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Spirals and Vortices

Part of the The Frontiers Collection Book Series

Editors: Tsuji, Kinko; Müller, Stefan C.

DOI: 10.1007/978-3-030-05798-5

ISBN: 978-3-030-05797-8

Publisher: Springer International Publishing - Springer Journals

Apr 5, 2019

1 - 10 of 17 Chapters

LitStream

Cultural History

Tsuji, Kinko; Müller, Stefan C.

Pages: 3 –29

[We introduce various spirals which were made during the time from 11,000 BC (Neolithic Period) to 1500 AD (early Renaissance)Renaissance. Concentric circlesConcentric circle were created much earlier (40,000–20,000 BC). For the period between 5000 and 2000 BC spirals in...
LitStream

Appearance in Nature

Müller, Stefan C.; Tsuji, Kinko

Pages: 31 –66

[Many spirals and vortices appear in nature both in the inanimate and the living world. As examples of the non-living nature some spirals and vortices of various sizes are selected: spiral galaxies, hurricanes and tornadoes, aerodynamic turbulence, crystal growth on surfaces and carbon nanotubes....
LitStream

The Arts and Beyond

Tsuji, Kinko; Müller, Stefan C.

Pages: 67 –87

[Spirals play a very favorite role as motives for modern European paintings. Here we assemble some examples for quiescent spirals (Klimt)Klimt/Gustav Klimt, spirals starting to move (IttenItten/Johannes Itten and Klee)Klee/Paul Klee and storming spirals (da Vinci, van GoghVan Gogh/Vincent van...
LitStream

Spirals, Their Types and Peculiarities

Polezhaev, Andrey

Pages: 91 –112

[In this chapter, we provide mathematical data concerning the description of spirals. Before starting with mathematical equations, Albrecht Dürer’sDürer/Albrecht Dürer pioneering works are briefly introduced. Subsequently, we discuss some properties of different spirals in a plane which make them...
LitStream

Acoustic Spirals: Analysis of Bach’s Prelude in C Major

Tsuji, Kinko

Pages: 113 –125

[Bach’s preludePrelude in C major of “The Well-Tempered ClavierWell-tempered clavier, Book I” is analyzed with a dynamical approach, by using phase portraitsPhaseportrait and their two and three-dimensional expressionsThree-Dimensional (3D)expression. Different from the traditional analysis based...
LitStream

Liesegang Rings, Spirals and Helices

Dietrich, Sabine

Pages: 129 –140

[The periodic precipitation process known as LiesegangLiesegang/R.E. Liesegang ring formation has been investigated during the past 120 years and is one of the most recognized spatial and temporal heterogeneous structures in physical chemistry. If a soluble electrolyte is placed in contact with a...
LitStream

Generation of Spirals in Excitable Media

Müller, Stefan C.

Pages: 141 –155

[The generation of dynamic spirals under conditions of excitability is presented. After a short description of some basic principles of nonlinear dynamicsNonlinear dynamics illustrated in the phase plane, wePhaseplane explain what excitable systemsExcitablesystem are, how excitation...
LitStream

Chemical Oscillations and Spiral Waves

Pfeiffer, Patricia

Pages: 157 –173

[Pattern formation is one of nature’s most fascinating phenomena. Starting with the evolution of life: cells and compartments start to differentiate such that they are able to undertake different tasks leading to life of complex organisms. Additionally, cells are able to release messenger...
LitStream

Shedding Light on Chaos - Controlling Surface Reactions

Rotermund, Harm H.

Pages: 175 –189

[Although heterogeneous surface reactionsSurface reaction have been studied for more than 200 years, only the introduction of several unique imaging techniques in the 1990s made it possible to visualize simple catalytic reactions occurring on the surface of platinumPlatinum/Pt(110) single...
LitStream

Spiral Waves of the Chemo-Attractant cAMP Organise Multicellular Development in the Social AmoebaeAmoebaeDictyostelium discoideumDictyostelium discoideum/Dictyostelium/Dictyostelids

Weijer, Cornelis J.

Pages: 193 –207

[Development of multicellular organisms requires precise spatial and temporal integration of key cellular behaviours such as cell division, cell differentiation and cell movement to form the complex tissues that make up the organism. These cell behaviours are controlled by highly dynamic...

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