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Anelastic-like nature of the rejuvenation of metallic glasses by cryogenic thermal cycling
Cryogenic thermal cycling (CTC) is an effective treatment for improving the room-temperature plasticity and toughness in metallic glasses. Despite considerable attention to characterizing the effects of CTC, they remain poorly understood. A prominent example is that, contrary to expectation, the stored energy in a metallic glass first rises, and then decreases, as CTC progresses. In this work, CTC is applied to bulk metallic glasses based on Pd, Pt, Ti, or Zr. The effects on calorimetric and mechanical properties are evaluated. Critically, CTC-induced effects, at whatever stage, are found to decay over about one week at room temperature after CTC, returning the properties to those of the as-cast glass. A model is proposed for CTC-induced effects, treating them as analogous to the accumulation of anelastic strain. The implications for analysis of existing data, and for future research on CTC effects, are highlighted
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
Six topics on inscribable polytopes
Inscribability of polytopes is a classic subject but also a lively research
area nowadays. We illustrate this with a selection of well-known results and
recent developments on six particular topics related to inscribable polytopes.
Along the way we collect a list of (new and old) open questions.Comment: 11 page
Realizability of Polytopes as a Low Rank Matrix Completion Problem
This article gives necessary and sufficient conditions for a relation to be
the containment relation between the facets and vertices of a polytope. Also
given here, are a set of matrices parameterizing the linear moduli space and
another set parameterizing the projective moduli space of a combinatorial
polytope
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
Intersecting Solitons, Amoeba and Tropical Geometry
We study generic intersection (or web) of vortices with instantons inside,
which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1
supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1}
\times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the
case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can
be beautifully understood in a mathematical framework of amoeba and tropical
geometry, and we propose a dictionary relating solitons and gauge theory to
amoeba and tropical geometry. A projective shape of vortex sheets is described
by the amoeba. Vortex charge density is uniformly distributed among vortex
sheets, and negative contribution to instanton charge density is understood as
the complex Monge-Ampere measure with respect to a plurisubharmonic function on
(C^\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin
function. The general form of the Kahler potential and the asymptotic metric of
the moduli space of a vortex loop are obtained as a by-product. Our discussion
works generally in non-Abelian gauge theories, which suggests a non-Abelian
generalization of the amoeba and tropical geometry.Comment: 39 pages, 11 figure
A Novel, Robust Quantum Detection Scheme
Protocols used in quantum information and precision spectroscopy rely on
efficient internal quantum state discrimination. With a single ion in a linear
Paul trap, we implement a novel detection method which utilizes correlations
between two detection events with an intermediate spin-flip. The technique is
experimentally characterized as more robust against fluctuations in detection
laser power compared to conventionally implemented methods. Furthermore,
systematic detection errors which limit the Rabi oscillation contrast in
conventional methods are overcome
A Single Laser System for Ground-State Cooling of 25-Mg+
We present a single solid-state laser system to cool, coherently manipulate
and detect Mg ions. Coherent manipulation is accomplished by
coupling two hyperfine ground state levels using a pair of far-detuned Raman
laser beams. Resonant light for Doppler cooling and detection is derived from
the same laser source by means of an electro-optic modulator, generating a
sideband which is resonant with the atomic transition. We demonstrate
ground-state cooling of one of the vibrational modes of the ion in the trap
using resolved-sideband cooling. The cooling performance is studied and
discussed by observing the temporal evolution of Raman-stimulated sideband
transitions. The setup is a major simplification over existing state-of-the-art
systems, typically involving up to three separate laser sources
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