arXiv subjects

Michael A. Jackson

Publications and source records attributed to Michael A. Jackson.

7 recordsLinked to original sources

arXiv2025

Accurate grain boundary plane distributions for textured microstructures from stereological analysis of orthogonal two-dimensional electron backscatter diffraction orientation maps

We present a method for obtaining qualitatively accurate grain boundary plane distributions (GBPD) for textured microstructures using a stereological calculation applied to two-dimensional electron backscatter diffraction (EBSD) orientation maps. Stereology, applied to 2D EBSD orientation maps, is currently the fastest method of obtaining GBPDs. Existing stereological methods are not directly applicable to textured microstructures because of the biased viewing perspectives for different grain boundary types supplied from a single planar orientation map. The method presented in this work successfully removes part of this bias by combining data from three orthogonal EBSD orientation maps for stereology. This is shown here to produce qualitatively correct GBPDs for heavily textured synthetic microstructures with hexagonal and tetragonal crystal symmetries. Synthetic microstructures were generated to compare the stereological GBPD to a known ground truth, as the true GBPD could be obtained from a triangular mesh of the full grain boundary network in 3D. The triangle mesh data contained all five macroscopic parameters to fully describe the grain boundary structure. It was observed that our stereological method overestimated the GBPD anisotropy. However, qualitative analysis of the GBPD remains useful. Furthermore, it was found that combining data from three orthogonal sections gives reliable results when sectioning the texture's primary axes.

cond-mat.mtrl-sci↗

arXiv2015

Rectified Simplex Polytope Numbers

Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope number sequences as sums of simplex number sequences. We focus on $r$-rectified simplices and show that the sequences for these polytopes can be written as alternating sums of simplex numbers analogous to the inclusion-exclusion given by the geometric process of $r$-rectification.

math.CO↗

arXiv2015

On interior polytope number sequences

Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope number sequences as sums of simplex number sequences. In addition, these works have given a process for writing the polytope number sequence in a recursive fashion by using the interior sequence for the various k-faces of the polytope, each viewed as a k-dimensional polytope. This paper shows that the coefficients of the linear combination of simplex number are the h-vector components for a certain type of triangulation of the polytope. In addition, reversing the order of the coefficients in the linear combination is shown to equal the interior polytope sequence for this polytope.

math.CO↗

arXiv2005

Qd(p)-free rank two finite groups act freely on a homotopy product of two spheres

In this paper we show that most rank two groups act freely on a finite homotopy product of two spheres. This makes new progress on a conjecture by Benson and Carlson which states that a finite group G acts freely on a finite complex with the homotopy type of n spheres if the rank of G is less than or equal to n. Recalling that Qd(p) is the semidirect product of a rank two elementary abelian p-group with SL(2,p), we show that a rank two finite group acts freely on a finite CW-complex homotopic to the product of two spheres if, it does not contain any subquotient isomorphic to Qd(p) for any odd prime p.

math.AT↗

arXiv2005

A Quotient of the Set [BG, BU(n)] for a Finite Group G of Small Rank

We construct a natural map from the set [BG,BU(n)] into a set of characters of the Sylow p-subgroups of G and prove that this natural map is a surjection for all finite groups G of rank two. We show, furthermore, that this same natural map is in fact a bijection for two types of finite groups G: those with periodic cohomology and those of rank two with odd order.

math.AT↗

arXiv2004

The strong symmetric genus of the hyperoctahedral groups

The strong symmetric genus of a group is the smallest genus of a surface on which the group acts faithfully as a group of orientation preserving automorphisms. In this paper we announce and prove the strong symmetric genus for the hyperoctahedral groups. This parameter is already known for the alternating and symmetric groups as well as the sporadic finite simple groups.

math.GR↗

arXiv2004

The strong symmetric genus of the finite Coxeter groups

The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving automorphisms. In this paper we complete the calculation of the strong symmetric genus for each finite Coxeter group excluding the group E8.

math.GT↗