scispace - formally typeset
Search or ask a question
Topic

Reaction–diffusion system

About: Reaction–diffusion system is a research topic. Over the lifetime, 5741 publications have been published within this topic receiving 94719 citations. The topic is also known as: Reaction-diffusion system.


Papers
More filters
Journal ArticleDOI
31 Aug 1995-Nature
TL;DR: The striking similarity between the actual and simulated pattern rearrangement strongly suggests that a reaction–diffusion wave is a viable mechanism for the stripe pattern of Pomacanthus.
Abstract: IN 1952, Turing proposed a hypothetical molecular mechanism, called the reaction–diffusion system1, which can develop periodic patterns from an initially homogeneous state. Many theoretical models based on reaction–diffusion have been proposed to account for patterning phenomena in morphogenesis2–4, but, as yet, there is no conclusive experimental evidence for the existence of such a system in the field of biology5–8. The marine angelfish, Pomacanthus has stripe patterns which are not fixed in their skin. Unlike mammal skin patterns, which simply enlarge proportionally during their body growth, the stripes of Pomacanthus maintain the spaces between the lines by the continuous rearrangement of the patterns. Although the pattern alteration varies depending on the conformation of the stripes, a simulation program based on a Turing system can correctly predict future patterns. The striking similarity between the actual and simulated pattern rearrangement strongly suggests that a reaction–diffusion wave is a viable mechanism for the stripe pattern of Pomacanthus.

781 citations

Journal ArticleDOI
TL;DR: This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.
Abstract: Dynamical reaction–diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities—such as density, potentials and particles—diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction–diffusion process (given by the reaction steps B→A and B+A→2B) defined on networks with heterogeneous topology and no limit on the nodes’ occupation number. We investigate the effect of network topology on the basic properties of the system’s phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density-driven phase transitions, whereas phase transition and critical points independent of the particle density are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.

755 citations

Journal ArticleDOI
TL;DR: In this article, the correlation length exponent ν and the order parameter exponent β are found toO(e2) in an ǫ-expansion around the upper critical dimension dc=4.
Abstract: It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlogl's first reaction) exhibit nevertheless a second order phase transition in non-zero dimensional macroscopic systems. The relation to Reggeon field theory is given more directly than by Grassberger et al. using the functional integral formalism of statistical dynamics. As a new result the correlation length exponent ν and the order parameter exponent β are found toO(e2) in an ɛ-expansion around the upper critical dimensiondc=4.

485 citations

Journal ArticleDOI
TL;DR: In this article, the bounds of solutions of reaction-diffusion equations are given for Partial Differential Equations (PDE) in the context of communication in partial differential equations.
Abstract: (1979). LP Bounds of solutions of reaction-diffusion equations. Communications in Partial Differential Equations: Vol. 4, No. 8, pp. 827-868.

483 citations

Journal ArticleDOI
TL;DR: It is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerskin method has a stabilization effect similar to a sub-grid scale model, which is in turn related to the introduction of bubble functions.

482 citations


Network Information
Related Topics (5)
Partial differential equation
70.8K papers, 1.6M citations
90% related
Differential equation
88K papers, 2M citations
88% related
Nonlinear system
208.1K papers, 4M citations
85% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
85% related
Bounded function
77.2K papers, 1.3M citations
85% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023257
2022532
2021344
2020316
2019278
2018271