Five dimensional Bianchi type-I string cosmological model in Brans-Dicke theory

A Bianchi type-I string cosmological model in Brans-Dicke theory in five dimension space-time has been investigated. For the determinate solution it has been assumed that the sum of energy density and tension density of the cosmic string dust source vanishes. Some physical and kinematical parameters are also discussed.     

A review of b-value imaging and fractal dimension studies in the Andaman Sumatra subduction

The present study analyses the spatial pattern of quaternary gravitational slope deformations (GSD) and historical/present-day instabilities (HPI) inventoried in the Swiss Rhone Valley. The main objective is to test if these events are clustered (spatial attraction) or randomly distributed (spatial independency). Moreover, analogies with the cluster behaviour of earthquakes inventoried in the same area were examined. The Ripley’s K-function was applied to measure and test for randomness. This indicator allows describing the spatial pattern of a point process at increasing distance values. To account for the non-constant intensity of the geological phenomena, a modification of the K-function for inhomogeneous point processes was adopted. The specific goal is to explore the spatial attraction (i.e. cluster behaviour) among landslide events and between gravitational slope deformations and earthquakes. To discover if the two classes of instabilities (GSD and HPI) are spatially independently distributed, the cross K-function was computed. The results show that all the geological events under study are spatially clustered at a well-defined distance range. GSD and HPI show a similar pattern distribution with clusters in the range 0.75–9 km. The cross K-function reveals an attraction between the two classes of instabilities in the range 0–4 km confirming that HPI are more prone to occur within large-scale slope deformations. The K-function computed for GSD and earthquakes indicates that both present a cluster tendency in the range 0–10 km, suggesting that earthquakes could represent a potential predisposing factor which could influence the GSD distribution.     

Modeling water-table fluctuations in a sloping aquifer with random hydraulic conductivity

To prevent environmental problems like water logging and increase in soil salinity which are responsible for the degradation of the top productive soils, an optimum ditch drainage design is required. For this purpose a knowledge of the spatio-temporal variation of the water table is essential. In this study the spatio-temporal variation of the water table in a sloping ditch drainage system has been modeled from a stochastic point of view, incorporating randomness in hydraulic conductivity to get the expression for the mean and the standard deviation of the water-table height. The hydraulic conductivity has been considered to be a realization of a log-normal distribution. Application of these expressions in the prediction of mean water-table variation with the associated error bounds has been demonstrated with the help of a ditch drainage problem of a sloping aquifer. The sensitivity analysis has also been carried out to see the effect of variability in the hydraulic conductivity on the water-table fluctuations. The error bounds quantified on the water-table height will thus help in the decision-making process for proper drainage design.     

A model for temperature variations in sedimentary basins due to random radiogenic heat sources

The thermal structure of a sedimentary basin is controlled by its thermal conductivity, its boundary conditions, water flow, rate of sedimentation and erosion and radiogenic heat sources. The radiogenic heat production in the sediments is known to vary over several orders of magnitude, with the lowest values in evaporites and carbonates and the highest values in black shales. Due to a paucity of information available on the existing heat sources, this parameter can be represented with a known mean value and a Gaussian correlation structure rather than a deterministic function. In this paper, the 1-D steady-state thermal structure in a sedimentary basin has been modelled in a stochastic framework with a random radiogenic heat source, and analytical expressions for the first two moments of the temperature field have been obtained. A synthetic example has been examined to quantify the error bounds on the temperature field due to uncertainties in the radiogenic heat sources.