10 papers
WKBJ approximation for linearly coupled systems: asymptotics of reaction-diffusion systems
Juraj Kováč, Václav Klika
Asymptotic analysis has become a common approach in investigations of reaction-diffusion equations and pattern formation, especially when considering generalizations to the origina…
Turing Patterning in Stratified Domains
Andrew L. Krause, Václav Klika, Jacob Halatek +4
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in developm…
Gradient and GENERIC evolution towards reduced dynamics
Miroslav Grmela, Vaclav Klika, Michal Pavelka
Let (M,J) be a dynamical model of macroscopic systems and (N,K) a less microscopic model (i.e. a model involving less details) of the same macroscopic systems; M and N are manifold…
Generalization of the dynamical lack-of-fit reduction
Michal Pavelka, Vaclav Klika, Miroslav Grmela
The lack-of-fit statistical reduction, developed and formulated first by Bruce Turkington, is a general method taking Liouville equation for probability density (detailed level) an…
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics
Michal Kozák, Eamonn A Gaffney, Václav Klika
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we impleme…
From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJ
Andrew L. Krause, Václav Klika, Thomas E. Woolley +1
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spati…