Gubernov, Vladimir Vladimirovich Kim, Jong Soo 2024-01-20T08:02:32Z 2024-01-20T08:02:32Z 2021-09-05 2015-01 0259-9791 https://pubs.kist.re.kr/handle/201004/125924 A detailed spectral map for the fast-time instability in LiAn's diffusion-flame regime is presented in order to clarify the origin of two bifurcations of co-dimension 2, causing the transitions from cellular to uniform-oscillatory instability and from uniform-oscillatory to traveling instability. The role of the real and continuous essential spectrum is found to be pivotal in understanding both transitions. Particular attention is paid to the spectral characteristics in the stable parametric regions, where the interaction with the essential spectrum leads to these transitions. When the Lewis number is increased above unity from below, the discrete real spectrum disappears by submerging below the essential spectrum, and the discrete complex spectrum emerges instead, eventually leading to uniform-oscillatory instability. The transition from uniform-oscillatory to traveling instability, associated with the Bogdanov-Takens bifurcation, involves a phenomenon called gap spectrum. For Lewis numbers slightly greater than unity and Damkohler numbers sufficiently large, the discrete complex spectrum intersects the plane corresponding to the essential spectrum, resulting in a gap in the discrete spectrum for small wave numbers. The discrete complex gap spectrum exhibits a local maximum as the parameter values are modified to approach the Hopf bifurcation boundary. The gap in the discrete complex spectrum disappears and traveling instability emerges when crossing the Hopf bifurcation boundary. English SPRINGER THERMAL INSTABILITY COMBUSTION WAVES STABILITY The fast-time instability map of LiAn's diffusion-flame regime Article 10.1007/s10910-014-0423-0 1 JOURNAL OF MATHEMATICAL CHEMISTRY, v.53, no.1, pp.220 - 235 JOURNAL OF MATHEMATICAL CHEMISTRY 53 1 220 235 scie scopus 000347719200016 2-s2.0-84922093228 Chemistry, Multidisciplinary Mathematics, Interdisciplinary Applications Chemistry Mathematics Article THERMAL INSTABILITY COMBUSTION WAVES STABILITY Activation energy asymptotics Linan&apos s diffusion-flame regime Fast-time instability Oscillatory instability Bogdanov-Takens bifurcation