메뉴 건너뛰기




Volumn 66, Issue 2, 2002, Pages

Example of a chaotic crystal: The labyrinth

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); GRAIN BOUNDARIES; LAPLACE TRANSFORMS; LIQUID CRYSTALS; NUMERICAL ANALYSIS; POLYCRYSTALLINE MATERIALS; QUANTUM THEORY;

EID: 41349115247     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.026203     Document Type: Article
Times cited : (34)

References (30)
  • 2
    • 85036324212 scopus 로고    scopus 로고
    • C. Szwaj (private communication)
    • C. Szwaj (private communication);
  • 6
    • 0011189154 scopus 로고
    • see also Magnétisme, Tome 1: Les Fondements (University of Grenoble Press, Grenoble, 2001)
    • R. E. Rosensweig, Sci. Am. 247, 135 (1982);see also Magnétisme, Tome 1: Les Fondements (University of Grenoble Press, Grenoble, 2001).
    • (1982) Sci. Am. , vol.247 , pp. 135
    • Rosensweig, R.E.1
  • 10
    • 85036222819 scopus 로고    scopus 로고
    • S. Metens, Ph.D thesis, University of Brussels, Belgium, 1998
    • S. Metens, Ph.D thesis, University of Brussels, Belgium, 1998.
  • 15
    • 85036276864 scopus 로고    scopus 로고
    • Eqs. (5) and (6), the damping coefficients (Formula presented) have been introduced to prevent divergence of the solutions. A weakly nonlinear analysis was performed for (Formula presented) by using the expansion (1) with (Formula presented) for w, and a similar expansion for u (with wave numbers varying between 0 and 2, due to the quadratic coupling). Using the same notation as in Refs. 1 18 the coupling coefficient between the two active and passive modes is (Formula presented) where (Formula presented) is the Lorentzian (Formula presented) and (Formula presented) and the self-interaction coefficient is (Formula presented) The condition required 1 for a turbulent crystal [i.e., that the coupling function β(θ) is flat and very small in the whole domain (0, π)] is fulfilled only for (Formula presented) very small (Formula presented) and (Formula presented) close to 3/2; but this case leads to a negative (Formula presented) A positive (Formula presented) is reachable only for peaked (nonflat) β(θ), so that it would lead to the usual N-gon structures, with (Formula presented) 2, 3
    • In Eqs. (5) and (6), the damping coefficients (Formula presented) have been introduced to prevent divergence of the solutions. A weakly nonlinear analysis was performed for (Formula presented) by using the expansion (1) with (Formula presented) for w, and a similar expansion for u (with wave numbers varying between 0 and 2, due to the quadratic coupling). Using the same notation as in Refs. 1, 18 the coupling coefficient between the two active and passive modes is (Formula presented) where (Formula presented) is the Lorentzian (Formula presented) and (Formula presented) and the self-interaction coefficient is (Formula presented) The condition required 1 for a turbulent crystal [i.e., that the coupling function β(θ) is flat and very small in the whole domain (0, π)] is fulfilled only for (Formula presented) very small (Formula presented) and (Formula presented) close to 3/2; but this case leads to a negative (Formula presented) A positive (Formula presented) is reachable only for peaked (nonflat) β(θ), so that it would lead to the usual N-gon structures, with (Formula presented) 2, 3.
  • 16
    • 0028386874 scopus 로고
    • The model in Eqs. (9) and (10) gives comparable results with the mean-field model introduced by G. L. Oppo, M. Brambilla, and L. Lugiato, Phys. Rev. A 49, 2028 (1994)
    • (1994) Phys. Rev. A , vol.49 , pp. 2028
    • Oppo, G.L.1    Brambilla, M.2    Lugiato, L.3
  • 21
    • 85036269545 scopus 로고    scopus 로고
    • P. Manneville, Structures Dissipatives Chaos et Turbulene (Aléa, Saclay, France, 1990)
    • P. Manneville, Structures Dissipatives Chaos et Turbulene (Aléa, Saclay, France, 1990).
  • 24
    • 85036205075 scopus 로고    scopus 로고
    • For nonanalytic functions, or for analytic functions (Formula presented) without any pole in the complex k plane, the result could be different. For example, in the case of a square shaped structure factor (Formula presented) for (Formula presented) the asymptotic behavior (Formula presented) leads to the power law behavior (Formula presented)
    • For nonanalytic functions, or for analytic functions (Formula presented) without any pole in the complex k plane, the result could be different. For example, in the case of a square shaped structure factor (Formula presented) for (Formula presented) the asymptotic behavior (Formula presented) leads to the power law behavior (Formula presented)
  • 25
    • 85036347425 scopus 로고    scopus 로고
    • This procedure was implemented by P. Manneville in the case of the SH equation (private communication)
    • This procedure was implemented by P. Manneville in the case of the SH equation (private communication).
  • 26
    • 85036296829 scopus 로고    scopus 로고
    • A weakly nonlinear analysis proves that the mean-field model, and therefore also Eqs. (9) and (10), reduce to the SH equation (2), in the limit of small negative mistunings 25 (Formula presented) But our study of the DOPO concerns the case (Formula presented) outside the validity range of the approximation of a DOPO by the SH equation
    • A weakly nonlinear analysis proves that the mean-field model, and therefore also Eqs. (9) and (10), reduce to the SH equation (2), in the limit of small negative mistunings 25 (Formula presented) But our study of the DOPO concerns the case (Formula presented) outside the validity range of the approximation of a DOPO by the SH equation.
  • 27
    • 85036181734 scopus 로고    scopus 로고
    • L. Di Menza, M. Le Berre, Y. Pomeau, E. Ressayre, and A. Tallet, Rencontre du Non-Linéaire (IHP, Paris, 2001)
    • L. Di Menza, M. Le Berre, Y. Pomeau, E. Ressayre, and A. Tallet, Rencontre du Non-Linéaire (IHP, Paris, 2001).
  • 30
    • 85036281523 scopus 로고    scopus 로고
    • Phys. Rev. ED. BoyerJ. Vinals65, 046119 (2002).
    • (2002) , vol.65 , pp. 46119
    • Boyer, D.1    Vinals, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.