Time-dependent Movements Research Articles

On analytic solutions of the drift equations for many ionic species

The charge-drift equations result from charge continuity considerations when viewed from a frame of reference moving with the gaseous ions. They are simple in form and have already been used to good effect for single-species drift for which references are given in the text. This paper systematically examines the theory for multiple species looking for algebraically expressible solutions, and has met with some success. It has been shown that the charge density of a packet of a particular species of ions can be written in terms of integrals involving the charge densities of other ions that it meets on its way. A power law governing the charge densities has been found for all time-dependent homogeneous ionic movements. Time-independent motions have also been considered and the constant ratios of charge densities and currents confirmed for all points in these flows. Situations with two ionic species are fully investigated, and an analytic solution has been found for homogeneous distributions of positive and negative ions with equal but opposite mobilities. Stable charged clouds with equal but opposite positive and negative ionic distributions are shown to be possible. When disturbed, the variations from equilibrium charge densities within such a cloud are found to be characterized by an exponential law. The destabilizing effect of an externally applied electric field on these clouds is shown to be resisted by the self-field of the resulting ionic displacements. Perturbation solutions and expansions are considered in some detail, and the paper concludes with a section giving explicit solutions for superimposed clouds of ions with either spherical or cylindrical symmetry. Fuller descriptions of the main findings can be found in the conclusions at the end of the text.

Evaluation of standardized methods for registration of time-dependent orthodontic tooth movements

An in vitro study was conducted to compare reproducibility of repeated recordings obtained from devices constructed for standardized registrations. An existing radiographic method and a new photographic technique were employed. On five in vitro models, half of the maxilla from dry skulls, special designed splints with a Troll-biten film holder were constructed. A stiff metal bar attached to the splints and to either an X-ray apparatus or a standard photographic camera made it possible to obtain standardized registrations. For each model 10 radiographs and photographs were taken before and after the canine was moved. Subtracting the values from well defined points for these pictures, 10 pairs of coordinates were available for each of the models with both methods. The findings showed very similar reproducibility for the two methods with 95 per cent of the discrepancies within a magnitude of 0.12 mm for the radiographic method and 0.14 mm for the photographic method. When evaluating the canine movements, similar results were observed. No significant difference could be detected in the five in vitro models. In addition, the results showed that a splint can be used as a stable reference for registration of tooth movements. Because of ethical objections to unnecessary radiation, the photographic registration technique might substitute the radiographs in future investigations where standardized periodic records are necessary for the description of tooth movement.

Tunnelling in compressible soils: large ground movements and structural implications : Attewell, P B; Selby, A R Tunnlg Underground Space TechnolV4, N4, 9, P481–487

When a tunnel is driven through soil by the conventional shield method, ground losses are inevitable due to face take proper and to shield and post-shield radial take. The relaxed soil movements inwards at the tunnel are propagated upward and outward, decreasing in magnitude because of the increasing volume disturbed, so that an inverted bell-shaped depression develops at the ground surface. This settlement trough moves forward as tunnelling progresses. If any buildings, roads or buried services lie within the settlement zone, it becomes necessary to estimate the magnitude of those settlements and to evaluate the risk of damage to the constructions. A well-constructed tunnel driven through stiff clays may cause surface settlements of less than 10 mm. However, when a tunnel is driven through soft, variable, compressible soils, consolidation settlements greater than 100 mm may occur. The effects of soil movements upon buried pipes and on structures can be assessed using a linear elastic form of soil-structure analysis. The consequences of small, short-term settlements and also of very large, time-dependent soil movements upon pipelines and foundation slabs are considered in the paper. This paper was first presented at the Third International Conference on Underground Space and Earth-Sheltered Buildings, held September 1-6, 1988, in Shanghai, China.

The use of an Elastic Recovery Index as a Criterion of Compactional Behaviour of Some Direct Compression Bases

AbstractThe effects of compression force and holding time on computer logged strain movements (at constant stress) and elasticviscoelastic expansions (on load release) of compacts made from eight pharmaceutical powders are reported. The feasibility of using an elastic recovery index (the ratio of elastic recovery to viscoelastic strain movements) to predict the quality of a material is also discussed.All compacts continued to consolidate by viscoelastic and plastic flow when held under constant stress during the holding period. The “compressible” bases Avicel PH-101 and Sta-Rx 1500 exhibited more time dependent movements than powders such as Paracetamol DC, Paracetamol, Emcompress and magnesium stearate. Poorly compressible materials such as magnesium carbonate and paracetamol showed the greatest elastic expansions on load release.It has been found that the elastic recovery indices of the compressible materials were lower than those of poorly compressible powders.

Uncertainty and models for creep of concrete

An engineer involved in practical design must often choose between using approximate rules of thumb, and more rigorous analyses. The problem may be tackled using decision theory. An important element in this analysis is the estimation of probabilities of future values of creep. Some factors that contribute to one's uncertainty are discussed and ranked. If it is decided to carry out a detailed structural analysis, it is necessary to have constitutive equations for creep. The importance of heterogeneity of concrete and cement paste is emphasized, together with the implications of this in the analysis of time-dependent movements using the activation energy approach. A qualitative interpretation of the dashpot elements in viscoelastic models from a thermodynamic standpoint is given; this relates primarily to an increase in configurational entropy. Lastly the effects of ageing and some disadvantages of the linear viscoelastic models are discussed.

プレート間巨大地震後の応力緩和過程と地表変位パターン

By means of two-dimensional finite element simulations of the stress relaxation in the asthenosphere induced by the occurrence of major underthrust earthquakes at subduction zones, characteristic features of the postseismic time-dependent surface displacements are investigated. In the model of the upper mantle structure involving a subduction zone, the following structural anomalies are taken into account; (1) the presence of a descending elastic slab in a Maxwell viscoelastic asthenosphere beneath a continental elastic plate, and (2) the difference between the thicknesses of oceanic and continental elastic plates.Both of the structural anomalies of (1) and (2) significantly affect not only the amounts but also the patterns of the displacements. Furthermore whether the coseismic faulting reaches the asthenosphere or not also has a notable effect on the patterns of the displacements. Therefore the displacements for the anomalous structure model are considerably different from those for a simpler layered structure model in amount and pattern. It is confirmed that time-dependent surface movements in subduction zones following megathrust earthquakes must be interpreted by using a realistic model of the upper mantlt structure.