Martingale solutions and Markov selections for stochastic partial differential equations

We present a general framework for solving stochastic porous medium equations and stochastic Navier–Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion processes, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 691–708] and Flandoli–Romito [F. Flandoli, N. Romito, Markov selections for the 3D stochastic Navier–Stokes equations, Probab. Theory Related Fields 140 (2008) 407–458], we also study the existence of Markov selections for stochastic evolution equations in the absence of uniqueness.     

掺杂对随机取向团簇粒子辐射特性的影响

利用Bruggeman有效介质理论得到了占有不同体积份额杂质的团簇粒子的等效复折射率.采用离散偶极子近似方法对包含有不同化学成分的随机取向团簇粒子的散射相函数、消光、吸收、散射效率因子、单次散射反照率以及不对称因子等辐射特性参量进行了数值计算,深入探讨了掺杂量对随机取向团簇粒子辐射特性的影响.研究表明,掺杂对随机取向团簇粒子的辐射特性产生显著的影响,并且此影响随着粒子尺度参量的变化而变化.这一工作对研究多种化学成分组成的混合气溶胶的辐射及气候效应具有重要科学价值.     

Influence of a Kerr-Like Medium and the Detuning Parameter on the Statistical Aspects of the Intensity-Dependent-Coupling Hamiltonian

We study the interaction between a one-mode electromagnetic field and a two-level atom in the presence of a Kerr-like medium when the atom is prepared initially in the momentum eigenstate. The wave function is calculated by using the Schrodinger equation for a coherent electromagnetic field and an atom in the excited state. The effects of the Kerr-like medium and the detuning parameters on the statistical aspects of the intensity-dependent-coupling Hamiltonian such as, atomic momentum increment, momentum diffusion, the radiation force, and the field entropy are calculated. We investigate the effect of the detuning, Kerr-like medium and photon number operator on the field entropy.     

Determination of the configuration in six-membered saturated heterocycles (N,P, S,Se) and their oxidation products using experimental and calculated NMR chemical shifts

The six-membered saturated heterocycles—4-tert-butyl-1-methylpiperidine, 4-tert-butyl-1-methylphosphine, 4-tert-butyl-tetrahydro-2H-thiopyran, and 4-tert-butyl-tetrahydro-2H-selenopyran—were prepared as suitable model compounds with well-defined geometry for an NMR study of their oxidation products. The corresponding epimeric N-oxides, phosphinoxides, sulfoxides, and selenoxides were obtained by standard chemical preparation and also by in situ oxidation with meta-chloroperbenzoic acid directly in the NMR tube. The experimental ¹H and ¹³C chemical shifts were compared with corresponding calculated data obtained by GIAO approach with DFT, MP2, and HF methods and various basis sets. The correlation of experimental versus calculated data showed the possibility to determine the stereochemistry of the epimeric oxidation products using fast DFT B3LYP/6-31G* method for both geometry optimization and NMR chemical shifts calculation.     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.     

Kerr介质中V型三能级原子与双模奇偶纠缠相干光场相互作用的纠缠特性

运用量子约化熵研究了Kerr介质中V型三能级原子与双模奇偶纠缠相干光场相互作用系统中场熵的演化特性.分析了Kerr介质、失谐量和光场的初始平均光子数对场熵的影响.结果表明:Kerr介质与光场的耦合系数对场熵的振荡特性有调制作用,增大失谐量,场熵的最大值减小,振荡频率增大,由初始时刻的零值增大到最大值所需的时间也增大;光场的平均光子数太大或太小都不利于原子与光场之间的纠缠.     

Effect of parton cascade to medium

Jet quenching has been proposed as a probe of the properties of the strongly interacting quarkgluon-plasma in high energy heavy ion collisions.At the meantime,it is also important to study the excitation of medium by propagating jets.Based on Boltzmann equation,a Monte Carlo was constructed to simulate the elastic collisions with thermal partons by energetic jets.Medium modification due to jet-medium interaction has been studied within this model in a uniform medium.     

烷基苯生产中循环烷烃的液固吸附色谱预分离和气相色谱/质谱分析

 利用 10 0目～ 2 0 0目的硅胶 ,选择正戊烷和二氯甲烷作为洗脱剂 ,采用吸附色谱法将烷基苯生产中的循环烷烃分离为饱和烃 (烷烃 +环烷烃 )及芳烃两部分。然后将饱和烃及芳烃分别进行色谱 /质谱 (GC/MS)联用分析 ,得到了有关循环烷烃构成的定性定量结果。定性结果如实地反映出烷基苯生产中的副反应产物 ,可直接用于指导生产。从定量结果可以看出 ,经过硅胶吸附分离后 ,试样中含量要求很低的芳烃被浓缩 ,提高了分析的准确度和灵敏度 ,可以检测出循环烷烃中含量很低的物质 ,为全面分析样品组成提供了有力的证据。     

均匀各向同性湍流的频率波数能量谱

对均匀各向同性湍流的频率波数能量谱进行了初步研究，得出均匀各向同性湍流中能量随时间、空间尺度分布的解析表达式，并运用直接数值模拟的方法对理论预测进行验证．数值结果很好地支持了理论预测：横扫速度是决定频率波数能量谱的特征量．     

Convective heat transfer flow of nanofluid in a porous medium over wavy surface

In this letter, water base nanofluid flow over wavy surface in a porous medium of spherical packing beds is investigated. The copper oxides particles are taken into account. These properties are rehabilitated when fluid interacts with porous walls. For porous medium, Dupuit–Forchheimer model; an extension of Darcy's law model is utilized. The natures of velocity and temperature profiles of nanofluid are discussed graphically whereas the values of convection heat transfer coefficient in the presence of different nanoparticles concentrations in porous medium is presented in tabular form. The obtained results illustrate that convection heat transfer is improved by nanoparticles concentration but reduces when fluid attract to pores structured medium. On the other hand, when particles are added in fluid, convection heat transfer rate is improved but flow velocity is declined.