papers

Publications (18)

astro-ph2008

Complete nucleosynthesis calculations for low-mass stars from NuGrid

Marco Pignatari, Falk Herwig, Michael Bennett +8

Many nucleosynthesis and mixing processes of low-mass stars as they evolve from the Main Sequence to the thermal-pulse Asymptotic Giant Branch phase (TP-AGB) are well understood (a…

astro-ph2008

NuGrid: Toward High Precision Double-Degenerate Merger Simulations with SPH in 3D

Steven Diehl, Christopher L. Fryer, Aimee Hungerford +11

We present preliminary results from recent high-resolution double-degenerate merger simulations with the Smooth Particle Hydrodynamics (SPH) technique. We put particular emphasis o…

math.NT2015

Rational Points on Erdos-Selfridge Superelliptic Curves

Michael Bennett, Samir Siksek

Given , we show that there are at most finitely many rational numbers and and integers (with ) for which $$ x (x+1) \cdo…

math.NT2018

Shifted powers in Lucas-Lehmer sequences

Michael Bennett, Vandita Patel, Samir Siksek

We develop a general framework for finding all perfect powers in sequences derived by shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer.…

math.NT2021

Odd values of the Ramanujan tau function

Michael Bennett, Adela Gherga, Vandita Patel +1

We prove a number of results regarding odd values of the Ramanujan -function. For example, we prove the existence of an effectively computable positive constant such that…

astro-ph2008

Nucleosynthesis simulations for a wide range of nuclear production sites from NuGrid

Falk Herwig, Michael Bennett, Steven Diehl +8

Simulations of nucleosynthesis in astrophysical environments are at the intersection of nuclear physics reaction rate research and astrophysical applications, for example in the ar…

astro-ph2008

44Ti and 56Ni in core-collapse supernovae

Georgios Magkotsios, Francis X. Timmes, Michael Wiescher +9

We investigate the physical conditions where 44Ti and 56Ni are created in core-collapse supernovae. In this preliminary work we use a series of post-processing network calculations…

math.CO2018

Occurrence of Right Angles in Vector Spaces Over Finite Fields

Michael Bennett

Here we examine some Erdos-Falconer-type problems in vector spaces over finite fields involving right angles. Our main goals are to show that a) a subset A of F_q^d of size >> q^[(…

astro-ph.SR2011

Convective-reactive proton-C12 combustion in Sakurai's object (V4334 Sagittarii) and implications for the evolution and yields from the first generations of stars

Falk Herwig, Marco Pignatari, Paul R. Woodward +5

Depending on mass and metallicity as well as evolutionary phase, stars occasionally experience convective-reactive nucleosynthesis episodes. We specifically investigate the situati…

astro-ph2008

Spatial Distribution of Nucleosynthesis Products in Cassiopeia A: Comparison Between Observations and 3D Explosion Models

Patrick Young, Carola I. Ellinger, Francis X. Timmes +10

We examine observed heavy element abundances in the Cassiopeia A supernova remnant as a constraint on the nature of the Cas A supernova. We compare bulk abundances from 1D and 3D e…

astro-ph2008

Difficulties in Probing Nuclear Physics: A Study of Ti and Ni

Aimee Hungerford, Christopher L. Fryer, Francis X. Timmes +8

The nucleosynthetic yield from a supernova explosion depends upon a variety of effects: progenitor evolution, explosion process, details of the nuclear network, and nuclear rates.…

astro-ph2008

Nucleosynthesis Calculations from Core-Collapse Supernovae

Christopher L. Fryer, Patrick Young, Michael Bennett +8

We review some of the uncertainties in calculating nucleosynthetic yields, focusing on the explosion mechanism. Current yield calculations tend to either use a piston, energy injec…

math.CO2019

Bounds on sizes of general caps in via the Croot-Lev-Pach polynomial method

Michael Bennett

In 2016, Ellenberg and Gijswijt employed a method of Croot, Lev, and Pach to show that a maximal cap in has size for some . In this paper, we show mor…

math.CO2012

Three-point configurations determined by subsets of via the Elekes-Sharir paradigm

Michael Bennett, Alex Iosevich, Jonathan Pakianathan

We prove that if , , has size greater than , then determines a positive proportion of all congruence classes of triangle…

math.NT2016

Sums of two -units via frey-hellegouarch curves

Michael Bennett, Nicolas Billerey

In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is…

astro-ph2008

Nucleosynthetic Yields from "Collapsars"

Gabriel Rockefeller, Christopher L. Fryer, Patrick Young +8

The "collapsar" engine for gamma-ray bursts invokes as its energy source the failure of a normal supernova and the formation of a black hole. Here we present the results of the fir…

math.NT2016

Perfect powers that are sums of consecutive cubes

Michael Bennett, Vandita Patel, Samir Siksek

Euler noted the relation and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gen…

astro-ph2008

NuGrid: s process in massive stars

Raphael Hirschi, Urs Frischknecht, F. -K. Thielemann +10

The s-process production in massive stars at very low metallicities is expected to be negligible due to the low abundance of the neutron source 22Ne, to primary neutron poisons and…