Publications

Ultra-long gamma-ray bursts (ULGRBs) are a distinct class of GRBs characterized by durations of several thousands of seconds, about two orders of magnitude longer than those of standard long GRBs (LGRBs). The driving engine of these events has not yet been uncovered, and ideas range from magnetars, to tidal disruption events, to extended massive stars, such as blue super giants (BSG). BSGs, a possible endpoint of stellar evolution, are attractive for the relatively long freefall times of their envelopes, allowing accretion to power a long-lasting central engine. At the same time, their large radial extension poses a challenge to the emergence of a jet. Here, we perform an end-to-end simulation aimed at assessing the viability of BSGs as ULGRB progenitors. The evolution to the core-collapse of a BSG star model is calculated with the MESA code. We then compute the accretion rate for the fraction of envelope material with enough angular momentum to circularize and form an accretion disk, and input the corresponding power into a jet, which we evolve through the star envelope with the FLASH code. Our simulation shows that the jet can emerge, and the resulting light curves resemble those observed in ULGRBs, with durations T90 ranging from ≈4000 s to ≈104 s, depending on the viewing angle.

We develop and apply a model to quantify the global efficiency of radial orbit migration among stars in the Milky Way disk. This model parameterizes the possible star formation and enrichment histories, radial birth profiles, and combines them with a migration model that relates present-day orbital radii to birth radii through a Gaussian probability, broadening with age τ as σRM8 τ/8 Gyr‾‾‾‾‾‾‾√. Guided by observations, we assume that stars are born with an initially tight age--metallicity relation at given radius, which becomes subsequently scrambled by radial orbit migration, thereby providing a direct observational constraint on radial orbit migration strength σRM8. We fit this model with MCMC to the observed age--metallicity distribution of low-α red clump stars with Galactocentric radii between 5 and 14 kpc from APOGEE DR12, sidestepping the complex spatial selection function and accounting for the considerable age uncertainties. This simple model reproduces well the observed data, and we find a global (in radius and time) radial orbit migration efficiency in the Milky Way of σRM8=3.6±0.1 kpc when marginalizing over all other model aspects. This shows that radial orbit migration in the Milky Way's main disk is indeed rather strong, in line with theoretical expectations: stars migrate by about a half-mass radius over the age of the disk. The model finds the Sun's birth radius at ∼5.2 kpc. If such strong radial orbit migration is typical, this mechanism plays indeed an important role in setting the structural regularity of disk galaxies.

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach involves a minor modification of a classical formulation. In the electrostatic or acoustic setting, we introduce a new vector partial differential equation, from which the desired solution is easily obtained. It is the vector equation for which we derive a well-conditioned integral equation. In addition to providing a unified framework for these solvers, we illustrate their performance using iterative solution methods coupled with the FFT-based technique of [1] to discretize and apply the relevant integral operators.

Upcoming cosmic microwave background (CMB) surveys will soon make the first detection of the polarized Sunyaev-Zel’dovich effect, the linear polarization generated by the scattering of CMB photons on the free electrons present in collapsed objects. Measurement of this polarization along with knowledge of the electron density of the objects allows a determination of the quadrupolar temperature anisotropy of the CMB as viewed from the space-time location of the objects. Maps of these remote temperature quadrupoles have several cosmological applications. Here we propose a new application: the reconstruction of the cosmological reionization history. We show that with quadrupole measurements out to redshift 3, constraints on the mean optical depth can be improved by an order of magnitude beyond the CMB cosmic variance limit.

The TREX is a recently introduced approach to sparse linear regression. In contrast to most well-known approaches to penalized regression, the TREX can be formulated without the use of tuning parameters. In this paper, we establish the first known prediction error bounds for the TREX. Additionally, we introduce extensions of the TREX to a more general class of penalties, and we provide a bound on the prediction error in this generalized setting. These results deepen the understanding of the TREX from a theoretical perspective and provide new insights into penalized regression in general.

Abstract Spindles are self-organized microtubule-based structures that segregate chromosomes during cell division. The mass of the spindle is controlled by the balance between microtubule turnover and nucleation. The mechanisms that control the spatial regulation of microtubule nucleation remain poorly understood. While previous work found that microtubule nucleators bind to microtubules in the spindle, it is still unclear whether this binding regulates the activity of those nucleators. Here we use a combination of experiments and mathematical modeling to investigate this issue. We measured the concentration of microtubules and soluble tubulin in and around the spindle. We found a very sharp decay in the concentration of microtubules at the spindle interface. This is inconsistent with a model in which the activity of nucleators is independent of their association with microtubules but consistent with a model in which microtubule nucleators are only active when bound to preexisting microtubules. This argues that the activity of microtubule nucleators is greatly enhanced when bound to microtubules. Thus, microtubule nucleators are both localized and activated by the microtubules they generate.

Density functional theory augmented with Hubbard-U corrections (DFT+U) is currently the most widely used method for first-principles electronic structure modeling of insulating transition metal oxides (TMOs). Since U is relatively large relative to band widths, the magnetic excitations in TMOs are expected to be well described by a Heisenberg model. However, in practice the calculated exchange parameters Jij depend on the magnetic configuration from which they are extracted and on the functional used to compute them. In this work we investigate how the spin polarization dependence of the underlying exchange-correlation functional influences the calculated magnetic exchange constants of TMOs. We perform a systematic study of the predictions of calculations based on the local density approximation plus U (LDA+U) and the local spin density approximation plus U (LSDA+U) for the electronic structures, total energies and magnetic exchange interactions Jij's extracted from ferromagnetic (FM) and antiferromagnetic (AFM) configurations of several transition metal oxide materials. We report that, for realistic choices of Hubbard U and Hund's J parameters, LSDA+U and LDA+U calculations result in different values of the magnetic exchange constants and band gap. The dependence of the band gap on the magnetic configuration is stronger in LDA+U than in LSDA+U and we argue that this is the main reason why the configuration dependence of the Jij's is found to be systematically more pronounced in LDA+U than in LSDA+U calculations. We report a very good correspondence between the computed total energies and the parameterized Heisenberg model for LDA+U calculations, but not for LSDA+U, suggesting that LDA+U is a more appropriate method for estimating exchange interactions.

A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified fast Gauss transform for this purpose in two dimensions, making use of an adaptive quad-tree discretization on a unit square which is assumed to contain all sources. Our implementation permits either free-space or periodic boundary conditions to be imposed, and is efficient for any choice of variance in the Gaussian.