微晶粘结成球的无机离子交换剂传质研究

无机离子交换剂以其选择性、耐热及抗辐照性很高一直受到重视.但由于它的交换过程缓慢,使其应用受到了限制,为了克服这一障碍,本文把十分之几微米的无机离子交换剂[Ti(HPO_4)_2·1/2H_2O]微晶粘结成球,以减低对流体阻力,同时大大增加交换表面.用这种交换剂研究了H~+-Li~+和Li~+-H~+互交换的动力学;同时,根据交换剂的几何模型,解出了相应界面条件的扩散方程.实验显示了在这种无机离子交换剂中的交换速度比在001×20的聚苯乙烯凝胶磺酸型阳离子交换树脂中的快3.5倍,它可能为提高无机离子交换剂的传质功能提供了新途径.     

基于梯度折射率透镜的管道内窥镜设计

 针对管道测试的需求,将梯度折射率透镜的光学性能与显微镜相结合,设计了具有大景深的管道内窥镜光学系统.在保证所需放大倍率的同时,利用梯度折射率透镜介质折射率渐变的特点,使该系统的景深增大为原来的200倍.该系统像面近似球面的特点使其更适合圆形管道内壁的检测,当它与CCD等器件相结合,不仅实现管道内窥镜的数字化测试,而且能通过监视器在更大景深范围内、方便的监测管道内壁的裂痕、磨损等清晰的图像.     

Phase Diagram and Phase Separation of a Trapped Interacting Bose-Fermi Gas Mixture

In six different regimes for a spatial phase diagram of a trapped interacting Bose-Fermi gas mixture at low temperatures, we present the conditions for the spatial demixing and separation of bosons and fermions. Starting from a semiclassically thermodynamic model for the local density functional of thermal bosons and fermions,the explicit analytical expressions for the fugacities of bosons and fermions are derived in different regimes by means of a first-order perturbation method in a local-density approximation. The critical values of the fermionboson interaction strength as a function of the fractional composition of fermions have a general feature: increase,extreme and decrease with increasing the fermionic composition slightly above Bose-Einstein critical temperature.     

火焰原子吸收分光光度法测定改性粘土催化剂中的铜

以无机天然粘土或用金属离子交换处理粘土制备的改性粘土作为固体酸催化剂 ,因其具有选择性好、廉价、易再生及无环境污染等特点 ,正成为目前绿色化学研究的热点 ,特别是经离子交换制备的改性粘土应用于芳烃的选择性硝化反应的研究 ,已取得较大的进展。该改性固体酸催化剂中改性元素的含量常影响催化剂的性能 ,但对改性粘土催化剂中改性元素的含量的测定却未见报道。微量铜的测定常采用紫外可见分光光度法 [1] 和原子吸收分光光度法 [2 ]。本文对经铜元素改性的粘土催化剂进行处理 ,采用了火焰原子吸收分光光度法 ,直接测定了铜元素的含量[3…     

利用留数定理对一类广义积分的推广

在数学物理问题中常常遇到一类广义积分■或■,其中正整数n和实数α满足n≥1和0<α±是I_±的线性组合。我们综合介绍了此广义积分的几种解法，分析了由高等数学知识求解此类实变函数积分的限制性，并讨论了传统方法的繁琐性。     

Variational Calculations for the Spectrum of Finite Bosons in Harmonic Potentials

Using both the Gaussian and Fetter‘‘s variational calculations for the N-body ground-state wavefunction of the trapped Bose-Einstein condensate, we give explicit analytic formulae for the spectrum of finite bosons in harmonic potentials based on the corrected sum rules and generalized virial identities. We compare the low-lying excitation spectra among the Gaussian and Fetter‘‘s variational calculations and the exact numerical results. The Gaussian approximation has the simplest reasonable results, valid for N→∞ and high-lying excitations.     

高温超导体玻色子超导弦理论及其应用

本文用 u(?)×u(1) 场论描述高温氧化物超导体.求得了玻色子超导弦场方程的孤子解,并把理论结果应用于讨论 Cu-O 型超导体的一些特性.     

Thermodynamic properties of a finite Bose gas in a harmonic trap

We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.     

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas--Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.     

Unitarity Schrodinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover

On the basis of quantum hydrodynamical equations we derive a unitarity Schrodinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg-Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross-Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrodinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.