Evidence for a solid phase of dodecahedral C 20

Evidence is presented for the formation of a solid phase based on the smallest fullerene, C₂₀, in thin diamond-like carbon films deposited by ultraviolet laser ablation from diamond onto nickel substrates at room temperature in the presence of 10^-4 torr of cyclohexane or benzene. Laser desorption mass spectrometry from the films shows the presence of C₂₀, C₂₁ and C₂₂ species, while micro-Raman spectroscopy and electron diffraction from selected particles together with first principle density-functional calculations, indicate a cubic solid with dodecahedral C₂₀ cages as building blocks. Unlike solid C₆₀ and fully protonated C₂₀, which are bound by van der Waals forces, the proposed structure is stabilized by linking of the C₂₀ dodecahedra with bridging carbon atoms at interstitial tetrahedral sites to form a face-centered-cubic lattice with 22 carbon atoms per unit cell. Received 10 October 2002 / Received in final form 24 December 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: zafar.iqbal@njit.edu     

Ab initio simulation of phase transitions and dissociation of H2S at high pressure

By ab initio constant pressure molecular dynamics, we have identified the structure of phase V and phase VI of H2S at 35 and 65 GPa, respectively. The theoretical IR spectra of both phases are consistent with experimental findings and support our proposed structural models. We find that phase V is characterized by the presence of charged SH+3 and SH- species which are created and destroyed dynamically, whereas phase VI is no longer a molecular phase but consists of sheets of S with the majority of H intercalated between the layers. The stability of the two phases with respect to dissociation into elemental crystalline hydrogen and sulfur is discussed.     

Correlations in a Mozart's music score (K-73x) with palindromic and upside-down structure

In this work, we study long-range correlations in a “Scherzo-Duetto di Mozart” score (K-73x) for two violins. This is a fascinating piece, as the second violin part is upside down on the same sheet below the first violin, and some parts are like a palindrome. Given such ingenious structure, it is expected the existence of long-range correlations in the score structure. In order to quantify long-range correlations, we considered the music score as a sequence of integer numbers, each of them corresponding to last common denominator units of note. By using detrended fluctuation analysis (DFA), correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note. The following conclusions can be drawn from the analysis: (a) For about 10-25 neighbor note distances, correlations are similar to 1/f-noise. This is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1/f noise. (b) As the neighbor note distance increases, the long-range correlations decays continuously. For some score sections, the music score behaves like non-correlated (i.e., purely random) noise. Summing up, the results show that the studied Mozart's score contains a certain degree of correlation for relatively small note distances, and becomes close to non-correlated behavior for long note distances. We considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins. Interestingly, for relatively small neighbor note distances, a scaling behavior similar to that found for individual violins is also displayed. In some sense, this is an expression of the specific structure (palindromes plus upside down construction) used by Mozart in the composition of this music score. Although we focused on a particular high-art music score, our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques.     

One‐pot Preparation,Spectroscopic and Structural Characterization of Mercury(II) Complexes of Bulky Diimines with Halides and Pseudohalides

The preparation and characterization of two novel HgCl₂ and Hg(SCN)₂ complexes with bis[N‐(2‐tert‐butylphenyl)imine]acenaphthene is here described. One‐pot reaction techniques were used, leading to high yields of 75 % and 81 %, respectively. The complexes were characterized by microanalysis, i.r. and ¹HNMR spectroscopy, and by single crystal X‐ray diffraction. The structures of the complexes present similar characteristics, the most outstanding being the formation of dimers via intermolecular interaction. Whereas the HgCl₂ complex shows a unidimensional network due to strong π–π interactions, its Hg(SCN)₂ counterpart displays a supramolecular arrangement resulting from non classical hydrogen bond formation.     

Phonon dispersion curves and densities of lithium-intercalated iron phosphorus trisulfide

Summary The lattice dynamics of Li-intercalated FePS₃ has been studied by means of a force constant model generated by a set of short-range two-body potentials. The intercalated phases have been investigated for the three stoichiometric compositions: Li_0.5FePS₃, LiFePS₃, Li_1.5FePS₃, with the aim of analysing the evolution of the host lattice normal modes as a function of the concentration, and of finding the dispersion of the new phonon branches induced by lithium. The above special values of lithium concentration have been chosen because the size of the unit cell keeps the same as in the host material. The force constants are fitted to the infrared data and the phonon dispersion curves and the phonon energy densities have been calculated. A spectroscopic method for monitoring lithium migration in the host material is proposed.     

Renormalization Group Flow¶of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L&\darr; 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t→∞, to one of the countably infinite equilibrium solutions. The j ^th nontrivial equilibrium solution bifurcates from the trivial one at . These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature β >0. Gallavotti and Nicoló's conjecture on infinite sequence of “phases transitions” is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz–Thouless phases, at least in the hierarchical model we consider. Received: 29 November 1999 / Accepted: 13 January 2001     

Topological duality for Tarski algebras

In this paper we will generalize the representation theory developed for finite Tarski algebras given in [7]. We will introduce the notion of Tarski space as a generalization of the notion of dense Tarski set, and we will prove that the category of Tarski algebras with semi-homomorphisms is dually equivalent to the category of Tarski spaces with certain closed relations, called T-relations. By these results we will obtain that the algebraic category of Tarski algebras is dually equivalent to the category of Tarski spaces with certain partial functions. We will apply these results to give a topological characterization of the subalgebras. Received August 21, 2005; accepted in final form December 5, 2006.