Surface undulations in explosive crystallization: A nonlinear analysis of a thermal instability

Saarloos, Wim van; Weeks, John D.

doi:10.1016/0167-2789(84)90532-3

Cited by 30 publications

(20 citation statements)

References 39 publications

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“…Such transitions have been observed in experiments for both the condensed phase and the premixed gaseous combustion [20,22]. Similar instabilities have been observed in the process of rapid solidification of thin films initiated by a laser beam (see [23]), and laser-induced evaporation of solid materials [15]. A variety of complex (including chaotic) auto-oscillatory regimes have also been found in numerical simulations of mathematical models of different degrees of complexity.…”

Section: Introductionmentioning

confidence: 71%

“…For higher number of high frequency oscillations, only selected dynamically stable solutions are shown in Fig. 9; the dots correspond to 8,12,16,19,23, and 90 accumulation oscillations.…”

Section: Subcritical Bifurcation: An Infinite Period Bifurcationmentioning

confidence: 99%

“…We note that in the context of condensed phase combustion, the kinetic boundary condition in (2.6) expresses the dependence of the propagation velocity on the temperature of the flame front. In the context of solidification of overcooled liquids (see, e.g., [5]) or the amorphous to crystalline transition (see [18,23]) the condition corresponds to the interface attachment kinetics, which are determined by various microscopic mechanisms of incorporating the product phase into the crystalline lattice at the interface.…”

Section: Motivation Of the Free Boundary Modelmentioning

confidence: 99%

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Finite-dimensional dynamical system modeling thermal instabilities

Frankel¹,

Kovačič²,

Roytburd³

et al. 2000

Physica D: Nonlinear Phenomena

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We describe a three-dimensional dynamical system, which is obtained as a pseudo-spectral approximation to a free boundary problem modeling solid combustion and rapid solidification, and is capable of generating its major dynamical patterns. These patterns include a Hopf bifurcation followed by a sequence of secondary period doubling and a transition to chaos, reverse sequences, and sequences followed by Shilnikov type trajectories. A computer-assisted bifurcation analysis uncovers some novel mechanisms of stability exchange. The most striking of them is an infinite period bifurcation which resembles the classical Shilnikov bifurcation, but instead of a funnel-shaped spiral along which the period is continually increasing, the continuation produced a series of isolas. Each isola is a closed branch of solutions of roughly the same period, and with the same number of oscillations. The isolas corresponding to consecutive numbers of low amplitude oscillations about the equilibrium are adjacent to each other, and appear to accumulate on a saddle-focus homoclinic connection of Shilnikov type.

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Section: Introductionmentioning

confidence: 71%

“…For higher number of high frequency oscillations, only selected dynamically stable solutions are shown in Fig. 9; the dots correspond to 8,12,16,19,23, and 90 accumulation oscillations.…”

Section: Subcritical Bifurcation: An Infinite Period Bifurcationmentioning

confidence: 99%

Section: Motivation Of the Free Boundary Modelmentioning

confidence: 99%

See 1 more Smart Citation

Finite-dimensional dynamical system modeling thermal instabilities

Frankel¹,

Kovačič²,

Roytburd³

et al. 2000

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…In the context of solidification with undercooling [4] or rapid crystallization of thin films [8], the free-interface model studied below is conceptually even simpler: the latent heat of the phase transition released at the interface must be diffused by the surrounding matter.…”

Section: Free-interface Problemmentioning

confidence: 99%

“…The free-boundary problem that is the subject of the paper arises naturally as a mathematical model of a variety of exothermic phase transition type processes, such as condensedstate combustion (also known as Self-propagating High-temperature Synthesis or SHS [7,9]), solidification with undercooling [4], laser induced evaporation [3], rapid crystallization in thin films [8] etc.…”

Section: Introductionmentioning

confidence: 99%