Tricritical point as a crossover between type-Is and type-IIs bifurcations

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Rajamanickam, Prabakaran and Daou, Joel (2023) Tricritical point as a crossover between type-Is and type-IIs bifurcations. Progress in Scale Modeling, an International Journal, 4 (1). 2. ISSN 2693-969X (https://doi.org/10.13023/psmij.2023.04-01-02)

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Abstract

A tricritical point as a crossover between (stationary finite-wavelength) type-Is and (stationary longwave) type-IIs bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto­­­­­­–­­Sivashinsky equation which is not applicable near the tricritical point.

ORCID iDs

Rajamanickam, Prabakaran ORCID logoORCID: https://orcid.org/0000-0003-1240-0362 and Daou, Joel;
CORE (COnnecting REpositories)