Geometry and combinatorics of Julia sets of real quadratic maps

For real a correspondence is made between the Julia setB forz(z–)², in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325.     

Four-component Pd-catalysed cascade/ring closing metathesis. Synthesis of heterocyclic enones

A palladium-catalysed four-component process is described involving carbon monoxide, allene and aryl/heteroaryl iodides generating (π-allyl) palladium species, which are intercepted by alkene tethered nitrogen nucleophiles to afford 1,6- and 1,7-dienones. Subsequent ring closing metathesis affords five- and six-membered N-heterocyclic enones. The N-heterocyclic enones are active dipolarophiles in 1,3-dipolar cycloaddition reactions as exemplified by azomethine ylide and nitrone cycloadditions.     

Molecular dynamics simulations of displacement cascades in Fe-10%Cr systems

Molecular dynamics simulations of the displacement cascades in Fe-10%Cr systems are used to simulate the primary knocked-on atom events of the irradiation damage at temperatures 300,600,and 750 K with primary knockedon atom energies between 1 and 15 keV.The results indicate that the vacancies produced by the cascade are all in the central region of the displacement cascade.During the cascade,all recoil Fe and Cr atoms combine with each other to form Fe-Cr or Fe-Fe interstitial dumbbells as well as interstitial clusters.The number and the size of interstitial clusters increase with the energy of the primary knocked-on atom and the temperature.A few large clusters consist of a large number of Fe interstitials with a few Cr atoms,the rest are Fe-Cr clusters with small and medium sizes.The interstitial dumbbells of Fe-Fe and Fe-Cr are in the 111 and 110 series directions,respectively.     

Energy flow along the medium-induced parton cascade

We discuss the dynamics of parton cascades that develop in dense QCD matter, and contrast their properties with those of similar cascades of gluon radiation in vacuum. We argue that such cascades belong to two distinct classes that are characterized respectively by an increasing or a constant (or decreasing) branching rate along the cascade. In the former class, of which the BDMPS, medium-induced, cascade constitutes a typical example, it takes a finite time to transport a finite amount of energy to very soft quanta, while this time is essentially infinite in the latter case, to which the DGLAP cascade belongs. The medium induced cascade is accompanied by a constant flow of energy towards arbitrary soft modes, leading eventually to the accumulation of the initial energy of the leading particle at zero energy. It also exhibits scaling properties akin to wave turbulence. These properties do not show up in the cascade that develops in vacuum. There, the energy accumulates in the spectrum at smaller and smaller energy as the cascade develops, but the energy never flows all the way down to zero energy. Our analysis suggests that the way the energy is shared among the offsprings of a splitting gluon has little impact on the qualitative properties of the cascades, provided the kernel that governs the splittings is not too singular.     

An Endo-Selective Epoxide-Opening Cascade for the Fast Assembly of the Polycyclic Core Structure of Marine Ladder Polyethers

The rapid synthesis of marine ladder polyethers from polyepoxide precursors (in analogy with the biosynthetic pathway hypothesized by Nakanishi) is hampered by the fact that the exo-selective epoxide-opening cyclization cascade that gives THF-type polyethers is preferred over the endo-selective cascade that gives the desired products. We found that perfluoro-tert-butanol (PFTB) cooperating with 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM]BF₄) can promote endo-selective epoxide-opening cyclization reactions of trisubstituted epoxy alcohols. Starting from readily accessible homochiral polyepoxy alcohols with a methyl group at all the endo-cyclization sites, we were able to construct polyethers up to five consecutive fused 6-, 7-, and/or 8-membered rings in one step. Notably, molecules with the 7/7/6/6 and 7/7/6/7/6 polyether frameworks of hemibrevetoxin B and brevenal, respectively, could be synthesized in 40 % and 17 % chemical yields.     

Intranuclear-Cascade model calculation of photofission probabilities for actinide nuclei

We have calculated the fission probabilities for ²³⁷Np, ^{233, 235, 238}U, ²³²Th, and ^natPb following the absorption of photons with energies from 68 MeV to 3.77 GeV using the RELDIS Monte Carlo code. This code implements the cascade-evaporation-fission model of intermediate-energy photonuclear reactions. It includes multiparticle production in photoreactions on intranuclear nucleons, pre-equilibrium emission, and the statistical decay of excited residual nuclei via competition of evaporation, fission, and multifragmentation processes. The calculations show that in the GeV energy region the fission process is not solely responsible for the entire total photoabsorption cross-section, even for the actinides. The fission probabilities are 80-95% for ²³³U, ²³⁵U, and ²³⁷Np, 70-80% for ²³⁸U, and only 55-70% for ²³²Th. This is because certain residual nuclei that are created by deep photospallation at GeV photon energies have relatively low fission probabilities. The results of those model calculations are in reasonable agreement (at the 10% level) with recent experimental data on relative photofission cross-sections for ²³⁷Np and ^{233, 235, 238}U (but not for ²³²Th or ^natPb) from the Saskatchewan and Jefferson Laboratories over a very wide range in photon energy. Using our calculated fission probabilities plus the total photoabsorption cross-sections per nucleon, estimated from previous cross-section data for nuclei from C to Pb, we can infer absolute photofission cross-sections for the actinide nuclei and compare them with the SAL and JLab results. The resulting discrepancies, however, clearly demonstrate the need for direct measurement of the total photoabsorption cross-sections for the heavy actinides.     

两种透平叶栅三维流动的计算分析

本文以数值手段分析研究两种不同叶片造型的三维环形叶棚内的定常粘性流动及损失情况，数值方法采用三维可压缩粘性流动压力校正其法求解N－S方程及k－ε双方程湍流模型．新一代透平叶片型线设计与传统叶片型线的差别在于叶片型线的后部加载特性．本文通过计算分析了这种后加载叶片与传统加教叶片应用于汽轮机时对控制三级叶栅损失与二次流发展的作用．     

Remarkable synergistic effect between MonBI and MonBII on epoxide opening reaction in ionophore polyether monensin biosynthesis

Enzymatic epoxide-opening cascade is one of the key biosynthetic processes for constructing structurally diverse polyethers. Here we report the first in vitro analysis of the cyclization catalyzed by two epoxide hydrolases, MonBI and MonBII involved in monensin biosynthesis, using simple epoxy-alcohols and the unprecedented synergistic effect on the epoxide-opening activity between these epoxide hydrolases.     

Development of the Monte Carlo model CASCADE-2004 of high-energy nuclear interactions

The Monte Carlo code CASCADE for the calculation of inelastic hadron- and nucleus-nucleus interactions at energies from several tens of MeV up to several tens of GeV and for modelling of nuclear-physical processes accompanying the transport of particles and nuclei in matter is improved by considering a more detailed model of decay of highly excited residual (after-intranuclear-cascade) nuclei. Results of calculations are in good agreement with experiment. However, there are some deviations for light-isotope production, which prompt the necessity of developing more correct models of evaporation and strong asymmetric high-energy fission.