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

1996 ◽  
Vol 53 (1) ◽  
pp. 400-407 ◽  
Author(s):  
P. L. Ramazza ◽  
S. Residori ◽  
E. Pampaloni ◽  
A. V. Larichev
Keyword(s):  
Optical System ◽  
Nonlinear Optical ◽  
Space Time ◽  
Two Dimensional

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

Experimental observation of space-time chaos in a nonlinear optical system with 2D feedback

1995 ◽  
Vol 117 (5-6) ◽  
pp. 492-496 ◽  
Author(s):  
F.T. Arecchi ◽  
A.V. Larichev ◽  
P.L. Ramazza ◽  
S. Residori ◽  
J.C. Ricklin ◽  
...  
Keyword(s):  
Experimental Observation ◽  
Optical System ◽  
Nonlinear Optical ◽  
Space Time

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 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 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

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.

scholarly journals Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

2021 ◽  
Vol 11 (8) ◽  
pp. 3421
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang
Keyword(s):  
Porous Media ◽  
Time Domain ◽  
Numerical Solutions ◽  
Space Time ◽  
Two Dimensional ◽  
Transient Flows ◽  
Layered Porous Media ◽  
Time Marching ◽  
Time Basis ◽  
Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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