9,816 research outputs found
Applications of DFT to the theory of twentieth-century harmony
Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip
Non-perturbative embedding of local defects in crystalline materials
We present a new variational model for computing the electronic first-order
density matrix of a crystalline material in presence of a local defect. A
natural way to obtain variational discretizations of this model is to expand
the difference Q between the density matrix of the defective crystal and the
density matrix of the perfect crystal, in a basis of precomputed maximally
localized Wannier functions of the reference perfect crystal. This approach can
be used within any semi-empirical or Density Functional Theory framework.Comment: 13 pages, 4 figure
Decontextualizing contextual inversion
Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip
Evaluation of a ln tan integral arising in quantum field theory
We analytically evaluate a dilogarithmic integral that is prototypical of
volumes of ideal tetrahedra in hyperbolic geometry. We additionally obtain new
representations of the Clausen function Cl_2 and the Catalan constant
G=Cl_2(\pi/2), as well as new relations between sine and Clausen function
values.Comment: 24 pages, no figure
Carbon release by selective alloying of transition metal carbides
We have performed first principles density functional theory calculations on
TiC alloyed on the Ti sublattice with 3d transition metals ranging from Sc to
Zn. The theory is accompanied with experimental investigations, both as regards
materials synthesis as well as characterization. Our results show that by
dissolving a metal with a weak ability to form carbides, the stability of the
alloy is lowered and a driving force for the release of carbon from the carbide
is created. During thin film growth of a metal carbide this effect will favor
the formation of a nanocomposite with carbide grains in a carbon matrix. The
choice of alloying elements as well as their concentrations will affect the
relative amount of carbon in the carbide and in the carbon matrix. This can be
used to design the structure of nanocomposites and their physical and chemical
properties. One example of applications is as low-friction coatings. Of the
materials studied, we suggest the late 3d transition metals as the most
promising elements for this phenomenon, at least when alloying with TiC.Comment: 9 pages, 6 figure
Electronic structure and chemical bonding of nc-TiC/a-C nanocomposites
The electronic structure of nanocrystalline (nc-) TiC/amorphous C
nanocomposites has been investigated by soft x-ray absorption and emission
spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the
nanocomposites are compared to those of Ti metal and amorphous C. The
corresponding intensities of the electronic states for the valence and
conduction bands in the nanocomposites are shown to strongly depend on the TiC
carbide grain size. An increased charge-transfer between the Ti 3d-eg states
and the C 2p states has been identified as the grain size decreases, causing an
increased ionicity of the TiC nanocrystallites. It is suggested that the
charge-transfer occurs at the interface between the nanocrystalline TiC and the
amorphous C matrix and represents an interface bonding which may be essential
for the understanding of the properties of nc-TiC/amorphous C and similar
nanocomposites.Comment: 13 pages, 6 figures, 1 table;
http://link.aps.org/doi/10.1103/PhysRevB.80.23510
Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions
Formulas are presented for the recursive generation of four-body integrals in
which the integrand consists of arbitrary integer powers (>= -1) of all the
interparticle distances r_ij, multiplied by an exponential containing an
arbitrary linear combination of all the r_ij. These integrals are
generalizations of those encountered using Hylleraas basis functions, and
include all that are needed to make energy computations on the Li atom and
other four-body systems with a fully exponentially correlated Slater-type basis
of arbitrary quantum numbers. The only quantities needed to start the recursion
are the basic four-body integral first evaluated by Fromm and Hill, plus some
easily evaluated three-body "boundary" integrals. The computational labor in
constructing integral sets for practical computations is less than when the
integrals are generated using explicit formulas obtained by differentiating the
basic integral with respect to its parameters. Computations are facilitated by
using a symbolic algebra program (MAPLE) to compute array index pointers and
present syntactically correct FORTRAN source code as output; in this way it is
possible to obtain error-free high-speed evaluations with minimal effort. The
work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009
Rapid fluctuations in the high-energy X-ray flux from a source in Crux
Balloonborne X ray telescopic observations of two point sources in Cru
A 2D systems approach to iterative learning control for discrete linear processes with zero Markov parameters
In this paper a new approach to iterative learning control for the practically relevant case of deterministic discrete linear plants with uniform rank greater than unity is developed. The analysis is undertaken in a 2D systems setting that, by using a strong form of stability for linear repetitive processes, allows simultaneous con-sideration of both trial-to-trial error convergence and along the trial performance, resulting in design algorithms that can be computed using Linear Matrix Inequalities (LMIs). Finally, the control laws are experimentally verified on a gantry robot that replicates a pick and place operation commonly found in a number of applications to which iterative learning control is applicable
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