62 research outputs found

    Three-dimensional Boltzmann-Hydro code for core-collapse in massive stars I. special relativistic treatments

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    We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled to hydrodynamics equations. It is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of advection and collision terms in the Boltzmann equations is the source of difficulties, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce and shock-stall for a 15M_{sun} progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects in our method.Comment: 25 pages, 22 figures, submitted to Ap

    A Detailed Comparison of Multi-Dimensional Boltzmann Neutrino Transport Methods in Core-Collapse Supernovae

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    The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. We carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to both methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are sub-dominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic Monte Carlo random walk approximation.Comment: Accepted to ApJS. 24 pages, 19 figures. Key simulation results and codes are available at https://stellarcollapse.org/MCvsD

    On the Neutrino Distributions in Phase Space for the Rotating Core-collapse Supernova Simulated with a Boltzmann-neutrino-radiation-hydrodynamics Code

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    With the Boltzmann-radiation-hydrodynamics code, which we have developed to solve numerically the Boltzmann equations for neutrino transfer, the Newtonian hydrodynamics equations, and the Newtonian self-gravity simultaneously and consistently, we simulate the collapse of a rotating core of the progenitor with a zero-age-main-sequence mass of 11.2M11.2\,M_\odot and a shelluler rotation of 1rads11\,{\rm rad\,s^{-1}} at the center. We pay particular attention in this paper to the neutrino distribution in phase space, which is affected by the rotation. By solving the Boltzmann equations directly, we can assess the rotation-induced distortion of the angular distribution in momentum space, which gives rise to the rotational component of the neutrino flux. We compare the Eddington tensors calculated both from the raw data and from the M1-closure approximation. We demonstrate that the Eddington tensor is determined by complicated interplays of the fluid velocity and the neutrino interactions and that the M1-closure, which assumes that the Eddington factor is determined by the flux factor, fails to fully capture this aspect, especially in the vicinity of the shock. We find that the error in the Eddington factor reaches 20%\sim 20\% in our simulation. This is due not to the resolution but to the different dependence of the Eddington and flux factors on the angular profile of the neutrino distribution function, and hence modification to the closure relation is needed.Comment: 24 pages, 23 figures, 0 explosion, published in Ap

    Orthodontic Treatment of a Patient with Bilateral Congenitally Missing Maxillary Canines: The Effects of First Premolar Substitution on the Functional Outcome

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    Permanent canines are thought to play a pivotal role in obtaining an ideal occlusion. Dentists occasionally encounter patients who lack canines and are therefore missing a key to harmonious guidance during functional mandibular excursions. This case report describes the substitution of maxillary first premolars for congenitally missing canines in the context of an orthodontic treatment plan. A boy, age 10 years and 11 months, with a chief complaint of crooked teeth was diagnosed with Class II division 2 malocclusion associated with a high mandibular plane angle and deep overbite. A stable occlusion with a satisfactory facial profile and functional excursions without interference were achieved after a comprehensive two-stage orthodontic treatment process. The resulting occlusion and satisfactory facial profile were maintained for 12 months. These results indicate that substituting the first premolars for the canines is an effective option in treating patients with missing canines while maintaining functional goals
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