Modeling the depletion of dissolved oxygen in a lake due to algal bloom: Effect of time delay

We propose and analyze a non-linear mathematical model for algal bloom in a lake to account for the delay in conversion of detritus into nutrients. It is assumed that there is a continuous inflow of nutrients in the lake due to agricultural run off. The model involves four variables, namely nutrient concentration, algal population density, detritus density and dissolved oxygen concentration. The dynamics of the model is studied in terms of local stability analysis and Hopf-bifurcation analysis. It is found that the positive equilibrium of the model may switch from stability to instability to stability, and eventually instability sets in under certain conditions. The numerical simulation is performed to support the analytical results.     

On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation

Pure and Applied Geophysics - Deflection and bending moments of a thin isotropic rectangular plate, having its edges simply supported and maintained at zero temperature, have been investigated in...     

Escalation of salinity levels in the quaternary aquifers of the Ganga alluvial plain,India

A detailed water quality analysis was carried out in the quaternary aquifer system of the marginal alluvial plain (Ganga Plain) in Bah Tahsil, Agra district, India. The electrical conductivity of 50 samples each from dug wells, hand pumps and tube wells was analysed for the study of salinity levels in shallow, intermediate and deep aquifers. Out of 50, 20 samples of each were also analysed for other chemical constituents such as Na⁺, K⁺, Cl⁻, F⁻ and TDS. The analyses show drastic changes in the salinity levels of shallow, intermediate and deep aquifers. The deep aquifers are more saline compared to the shallow and intermediate aquifers. On the contrary, the concentration of chemical constituents such as Na⁺, K⁺, Cl⁻ and F⁻ was more in the shallow aquifers compared to the deep aquifers. Moreover, there is an indication that the salinity and concentration of the above chemical constituents also escalate with time in each aquifer. The chemical constituents such as Na⁺, K⁺, Cl⁻, F⁻ and TDS range from 51 to 165 mg/l, 1 to 14 mg/l, 224 to 1,459 mg/l, 0 to 1.5 mg/l and 750 to 2,650 mg/l, respectively. Over a 3-year period, the salinity levels have sharply increased and the average F level has increased by 0.1–0.3 mg/l. An attempt has been made here to discuss the factors causing the variation and escalation of chemical constituents and salinity in the water of the three aquifers.     

Age of granitic activity associated with copper–molybdenum mineralization at Malanjkhand, Central India

The Malanjkhand copper–molybdenum deposit in the Bhandara Craton, Central India, is hosted by a granite complex which consists of regionally dominant grey granitoid and pink granitoid confined to the mineralized zone. New SHRIMP RG data on zircons from both granite types are inferred to have crystallized during the same magmatic pulse at ca 2.48 Ga. The discrepancy between zircon age and earlier obtained Rb–Sr whole-rock age is attributed to modification of the Rb–Sr system by hydrothermal overprint. Similarity in petrographic features and chemical affinity in combination with identical age strongly indicate that the pink granite is the hydrothermally altered variety (microclinization and silicification) of the grey granite. The spatially associated, main Cu–Mo mineralization event at Malankhand appears to be broadly contemporaneous with and genetically related to the emplacement of the host granitoids at about 2.48 Ga.     

Laboratory investigations on rotary diamond drilling

Extensive laboratory drilling investigations were conducted on a wide variety of rocks to study the inter-dependence of machine as well as rock parameters on the performance of the drilling operation. Detailed physical and mechanical properties of all the rock types were determined to study the influence of the rock properties on the drilling performance. The effect of PEO (poly-ethylene-oxide) added to the drilling water was also studied. Slake durability tests were conducted in plain water as well as a PEO mixed water medium to observe the effects of PEO on the surface properties of the rock. An attempt is also made to understand the different modes of wear of impregnated diamond bits in the rotary drilling operation.     

Evolution of Mayurbhanj Granite Pluton, eastern Singhbhum, India: a case study of petrogenesis of an A-type granite in bimodal association

The A-type Mayurbhanj Granite Pluton (3.09 Ga), occurring along the eastern margin of the Singhbhum-Orissa Craton, eastern India, represents the final phase of acid plutonism in this crustal block of Archean age. The granite shows a bimodal association with a voluminous gabbroid body, exposed mainly along its western margin, and is associated with the Singhbhum Shear zone. The granite pluton is composed mainly of a coarse ferrohastingsite–biotite granite phase, with an early fine-grained granophyric microgranitic phase and a late biotite aplogranitic phase. Petrogenetic models of partial melting, fractional crystallisation and magma mixing have been advocated for the evolution of this pluton. New data, combined with earlier information, suggest that two igneous processes were responsible for the evolution of the Mayurbhanj Granite Pluton: partial melting of the Singhbhum Granite; followed by limited amount of mixing of acid and basic magmas in an anorogenic extensional setting. The necessary heat for partial melting was provided by the voluminous basaltic magma, now represented by the gabbroid body, emplaced at a shallow crustal level and showing a bimodal association with the Mayurbhanj Granite Pluton. The Singhbhum Shear Zone provided a possible channel way for the emplacement of the basic magma during crustal extension. It is concluded that all three phases of the Mayurbhanj Granite Pluton were derived from the same parent magma, generated by batch partial melting of the Singhbhum Granite at relatively high temperatures (980 °C) and low pressures (4 to <2 kbar) under anhydrous conditions. The coarse ferrohastingsite biotite granite phase shows evidence of limited and heterogeneous assimilation of country rock metasediments. However, the early microgranite phase and late aplogranite phase have not assimilated any metasediments. Compositional irregularities observed along the western margin of the Mayurbhanj Granite Pluton in contact with the gabbro body including a continuous fractionating sequence from quartz diorite to alkali-feldspar granite in the Notopahar area. Gradational contacts between the gabbro and the Mayurbhanj Granite Pluton in the Gorumahisani area etc., may be attributed to a limited amount of mixing between the gabbroid magma and the newly generated Mayurbhanj Granite magma. The mixing was mainly of liquid–liquid diffusive type, with a subordinate amount of mixing of solid–liquid type. Although A-type granites are commonly described as having high total REE (e.g. 270–400 ppm), studies on the late aplogranite phase of the Mayurbhanj Granite show that total REE values (100 ppm) are low. This low REE abundance may be attributed to the progressive residual nature of the Singhbhum Granite source during continued partial melting, when the magmas of the microgranite and coarse granite phases had already been removed from the source region.     

Hydrometeorological assessments and suspended sediment delivery from a central Himalayan glacier in the upper Ganga basin

Integrated hydrometeorological investigations are not frequently available at a regional scale over a longer time period, especially near the terminus of Indian Himalayan glaciers. An integrated approach to the collection of hydrological data has major advantages for understanding the runoff generation mechanisms at basin scale, particularly when coupled with meteorological observations. The current study involves time series analysis of hydrometeorological records collected near the terminus of the Chorabari Glacier, for four consecutive ablation seasons(June-Sept.) 2009-2012. The analysis shows that variation in rainfall was higher(c_v= 0.9) at the same elevation over proximal sites, while the intensity of extreme rainfall events was 121-160 mm/d. The diurnal temperature range(DTR) has a tendency to reduce over the ablation season because of the onset of the Indian Summer Monsoon(ISM) and then further increases during the ISM withdrawal indicating humid-temperate conditions. The peak discharge(Qpeak) was found to be higher during July and August. Snow and glacier melt contributed 76% of the total suspended sediment transport during peak ISM months(July and August) reflecting seasonal evolution of the hydrologic conduits. The results indicate that Karakoram and western Himalayan glaciers produce comparatively low sediment yield compared to central Himalayan glaciers. The hydrological variations are depicted through flow duration curves(FDC) for meltwater discharge and sediment load. The flow corresponding to Q_(50), Q_(75), and Q_(90)(where Qx is the discharge that is exceeded x percent of the time referred to as % dependability) are 4.2, 3.7, and 2.8 m~3/s; and the corresponding dependability for suspended sediment loads(SSLs) are 409.0, 266.0, and 157.2 t/d, respectively. The daily SSL and discharge(Q) from 2009 to 2012 were used to develop a sediment rating curve(SSL = 39.55 × Q~(1.588). R~2 = 0.8).Multiple regressions are used to determine the impacts of meteorological parameters on glacier melt.The meteorological conditions, hydrological characteristics, and suspended sediment delivery for the Chorabari Glacier provide insight on meltwater generation processes and sediment transport patterns during the ISM season.