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 $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism between two cluster algebras associated to the matrix $A$ (see section 4 for precise meaning). When $A$ 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 $q$ generic and $q$ at roots of unity. Some of the representations have no classical analog even for generic $q$. Some of the representations have no analog to the finite-dimensional representations of the quantised enveloping algebra $U_q(sl(2))$, 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