Rotation and strain of linear and planar structures in three-dimensional progressive deformation

Rotation and progressive strain have been studied for a sheet embedded in a matrix which undergoes rotational three-dimensional strain under constant volume conditions. The mathematics gives explicit information on the following features:

1. (1) The length and position (relative to a defined coordinate system) of the principal axes of the strain ellipsoid at any stage of the progressive deformation.

2. (2) The position and length of the principal axes in any plane intersecting the strain ellipsoid, also at any stage of the deformation.

3. (3) The position and length of passive markers which initially coincided with the principal axes in an intersecting plane. This is of consequence for the distinction between passively rotating structures and actively forming structures.

4. (4) The shear strain parallel to an intersecting plane or sheet, as indicated by the angular difference between the normal to an intersecting plane at any time and the marker at the same time which initially, however, was parallel to the normal. This layer-parallel shear causes boudins to rotate and the axial plane of buckles to tilt.

The relationships have been expressed quantitatively in the bulk of the paper and illustrated in diagrams. The analysis presented is basic for the study of the deformational behavior of competent sheets of rocks embedded in less competent ones.     

Retrieval of vertical wind profiles during monsoon from satellite observed winds over the Indian ocean using complex EOF analysis

The aim of this paper is to study the feasibility of deriving vertical wind profiles from current satellite observations. With this aim, we carried out complex empirical orthogonal function (CEOF) analysis of a large number of radiosonde observations of wind profiles over the Indian Ocean during the monsoon months. It has been found that the first two CEOFs explain 67% of the total variance in wind fields. While the first principal component is well correlated with the winds at 850 mb (r = 0:80), the second one is highly correlated with winds at 200 mb (r = 0:89). This analysis formed the basis of a retrieval algorithm which ensures the retrieval of vertical profiles of winds using satellite tracked cloud motion vector winds. Under the assumption that accurate measurements of wind are available at the above mentioned levels, the r.m.s. error of retrieval of each component of wind is estimated to range between 2 ms^-1 and 6 ms^-1 at different levels, which is much less than the natural variance of winds at these levels. For a better visualization of retrieval, we have provided retrieved and true wind profiles side by side for four typical synoptic conditions during the monsoon season.     

Estimation of critical convergence and rock load in coal mine roadways — an approach based on rock mass rating

Summary Based on field instrumentation in eight different coal mines representing varying depths and strata conditions, a relation for obtaining the critical convergence value has been established. In development heading for bord and pillar workings this relation can be used successfully to control the premature collapse of the roof. An empirical relation for rock load has been established. This can be utilized for optimum design of support system. The roofs have been categorized as stable, short-term stable and unstable. Proper attention should be provided for an unstable roof and the support design is to be changed before the convergence reaches the critical value.     

The variational technique of data assimilation using adjoint equations in a shallow water model

The variational technique of data assimilation using adjoint equations has been illustrated using a nonlinear oceanographic shallow water model. The technique consists of minimizing a cost function representing the misfit between the model and the data subject to the model equations acting as constraints. The problem has been transformed into an unconstrained one by the use of Lagrange multipliers. Particular emphasis has been laid on finite difference formulation of the algorithm. Several numerical experiments have been conducted using simulated data obtained from a control run of the model. Implications of this technique for assimilating asynoptic satellite altimeter data into ocean models have been discussed.     

Interaction of Aquifer and River‐Canal Network near Well Field

The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified.     

Higher dimensional thick domain wall in Lyra geometry

An exact solution is obtained for a thick domain wall in a five dimensional Kaluza-Klein space time within the framework of Lyra geometry. The space time is nonsingular both in its spatial and temporal behavior. It is shown that the domain wall has no particle horizon and the gravitational force due to them is attractive. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonplanar ion-acoustic Gardner solitons in a pair-ion plasma with nonextensive electrons and positrons

The properties of nonplanar (cylindrical and spherical) ion-acoustic solitary waves (IA SWs) in an unmagnetized, collisionless electron-positron-ion (e-p-i) plasma, whose constituents are q-distributed electrons and positrons and inertial ions, are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar IA Gardner solitons (GSs) are discussed. It is found that the properties of nonplanar IA GSs (rarefactive and compressive) are significantly affected by the particle nonextensivity.     

Rapid variations of Hα emission strength of eight Be stars

Rapid observations of H profiles of eight Be stars have been obtained and it is found that rapid (in a time-scale of 4 to 6 minutes) and irregular variations of total emission strength of H line are present in these stars. It has been suggested that these variations may be due to the material circulation in the envelope of Be stars.