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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)
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 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)
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)
We present a detailed analysis of the solution of the focusing nonlinear Schrödinger equation with initial condition ψ(x, 0) = N sech(x) in the limit N → ∞. We begin by presenting new and more accurate numerical reconstructions of the N-soliton by inverse scattering (numerical linear algebra) for N = 5, 10, 20, and 40. We then recast the inverse-scattering(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)
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)
We consider the problem of multi-dimensional linearized stability of planar, inviscid detonation waves. For an abstract, multi-step reaction model a normal mode analysis leads to a stability function similar to the Lopatinski determinant for gas dynamics. In the low-frequency/long wave limit of the perturbation we obtain explicit criteria for uniform(More)