Pattern Formation and Dynamics in Nonequilibrium Systems
By Michael C. Cross, H. Greenside. 2004
771 citations recorded by the source corpus.
Subfields: Computer Networks and Communications, Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ba7e35282b7d2e928fd13b50a9f6775ee104ec6f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Networks and Communications
- José Manuel Vega
- A. Krekhov
- Salvatore Torquato
- Soledad Le Clainche Martínez
- W. Saarloos
- Pierre Hohenberg
In Molecular Biology
- José Manuel Vega
- A. Krekhov
- Salvatore Torquato
- Soledad Le Clainche Martínez
- W. Saarloos
- Pierre Hohenberg
In Statistical and Nonlinear Physics
- José Manuel Vega
- A. Krekhov
- Salvatore Torquato
- Soledad Le Clainche Martínez
- W. Saarloos
- Pierre Hohenberg
Citations in the corpus
- Front propagation into unstable states (2003, methodology): “Just above onset, the patterns can be described by a so-called amplitude expansion by writing the physical fields in terms of the complex amplitude as [105,189,193,316,320]”
- Higher Order Dynamic Mode Decomposition (2017, methodology): “This is a very convenient pattern forming system to illustrate the methods in this paper because (i) it exhibits fairly complex dynamics, (ii) it is a “normal form” that applies to a variety of oscillatory bifurcations in infinite-dimensional systems [19, 26], and (iii) it is simple enough”
- Hyperuniform states of matter (2018, background): “[336] M.”
- An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns (2014, methodology): “The classification of instability type in time and space is based on the values of q0 and ω0, see Cross and Hohenberg (1993), Cross and Greenside (2009).”
- Pattern formation driven by cross-diffusion in a 2D domain (2012, background): “A systematic approach to derive the normal forms and the correspondent amplitude equations for flows at local bifurcations can be found in [14, 34, 29, 13, 28].”
- Pattern-formation approach to modelling spatially extended ecosystems (2012, neutral): “This is an important difference between the two modelling approaches; continuum models lend themselves to the powerful tools of pattern formation theory (Cross and Hohenberg, 1993; Pismen, 2006; Cross and Greenside, 2009), whereas no mathematical theory of this kind is available for discrete models.”