Patterns and waves in theory, experiment, and application

Instantanés de recherche mathématique à Oberwolfach

Patterns and waves in theory, experiment, and application

In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social processes. We begin by focussing on two types of patterns that do not change in time: space-filling patterns and localized patterns. We then discuss two types of waves that evolve predictably as time goes on: spreading waves and rotating waves. All our examples are motivated with real-world applications and we highlight some of the main lines of research that mathematicians pursue to better understand them.

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Sujet mathématique

Analyse
Calcul numérique et calcul scientifique

Auteur(s)

Jason J. Bramburger

Licence

DOI

10.14760/SNAP-2023-001-EN

Télécharger PDF

snapshot-2023-001.pdf

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snapshots: overview

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The periodic tables of algebraic geometry
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Closed geodesics on surfaces
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A tale of three curves
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What is Pattern?
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Representations and degenerations
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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Invitation to quiver representation and Catalan combinatorics
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Rotating needles, vibrating strings, and Fourier summation
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Quantum symmetry
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A few shades of interpolation
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Molecular quantum dynamics
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Closed geodesics on surfaces and Riemannian manifolds
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Aperiodic Order and Spectral Properties
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News on quadratic polynomials
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Profinite groups
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The adaptive finite element method
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The Willmore Conjecture
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Prime Tuples in Function Fields
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Polyhedra and commensurability
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Sujet mathématique

Algèbre et théorie des nombres
Analyse
Pédagogie et éducation
Mathématiques discrètes et fondements des mathématiques
Géométrie et Topologie
Calcul numérique et calcul scientifique
Théorie des probabilités et statistique

Liens avec d'autres domaines

Chimie et sciences de la terre
Informatique
Ingénierie et technologie
Finances
Humanités et sciences sociales
Sciences de la vie
Physique
Pensées mathématiques

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