Fifth order coupling coefficients

Here we list the coupling coefficients of the fifth order amplitude equations Eq. (6.16).

g_iii = 0

N₃h

N₃h

N₃h

N₃h

e^ı~kj~x,( ˆL⁰)⁻¹N₃[e^−ı~kj~x, e^ı~ki~x, e^−ı~kk~x], e^ı~kk~xi + N₃h

e^ı~kj~x,( ˆL⁰)⁻¹N₃[e^ı~ki~x, e^−ı~kj~x, e^−ı~kk~x], e^ı~kk~xi + N₃h

e^−ı~kj~x,( ˆL⁰)⁻¹N₃[e^ı~kj~x, e^ı~ki~x, e^ı~kk~x], e^−ı~kk~xi + N3

h

e^−ı~kj~x,( ˆL⁰)⁻¹N3[e^ı~ki~x, e^ı~kj~x, e^ı~kk~x], e^−ı~kk~xi + N₃h

e^−ı~kj~x,( ˆL⁰)⁻¹N₃[e^ı~kj~x, e^ı~ki~x, e^−ı~kk~x], e^ı~kk~xi + N3

h

e^−ı~kj~x,( ˆL⁰)⁻¹N3[e^ı~ki~x, e^ı~kj~x, e^−ı~kk~x], e^ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^−ı~kj~x, e^ı~ki~x, e^ı~kk~x], e^ı~kj~x, e^−ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^ı~ki~x, e^−ı~kj~x, e^ı~kk~x], e^ı~kj~x, e^−ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^−ı~kj~x, e^ı~ki~x, e^−ı~kk~x], e^ı~kj~x, e^ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^ı~ki~x, e^−ı~kj~x, e^−ı~kk~x], e^ı~kj~x, e^ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^ı~kj~x, e^ı~ki~x, e^ı~kk~x], e^−ı~kj~x, e^−ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^ı~ki~x, e^ı~kj~x, e^ı~kk~x], e^−ı~kj~x, e^−ı~kk~xi + N3

h

( ˆL⁰)⁻¹N3[e^ı~kj~x, e^ı~ki~x, e^−ı~kk~x], e^−ı~kj~x, e^ı~kk~xi + N₃h

( ˆL⁰)⁻¹N₃[e^ı~ki~x, e^ı~kj~x, e^−ı~kk~x], e^−ı~kj~x, e^ı~kk~xi

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After all those years, there is a long list of people who contributed in some way to this thesis, for which I would like to express thanks.

I thank Theo Geisel for giving me the opportunity to work in his group. He provided excellent working conditions and heads an vigorous institute with a great atmosphere.

I would like to thank my supervisor Fred Wolf. He provided me with many helpful suggestions, important advice and gave me the freedom to pursue own ideas. His en-thusiasm on the project often helped me to overcome doubts and frustration.

I also wish to thank Siegrid L¨owel for helpful suggestions and many biological insights.

I would like to thank the map folks: Ghazaleh Afshar, Matthias Kaschube, Michael Schnabel, Min Huang, and Wolfgang Keil. In particular, I would like to thank Dominik Heide for his constant help with numerical problems. I thank Dmitry Tsigankov for interesting discussions and re-establishing the ’map club’.

I thank Oliver Bendix with whom I shared a room for all these years. Oliver has always a helping hand and found quick solutions whenever I felt in trouble with linux. Owing to him I learned a lot of science beyond the borders of my own work.

Denny Fliegner and Yorck-Fabian Beensen provided me assistance in numerous com-puter problems.

I thank Corinna Trautsch, Katharina Jeremias, Regina Wunderlich, Tanja Gindele, and Tobias Niemann for management and support.

I thank Michelle Monteforte and Hecke Degering for critically reading the manuscript.

Thanks to all the members of the Department of Nonlinear Dynamics.

I owe many thanks to friends for their patience in the past years.

I would like to thank my family for their constant support.

Finally, I want to thank Jasmin Held. Without her understanding, help, and encour-agement this study would not have been completed.

Name: Lars Reichl Geburtsdatum: 26. Oktober 1976

Geburtsort: Sinsheim

Staatsangeh¨origkeit: deutsch

Familienstand: ledig

Ausbildung

6/1997 Abitur, Willy-Hellpach-Schule, Heidelberg 10/1998–12/2003 Studium der Physik,

Ruprecht-Karls-Universit¨at, Heidelberg

10/2000 Vordiplom in Physik

12/2002–12/2003 Diplomarbeit, Institut f¨ur theoretische Physik, Ruprecht-Karls-Universit¨at, Heidelberg

Titel der Arbeit: “Composite gauge fields and localization in extra dimensions”

12/2003 Diplom in Physik

seit 05/2004 Wissenschaftlicher Mitarbeiter am Max Planck Institut f¨ur Dynamik und Selbstorganisation, G¨ottingen

seit 04/2005 Promotionsstudium, Institut f¨ur Nichtlineare Dynamik, Georg-August-Universit¨at, G¨ottingen

G¨ottingen, 5. April 2010

Im Dokument Symmetry Breaking and Pattern Selection in Models of Visual Development (Seite 178-195)