Finite element formulation and algorithms for unsaturated soils. Part I: Theory

This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd.     

A concept for a superconducting tunnelling junction based spectrograph

We describe a multi-order spectrograph concept suitable for 8-m class telescopes, using the intrinsic spectral resolution of superconducting tunnelling junction detectors to sort the spectral orders. The spectrograph works at low orders, 1–5 or 1–6, and provides spectral coverage with a resolving power of   R ≃ 8000  from the atmospheric cut-off at 320 nm to the long-wavelength end of the infrared H or K band at 1800 nm or 2400 nm. We calculate that the spectrograph would provide substantial throughput and wavelength coverage, together with high time resolution and sufficient dynamic range. The concept uses currently available technology, or technologies with short development horizons, restricting the spatial sampling to two linear arrays; however, an upgrade path to provide more spatial sampling is identified. All of the other challenging aspects of the concept – the cryogenics, thermal baffling and magnetic field biasing – are identified as being feasible.     

Numerical simulation of shear band formation in soils

Zones of localized shear strain, called bands, are initiated numerically within idealized cohesive and frictional soil specimens both by inhomogeneities and by imperfect boundaries. Qualitatively the results agree with experimental evidence, and give promise of quantitative analyses using better soil models, when the presence of porewater pressures will be of particular significance.     

1986年2月4日太阳耀斑的演化研究

本文根据乌鲁木齐天文站的H_α耀斑及3.2cm射电流量观侧资料、云南天文台的黑子精细结构照相和Marshall Space Flight Center的向量磁场图,对1986年2月4日的六个耀斑的形态相关及演化联系,特别是0736UT 4B/3X大耀斑的发展过程进行了综合分析。主要结果是: 1.4日大耀斑的初始亮点和闪光相的主要形态演化,与活动区中沿中性线新浮现的强大电流/磁环系密切相关。后者的主要标志是沿中性线的长的剪切半影纤维及它两端的偶极旋涡黑子群(1_3F_3)。 2.上述大耀斑与1972年8月4日0624 UT大耀斑爆发的磁场背景及主要形态特征相似,表明两者的储能和触发机制可能相同。 3.大耀斑爆发的H_α初始亮点,双带出现,环系形成,亮物质抛射和吸收冕珥等现象同3.2cm射电流量的变化在时间上有较好的对应关系。 4.重复性的前期小耀斑爆发位置和发展趋势与大耀斑的主要形态及演化特征相似。它们相对于剪切的纵场中性线两侧的位置相近或相同。因而,可以看作上述强大电流/磁环系不稳性发展过程中的前置小爆发。     

Towards a theory for type III solar radio bursts

The procedure developed in Smith (1974) to model the radiation source for type III bursts is modified to include scattering of radiation in the source itself. Since the inhomogeneities in the source must have the same statistical properties as the inhomogeneities used in tracing radiation from the source to the observer, these two parts of the type III problem are no longer uncoupled. Thus we use inhomogeneities consistent with the scattering inhomogeneities of Steinberg et al. (1971) and Riddle (1974) and apply the procedure to an archetype ‘fundamental-harmonic’ pair observed at Culgoora on 28 September, 1973 at 0319 UT. We find that it is impossible to model this burst with a source which is homogeneous in the sense that every part of the source has the same energy density in plasma waves. The density inhomogeneities in the source severely hamper amplification of the supposed fundamental. Possible ways out of this dilemma are discussed, including second harmonic pairs and a source with an inhomogeneous distribution of plasma waves. It is concluded that none of the possibilities are completely satisfactory to explain present observations and suggested that critical observations are missing.     

3.3 Millimeter limb brightening measurements during the 30 June 1973 total solar eclipse

Solar limb brightening measurements at a wavelength of 3.3 mm were made during the 30 June 1973 total solar eclipse from a site at Lake Rudolf, Kenya. The results show that at this wavelength there is a limb brightening of about 20%, occurring within one half arc min of the limb.     

Beta-dispersion of low-frequency Rossby waves

An investigation is made into the dispersion of oceanic internal Rossby waves at annual and semi-annual frequencies. Turning of the group velocity vector due to latitudinal variations in the radius of deformation cannot be neglected, particularly in basins as large as the Pacific. This turning allows disturbances to propagate from high lattitudes into the equatorial zone and distorts the solutions in the western part of the basin. For no mean flow, and a coastline aligned north-south, an almost exact focus of wave energy is found very close to the equator at a distance of just under $\text{πc/4ω}$ from the eastern boundary, where $\text{c}$ is the eigenspeed of a high-frequency internal wave mode, and ω is the angular frequency of the low-frequency wave being studied. The focus depends on a long meridional wavelength excited at the coast, and a frequency small compared with $\text{c/a}$, where $\text{a}$ is the radius of the Earth. For the lowest baroclinic mode and waves of annual period, this distance is about 12 000 km. Equivalence of the ray theory and the theory of equatorial meridional modes is demonstrated for the simple cases where the latter applies.The effects of mean currents and irregular coastlines are examined. Barotropic mean currents may change the turning latitude and ray shapes, inducing critical layers and enhancing reflection. Baroclinic mean currents are seen to affect the rays by simply changing the speed in proportion to the depth of the thermocline. As long as the mean currents are geostrophically balanced, no “effective beta” term from variations in the thermocline depth appears, in contrast to the topographic Rossby wave problem.