A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Geometric Characterizations for Subgroups of PU（1, n; C）

In this paper, we discuss non-elementary subgroups and discontinuous subgroups of PU(1,n; C), and give their geometric characterizations.     

Error estimation,adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization

In this paper, an adaptive FE analysis is presented based on error estimation, adaptive mesh refinement and data transfer for enriched plasticity continua in the modelling of strain localization. As the classical continuum models suffer from pathological mesh-dependence in the strain softening models, the governing equations are regularized by adding rotational degrees-of-freedom to the conventional degrees-of-freedom. Adaptive strategy using element elongation is applied to compute the distribution of required element size using the estimated error distribution. Once a new mesh is generated, state variables and history-dependent variables are mapped from the old finite element mesh to the new one. In order to transfer the history-dependent variables from the old to new mesh, the values of internal variables available at Gauss point are first projected at nodes of old mesh, then the values of the old nodes are transferred to the nodes of new mesh and finally, the values at Gauss points of new elements are determined with respect to nodal values of the new mesh. Finally, the efficiency of the proposed model and computational algorithms is demonstrated by several numerical examples.     

催化极谱法连续测定岩石中钨和钼

本文提出了在二苯基乙醇酸-二苯胍-氯酸钠催化极谱体系测钨后,加入少许钛铁试剂,使钼产生一个极灵敏的导数波。谊波形尖锐、对称,便于测量钼。建立的连测体系简便灵敏,用于岩石样品中钨和钼的测定,取得了满意的效果。     

岩石的核磁共振自旋密度微成像

岩，心是油气储层的基本单元，其内部结构和渗流性质反映了油藏的基本特征．岩。心的精细描述是油藏描述、储层动态监测及设计强化采油方案的重要基础．本文利用核磁共振（NMR）自旋密度做成像，快速无损地观测到两类基本储油岩石——砂岩和灰岩的内部结构，提供了岩石渗透性、孔隙性及灰岩沉积环境等重要信息．1实验方法以自旋回波单片NMR成像脉冲序列为基础，设。P平面内样品的目施密度为P（。，v）．演化期t。，在。方向梯度场G。作用下，各处横向磁化矢量获得的相移为式中，7为共振核（在成像中一般为质子）的旋磁比，g为坐标位置·…     

Thermal analysis and X-ray studies of chiral ferroelectric liquid crystalline materials and their binary mixtures

Summary Thermal properties of a homologous series of ferroelectric liquid crystals S-(-)-[4-(2-n-alkoxy-propionyloxy)]biphenyl-4'-[n-alkoxy-(3,5-dimethyl)]benzoate have been investigated by polarizing optical microscopy and differential scanning calorimetry. The mesophases were identified and confirmed by X-ray too. Three binary mixtures were prepared from the individual homologues. In one of the mixtures (Mix1), the ferroelectric SmC* phase has broadened and became enantiotropic. This mesophase remained monotropic in the other two mixtures (Mix2, Mix3). The chiral nematic N* phase did not appear in Mix1, but remained monotropic for the other two mixtures. Two molecular parameters, the layer spacing and the average intermolecular distance have been calculated from the X-ray results for the homologues and their mixtures. An intercalated tail-to-tail packing of molecules was found both in the single compounds and their mixtures resulting in the layer spacing about half of the molecular length of the single compounds.     

Elastic moduli and structure of low density polyethylene

Summary Low density polyethylene film is drawn at room temperature four times the original length and subjected to thermal annealing at 60, 80, and 100 °C keeping the film length constant. Long spacing measured by SAXS increased with increasing temperature of annealing; the increase of the long spacing is presumed to be due to the decrease of the number of micelles through relaxation during the annealing. Simultaneous measurement of the changes of the long spacing and the film length by stretching is carried out and stress-extension curves are obtained. The values of the initial moduli of the long spacingE ₁ and the film lengthY are very near to each other. Elastic modulus of the crystal latticeE _c is known to be 235 GN/m² and that of the amorphous regionE _a is found to be 0.15 GN/m². When higher stress is applied than in the case of the initial modulus, the percentage of extension of film is much greater than that of the long spacing. The discrepancy is explained by the increase of the number of micelles through stress crystallization.Dedicated to Professor Dr. K. Ueberreiter on the occasion of his 70th birthday.     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf