"Stable localized structures in one and two spatial dimensions: a review and a perspective"
Prof. Helmut R. Brand

Aug 19, 2013

講演題目：　 Stable localized structures in one and two spatial dimensions: a review and a perspective
講　師　：　Prof. Helmut R. Brand
　　　　　Technische Universitat Braunschweig, Institute for Condensed Matter Physics, 38106 Braunschweig, Germany
日　時　：　平成25年8月19日 (木) 13:00-14:00
場　所　：　北海道大学理学部２号館211室（2-2-11）

要　旨　：
We give an overview over stable localized solutions in nonlinear driven non-equilibrium systems, often denoted as dissipative solitons [1]. We cover different mechanisms to generate stable localized structures in various types of prototype equations, namely, envelope equations, order parameter equations and phase equations.For envelope equations nonvariational effects are a key ingredient as emphasized first by Thual and Fauve [2]. This mechanism turns out to be very robust and allows for many different stable particle- and hole-like solutions in one and two spatial dimensions. The interaction of localized solutions can give rise to many different types of outcomes including propagating holes as a result of a collision of propagating particles of fixed shape [3]. For order parameter equations a trapping mechanism can generate localized solutions of arbitrary lengths [4]. A third type of localized solutions involves nonlinear phase dynamics giving rise to stable localized patterns in the wavelength for a nonlinear phase equation [5] or in coupled envelope and phase equations [6]. We also cover briefly recent work on the effects of noise on localized solutions in envelope equations [7,8] and close with an overview of possible applications to systems as diverse as surface reactions under UHV conditions [9], binary fluid convection [10] or holes observed in corn and potato starch suspensions [11].

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[2] O. Thual and S. Fauve, J.Phys. France 49, 1829 (1988).
[3] O. Descalzi, J. Cisternas, and H.R. Brand, Phys. Rev. E 74, 065201 (2006).
[4] H. Sakaguchi and H.R. Brand, Physica D 97, 274 (1996).
[5] H.R. Brand and R.J. Deissler, Phys. Rev. Lett. 63, 508 (1989).
[6] H. Sakaguchi, Prog. Theor. Phys. 87, 1049 (1992).
[7] O. Descalzi, J. Cisternas, D. Escaff, and H.R. Brand, Phys. Rev. Lett. 102, 188302 (2009).
[8] C. Cartes, J. Cisternas, O. Descalzi, and H.R. Brand, Phys. Rev. Lett. 109, 178303 (2012).
[9] H.H. Rotermund, S. Jakubith, A. von Oertzen, and G. Ertl, Phys. Rev. Lett. 66, 3083 (1991).
[10] P. Kolodner, Phys. Rev. A 44, 6448 (1991); Phys. Rev. A 44, 6466 (1991).
[11] H. Ebata and M. Sano, Phys. Rev. Lett. 107, 088301 (2011).

世話人　 北　孝文
(kita@phys.sci.hokudai.ac.jp)
北海道大学大学院理学研究院物理学部門