Results 231 to 240 of about 9,418 (264)
Some of the next articles are maybe not open access.
Complex Systems, 2023
The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called “Turing instability.” In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing ...
Elizabeth Alejandra Ortiz Durán +1 more
openaire +1 more source
The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called “Turing instability.” In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing ...
Elizabeth Alejandra Ortiz Durán +1 more
openaire +1 more source
Physical Review E, 1999
We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the ...
C, Varea, J L, Aragón, R A, Barrio
openaire +2 more sources
We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the ...
C, Varea, J L, Aragón, R A, Barrio
openaire +2 more sources
Effect of obstructions on growing Turing patterns
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel–Epstein reaction–diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a variety of obstruction geometries, including obstructions spanning the length of the domain ...
Milos Dolnik +3 more
openaire +2 more sources
Membrane-bound Turing patterns
Physical Review E, 2005Motivated by recent observations in biological cells, we study Turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk. Within a generic model, we formulate the stability problem and discuss the conditions for the occurrence of a Turing instability. By choosing other
Herbert, Levine, Wouter-Jan, Rappel
openaire +2 more sources
1998
In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length.
Irving R. Epstein, John A. Pojman
openaire +1 more source
In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length.
Irving R. Epstein, John A. Pojman
openaire +1 more source
Turing Bifurcations and Pattern Selection
1995Pattern forming instabilities in spatially extended dissipative systems driven away from equilibrium have been the focus of a large activity for many years. The goal of this chapter is to present some theoretical concepts that have been developed to understand and describe these dissipative structures [1] from a macroscopic point of view.
Borckmans, Pierre +3 more
openaire +2 more sources
Turing pattern formation in heterogenous media
Physica D: Nonlinear Phenomena, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Voroney, J.-P. +2 more
openaire +2 more sources
Science, 2011
Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
openaire +1 more source
Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
openaire +1 more source
Turing patterns beyond hexagons and stripes
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive ...
Lingfa, Yang +3 more
openaire +2 more sources
Turing-Type Patterns on Electrode Surfaces
Science, 2001We report stationary, nonequilibrium potential and adsorbate patterns with an intrinsic wavelength that were observed in an electrochemical system with a specific type of current/electrode-potential ( I- φ DL ) characteristic.
Li, Y. +5 more
openaire +3 more sources