13,729 research outputs found
Tight-binding study of structure and vibrations of amorphous silicon
We present a tight-binding calculation that, for the first time, accurately
describes the structural, vibrational and elastic properties of amorphous
silicon. We compute the interatomic force constants and find an unphysical
feature of the Stillinger-Weber empirical potential that correlates with a much
noted error in the radial distribution function associated with that potential.
We also find that the intrinsic first peak of the radial distribution function
is asymmetric, contrary to usual assumptions made in the analysis of
diffraction data. We use our results for the normal mode frequencies and
polarization vectors to obtain the zero-point broadening effect on the radial
distribution function, enabling us to directly compare theory and a high
resolution x-ray diffraction experiment
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
Transformation laws of the components of classical and quantum fields and Heisenberg relations
The paper recalls and point to the origin of the transformation laws of the
components of classical and quantum fields. They are considered from the
"standard" and fibre bundle point of view. The results are applied to the
derivation of the Heisenberg relations in quite general setting, in particular,
in the fibre bundle approach. All conclusions are illustrated in a case of
transformations induced by the Poincar\'e group.Comment: 22 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. For
other papers on the same topic, view http://theo.inrne.bas.bg/~bozho/ . arXiv
admin note: significant text overlap with arXiv:0809.017
Dual equilibrium in a finite aspect ratio tokamak
A new approach to high pressure magnetically-confined plasmas is necessary to
design efficient fusion devices. This paper presents an equilibrium combining
two solutions of the Grad-Shafranov equation, which describes the
magnetohydrodynamic equilibrium in toroidal geometry. The outer equilibrium is
paramagnetic and confines the inner equilibrium, whose strong diamagnetism
permits to balance large pressure gradients. The existence of both equilibria
in the same volume yields a dual equilibrium structure. Their combination also
improves free-boundary mode stability
Realistic atomistic structure of amorphous silicon from machine-learning-driven molecular dynamics
Amorphous silicon (a-Si) is a widely studied noncrystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained using a machine-learning-based interatomic potential. Our best a-Si network is obtained by simulated cooling from the melt at a rate of 1011 K/s (that is, on the 10 ns time scale), contains less than 2% defects, and agrees with experiments regarding excess energies, diffraction data, and 29Si NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4096-atom system that correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with experiments to date. Our study demonstrates the broader impact of machine-learning potentials for elucidating structures and properties of technologically important amorphous materials
The Evolution of Distorted Rotating Black Holes III: Initial Data
In this paper we study a new family of black hole initial data sets
corresponding to distorted ``Kerr'' black holes with moderate rotation
parameters, and distorted Schwarzschild black holes with even- and odd-parity
radiation. These data sets build on the earlier rotating black holes of Bowen
and York and the distorted Brill wave plus black hole data sets. We describe
the construction of this large family of rotating black holes. We present a
systematic study of important properties of these data sets, such as the size
and shape of their apparent horizons, and the maximum amount of radiation that
can leave the system during evolution. These data sets should be a very useful
starting point for studying the evolution of highly dynamical black holes and
can easily be extended to 3D.Comment: 16 page
Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion
For a multicomponent wave field propagating into a multidimensional
conversion region, the rays are shown to be helical, in general. For a
ray-based quantity to have a fundamental physical meaning it must be invariant
under two groups of transformations: congruence transformations (which shuffle
components of the multi-component wave field) and canonical transformations
(which act on the ray phase space). It is shown that for conversion between two
waves there is a new invariant not previously discussed: the intrinsic helicity
of the ray
Representations of the Generalized Lie Algebra sl(2)_q
We construct finite-dimensional irreducible representations of two quantum
algebras related to the generalized Lie algebra \ssll (2)_q introduced by
Lyubashenko and the second named author. We consider separately the cases of
generic and at roots of unity. Some of the representations have no
classical analog even for generic . Some of the representations have no
analog to the finite-dimensional representations of the quantised enveloping
algebra , while in those that do there are different matrix
elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de
The Keck+Magellan Survey for Lyman Limit Absorption I: The Frequency Distribution of Super Lyman Limit Systems
We present the results of a survey for super Lyman limit systems (SLLS;
defined to be absorbers with 19.0 <= log(NHI) <= 20.3 cm^-2) from a large
sample of high resolution spectra acquired using the Keck and Magellan
telescopes. Specifically, we present 47 new SLLS from 113 QSO sightlines. We
focus on the neutral hydrogen frequency distribution f(N,X) of the SLLS and its
moments, and compare these results with the Lyman-alpha forest and the damped
Lyman alpha systems (DLA; absorbers with log(NHI) >= 20.3 cm^-2). We find that
that f(N,X) of the SLLS can be reasonably described with a power-law of index
alpha = -1.43^{+0.15}_{-0.16} or alpha = -1.19^{+0.20}_{-0.21} depending on
whether we set the lower N(HI) bound for the analysis at 10^{19.0} cm^-2 or
10^{19.3}$ cm^-2, respectively. The results indicate a flattening in the slope
of f(N,X) between the SLLS and DLA. We find little evidence for redshift
evolution in the shape of f(N,X) for the SLLS over the redshift range of the
sample 1.68 < z < 4.47 and only tentative evidence for evolution in the zeroth
moment of f(N,X), the line density l_lls(X). We introduce the observable
distribution function O(N,X) and its moment, which elucidates comparisons of HI
absorbers from the Lyman-alpha through to the DLA. We find that a simple three
parameter function can fit O(N,X) over the range 17.0 <= log(NHI) <=22.0. We
use these results to predict that f(N,X) must show two additional inflections
below the SLLS regime to match the observed f(N,X) distribution of the
Lyman-alpha forest. Finally, we demonstrate that SLLS contribute a minor
fraction (~15%) of the universe's hydrogen atoms and, therefore, an even small
fraction of the mass in predominantly neutral gas.Comment: 15 pages, 10 figures, accepted to the Astrophysical Journal. Revision
includes updated reference
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