Propagation velocity of a cold flame

Novozhilov, B. V.; Posvyanskiǐ, V. S.

doi:10.1007/bf00814812

Cited by 8 publications

(13 citation statements)

References 1 publication

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“…Solution exists for h < h** ≈ 0.045, in agreement with h** = 0.04611 13 and 0.0465. 16 At the zero inhibition rate, velocity c(h = 0) ≈ 0.7 also agrees with the published results 13,16 (eq 20, dotted line in Figure 4A). Comparison of solution with and without diffusion of v (Figure 4A,B, dashed vs solid curves) shows that diffusion of v, at least in the range 0 ≤ D v /D ≤ 1, affects properties of the system quantitatively but not qualitatively: it reduces autowave velocity and amplitude as well as h* but does not disrupt V(h), A(h), and VA relations.…”

Section: Discussionsupporting

confidence: 67%

“…Novozhilov and Posvyanski obtained similar V ( h ) curves when varied the ratio D / D v in the range 0.5–2. 13 Qualitative unimportance of diffusion of v (at not very high ratio D v / D ) can be well understood as it acts to smooth the v ( x ) profile: to decrease v at the wave front (where v ≈ 1) and to increase v in the wave tail (where v ≈ 0). Some decrease of v compared to v ≈ 1 at the wave front can indeed decrease the velocity, but the wave tail does not influence the system behavior.…”

Section: Discussionmentioning

confidence: 99%

“…Various complex systems can be studied after reducing their kinetic scheme to the GS model . Examples include glycolysis, catalytic chemical reactors and cold flame propagation, ,,− fungal mycelia growth, and disease spreading . However, available studies in the spatial-distributed conditions are almost always limited to open conditions, ,− the dependence of autowave velocity on parameters in isolated conditions is rarely studied, , and the VA relationship in the GS model in isolated conditions has never been reported, to the best of our knowledge.…”

Section: Introductionmentioning

confidence: 99%

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Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions

Tokarev

2019

ACS Omega

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Velocity and amplitude are two basic characteristics of any autowave, and their relationship reflects the internal regulation of the autowave system. This study proposes an approach to approximately estimate steady velocity–amplitude (VA) relation without deriving separate formulas for V and A. The approach presumes constructing an ansatz which represents the “petal” form of phase trajectory and contains V, A, and a free parameter (parameters). After substituting this ansatz, integration of model equations leads to a VA relation analytically. A free parameter (parameters) can be determined by comparing the analytical VA relation to the numerical data. As an example, we used the simplest autowave model possessing threshold, that is, the Gray–Scott model (cubic autocatalysis with linear inhibition) in isolated conditions with an immobilized precursor and a diffusible reactant. For all values of the inhibition rate constant allowing autowave solution (i.e., except approaching zero), the free parameter of ansatz belongs to a narrow interval has little effect on VA relation and can be regarded as fixed. Assumption of precursor immobilization does not influence the results qualitatively. This approach will be useful in investigations of more complex active media systems in biochemistry, combustion, and disease control.

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Section: Discussionsupporting

confidence: 67%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions

Tokarev

2019

ACS Omega

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“…This yields Thus, the flame becomes extinguished before the wave velocity becomes equal to zero, and this had already been seen in early experiments on the "cold" oxidation of CS 2 (an alternative explanation is given in Ref. 135).…”

Section: P-2mentioning

confidence: 58%

Localized waves in inhomogeneous media

Gurevich¹,

Mint︠s︡²

1984

Sov. Phys. Usp.

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This review examines the localization of one-dimensional nonlinear waves in an inhomogeneous multiphase medium. Particular attention is devoted to the localization of two types of waves, namely, solitary waves (domains) and switching waves that are the separation boundaries between the corresponding phases (domain walls). The localized state of such waves on both point and slowly-varying (in space) inhomogeneities is investigated. It is shown that several types of waves can become localized on inhomogeneities, and variation of external parameters may be accompanied by abrupt transitions between different types of localized waves. The stability of waves localized on inhomogeneities is examined together with various hysteresis phenomena that may occur in an inhomogeneous medium. The general results presented in the first part of the review are illustrated by examples of different physical systems, including superconductors, normal metals, semiconductors, plasmas, and chemical-reaction waves. CONTENTS 1. Introduction 19 2. Nonlinear quasistationary waves 20 A. Waves in a homogeneous medium. B. Waves in an inhomogeneous medium (qualitative analysis). C. Exactly solvable model. D. Dynamics of localized waves. 3. Localized static waves (general approach) 29 A. Static distributions. B. Stability of localized waves. 4. Examples 30 A. Resistive domains in superconductors. B. Optical discharge in gases. C. Temperature-electric domains in normal metals. D. Chemical-reaction waves. E. Superconductor exposed to laser radiation. F. Dielectric-metal phase transition. G. Dissipative structures in an inhomogeneous medium. 5. Conclusions 39 References 39

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“…Travelling waves in this context have been considered by Novozhilov and Posvyanskii [37], [38], [46] and reviewed by Zel'dovich et al [49]. Travelling waves in this context have been considered by Novozhilov and Posvyanskii [37], [38], [46] and reviewed by Zel'dovich et al [49].…”

Section: Introductionmentioning

confidence: 99%

The Evolution of Travelling Waves in Fractional Order Autocatalysis with Decay. I. Permanent Form Travelling Waves

McCabe¹,

Leach²,

Needham³

1998

SIAM J. Appl. Math.

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This paper considers a model, isothermal, autocatalytic reaction scheme with termination when the reaction orders m, n are fractional, i.e., 0 < m, n < 1. With k measuring the strength of the termination step, it is shown that finite speed propagating wavefronts can persist in the system if and only if m > n and k ∈ (0, kc), where kc depends upon m and n. It is further established that these wavefronts are of excitable (rather than Fisher-Kolmogorov) type and have only semi-infinite support (that is, the reaction is totally dormant ahead of the wavefront). These features are in contrast to the case when m, n ≥ 1 as studied by Merkin, Needham, and Scott [Proc.

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Propagation velocity of a cold flame

Cited by 8 publications

References 1 publication

Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions

Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions

Localized waves in inhomogeneous media

The Evolution of Travelling Waves in Fractional Order Autocatalysis with Decay. I. Permanent Form Travelling Waves

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