Time-dependent Diffusion Calculations Research Articles

Fast reproduction of time-dependent diffusion calculations using the reduced order model based on the proper orthogonal and singular value decompositions

ABSTRACT An efficient reduced order model (ROM) for time-dependent diffusion calculations using the proper orthogonal decomposition (POD) is proposed. Employing the singular value decomposition (SVD) and low-rank approximation (LRA) for the flux distributions sampled from the detail full order model (FOM) solutions, the orthogonal basis suitable for a target problem is numerically obtained. In the present ROM, flux distribution is expanded with an orthogonal basis on space. Then, the dimensionality reduction is performed for the neutron diffusion equation using the orthogonal basis, and the equation for the expansion coefficients is obtained. Since any flux distributions can be used to construct the orthogonal bases, different orthogonal bases calculated from different flux distribution sets are tested. The accuracy and computation time of the present ROM are verified in the TWIGL benchmark problem. The calculation results show that the present ROM is approximately 100 times faster than the FOM for kinetic calculations in the present conditions. The present method can be substituted as real-time FOM simulations when typical flux distributions of a target problem can be precalculated to represent the solution space with less degree of freedom (DOF).

Asteroseismology of GD358 with complex core carbon and oxygen profiles

AbstractGD 358 is the brightest (mv=13.7) and best studied helium atmosphere white dwarf pulsator. We present an analysis based on over 1000 hours of observations spanning 2007-2014 as well as archival data going back to 1982. From the complete data set, we identify a total of 27 independent frequencies and fit 14 of them as m=0 modes in our asteroseismic analysis. We add GD358 to a set of helium atmosphere white dwarfs fitted with similar models. With this consistent set, we can see a trend in the thickness of the pure helium layer that are quantitatively consistent with time-dependent diffusion calculations.

Radiative levitation of silicon in the atmospheres of two Hyades DA white dwarfs

Abstract The presence of silicon at the surface of the two Hyades DA white dwarfs WD 0421+162 and WD 0431+126 requires mechanisms that counteract the effects of the downward diffusion. Radiative levitation calculations indicate that the silicon abundance observed in WD 0431+126 corresponds to the abundance supported by radiative levitation. Detailed time-dependent diffusion calculations that take into account radiative levitation and accretion indicate that accretion with rates of $\dot{M}_{\rm {Si}} \lesssim 10^4$ g s−1 could also be present without disrupting the abundance supported by radiative levitation. In the case of WD 0421+162, accretion with a rate of $\dot{M}_{\rm {Si}} = 10^{5.1}$ g s−1 must be invoked, because its observed silicon abundance is larger than the abundance supported by radiative levitation. This accretion rate is lower than the accretion rate given by the accretion–diffusion model, because the radiative levitation slows down the downward diffusion of silicon. The silicon abundances observed in the two Hyades white dwarfs cannot be interpreted solely in terms of accretion. The interpretation of the silicon abundances must take into account the interplay between radiative levitation and accretion.

Self-consistent, time-dependent diffusion calculations for iron-peak elements

We present time-dependent, self-consistent diffusion calcu- lations for Cr, Mn and Fe in a Teff = 12000K and log g = 4.0 stellar atmosphere. The temporal evolution of the chemical stratifications is followed for the zero field case and for magnetic fields of varying strength and direction relative to the stellar surface. Preliminary con- clusions are preceded by a comparison of the present results to equilib- rium solutions.

Modelling ApBp star atmospheres with stratified abundances consistent with atomic diffusion

Elemental abundances have been found – both empirically and theoretically – to be stratified in the magnetic atmospheres of many chemically peculiar (CP) stars, but these findings are rarely if ever taken into account for example in (Zeeman) Doppler mapping, resulting in a disturbing problem of self-consistency. Such a lack of self-consistency is also present in many studies of atomic diffusion which have usually been based on vertically homogeneous atmospheric models. In this paper we go one step further in our modelling of diffusion in magnetic CP star atmospheres and discuss self-consistent equilibrium stratifications of elements, in particular of Fe. In an iterative approach, the atmospheric structure is adjusted to the latest stratification profiles of the various elements until zero particle flux throughout the atmosphere is achieved. It can be shown that the resulting stratifications are different from those calculated with vertically homogeneous atmospheres – mainly on account of the change in temperature structure – and that the unphysical behaviour resulting from the latter atmospheres may be avoided. An important finding concerns the mutual interaction between the various elements, leading to stratification profiles that differ substantially depending on whether e.g. Fe alone is allowed to diffuse or whether other elements may diffuse too. This presentation ends with a discussion of these interactions in the context of time-dependent diffusion calculations.

Asteroseismic constraints on diffusion in white dwarf envelopes

The asteroseismic analysis of white dwarfs allows us to peer below their photospheres and determine their internal structure. At ~ 28,000 K EC20058-5234 is the hottest known pulsating helium atmosphere white dwarf. As such, it constitutes an important link in the evolution of white dwarfs down the cooling track. It is also astrophysically interesting because it is at a temperature where white dwarfs are expected to cool mainly through the emission of plasmon neutrinos. In the present work, we perform an asteroseismic analysis of EC20058-5234 and place the results in the context of stellar evolution and time dependent diffusion calculations. We use a parallel genetic algorithm complemented with targeted grid searches to find the models that fit the observed periods best. Comparing our results with similar modeling of EC20058-5234's cooler cousin CBS114, we find a helium envelope thickness consistent with time dependent diffusion calculations and obtain a precise mode identification for EC20058-5234.

FUSE Observations of EC14026 Stars

We present a FUSE abundance analysis of EC14026 stars. We compare the abundances of heavy elements in the atmospheres of EC14026 stars to non-pulsating stars with similar atmospheric parameters, and investigate whether weak stellar winds could explain the coexistence of variable and non-variable sdB stars in the log g – Teff diagram. We also present preliminary results on time-dependent diffusion calculations of iron in presence of radiative levitation and mass loss, and show how weak stellar winds can affect the diffusive equilibrium between gravitational settling and radiative support.

Probing the core and envelope structure of DBV white dwarfs

We investigate the global pulsation properties of DBV white dwarf models that include both the double-layered envelope structure expected from time-dependent diffusion calculations, as well as a non-uniform C/O core expected from prior nuclear burning. We compare these models to otherwise identical models containing a pure C core to determine whether the addition of core structure leads to any significant improvement. Our double-layered envelope model fit to GD 358 that includes an adjustable C/O core is significantly better than our pure C core fit (7sigma improvement). We find a comparable improvement from fits to a second DBV star, CBS 114, though the values of the derived parameters may be more difficult to reconcile with stellar evolution theory. We find that our models are systematically cooler by 1,900 K relative to the similar models of Fontaine & Brassard (2002). Although a fit to their model reproduces the mass and envelope structure almost exactly, we are unable to reproduce the absolute quality of their fit to GD 358. Differences between the constitutive physics employed by the two models may account for both the temperature offset and the period residuals.

Persistent particle anisotropies and magnetospheric models

The influence of an interplanetary particle anisotropy on the asymmetry of solar particle entry into the magnetotail is analysed in the diffusion as well as in the reconnection model. By time dependent diffusion calculations with an asymmetric boundary condition in a cylindrical tail lobe it can be shown that a north-south interplanetary anisotropy leads in the open as well as in the closed magnetosphere to essentially the same polar cap structures when observed with a dawn-dusk polar orbiting satellite. However, depending on the satellite orbit, an east-west interplanetary anisotropy can serve to distinguish between rival magnetospheric models. Comparison of our diffusion calculations with polar cap measurements during an east-west interplanetary anisotropy, as presented in Morfill and Scholer (1972), show a large discrepancy, whereas an open tail model fits these observations best.