4,716 research outputs found
Time-dependent approach to many-particle tunneling in one-dimension
Employing the time-dependent approach, we investigate a quantum tunneling
decay of many-particle systems. We apply it to a one-dimensional three-body
problem with a heavy core nucleus and two valence protons. We calculate the
decay width for two-proton emission from the survival probability, which well
obeys the exponential decay-law after a sufficient time. The effect of the
correlation between the two emitted protons is also studied by observing the
time evolution of the two-particle density distribution. It is shown that the
pairing correlation significantly enhances the probability for the simultaneous
diproton decay.Comment: 9 pages, 10 eps figure
Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames
It has been proposed that mixing induced by convective overshoot can disrupt
the inward propagation of carbon deflagrations in super-asymptotic giant branch
stars. To test this theory, we study an idealized model of convectively bounded
carbon flames with 3D hydrodynamic simulations of the Boussinesq equations
using the pseudospectral code Dedalus. Because the flame propagation timescale
is much longer than the convection timescale, we approximate the flame as fixed
in space, and only consider its effects on the buoyancy of the fluid. By
evolving a passive scalar field, we derive a {\it turbulent} chemical
diffusivity produced by the convection as a function of height, .
Convection can stall a flame if the chemical mixing timescale, set by the
turbulent chemical diffusivity, , is shorter than the flame
propagation timescale, set by the thermal diffusivity, , i.e., when
. However, we find for most of the flame
because convective plumes are not dense enough to penetrate into the flame.
Extrapolating to realistic stellar conditions, this implies that convective
mixing cannot stall a carbon flame and that "hybrid carbon-oxygen-neon" white
dwarfs are not a typical product of stellar evolution.Comment: Accepted to Ap
Ordering of timescales predicts applicability of quasi-linear theory in unstable flows
We discuss the applicability of quasilinear-type approximations for a
turbulent system with a large range of spatial and temporal scales. We consider
a paradigm fluid system of rotating convection with a vertical and horizontal
temperature gradients. In particular, the interaction of rotating with the
horizontal temperature gradient drives a ``thermal wind'' shear flow whose
strength is controlled by a horizontal temperature gradient. Varying the
parameters systematically alters the ordering of the shearing timescale, the
convective timescale, and the correlation timescale. We demonstrate that
quasilinear-type approximations work well when the shearing timescale or the
correlation timescale is sufficiently short. In all cases, the Generalised
Quasilinear approximation (GQL) systematically outperforms the Quasilinear
approximation (QL). We discuss the consequences for statistical theories of
turbulence interacting with mean gradients. We conclude with comments about the
general applicability of these ideas across a wide variety of non-linear
physical systems.Comment: 5 pages, 3 figure
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