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Catastrophic stress corrosion failure of Zr-base bulk metallic glass through hydrogen embrittlement
Zr-base bulk metallic glasses (BMG) are prone to pitting corrosion in halide containing solutions and also stress corrosion cracking (SCC) is often interpreted in this context. This work presents in situ SCC experiments on notched Zr52.5Cu17.9Ni14.6Al10Ti5 (at.%) BMG bars under 3-point bending in dilute NaCl solution. They show that pitting corrosion is only the initiating process. The pitted areas have a lower local corrosion potential and the reaction of Zr4+ to zirconyl ions in solution produces H+ that can be reduced and absorbed in the local acidic environment. So, hydrogen embrittlement causes the observed catastrophic failure and peculiar fracture surface characteristics. © 2019 The Author
On the fundamental representation of Borcherds algebras with one imaginary simple root
Borcherds algebras represent a new class of Lie algebras which have almost
all the properties that ordinary Kac-Moody algebras have, and the only major
difference is that these generalized Kac-Moody algebras are allowed to have
imaginary simple roots. The simplest nontrivial examples one can think of are
those where one adds ``by hand'' one imaginary simple root to an ordinary
Kac-Moody algebra. We study the fundamental representation of this class of
examples and prove that an irreducible module is given by the full tensor
algebra over some integrable highest weight module of the underlying Kac-Moody
algebra. We also comment on possible realizations of these Lie algebras in
physics as symmetry algebras in quantum field theory.Comment: 8 page
Precision spectroscopy by photon-recoil signal amplification
Precision spectroscopy of atomic and molecular ions offers a window to new
physics, but is typically limited to species with a cycling transition for
laser cooling and detection. Quantum logic spectroscopy has overcome this
limitation for species with long-lived excited states. Here, we extend quantum
logic spectroscopy to fast, dipole-allowed transitions and apply it to perform
an absolute frequency measurement. We detect the absorption of photons by the
spectroscopically investigated ion through the photon recoil imparted on a
co-trapped ion of a different species, on which we can perform efficient
quantum logic detection techniques. This amplifies the recoil signal from a few
absorbed photons to thousands of fluorescence photons. We resolve the line
center of a dipole-allowed transition in 40Ca+ to 1/300 of its observed
linewidth, rendering this measurement one of the most accurate of a broad
transition. The simplicity and versatility of this approach enables
spectroscopy of many previously inaccessible species.Comment: 25 pages, 6 figures, 1 table, updated supplementary information,
fixed typo
Computing Tropical Varieties
The tropical variety of a -dimensional prime ideal in a polynomial ring
with complex coefficients is a pure -dimensional polyhedral fan. This fan is
shown to be connected in codimension one. We present algorithmic tools for
computing the tropical variety, and we discuss our implementation of these
tools in the Gr\"obner fan software \texttt{Gfan}. Every ideal is shown to have
a finite tropical basis, and a sharp lower bound is given for the size of a
tropical basis for an ideal of linear forms.Comment: 22 pages, 2 figure
Top Management Team Diversity: A systematic Review
Empirical research investigating the impact of top management team (TMT)
diversity on executives’ decision making has produced inconclusive results.
To synthesize and aggregate the results on the diversity-performance
link, a meta-regression analysis (MRA) is conducted. It integrates more
than 200 estimates from 53 empirical studies investigating TMT diversity
and its impact on the quality of executives’ decision making as reflected
in corporate performance. The analysis contributes to the literature by
theoretically discussing and empirically examining the effects of TMT diversity
on corporate performance. Our results do not show a link between TMT
diversity and performance but provide evidence for publication bias. Thus,
the findings raise doubts on the impact of TMT diversity on performance
Minimal external representations of tropical polyhedra
Tropical polyhedra are known to be representable externally, as intersections
of finitely many tropical half-spaces. However, unlike in the classical case,
the extreme rays of their polar cones provide external representations
containing in general superfluous half-spaces. In this paper, we prove that any
tropical polyhedral cone in R^n (also known as "tropical polytope" in the
literature) admits an essentially unique minimal external representation. The
result is obtained by establishing a (partial) anti-exchange property of
half-spaces. Moreover, we show that the apices of the half-spaces appearing in
such non-redundant external representations are vertices of the cell complex
associated with the polyhedral cone. We also establish a necessary condition
for a vertex of this cell complex to be the apex of a non-redundant half-space.
It is shown that this condition is sufficient for a dense class of polyhedral
cones having "generic extremities".Comment: v1: 32 pages, 10 figures; v2: minor revision, 34 pages, 10 figure
Small grid embeddings of 3-polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a
convex 3-polytope with integer coordinates. The size of the coordinates is
bounded by . If the graph contains a triangle we can
bound the integer coordinates by . If the graph contains a
quadrilateral we can bound the integer coordinates by . The
crucial part of the algorithm is to find a convex plane embedding whose edges
can be weighted such that the sum of the weighted edges, seen as vectors,
cancel at every point. It is well known that this can be guaranteed for the
interior vertices by applying a technique of Tutte. We show how to extend
Tutte's ideas to construct a plane embedding where the weighted vector sums
cancel also on the vertices of the boundary face
Gene Expressio Array Exploration Using K-Formal Concept Analysis
Proceeding of: 9th International Conference, ICFCA 2011, Nicosia, Cyprus, May 2-6, 2011.DNA micro-arrays are a mechanism for eliciting gene expression values, the concentration of the transcription products of a set of genes, under different chemical conditions. The phenomena of interest—up-regulation, down-regulation and co-regulation—are hypothesized to stem from the functional relationships among transcription products. In [1,2,3] a generalisation of Formal Concept Analysis was developed with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the usual Boolean carrier set. In this paper, we use (Rmin+)- and (Rmax+) to analyse gene expression data for Arabidopsis thaliana. We introduce the mechanism to render the data in the appropriate algebra and profit by the wealth of different Galois Connections available in Generalized Formal Concept Analysis to carry different analysis for up- and down-regulated genes.Spanish Government-Comision Interministerial de Ciencia y TecnologĂa projects 2008-06382/TEC and 2008-02473/TEC and the regional projects S-505/TIC/0223 (DGUI-CM) and CCG08-UC3M/TIC- 4457 (Comunidad Aut onoma de Madrid - UC3M)
Signatures of partition functions and their complexity reduction through the KP II equation
A statistical amoeba arises from a real-valued partition function when the
positivity condition for pre-exponential terms is relaxed, and families of
signatures are taken into account. This notion lets us explore special types of
constraints when we focus on those signatures that preserve particular
properties. Specifically, we look at sums of determinantal type, and main
attention is paid to a distinguished class of soliton solutions of the
Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures
preserving the determinantal form, as well as the signatures compatible with
the KP II equation, is provided: both of them are reduced to choices of signs
for columns and rows of a coefficient matrix, and they satisfy the whole KP
hierarchy. Interpretations in term of information-theoretic properties,
geometric characteristics, and the relation with tropical limits are discussed.Comment: 42 pages, 11 figures. Section 7.1 has been added, the organization of
the paper has been change
Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity
We analyze combinatorial structures which play a central role in determining
spectral properties of the volume operator in loop quantum gravity (LQG). These
structures encode geometrical information of the embedding of arbitrary valence
vertices of a graph in 3-dimensional Riemannian space, and can be represented
by sign strings containing relative orientations of embedded edges. We
demonstrate that these signature factors are a special representation of the
general mathematical concept of an oriented matroid. Moreover, we show that
oriented matroids can also be used to describe the topology (connectedness) of
directed graphs. Hence the mathematical methods developed for oriented matroids
can be applied to the difficult combinatorics of embedded graphs underlying the
construction of LQG. As a first application we revisit the analysis of [4-5],
and find that enumeration of all possible sign configurations used there is
equivalent to enumerating all realizable oriented matroids of rank 3, and thus
can be greatly simplified. We find that for 7-valent vertices having no
coplanar triples of edge tangents, the smallest non-zero eigenvalue of the
volume spectrum does not grow as one increases the maximum spin \jmax at the
vertex, for any orientation of the edge tangents. This indicates that, in
contrast to the area operator, considering large \jmax does not necessarily
imply large volume eigenvalues. In addition we give an outlook to possible
starting points for rewriting the combinatorics of LQG in terms of oriented
matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos
corrected, presentation slightly extende
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