Periodic Pattern Formation in Side-Group Polymer Nematic Solutins at the Twist Frederiks Transition

1995 ◽  
Vol 5 (3) ◽  
pp. 397-411 ◽  
Author(s):  
E. E. Pashkovsky ◽  
W. Stille ◽  
G. Strobl
Keyword(s):  
Pattern Formation ◽  
Periodic Pattern ◽  
Side Group

Pattern formation in the splay Freedericks transition of a nematic side-group polysiloxane

1993 ◽  
Vol 3 (6) ◽  
pp. 865-889 ◽  
Author(s):  
Norbert Schwenk ◽  
Hans Wolfgang Spiess
Keyword(s):  
Pattern Formation ◽  
Side Group

Periodic pattern formation in solid state reactions related to the Kirkendall effect

1998 ◽  
Vol 46 (18) ◽  
pp. 6521-6528 ◽  
Author(s):  
A.A. Kodentsov ◽  
M.R. Rijnders ◽  
F.J.J. van Loo
Keyword(s):  
Solid State ◽  
Pattern Formation ◽  
Kirkendall Effect ◽  
Solid State Reactions ◽  
Periodic Pattern

Laser Ablation Modeling of Periodic Pattern Formation on Polymer Substrates

2008 ◽  
Vol 10 (5) ◽  
pp. 488-493 ◽  
Author(s):  
A. Lasagni ◽  
M. Cornejo ◽  
F. Lasagni ◽  
F. Muecklich
Keyword(s):  
Laser Ablation ◽  
Pattern Formation ◽  
Periodic Pattern ◽  
Polymer Substrates ◽  
Ablation Modeling

Bifurcations and Pattern Formation in a Predator–Prey Model

2018 ◽  
Vol 28 (11) ◽  
pp. 1850140 ◽  
Author(s):  
Yongli Cai ◽  
Zhanji Gui ◽  
Xuebing Zhang ◽  
Hongbo Shi ◽  
Weiming Wang
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Global Bifurcation ◽  
Periodic Pattern ◽  
Spatiotemporal Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Steady State Bifurcation

In this paper, we investigate the spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge subject to the Neumann boundary conditions. We mainly consider Hopf bifurcation and steady-state bifurcation which bifurcate from the constant positive steady-state of the model. In the case of Hopf bifurcation, by the center manifold theory and the normal form method, we establish the bifurcation direction and stability of bifurcating periodic solutions; in the case of steady-state bifurcation, by the local and global bifurcation theories, we prove the existence of the steady-state bifurcation, and find that there are two typical bifurcations, Turing bifurcation and Turing–Hopf bifurcation. Via numerical simulations, we find that the model exhibits not only stationary Turing pattern induced by diffusion which is dependent on space and independent of time, but also temporal periodic pattern induced by Hopf bifurcation which is dependent on time and independent of space, and spatiotemporal pattern induced by Turing–Hopf bifurcation which is dependent on both time and space. These results may enrich the pattern formation in the predator–prey model.

Theoretical Aspects of Laser-Induced Periodic Surface Structure Formation

1983 ◽  
Vol 29 ◽  
Author(s):  
Michael Hutchinson ◽  
Ki-Tung Lee ◽  
William C. Murphy ◽  
A. C. Beri ◽  
Thomas F. George
Keyword(s):  
Pattern Formation ◽  
Maxwell’S Equations ◽  
Smooth Surface ◽  
Maxwell's Equations ◽  
Periodic Pattern ◽  
Periodic Surface ◽  
Periodic Surface Structure ◽  
Surface Grating ◽  
Perturbative Solution ◽  
Initial Deposition

ABSTRACTLaser-induced periodic pattern formation has been observed on a variety of substances. In particular, low-power lasers have been used to deposit a pattern on a metal surface. For a relatively smooth surface grating, this pattern can be explained in terms of a perturbative solution of Maxwell's equations. However, as the surface grating is enhanced by this initial deposition, the perturbative solution breaks down. An alternate non-perturbative solution of Maxwell's equations for such rough surfaces is considered here.

Kinetics of spatially confined precipitation and periodic pattern formation

1997 ◽  
Vol 239 (1-3) ◽  
pp. 390-403 ◽  
Author(s):  
Chein-Shiu Kuo ◽  
E. Lo´pez Cabarcos ◽  
A. Scala ◽  
R. Bansil
Keyword(s):  
Pattern Formation ◽  
Periodic Pattern ◽  
Kinetics Of
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