Zobrazeno 1 - 10
of 1 060
pro vyhledávání: '"Knobloch, E."'
We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a ric
Externí odkaz:
http://arxiv.org/abs/2308.08789
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in one spatial d
Externí odkaz:
http://arxiv.org/abs/2208.04009
Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, which supports a large variety of dynamical solutions. Here, we review
Externí odkaz:
http://arxiv.org/abs/2010.03375
Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion
Publikováno v:
Phys. Rev. E 98, 042212 (2018)
We study the stability and bifurcation structure of spatially extended patterns arising in nonlin- ear optical resonators with a Kerr-type nonlinearity and anomalous group velocity dispersion, as described by the Lugiato-Lefever equation. While there
Externí odkaz:
http://arxiv.org/abs/1805.02555
Publikováno v:
Phys. Rev. E 97, 042204 (2018)
The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and
Externí odkaz:
http://arxiv.org/abs/1801.04796
Publikováno v:
New J. Phys. 20 (2018) 122002
We investigate quasicrystal-forming soft matter using a two-scale phase field crystal model. At state points near thermodynamic coexistence between bulk quasicrystals and the liquid phase, we find multiple metastable spatially localized quasicrystals
Externí odkaz:
http://arxiv.org/abs/1709.06401
Autor:
Rucklidge, A. M., Knobloch, E.
Publikováno v:
Dynamical Systems, 32:3, 354-373 (2017)
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no left-right prefer
Externí odkaz:
http://arxiv.org/abs/1609.02730
Publikováno v:
Phys. Rev. Lett. 117, 075501 (2016)
We investigate the formation and stability of icosahedral quasicrytalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine
Externí odkaz:
http://arxiv.org/abs/1602.05361
Autor:
Ma, Y. -P., Knobloch, E.
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous occurrence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcati
Externí odkaz:
http://arxiv.org/abs/1508.03521