Collective diffusion of Brownian particles with square well and hydrodynamic interaction

The low wavenumber collective diffusion coefficient of a semi-dilute suspension of spherical Brownian particles interacting via square well potential and hydrodynamic pair interaction is considered. The first two nonvanishing terms of an expansion in powers of the wavenumber are calculated. Analytical expressions are found for extremely narrow wells and in the limit of large well diameters.     

Optical Reskponse of Metal—Dielectric Composite Containing Interfacial Layers

A phenomenological approach nto investigate the effect of interfacial layers on the absorption of metaldielectric composite at elevated temperatures is put forward by making use of a model in which weakly nonlinear spherical metallic particles with linear concentric shells are randomly embedded in a linear host.Corresponding formulae in terms of the interfacial factor are derived in detail by incorporating Taylor expansion and Drude model.We take Ag/MgF2 composite as numerical calculation.It is concluded that such absorption is dependent not only on the temperature,but also on the properties of interfacial layers.Many other interesting phenomena are shown.     

Collision induced spectrum decay constant for Lennard-Jones interaction potential

An expression of the collision induced spectrum decay constant has been derived for spherical molecules interacting with a (6–12) Lennard-Jones potential. Theoretical vakues for Hard-Sphere and Lennard-Jones potential are compared with the experimental values for gaseous Ar, CH₄, CF₄.     

Blood flow in microvascular networks: a study in nonlinear biology

Plasma skimming and the Fahraeus-Lindqvist effect are well-known phenomena in blood rheology. By combining these peculiarities of blood flow in the microcirculation with simple topological models of microvascular networks, we have uncovered interesting nonlinear behavior regarding blood flow in networks. Nonlinearity manifests itself in the existence of multiple steady states. This is due to the nonlinear dependence of viscosity on blood cell concentration. Nonlinearity also appears in the form of spontaneous oscillations in limit cycles. These limit cycles arise from the fact that the physics of blood flow can be modeled in terms of state dependent delay equations with multiple interacting delay times. In this paper we extend our previous work on blood flow in a simple two node network and begin to explore how topological complexity influences the dynamics of network blood flow. In addition we present initial evidence that the nonlinear phenomena predicted by our model are observed experimentally.     

Theoretical models for deuteron photodisintegration in the energy range between 250 MeV and 800 MeV

Two theoretical models of γd → pn are developed to study the differential cross-section and'the proton polarization data in a coherent way. The first model is an extension of conventional diagrammatic summations of Born terms and isobar excitation terms. The second model is novel in that the isobar excitation terms are replaced by experimentally determined _γN → N_π helicity amplitudes. The second model allows us to extend to higher energies with the introduction of only one arbitrary parameter. The differential cross-section data are fairly well reproduced in the whole energy range, while the proton polarization data are very far removed from the calculations.     

The Effective AC Response of Nonlinear Composites

A perturbative approach is used to study the AC response of nonlinear compostie media,which obey a current-field relation of the form J=σE χ|E|^2E with comp[onents having nonlinear response at finite frequencies.For a sinusoidal applied field,we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear comosites.For nonlinear composite media with a low concentrations of spherical inclusions,we give the formulae of the nonlinear effective AC susceptibility χ3ω at the third harmonic frequency.     

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.     

CdSe:Nd纳米晶及CdSe:Nd@SiO2核壳结构的合成及发光性能

利用有机相法合成Nd³⁺掺杂CdSe纳米晶（CdSe∶Nd）,通过X射线粉末衍射（XRD）、透射电镜（TEM）、紫外吸收光光谱及荧光光谱表征,证明Nd³⁺已经成功掺入到CdSe的晶格中。与纯CdSe纳米晶相比,CdSe∶Nd纳米晶的结构仍为立方晶型,且形貌近似球形,均匀分散,粒径约为2~4 nm。紫外吸收峰和荧光发射峰都发生红移,而且掺杂后的CdSe∶Nd纳米晶量子产率也提高,这可能是由于掺杂Nd³⁺引入了新的杂质能级,带隙减小。为了实现CdSe∶Nd纳米晶的可加工性和功能性,通过微乳法合成SiO₂壳包覆的CdSe∶Nd纳米球（CdSe∶Nd@SiO₂纳米球）,CdSe∶Nd@SiO₂纳米球呈均匀球形,直径约为100~115 nm,并且包壳后的CdSe∶Nd@SiO₂纳米球发射峰（581 nm）与CdSe∶Nd纳米晶（598 nm）相比,发光强度提高且发射峰蓝移,蓝移约为17 nm,可能是因为SiO₂壳可以减少纳米晶表面的非辐射跃迁以及改善表面缺陷导致的。     

Breit夸克势的不同次正规化与ηc-J/ψ等的质量劈裂

用夸克势模型研究结构相同而自旋和轨道量子数不同的介子之间质量劈裂是检验势模型有效性的重要手段之一. 在以往的用各种夸克势模型计算质量劈裂工作中, 当轻介子和重介子一起计算时, π-ρ很容易劈裂, 而η_c-J/ψ等的劈裂都很 难达到实验值. 这里首先用正规化形状因子μ²/(q²+μ²), 对完整的动量空间中的Breit夸克势的第三项实施二次正规化, 除了第一项 库仑势和第七项常数项势, 对其余的项实施一次正规化, 然后用来计算 质量劈裂. 研究计算发现, 只有当屏蔽质量μ取为关于 折合质量μ_r=m_r m_j/(m_r+m_j) 的三阶多项式时, 轻介子π-ρ和重介子η_c-J/ψ, η_b-Υ(1s), 还有χ_c0-χ_c1-χ_c2 等的劈裂 精确达到实验值, 同时其他介子质量也都比以往得到较大的改善. 因此, 本文给出了一个有效的夸克势模型.     

Cluster integrals of convex molecule systems

Cluster integrals assigned to particles interacting via the Kihara non-spherical potential are studied theoretically. An exact formula is derived which allows one to consider the effect of molecular shape separately from the effect of soft interactions. Employing the proposed formalism, the cluster integrals are analysed. The approach is applied to determine the third virial coefficient and an efficient computational method is developed. The third virial coefficient was calculated for a combination of molecules with hard cores of prolate spher-ocylindrical- and spherical shapes interacting via the square-well, triangle-well and 12-6 pair potentials. Comparison with numerical results obtained by Monte Carlo integration is made and fair agreement is found.     

Total Cross Sections for Electron Scattering on Polyatomic Molecules (CH4, CO2,NO2, and N2O) at 10 ～ 3000 eV

A new modified formulation of the Additivity Rule (AR) was proposed to calculate the total electron scattering cross sections for CH₄, CO₂, NO₂, and N₂O, considering the overlapping between atoms in molecules and the not fully transparency of the molecules. The present calculation covers the range of impact energy from 10 to 3000 eV. The results are compared with experimental data and other theories where available. The atoms are presented by spherical complex optical potential, which is composed of static, exchange, polarization, and absorption terms.     

氢化铁的自旋极化效应及势能函数

B3LYP/6-311++g**水平上预测了FeH2及FeH稳定构型讨论了其自旋极化效应,并与实验结果进行了比较.结果表明其基态分别为FeH2(5A1)和FeH(4?),自旋态对构型和物理性质均有显著影响.FeH2具有C2v对称性.势能与核间距的关系用4参数Murrell-Sorbie函数进行拟合得到其分析势能函数.由此推导出力常数和光谱数据,并由多体项展式理论导出了基态FeH2分子的分析势能函数.用这个分析势能函数分析表明:H+FeH生成FeH2(C2v)分子通道存在一个4.68 eV深的势阱,易生成H—Fe—H络合物分子.反应Fe+H2→HFeH,?H=-0.08305 eV,是放热反应.     

Classification of the Phenomenological Models of Phase Transitions with Two Interacting Order Parameters Using the Catastrophe Theory: <Emphasis Type="Italic">L</Emphasis> = <Emphasis Type="Italic">C</Emphasis><Subscript>2<Emphasis Type="Italic">v</Emphasis></Subscript>

The phenomenological models of phase transitions for two one-component interacting order parameters have been classified using the methods of the equivariant catastrophe theory. The models have been constructed based on the number of control parameters, which depend on the thermodynamic parameters varied in experiments (temperature, pressure, chemical potentials of impurities, etc.), rather than by simple expansion of the thermodynamic potential in series of order-parameter powers. The models with the order-parameter symmetry group L = C_2v are classified in terms of the number of control parameters from two to five. An infinite series of the phenomenological models with biquadratic interaction of the order parameters was also obtained.     

Mean Spherical Approximation-Based Partitioned Density Functional Theory

Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0^(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ^3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.     

Statistical ensembles for money and debt

We build a statistical ensemble representation of two economic models describing respectively, in simplified terms, a payment system and a credit market. To this purpose we adopt the Boltzmann–Gibbs distribution where the role of the Hamiltonian is taken by the total money supply (i.e. including money created from debt) of a set of interacting economic agents. As a result, we can read the main thermodynamic quantities in terms of monetary ones. In particular, we define for the credit market model a work term which is related to the impact of monetary policy on credit creation. Furthermore, with our formalism we recover and extend some results concerning the temperature of an economic system, previously presented in the literature by considering only the monetary base as a conserved quantity. Finally, we study the statistical ensemble for the Pareto distribution.     

Generalized Integral Fluctuation Relation with Feedback Control for Diffusion Processes

We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation. This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.     

A generalized approach to complex networks

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.     

一类新的Stückelberg全息超导模型

本文研究了含Stückelberg机理的黑洞全息超导模型. 通过选取标量场新的高阶修正形式, 建立了新的Stückelberg黑洞全息超导模型. 通过研究模型参数对标量场凝聚的影响, 发现了当模型参数大于临界值时, 高阶修正可以引起一阶相变. 同时本文还考查了反作用对临界值的影响.     

A generalized Hartree-Fock-Bogoliubov approach for the description of band structures in nuclei: (II). The generalized Hartree-Fock-Bogoliubov theory in the intrinsic frame of reference

The problem of the occupation number calculation for the generalized Hartree-Fock-Bogoliubov (GHFB) approach is solved by introducing an intrinsic frame of reference, where the generalized density matrix and the average field Hamiltonian becomes diagonal with respect to the nulcear spin I. Using variational methods a dynamical equation is obtained, which determines the intrinsic density matrix. Its eigenvalues are defined by means of additional kinematical conditions following from the Pauli principle. A special symmetry of the intrinsic average field Hamiltonian allows us to divide the quasiparticle states in to two conjugated groups having positive quasiparticle energies and the corresponding negative quasiparticle energies, respectively. A generalized Coriolis interaction and new self-consistency conditions are derived. The relation of the present model to the self-consistent cranking model is discussed. As a numerical example the equilibrium deformation for a system of nucléons moving in a spherical oscillator potential and interacting via simple quadrupole forces is calculated.     

Molecular dynamics computation of clusters in liquid Fe–Al alloy

By means of constant pressure molecular dynamics (MD) simulation technique, a series of simulations of the Fe₅₀Al₅₀ alloy have been carried out. The atoms interact via semi-empirical n-body noncentral potential. The pair correlation functions and the pair analysis technique is applied to reveal the cluster evolution in the process of quick solidification. By using the bond orientation order parameters, we have measured both local and extended orientation symmetries for computer-generated models of dense liquid and glass. A lot of polyhedra in liquid system, for example, icosahedra, are also obtained. In order to test the reliance of the computation results, corresponding X-ray diffraction experiments have been performed on the material.