Numerical simulations of nonparaxial beam self-action and transverse pattern formation in nonlinear media

1995 ◽  
Author(s):  
Vladimir L. Derbov ◽  
Leonid A. Melnikov
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Nonlinear Media ◽  
Transverse Pattern

Transverse-Pattern Formation for Counterpropagating Laser Beams in Rubidium Vapour

1992 ◽  
Vol 18 (8) ◽  
pp. 689-695 ◽  
Author(s):  
A Petrossian ◽  
M Pinard ◽  
A Maître ◽  
J.-Y Courtois ◽  
G Grynberg
Keyword(s):  
Pattern Formation ◽  
Laser Beams ◽  
Transverse Pattern

Transverse pattern formation and its control in photorefractive optics

2004 ◽  
Vol 13 (78) ◽  
pp. 391-402 ◽  
Author(s):  
C. Denz ◽  
Ph. Jander ◽  
M. Schwab ◽  
O. Sandfuchs ◽  
M. Belić ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Transverse Pattern

SINGLE-ELECTRON CIRCUITS PERFORMING DENDRITIC PATTERN FORMATION WITH NATURE-INSPIRED CELLULAR AUTOMATA

2007 ◽  
Vol 17 (10) ◽  
pp. 3651-3655 ◽  
Author(s):  
TAKAHIDE OYA ◽  
IKUKO N. MOTOIKE ◽  
TETSUYA ASAI
Keyword(s):  
Pattern Formation ◽  
Cellular Automata ◽  
Physical Properties ◽  
Cellular Automaton ◽  
Numerical Simulations ◽  
Thermal Effects ◽  
Semiconductor Device ◽  
Single Electron ◽  
Dendritic Trees ◽  
Single Electron Devices

We propose a novel semiconductor device in which electronic-analogue dendritic trees grow on multilayer single-electron circuits. A simple cellular-automaton circuit was designed for generating dendritic patterns by utilizing the physical properties of single-electron devices, i.e. quantum and thermal effects in tunneling junctions. We demonstrate typical operations of the proposed circuit through extensive numerical simulations.

Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

2017 ◽  
Vol 10 (05) ◽  
pp. 1750073 ◽  
Author(s):  
Peng Feng
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Spatial Pattern ◽  
Numerical Simulations ◽  
Functional Response ◽  
Allee Effect ◽  
Turing Instability ◽  
Spatial Pattern Formation ◽  
The Stability ◽  
Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

Numerical Simulations of Elliptical Hollow Gaussian Beams Propagating in Strongly Nonlocal Media

2015 ◽  
Vol 713-715 ◽  
pp. 2085-2088
Author(s):  
Zhen Feng Yang
Keyword(s):  
Numerical Simulations ◽  
Beam Width ◽  
Input Power ◽  
Gaussian Beams ◽  
Nonlinear Media ◽  
Nonlocal Nonlinear Media ◽  
Strongly Nonlocal Nonlinear Media ◽  
Nonlocal Media ◽  
Nonlocal Nonlinear ◽  
Evolution Period

The evolution of elliptical hollow Gaussian beams propagating in strongly nonlocal nonlinear media is investigated. As examples, this paper mainly focuses on the evolutions of the transverse intensity and the beam width of elliptical hollow Gaussian beams with the beam order being 1 and 3. The results show that the evolutions of the transverse intensity and the beam width are both periodical and the size of the evolution period is determined by the input power. There exists the transverse reverse transform for the beam width when selecting a proper input power, which is quiet different from the circularly symmetric hollow Gaussian beams.

scholarly journals Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion

2020 ◽  
pp. 1-31
Author(s):  
HAI-YANG JIN ◽  
ZHI-AN WANG
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Prey Density ◽  
Temporal Patterns ◽  
Steady States ◽  
Global Dynamics ◽  
Predator Prey ◽  
Density Dependent ◽  
Spatially Homogeneous ◽  
Spatio Temporal

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator–prey systems with density-dependent prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusiq‘dfdon) and mobility (prey-taxis) of the predator are correlated through a prey density-dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals. With numerical simulations, we further demonstrate that spatially homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns and chaotic spatio-temporal patterns are all possible for the parameters outside the stability regime. We also find from numerical simulations that the temporal dynamics between linearised system and nonlinear systems are quite different, and the prey density-dependent motility function can trigger the pattern formation.

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