Initial growth of Boltzmann entropy and chaos in a large assembly of weakly interacting systems

We introduce a high-dimensional symplectic map, modeling a large system, to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the initial growth of the Boltzmann entropy, S_B, as a function of the coarse-graining resolution (the late stage of the evolution is trivial, as the system is subjected to no external drivings). We show that a characteristic scale emerges, and that the behavior of S_B vs t, at variance with the Gibbs entropy, does not depend on the resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth, in its early stage, depends essentially on the single-particle chaotic dynamics. It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.     

Self-organized criticality in 1D stochastic traffic flow model

Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.     

Interfaces in perovskite heterostructures

Recent advances in film synthesis have made it possible to investigate the properties of well-controlled interfaces in perovskite metal-oxides. A review of published experimental data and computational results indicate that so far most interfaces that have been analyzed in ferroelectric materials—while necessary to impose large lattice strain on the polar material—contribute little to the ferroelectricity and may instead be detrimental to the desired properties. In contrast, a very different situation arises at interfaces that show changes in the electronic configuration as a consequence of a compositional discontinuity. Data is shown for LaMnO₃/SrTiO₃ superlattices as an example of electronic effects that produce enhanced properties, further illustrating the richness of interfacial properties that can be obtained at interfaces (as shown in numerous published results for different but related interfaces).     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,...     

Emission,Emissionslebensdauer und Absorption von [Cr urea6]X3-Einkristallen

Emission and absorption polarization spectra as well as emission lifetimes between room temperature and 5 °K have been measured of [Cr urea₆]X₃ single crystals, where X stands for ClO ₄ ^– , J^–, NO ₃ ^– , Br^–, Cl^–, F^–, and X₃ for JSO ₄ ^3– . The strong temperature dependence of the fluorescence/phosphorescence-ratios, and of the emission lifetimes is discussed. The differences between the spectra as well as the emission lifetimes of the various salts can be attributed to an anion dependent trigonal perturbation.kquote>kquote>Die Autoren danken dem Verband der Chemischen Industrie für finanzielle Unterstützung dieser Arbeit.     

Electronic structure of unstable intermediates

The geometry of the linear molecule HBO, has been investigated within the restricted Hartree-Fock LCAO-MO-SCF approximation. The calculated bond lengths for the near Hartree-Fock calculation were R(H-B)=2.1913 bohr, R(B-O)=2.2284 bohr. Several one electron properties have been calculated for the minimum energy configuration.     

Synthesis of N-unsubstituted ketene aminals from β-ketocarboxylic esters and cyanamide

The interaction of cyanamide with k281t660/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-ketocarboxylic esters in the presence of Ni(acac)₂ affords N-unsubstituted aminals of acyl(alkoxycarbonyl)ketenes.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 419–421, February, 1993.     

Inter-ring η6⇌η5 haptotropic rearrangements of 18ē and 19ē (η5-pentamethylcyclopentadienyl)(η6-9-methylfluorenyl)iron complexes

New cationic complexes [(k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁶-C₁₃H₁₀)Fe(k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁵-Cp^*)]PF₆ and [(k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁶-9-CH₃-C₁₃H₉)Fe(k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁵-Cp^*)]PF₆ were obtained by the reaction of Cp^*Fe(CO)₂Br with fluorene and 9-methylfluorene, respectively. Deprotonation of these complexes byt-BuOK in THF affords zwitter-ionic compounds (k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁶-C₁₃H₉)Fe(k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁵-Cp^*) and (k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁶-9-CH₃-C₁₃H₈)Fe(k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁵-Cp^*) (A). WhenA is heated in nonane at 150 °C it undergoes k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁶k4439vn/xxlarge8652.gif" alt="rlhar" align="MIDDLE" BORDER="0">k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁵ inter-ring rearrangement with the formation of hexamethyldibenzoferrocene (B). The electrochemical behavior ofA andB was studied by cyclic voltammetry. One-electron reduction ofA andB to the corresponding radical anions induces inter-ring haptotropic rearrangementA ^.–k4439vn/xxlarge8652.gif" alt="rlhar" align="MIDDLE" BORDER="0">k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">B ^.–. The equilibrium in the 19k4439vn/xxlarge275.gif" alt="emacr" align="BASELINE" BORDER="0"> state is shifted to the k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁶-isomeric radical anionA ^.–, while in the 18k4439vn/xxlarge275.gif" alt="emacr" align="BASELINE" BORDER="0"> precursors, it shifts to the k4439vn/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0">⁵-isomerB.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 319–324, February, 1994.The authors are grateful to D. V. Zagorevskii (A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences) for recording and interpreting the mass spectra, and to A. A. Borisenko (Moscow State University) for recording the NMR spectra.This work was financially supported by the Russian Foundation for Basic Research (Grant 93-03-5209).     

Transformed steroids

A preparative method for 9a-hydroxylation of k51191/xxlarge916.gif" alt="Delta" align="BASELINE" BORDER="0">⁵-3k51191/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-hydroxysteroids using the fungi ofCircinella sp. 10Kh-1220 not capable of modifying theA ring has been developed. It is established that the yields of the main and the side products greatly depend on the transformation conditions, mycelium age, and the structure of the steroid substrate. Under the optimal transformation conditions novel 9k51191/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-hydroxysubstituted derivatives of androstenolone, pregnenolone, 16-dehydro-16k51191/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">,17k51191/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-epoxy-, and-16k51191/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-methoxypregnenolone have been obtained in 36–80 % yields.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 737–743, April, 1994.