现代热力学的完整分类系统--非平衡非耗散热力学新领域

在同一体系中同时有多个不可逆过程时，不可逆过程之间会有相互影响，原来的非自发过程有可能在其他自发过程的影响下得以进行，这种现象就称为热力学耦合或反应耦合，长期以来，经典热力学把热力学第二定律的等式作为平衡体系的充分必要条件，其中隐含了一个前提性的假定，即经典热力学的对象只限于非耦合的体系，摈弃这一隐含的前提性假定以后，热力学自身就发展成为一个现代热力学的完整学术体系，适用于任何宏观体系（包括极其复杂的生命体系），现代热力学的完整学术体系中包含了一个崭新的非平衡非耗散热力学新领域，由于该领域属于热力学第二定律的等式部分，因此可以定量计算，并得到一系列理论计算的非平衡相图，与文献上报道的激尖低压金刚石合成等的大量实验数据相符。     

Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

Christoffel functions and mean convergence for Lagrange interpolation for exponential weights

For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.     

The Design of Single Mode Large Cross-section Glass-based Waveguides for Photonic Integrated Circuits

This paper presents our recent simulation results and novel designs of single mode large cross-section glass-based waveguides for photonic integrated circuits (PICs). Simulations were performed using an in-house Finite Difference (FD) based mode solver and the FD Beam propagation Method (FD-BPM). Our simulation results show that this innovative technology could provide a simplified means to couple optical energy efficiently between optical components in a single chip. This would provide the base for the future large-scale integration of optical components in PICs. The novel idea of using single mode large cross-section glass-based waveguides as an optical integration platform is an evolutionary innovative solution for the monolithic integration of optical components, in which the glass-based structures act both as waveguides and as an optical bench for integration. This allows easy and efficient optical coupling between optical components and optical fibres, removing costly and tedious alignment problems and considerably reducing optical coupling losses in PICs. We expect that the glass-based waveguide PICs technology will enable the emergence of a new generation of compact, reliable, high speed, and multifunctional devices.     

On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.     

Structural characterization and ferromagnetic behavior of Fe-doped TiO2 powder by high-energy ball milling

Fe-doped TiO₂ powder was prepared by high-energy ball milling, using TiO₂ Degussa P-25 and α-Fe powders as the starting materials. The structure and magnetic properties of the Fe-doped TiO₂ powder were studied by X-ray diffraction, ⁵⁷Fe Mossbauer spectroscopy and vibrating sample magnetometer. The Reitveld refinement of XRD revealed that ball milling not only triggered incorporation of Fe in TiO₂ lattice but also induced the phase transformation from anatase to rutile in TiO₂ and consequently the milled Fe-doped TiO₂ powder contained only rutile.⁵⁷Fe Mössbauer effect measure showed that Fe atoms existed in Fe²⁺ and Fe³⁺ state, which were assigned to the solid solution Fe_xTi_1−xO₂. The magnetization measurements indicated that the milled Fe-doped TiO₂ powder was ferromagnetic above room temperature. The ferromagnetism in our milled Fe-doped TiO₂ powder seemingly does not come from Fe and iron oxides particles/clusters but from the Fe-doped TiO₂ powder matrices.     

Spin tunneling properties in mesoscopic magnets: effects of a magnetic field

The tunneling of a giant spin at excited levels is studied theoretically in mesoscopic magnets with a magnetic field at an arbitrary angle in the easy plane. Different structures of the tunneling barriers can be generated by the magnetocrystalline anisotropy, the magnitude and the orientation of the field. By calculating the nonvacuum instanton solution explicitly, we obtain the tunnel splittings and the tunneling rates for different angle ranges of the external magnetic field ( θ _H = π/2 and π/2 < θ _H < π). The temperature dependences of the decay rates are clearly shown for each case. It is found that the tunneling rate and the crossover temperature depend on the orientation of the external magnetic field. This feature can be tested with the use of existing experimental techniques. Received 12 March 2001 and Received in final form 18 October 2001     

Effects of Nb2O5 on thermal stability and optical properties of Er3+-doped tellurite glasses

Er³⁺-doped tellurite glasses with molar compositions of xNb₂O₅-(14.7-x)Na₂O--10ZnO--5K₂O--10GeO₂-- 60TeO₂--0.3Er₂O₃ (x=0, 3, 5, 7 and 9) have been investigated for developing 1.5~μm fibre and planar amplifiers. The effects of Nb₂O₅ on the thermal stability and optical properties of Er³⁺-doped tellurite glasses have been discussed. It is noted that the incorporation of Nb₂O₅ (x=5) increases the thermal stability of tellurite glasses significantly. Er³⁺-doped niobium tellurite glasses exhibit a large stimulated emission cross-section (7.2\times 10^-21- 10.7×10^-21~cm² and the gain bandwidth, FWHM×\sigma_e^{\rm peak} (274\times 10^-28 - 480×10^-28~cm³), which are significantly higher than that of silicate and phosphate glasses. In addition, the intensity of upconversion luminescence of the Er³⁺-doped niobium tellurite glasses decreases rapidly with increasing Nb₂O₅ content. As a result, Er³⁺-doped niobium tellurite glasses might be a potential candidate for developing laser or optical amplifier devices.     

A Lower Bound for {a+b:aA, bB, and P(a,b)≠0}

Let A and B be two finite subsets of a field . In this paper, we provide a non-trivial lower bound for {a+b:aA, bB, and P(a,b)≠0} where P(x,y) [x,y].     

Modeling of the microwave drying process of aqueous dielectrics

We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz Field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.