretical results are validated against an extensive simulation of a sheared system. | method 0.46 | 0.93 | 0.11 | asserted 1.00 |
| s5 | The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems. | future work 0.89 | 0.40 | 0.17 | asserted 0.66 |
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A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy detailed balance-like condition when the CO$\,\leq 6$. Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems.
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