scholarly journals Localized States in Bi-Pattern Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
U. Bortolozzo ◽  
M. G. Clerc ◽  
F. Haudin ◽  
R. G. Rojas ◽  
S. Residori
Keyword(s):  
Optical System ◽  
Nonlinear Optical ◽  
Amplitude Equation ◽  
Localized States ◽  
Two Dimensional ◽  
One Dimensional ◽  
Self Organized ◽  
Localized Structures ◽  
Spatially Periodic ◽  
Different Shapes

We present a unifying description of localized states observed in systems with coexistence of two spatially periodic states, calledbi-pattern systems. Localized states are pinned over an underlying lattice that is either a self-organized pattern spontaneously generated by the system itself, or a periodic grid created by a spatial forcing. We show that localized states are generic and require only the coexistence of two spatially periodic states. Experimentally, these states have been observed in a nonlinear optical system. At the onset of the spatial bifurcation, a forced one-dimensional amplitude equation is derived for the critical modes, which accounts for the appearance of localized states. By numerical simulations, we show that localized structures persist on two-dimensional systems and exhibit different shapes depending on the symmetry of the supporting patterns.

scholarly journals Pulsating and Rotating Spirals in a Delayed Feedback Diffractive Nonlinear Optical System

2021 ◽  
Vol 31 (01) ◽  
pp. 2130002
Author(s):  
Stanislav Budzinskiy ◽  
Alexander Razgulin
Keyword(s):  
Diffusion Equation ◽  
Optical System ◽  
Feedback Loop ◽  
Nonlinear Optical ◽  
Spiral Waves ◽  
Two Dimensional ◽  
One Dimensional ◽  
Existence And Stability ◽  
The One ◽  
Scalar Diffusion

We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and derive the limiting equation on a circle. Based on the explicitly constructed normal form of the Hopf bifurcation for the one-dimensional delayed scalar diffusion equation, we make predictions about the existence and stability of two-dimensional spirals that we verify in direct numerical simulations, observing pulsating and rotating spiral waves.

Periodic travelling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples

2018 ◽  
Vol 30 (04) ◽  
pp. 756-790 ◽  
Author(s):  
BENJAMIN F. AKERS ◽  
DAVID M. AMBROSE ◽  
DAVID W. SULON
Keyword(s):  
Travelling Waves ◽  
Global Bifurcation ◽  
Travelling Wave ◽  
Two Dimensional ◽  
Wave Problem ◽  
Bifurcation Theorem ◽  
One Dimensional ◽  
Spatially Periodic ◽  
Parameter Values ◽  
The Waves

In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic travelling waves on infinite depth, and computed such travelling waves. The formulation of the travelling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of travelling waves in both of these situations. We compute the waves numerically as well, in both the resonant and non-resonant cases.

Erratum: Transition to space-time chaos in a nonlinear optical system with two-dimensional feedback

1996 ◽  
Vol 54 (1) ◽  
pp. 982-982 ◽  
Author(s):  
P. L. Ramazza ◽  
S. Residori ◽  
E. Pampaloni ◽  
A. Larichev
Keyword(s):  
Optical System ◽  
Nonlinear Optical ◽  
Space Time ◽  
Two Dimensional

Stochastic resonance on two-dimensional arrays of bistable oscillators in a nonlinear optical system

2003 ◽  
Vol 67 (5) ◽  
Author(s):  
J. P. Sharpe ◽  
N. Sungar ◽  
M. Swaney ◽  
K. Carrigan ◽  
S. Wheeler
Keyword(s):  
Stochastic Resonance ◽  
Optical System ◽  
Nonlinear Optical ◽  
Two Dimensional

scholarly journals MAGNETISM IN GRAPHENE SYSTEMS

NANO ◽  
2008 ◽  
Vol 03 (06) ◽  
pp. 433-442 ◽  
Author(s):  
ERJUN KAN ◽  
ZHENYU LI ◽  
JINLONG YANG
Keyword(s):  
Electronic Structures ◽  
Materials Science ◽  
Graphene Nanoribbons ◽  
Localized States ◽  
Theoretical Research ◽  
Two Dimensional ◽  
Spin Filter ◽  
Comprehensive Review ◽  
One Dimensional ◽  
Half Metal

Graphene has attracted great interest in materials science, owing to its novel electronic structures. Recently, magnetism discovered in graphene-based systems has opened up the possibility of their spintronics application. This paper provides a comprehensive review of the magnetic behaviors and electronic structures of graphene systems, including two-dimensional graphene, one-dimensional graphene nanoribbons, and zero-dimensional graphene nanoclusters. Theoretical research suggests that such metal-free magnetism mainly comes from the localized states or edges states. By applying an external electric field, or by chemical modification, we can turn the zigzag nanoribbon systems into half metal, thus obtaining a perfect spin filter.

scholarly journals Two-Dimensional Front Dynamics and Spatial Solitons in a Nonlinear Optical System

2007 ◽  
Vol 99 (15) ◽  
Author(s):  
M. Pesch ◽  
W. Lange ◽  
D. Gomila ◽  
T. Ackemann ◽  
W. J. Firth ◽  
...  
Keyword(s):  
Optical System ◽  
Nonlinear Optical ◽  
Two Dimensional ◽  
Spatial Solitons ◽  
Front Dynamics
Sign in / Sign up

Export Citation Format

Share Document