تقرير
Continuum descriptions for the dynamics in discrete lattices: Derivation and justification
| العنوان: | Continuum descriptions for the dynamics in discrete lattices: Derivation and justification |
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| المؤلفون: | Giannoulis, Johannes, Herrmann, Michael, Mielke, Alexander |
| سنة النشر: | 2006 |
| المجموعة: | Weierstrass Institute for Applied Analysis and Stochastics publication server |
| مصطلحات موضوعية: | article, ddc:510, 34C20, 34E13, 37K60, 37K05, 70F45, 70K70, Discrete lattice systems -- modulation equations -- Hamiltonian structure -- multiscale ansatz -- dispersive wave propagation |
| الوصف: | The passage from microscopic systems to macroscopic ones is studied by starting from spatially discrete lattice systems and deriving several continuum limits. The lattice system is an infinite-dimensional Hamiltonian system displaying a variety of different dynamical behavior. Depending on the initial conditions one sees quite different behavior like macroscopic elastic deformations associated with acoustic waves or like propagation of optical pulses. We show how on a formal level different macroscopic systems can be derived such as the Korteweg-de Vries equation, the nonlinear Schroedinger equation, Whitham's modulation equation, the three-wave interaction model, or the energy transport equation using the Wigner measure. We also address the question how the microscopic Hamiltonian and the Lagrangian structures transfer to similar structures on the macroscopic level. Finally we discuss rigorous analytical convergence results of the microscopic system to the macroscopic one by either weak-convergence methods or by quantitative error bounds. |
| نوع الوثيقة: | report |
| اللغة: | English |
| العلاقة: | https://doi.org/10.20347/WIAS.PREPRINT.1126Test; https://archive.wias-berlin.de/receive/wias_mods_00001460Test; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00001378/wias_preprints_1126.pdfTest; http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2006&number=1126Test |
| DOI: | 10.20347/WIAS.PREPRINT.1126 |
| الإتاحة: | https://doi.org/10.20347/WIAS.PREPRINT.1126Test https://archive.wias-berlin.de/receive/wias_mods_00001460Test https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00001378/wias_preprints_1126.pdfTest http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2006&number=1126Test |
| حقوق: | all rights reserved ; info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.42E4083E |
| قاعدة البيانات: | BASE |
| DOI: | 10.20347/WIAS.PREPRINT.1126 |
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