Rapid evaluation of synthetic and molecular complexity for in silico chemistry

Methods that rapidly evaluate molecular complexity and synthetic feasibility are becoming increasingly important for in silico chemistry. We propose a new metric based on relative atomic electronegativities and bond parameters that evaluate both synthetic and molecular complexity (SMCM) starting from chemical structures. Against molecular weight, SMCM has the lowest fraction of adjusted variance (R2=0.535) on a series of 261,048 diverse compounds, when compared to the complexity metric of Baron and Chanon (R2=0.777; J. Chem. Inf. Comput. Sci. 2001, 41, 269-272) and Rücker (R2=0.895 for log complexity values; J. Chem. Inf. Comput. Sci. 2004, 44, 378-386), respectively. These metrics are in general agreement when the metabolic synthesis of cholesterol from S-3-hydroxy-3-methyl-glutaryl coenzyme A is monitored, indicating that SMCM can be useful in discerning increases in complexity. Because the presence of substructure patterns can be directly incorporated into this scheme, SMCM is relatively straightforward and can be easily tailored to rapidly evaluate virtual (combinatorial) libraries and high throughput screening hits.     

The level-rank duality for non-abelian theta functions

We prove that the strange duality conjecture of Beauville–Donagi–Tu holds for all curves. We establish first a more extended level-rank duality, interesting in its own right, from which the standard level-rank duality follows by restriction.     

Modulational Stability of Travelling Waves in 2D Anisotropic Systems

The modulational stability of travelling waves in 2D anisotropic systems is investigated. We consider normal travelling waves, which are described by solutions of a globally coupled Ginzburg–Landau system for two envelopes of left- and right-travelling waves, and oblique travelling waves, which are described by solutions of a globally coupled Ginzburg–Landau system for four envelopes associated with two counterpropagating pairs of travelling waves in two oblique directions. The Eckhaus stability boundary for these waves in the plane of wave numbers is computed from the linearized Ginzburg–Landau systems. We identify longitudinal long and finite wavelength instabilities as well as transverse long wavelength instabilities. The results of the stability calculations are confirmed through numerical simulations. In these simulations we observe a rich variety of behaviors, including defect chaos, elongated localized structures superimposed to travelling waves, and moving grain boundaries separating travelling waves in different oblique directions. The stability classification is applied to a reaction–diffusion system and to the weak electrolyte model for electroconvection in nematic liquid crystals.      

综放极限平衡区顶煤渗透性的计算模型

基于放顶煤开采中顶煤渗透率对工作面安全生产的重要性, 对煤壁前方极限平衡区内顶煤渗透率的变化规律进行了研究. 应用损伤力学和数理统计方法对顶煤垂直和水平应变进行了研究分析, 并建立了数学模型. 以甲烷气体为渗流体, 应用自制三轴实验机对煤样体积应变与渗透率的关系进行了试验研究, 并利用多项式拟合方法对试验结果进行了分段拟合. 结果表明：根据所建立的顶煤应变计算模型, 可以求出综放顶煤内任意点的体积应变, 且顶煤的水平应变与其距底板的高度无关. 依据试验及拟合所得到的煤体体积应变与渗透率的函数关系, 可以求得顶煤内任意点渗透率. 最后对计算模型进行了实践检验.