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.     

Functional Carbazole-Fullerene Complexes: A New Perspective of Carbazoles Acting as Nano-Octopus to Capture Globular Fullerenes

Fullerene host-guest constructs have attracted increasing attention owing to their molecular-level hybrid arrangements. However, the usage of simple carbazolic derivatives to bind with fullerenes is rare. In this research, three novel carbazolic derivatives, containing a tunable bridging linker and carbazole units for the capturing of fullerenes, are rationally designed. Unlike the general concave-convex interactions, fullerenes could interact with the planar carbazole subunits to form 2-dimensional hexagonal/quadrilateral cocrystals with alternating stacking patterns of 1 : 1 or 1 : 2 stoichiometry, as well as the controllable fullerene packing modes. At the meanwhile, good electron-transporting performances and significant photovoltaic effects were realized when a continuous C_60⋅⋅⋅C₆₀ interaction channel existed. The results indicate that the introduction of such carbazolic system into fullerene receptor would provide new insights into novel fullerene host-guest architectures for versatile applications.     

Twofold-broken rational tori and the uniform semiclassical approximation

We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top. Received 3 August 1999     

Towards understanding the critical heat flux for industrial applications

Understanding CHF is of an upmost importance in many industries, especially in the design and operation of boilers, nuclear power plants, cryogenic systems, etc. Due to safety issues related to the nuclear power plants, and the adaptation of CHF as the limiting criterion of power generation, it is important to understand the mechanisms of CHF relevant to nuclear systems operation. Moreover, CHF is expected to occur during transients than steady-state conditions. Therefore, knowledge of transient CHF is of great importance for the safety evaluation of nuclear reactors under transient condition. In this paper, the existing CHF experimental and modeling studies are discussed in order to understand the phenomena leading to CHF. Also, the effect of transient conditions on CHF for nuclear fuels has been evaluated.     

Thermal decomposition of butylindium thiolates and preparation of indium sulfide powders

Thermal properties of organoindium thiolates were investigated by means of thermogravimetric (TG) and differential thermal (DT) analysis. Dibutyl-indium propylthiolates (Buⁿ₂InSPrⁿ, Buⁿ₂InSPrⁱ, Buⁱ₂InSPrⁿ and Buⁱ₂InSPrⁱ) decomposed up to 280°C along with an exothermic DT peak and gave indium(I) sulfide (InS) powders. Although the arylthiolate Buⁿ₂InSPh also afforded InS powders, it decomposed at a slightly higher temperature. In contrast, the dithiolate and the dithiocarbamate complexes [BuⁿIn(SPrⁱ)₂ and In (S₂CNBu₂)₃] gave indium(III) sulfide (In₂S₃) powders.     

Recent advances in photofunctional polymorphs of molecular materials

Crystalline polymorph is an intriguing phenomenon that the presence of multiple packing and aggregate architectures of the same molecular system.In this review,we focus on the recent progress in various feasible methods of molecule-based crystalline polymorphism growth,their adjustable photofunctional properties and multifunctional applications,which will help to illustrate the structure-property relationship.     

Laccase‐catalyzed polymerization of lignocatechol and affinity on proteins of resulting polymers

For the synthesis of a new biologically functional polymer from a natural resource by an environment‐friendly method, the laccase‐catalyzed polymerization of a lignin‐based macromonomer, lignocatechol, was carried out for the first time in ethanol–phosphate buffer solvent system to give crosslinked polymers in good yields. Lignocatechol was prepared by the phase separation system of lignin and catechol in aqueous sulfuric acid. The copolymerization was also performed with urushiol to afford the corresponding copolymers in high yields. The polymerization mechanism was estimated by the IR and pyrolysis GC‐MS measurements, suggesting that the polymerization proceeded mainly at the catechol ring through a quinone radical intermediate. The thermal properties were measured by the DSC, TG, and TMA analyses, indicating that the polymers had high thermal stabilities because of the crosslinked structures. In addition, it was found that the resulting polymers had the affinity of bovine serum albumin (BSA) and glucoamylase. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 824–832, 2009     

Fermion gases in magnetic fields: a semiclassical treatment

The study of quantum degenerate gases has received much interest in these last years essentially thanks to the extremely important experimental results of the achievement of Bose-Einstein condensation of atoms and, very recently, of almost complete degeneracy of atomic fermion gases. Here we want to present the results of a semi-analytical method for the study of an interacting degenerate fermion gas based on semiclassical kinetic theory; special care has been devoted to the study of a rotating electron gas, in a cylindrically symmetrical configuration, radially confined by a uniform magnetic field. The model will lead to a particular Thomas-Fermi equation which is generalized to take into account finite temperature and average velocity of the gas, and which is further developed to consider the effects of external fields. Received 10 March 2000