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We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-Stokes (RNS) model, and the simpler Zeldovich-von Neumann-Döring (ZND) and Chapman-Jouguet (CJ) models. The determinants… (More)

- Gregory Lyng
- 2008

Using Evans function techniques, we develop a stability index for weak and strong detonation waves analogous to that developed for shock waves in [GZ,BSZ], yielding useful necessary conditions for stability. Here, we carry out the analysis in the context of the Majda model, a simplified model for reacting flow; the method is extended to the full… (More)

- Elin Synnøve Mortensen, Gregory Lyng, Erik Juhl, J Egense, Mikael Schwartz
- Lancet
- 1972

- Katrin Egge, Gregory Lyng, Jan Martin Maltau
- Acta obstetricia et gynecologica Scandinavica
- 1981

The frequency and severity of retinal hemorrhages were studied in 200 newborns within the first 72 hours of life. One hundred of the neonates were delivered instrumentally by either forceps (49 cases) or vacuum extraction (51 cases). Another hundred neonates were delivered spontaneously and served as controls. Both the highest and the lowest frequency of… (More)

- Katrin Egge, Gregory Lyng, Jan Martin Maltau
- Acta ophthalmologica
- 1980

The present study shows the frequency and severity of retinal haemorrhages in 200 newborn, of which 100 were delivered spontaneously, 51 delivered by vacuum extractor and 49 by forceps. The incidence of retinal haemorrhages was highest in the vacuum group (50%), lowest in the forceps group (16%), while the spontaneously delivered children showed an… (More)

Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier–Stokes equations with ideal gas equation of state. Our main results are that, in appropriately rescaled coordinates, the Evans… (More)

The rigorous study of spectral stability for ZND detonations was begun by J.J. Erpenbeck in [E1]. He used a normal mode analysis to define a stability function V (λ, η), whose zeros in Rλ > 0 correspond to multidimensional perturbations of a steady planar profile that grow exponentially with time. In [E3] he was able to prove that for large classes of… (More)

- Gregory Lyng, MOHAMMADREZA ROOFI
- 2006

Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave solutions of an abstract viscous combustion model including both Majda’s model and the full reacting compressible Navier–Stokes equations with artificial viscosity with general… (More)

- Blake Barker, Jeffrey Humpherys, Gregory Lyng, Kevin Zumbrun
- SIAM Journal of Applied Mathematics
- 2015

It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such waves, we use numerical Evans-function techniques to study the (spectral) stability of viscous strong detonation… (More)

There is a large body of literature on the problem of stability for inviscid shock waves and in particular for gas dynamics, see [2, 17, 3, 5, 6, 9, 10, 16, 4, 7, 21, 12, 13, 1, 14, 15, 24]. The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function,” for the Euler equations of compressible gas dynamics. We describe two… (More)