An investigation of the linear driving force approximation to diffusion in spherical particles

The linear driving force approximation is studied for three cases of batch adsorption and one of leaching in a CSTR, for which exact analytical solutions are available. Common pitfalls in its application are underlined and it is shown that, for adsorption from a finite volume of fluid, very large errors can arise when the fractional uptake approaches unity.     

An elgenvalue and eigenfunction study of time-dependent fast-neutron spectra in 232Th

The pulsed problem for fast neutrons in Th has been studied using the multigroup diffusion equation and eigenfunction expansion method. The time-dependent fast-neutron spectra have been obtained up to 8000 ns inside Th systems with buckling ranging from 0.0 to 0.015 cm⁻². The results have been obtained using the 27-group BARC data set. It has been shown that for a fast Th system, unlike a fast U system, all the time eigenvalues lie in the continuum and no discrete time eigenvalue exists. A fast Th system behaves more like a non-multiplying system. The spectra shift continuously to lower energies with increasing time. However, pseudo-asymptotic conditions are established in certain time intervals. The start of pseudo-equilibrium conditions and the duration for which they persist is seen to increase with decreasing buckling. The reason for the establishment of pseudo-equilibrium conditions has been discussed. The theoretical results for the instantaneous decay constant inside a 40 cm cube of Th have been compared with the experimental results of Moo et al. (1973). The present results are in good agreement with the above experimental results based on the ²³⁹Pu detector.     

Oxidation of polycrystalline silicon carbide

The oxidation of densified silicon carbide has been studied by micrography and infrared reflection spectrometry, in addition to gravimetric techniques and X-ray diffraction. Of particular interest was the relative oxidation resistance of varieties of the material treated in various ways. The hot-pressed type oxidized less readily than the sintered, and annealing was found to impart substantial resistance to oxidation; these are thought to be impurity effects.     

Concept and design of a 3.5 MW pilot plant for high temperature electrolysis of water vapor

The high temperature electrolysis (HOT ELLY) of water vapor using zirconia as a solid oxide electrolyte has been demonstrated in laboratory experiments to be a very efficient method of hydrogen production. This program is a cooperation between Dornier Systems, Friedrichshafen and Lurgi, Frankfurt. In this paper, the thermodynamical advantages of electrolysis at very high temperatures, typically 900–1000°C, will be briefly reviewed first. After the principal technical realization has been explained the status of the advanced cell and module development will be illustrated. The process engineering for electrolysis plants will then be discussed and our concept for building up electrolysis units introduced. Finally a cost examination and comparison with conventional H₂-production plants will be reviewed.     

Elastic impact of spheres on thin shallow spherical shells

This investigation was concerned with the elastic impact of spheres on thin shallow spherical shells. A non-linear integro-differential equation of the impact process was developed on the basis of Reissner's approximate theory for transverse vibrations of shallow shells and the quasistatic Hertzian impact theory. This equation was numerically integrated and its main results were experimentally verified. Special attention was given to the apparently new observations that the rebound height of a sphere dropped onto a given shell has a minimum value for a critical size of the sphere, and that the contact time differs substantially for sphere sizes greater or less than this critical value.     

值域增长约束满足问题的无回溯与随机行走策略的算法复杂性分析

值域增长的约束满足问题模型是计算复杂性理论中一类重要的实际问题模型,针对解决这类问题的算法研究仍然很少。通过研究RB模型这一典型的值域增长约束满足问题,发现当问题规模很大时,无回溯策略比随机行走策略更加有效。这与典型的值域确定的约束满足问题如SAT问题不同,是值域增长的约束满足问题所特有的性质。通过实验研究了两种策略的表现,并进一步对两种策略的表现进行了分析。     

求分块周期三对角矩阵逆矩阵的新算法

根据分块三对角矩阵逆矩阵的特殊结构,利用其LU和UL分解,并使用Sheman-Morrison-Woodbury公式,得到一个求分块周期三对角矩阵逆矩阵的新算法,并由该算法得到求周期三对角矩阵和对称周期三对角矩阵逆矩阵的新算法。新算法比传统算法的计算复杂度和计算时间要低。     

Fast Algorithms to Enumerate All Common Intervals of Two Permutations

Given two permutations of n elements, a pair of intervals of these permutations consisting of the same set of elements is called a common interval . Some genetic algorithms based on such common intervals have been proposed for sequencing problems and have exhibited good prospects. In this paper we propose three types of fast algorithms to enumerate all common intervals: (i) a simple O(n ² ) time algorithm (LHP), whose expected running time becomes O(n) for two randomly generated permutations, (ii) a practically fast O(n ² ) time algorithm (MNG) using the reverse Monge property, and (iii) an O(n+K) time algorithm (RC), where K is the number of common intervals. It will also be shown that the expected number of common intervals for two random permutations is O(1) . This result gives a reason for the phenomenon that the expected time complexity O(n) of the algorithm LHP is independent of K . Among the proposed algorithms, RC is most desirable from the theoretical point of view; however, it is quite complicated compared with LHP and MNG. Therefore, it is possible that RC is slower than the other two algorithms in some cases. For this reason, computational experiments for various types of problems with up to n=10 ⁶ are conducted. The results indicate that (i) LHP and MNG are much faster than RC for two randomly generated permutations, and (ii) MNG is rather slower than LHP for random inputs; however, there are cases in which LHP requires Ω(n ² ) time, but MNG runs in o(n ² ) time and is faster than both LHP and RC. Received December 21, 1996; revised June 2, 1998.     

Application of mathematica to the direct semi-numerical solution of finite element problems

Several numerical methods, such as the finite element method, reduce applied mechanics and additional engineering problems to systems of linear algebraic equations. It has been already suggested that the inclusion of a symbolic parameter in the corresponding numerical results leads to a generality and a wide applicability of these results. Here we suggest the direct solution of these equations by using the popular computer algebra system MATHEMATICA. Assuming the results expressed in a Taylor-Maclaurin series form with respect to the selected symbolic parameter, the whole problem is reduced to the solution of an appropriate number of systems of purely numerical linear equations. This can be achieved either inside MATHEMATICA or by using efficient external numerical routines. As an application the above modification of the finite element method was used in the classical problem of a tapered elastic beam. The obtained semi-numerical results by the finite element method were seen to be in agreement with the available theoretical results. Further possibilities are also suggested in brief.