Long-Time behavior for crystal dislocation dynamics

S. Patrizi, E. Valdinoci

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the "smoothing effect" on the dislocation function occurring slightly after a "particle collision" (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the algebraic properties of the orientations of the initial transition layers). The results are endowed with explicit and quantitative estimates and, as a byproduct, we show that the ODE systems of particles that govern the evolution of the transition layers does not admit stationary solutions (i.e. roughly speaking, transition layers always move).
Original languageEnglish
Pages (from-to)2185-2228
Number of pages44
JournalMATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume27
Issue number12
DOIs
Publication statusPublished - 2017
Externally publishedYes

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Dislocation Dynamics
Transition Layer
Long-time Behavior
Dislocations (crystals)
Crystal
Dislocation
Atoms
Smoothing Effect
Nonlocal Equations
Constant function
Flow Time
Byproducts
Stationary Solutions
Trap
Superposition
Collision
Crystals
Estimate

Cite this

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Long-Time behavior for crystal dislocation dynamics. / Patrizi, S.; Valdinoci, E.

In: MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, Vol. 27, No. 12, 2017, p. 2185-2228.

Research output: Contribution to journalArticle

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