Pattern formation outside of equilibrium
By Michael C. Cross, Pierre Hohenberg. 1993
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Dirk Helbing
- Bjorn Sandstede
- Arjen Doelman
- Zhen Wang
- W. Saarloos
- Martin Treiber
- Arnd Scheel
- Erwin Frey
Citations in the corpus
- Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction‐diffusion equations invading an unstable equilibrium (2004, methodology): “Our method also allows us to obtain efficient lower and upper bounds for the propagation speed. c© 2004 Wiley Periodicals, Inc.”
- Active Turbulence (2021, methodology): “This approach is again similar in spirit to the Swift-Hohenberg equation for pattern formation [67, 68], and it had also been used in the context of granular media [81].”
- Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process (2001, unknown): “3Also Department of Physics, Rutgers.”
- Pattern-formation approach to modelling spatially extended ecosystems (2012, unknown): “to wavy modulations of the stripes (Cross and Hohenberg, 1993) can enhance the labyrinth nature of the patterns.”
- The physics of traffic jams (2002, unknown): “By sustaining the perturbed terms less than sixth-order term of ε (Cross and Hohenberg 1993), one obtains the TDGL equation (Kawasaki 1984, Nagatani 1998) from model (1): ∂S ∂t = − ( ∂ ∂X − 1 2 ∂2 ∂X2 ) δ (S) δS (54) with X = j + {2V ′(xc)2τ }t and S(X, t) = xj(t) − xc, (S) = ∫ dx ( V ′(xc) 48 (…”
- Waves and bumps in neuronal networks with axo-dendritic synaptic interactions (2003, methodology): “We refer in particular to the models reviewed by Cross and Hohenberg [37] and Champneys [38].”
- Spatiotemporal order out of noise (2007, unknown): “Cross and Hohenberg, 1993".”
- Computing absolute and essential spectra using continuation (2007, background): “Continuation of these quantities in systems parameters allows us to detect sign changes of the group velocity and certain Eckhaus instabilities, in particular of sideband type, where the onset is via zero wavenumber [3].”