Dispersive Shock Waves in Lattices: A Dimension Reduction Approach Article Swipe
Christopher Chong
,
Michael Herrmann
,
P. G. Kevrekidis
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2206.06413
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2206.06413
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is Whitham's modulation theory. While this framework has been successfully employed in many space-continuous settings to describe DSWs, the Whitham modulation equations are virtually intractable in most spatially discrete systems. In this article, we illustrate the relevance of the reduction of the DSW dynamics to a planar ODE in a broad class of lattice examples. Solutions of this low-dimensional ODE accurately describe the orbits of the DSW in self-similar coordinates and the local averages in a manner consistent with the modulation equations. We use data-driven and quasi-continuum approaches within the context of a discrete system of conservation laws to demonstrate how the underlying low dimensional structure of DSWs can be identified and analyzed. The connection of these results to Whitham modulation theory is also discussed.
Related Topics
Concepts
Ode
Modulation (music)
Nonlinear system
Planar
Dimensional reduction
Reduction (mathematics)
Dimension (graph theory)
Shock wave
Conservation law
Lattice (music)
Context (archaeology)
Mathematical analysis
Mathematics
Physics
Classical mechanics
Computer science
Mechanics
Geometry
Mathematical physics
Pure mathematics
Quantum mechanics
Computer graphics (images)
Acoustics
Biology
Paleontology
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2206.06413
- https://arxiv.org/pdf/2206.06413
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4310658457
All OpenAlex metadata
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- DOI
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https://doi.org/10.48550/arxiv.2206.06413Digital Object Identifier
- Title
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Dispersive Shock Waves in Lattices: A Dimension Reduction ApproachWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-06-13Full publication date if available
- Authors
-
Christopher Chong, Michael Herrmann, P. G. KevrekidisList of authors in order
- Landing page
-
https://arxiv.org/abs/2206.06413Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2206.06413Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2206.06413Direct OA link when available
- Concepts
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Ode, Modulation (music), Nonlinear system, Planar, Dimensional reduction, Reduction (mathematics), Dimension (graph theory), Shock wave, Conservation law, Lattice (music), Context (archaeology), Mathematical analysis, Mathematics, Physics, Classical mechanics, Computer science, Mechanics, Geometry, Mathematical physics, Pure mathematics, Quantum mechanics, Computer graphics (images), Acoustics, Biology, PaleontologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.the | 31, 54, 71, 74, 77, 98, 101, 107, 115, 125, 137 |
| abstract_inverted_index.use | 119 |
| abstract_inverted_index.via | 10 |
| abstract_inverted_index.DSWs | 35, 143 |
| abstract_inverted_index.also | 159 |
| abstract_inverted_index.been | 44 |
| abstract_inverted_index.form | 15 |
| abstract_inverted_index.laws | 133 |
| abstract_inverted_index.many | 48 |
| abstract_inverted_index.most | 62 |
| abstract_inverted_index.this | 41, 67, 93 |
| abstract_inverted_index.tool | 29 |
| abstract_inverted_index.wave | 13 |
| abstract_inverted_index.with | 114 |
| abstract_inverted_index.DSWs, | 53 |
| abstract_inverted_index.While | 40 |
| abstract_inverted_index.broad | 86 |
| abstract_inverted_index.class | 87 |
| abstract_inverted_index.local | 108 |
| abstract_inverted_index.media | 20 |
| abstract_inverted_index.shock | 1 |
| abstract_inverted_index.study | 33 |
| abstract_inverted_index.these | 152 |
| abstract_inverted_index.waves | 2 |
| abstract_inverted_index.which | 4 |
| abstract_inverted_index.abrupt | 23 |
| abstract_inverted_index.manner | 112 |
| abstract_inverted_index.orbits | 99 |
| abstract_inverted_index.planar | 82 |
| abstract_inverted_index.state. | 26 |
| abstract_inverted_index.states | 6 |
| abstract_inverted_index.system | 130 |
| abstract_inverted_index.theory | 157 |
| abstract_inverted_index.train, | 14 |
| abstract_inverted_index.within | 124 |
| abstract_inverted_index.(DSWs), | 3 |
| abstract_inverted_index.Whitham | 55, 155 |
| abstract_inverted_index.changes | 24 |
| abstract_inverted_index.connect | 5 |
| abstract_inverted_index.context | 126 |
| abstract_inverted_index.lattice | 89 |
| abstract_inverted_index.primary | 28 |
| abstract_inverted_index.results | 153 |
| abstract_inverted_index.theory. | 39 |
| abstract_inverted_index.article, | 68 |
| abstract_inverted_index.averages | 109 |
| abstract_inverted_index.describe | 52, 97 |
| abstract_inverted_index.discrete | 64, 129 |
| abstract_inverted_index.dynamics | 79 |
| abstract_inverted_index.employed | 46 |
| abstract_inverted_index.settings | 50 |
| abstract_inverted_index.systems. | 65 |
| abstract_inverted_index.Solutions | 91 |
| abstract_inverted_index.Whitham's | 37 |
| abstract_inverted_index.amplitude | 9 |
| abstract_inverted_index.analyzed. | 148 |
| abstract_inverted_index.different | 8 |
| abstract_inverted_index.equations | 57 |
| abstract_inverted_index.examples. | 90 |
| abstract_inverted_index.framework | 42 |
| abstract_inverted_index.modulated | 12 |
| abstract_inverted_index.nonlinear | 18 |
| abstract_inverted_index.reduction | 75 |
| abstract_inverted_index.relevance | 72 |
| abstract_inverted_index.spatially | 63 |
| abstract_inverted_index.structure | 141 |
| abstract_inverted_index.subjected | 21 |
| abstract_inverted_index.virtually | 59 |
| abstract_inverted_index.Dispersive | 0 |
| abstract_inverted_index.accurately | 96 |
| abstract_inverted_index.analytical | 32 |
| abstract_inverted_index.approaches | 123 |
| abstract_inverted_index.connection | 150 |
| abstract_inverted_index.consistent | 113 |
| abstract_inverted_index.discussed. | 160 |
| abstract_inverted_index.dispersive | 19 |
| abstract_inverted_index.equations. | 117 |
| abstract_inverted_index.identified | 146 |
| abstract_inverted_index.illustrate | 70 |
| abstract_inverted_index.modulation | 38, 56, 116, 156 |
| abstract_inverted_index.underlying | 138 |
| abstract_inverted_index.coordinates | 105 |
| abstract_inverted_index.data-driven | 120 |
| abstract_inverted_index.demonstrate | 135 |
| abstract_inverted_index.dimensional | 140 |
| abstract_inverted_index.generically | 16 |
| abstract_inverted_index.intractable | 60 |
| abstract_inverted_index.conservation | 132 |
| abstract_inverted_index.self-similar | 104 |
| abstract_inverted_index.successfully | 45 |
| abstract_inverted_index.low-dimensional | 94 |
| abstract_inverted_index.quasi-continuum | 122 |
| abstract_inverted_index.space-continuous | 49 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/15 |
| sustainable_development_goals[0].score | 0.6600000262260437 |
| sustainable_development_goals[0].display_name | Life in Land |
| citation_normalized_percentile |