From the conserved Kuramoto-Sivashinsky equation to a coalescing particles model |
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Authors: | Paolo Politi Daniel ben-Avraham |
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Affiliation: | a Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy b Physics Department, Clarkson University, Potsdam, NY 13699-5820, United States |
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Abstract: | The conserved Kuramoto-Sivashinsky (CKS) equation, , has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show that this equation can be mapped into the motion of a system of particles with attractive interactions, decaying as the inverse of their distance. Particles represent vanishing regions of diverging curvature, joined by arcs of a single parabola, and coalesce upon encounter. The coalescing particles model is easier to simulate than the original CKS equation. The growing interparticle distance ? represents coarsening of the system, and we are able to establish firmly the scaling . We obtain its probability distribution function, g(?), numerically, and study it analytically within the hypothesis of uncorrelated intervals, finding an overestimate at large distances. Finally, we introduce a method based on coalescence waves which might be useful to gain better analytical insights into the model. |
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Keywords: | 02.50.Ey 05.45.-a 05.70.Ln 81.10.Aj |
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