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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)
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)
Polychlorinated biphenyls (PCBs) are ubiquitous environmental contaminants that have been demonstrated to be toxic to the dopamine (DA) systems of the central nervous system. One proposed mechanism for PCB-induced DA neurotoxicity is inhibition of the vesicular monoamine transporter (VMAT); such inhibition results in increased levels of unsequestered DA and(More)
Polychlorinated biphenyls (PCBs) are persistent environmental contaminants that are highly toxic to the developing nervous system, particularly via their disruption of dopamine (DA) function. In order to characterize the effects of PCBs on the developing basal ganglia DA system, we utilized an organotypic coculture system of developing rat striatum and(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)
Organotypic cocultures of striatum, cortex, and ventral mesencephalon were used to study the anatomical and physiological development of striatal neurons in the presence or absence of cortical and nigral (SN/VTA) inputs. Striatum and cortex were dissected from prenatal (E18-E22) or early postnatal (P0-P2) rats, and SN/VTA was dissected from E14-15 fetuses;(More)
Using organotypic co-cultures of rat embryonic day 14 (E14) ventral mesencephalon (VM) and E21 striatum, we have described the developmental changes in (i) dopamine (DA) neurochemistry; (ii) numbers of DA neurons; and (iii) protein expression of tyrosine hydroxylase (TH), DA transporter (DAT), and glutamic acid decarboxylase (GAD 65/67), over 17 days in(More)