• Volume 108, Issue 3

      September 1999,   pages  117-221

    • Fourier’s heat conduction equation: History, influence, and connections

      T N Narasimhan

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      The equation describing the conduction of heat in solids has, over the past two centuries, proved to be a powerful tool for analyzing the dynamic motion of heat as well as for solving an enormous array of diffusion-type problems in physical sciences, biological sciences, earth sciences, and social sciences. This equation was formulated at the beginning of the nineteenth century by one of the most gifted scholars of modern science, Joseph Fourier of France. A study of the historical context in which Fourier made his remarkable contribution and the subsequent impact his work has had on the development of modern science is as fascinating as it is educational. This paper is an attempt to present a picture of how certain ideas initially led to Fourier’s development of the heat equation and how, subsequently, Fourier’s work directly influenced and inspired others to use the heat diffusion model to describe other dynamic physical systems. Conversely, others concerned with the study of random processes found that the equations governing such random processes reduced, in the limit, to Fourier’s equation of heat diffusion. In the process of developing the flow of ideas, the paper also presents, to the extent possible, an account of the history and personalities involved.

    • Application of Weibull model for redefined significant wave height distributions

      G Muraleedharan N Unnikrishnan Nair P G Kurup

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      It is well accepted that the parent distribution for individual ocean wave heights follows the Weibull model. However this model does not simulate significant wave height which is the average of the highest one-third of some ‘n’ (n- varies) wave heights in a wave record. It is now proposed to redefine significant wave height as average of the highest one-third of a constant number (n-constant, say,n = 100) of consecutive individual wave heights. The Weibull model is suggested for simulating redefined significant wave height distribution by the method of characteristic function. An empirical support of 100.00% is established by Χ2-test at 0.05 level of significance for 3 sets of data at 0900, 1200 and 1500 hrs at Valiathura, Kerala coast. Parametric relations have been derived for the redefined significant wave height parameters such as mean, maximum one-third average, extreme wave heights, return periods of an extreme wave height and the probability of realising an extreme wave height in a time less than the designated return period.

    • Tidal propagation in the Gulf of Khambhat, Bombay High, and surrounding areas

      A S Unnikrishnan S R Shetye G S Michael

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      The continental shelf on the west coast of India is widest off Bombay and leads into a strongly converging channel, the Gulf of Khambhat. Tides in the Gulf are among the largest on the coast. We use data on amplitude and phase of major semi-diurnal and diurnal constituents at forty-two ports in the Gulf and surrounding areas to define characteristics of the tides. We then use a barotropic numerical model based on shallow water wave equations to simulate the sea level and circulation in the region. The model is forced by prescribing the tide along the open boundaries of the model domain. Observed sea level at Bombay and currents from the Bombay High region at the centre of the model domain and from a shallow station off the port of Dahanu compare favourably with the fields simulated by the model. The simulated amplitudes and phases of the four most prominent tidal constituents also compare favourably with those observed along the coast, except at a few locations where the model spatial resolution (6.37 km × 6.37 km) appears to be inadequate to resolve the local geometry. Though this encourages us to conclude that the circulation in the region is dominated by barotropic tides, a concern is that the observational database on hydrography and directly measured currents in the region is weak.

    • 187Re-187Os in Lesser Himalayan sediments: Measurement techniques and preliminary results

      J R Trivedi Sunil K Singh S Krishnaswami

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      The applications of the187Re-187Os isotope pair as a petrogenetic and geologic tracer are increasing in recent years due to several advances in the chemical extraction and purification of Re and Os, occurring at ppb levels in environmental samples, and in the precise determination of the Os isotope composition. We have established in our laboratory; based on available methods, chemical procedures and Negative Thermal Ionisation Mass Spectrometric techniques for the measurement of Re-Os concentrations in environmental samples and the Os isotope composition in them. Using these techniques, we are able to determine187Os/186Os ratios with a precision of ∼ 1% (±2σμ; twice the standard error of the mean) in several tens of picogram of Os. Preliminary analysis of black shales from the Lower Tal section of the Maldeota phosphorite mine yields a mean187Re-187Os model age of 597 ± 30 Ma. The187Os/186Os and Os concentration in black shales of the Lesser Himalaya range from 8 to 96 and 0.02 to 13 ng g-1 respectively. The mean187Os/186Os in these samples is ∼ 25, significantly higher than the crustal value of ∼ 10.5, suggesting that these black shales could be an important source of radiogenic Os to the rivers draining the Himalaya and to the steady increase in187Os/186Os of the oceans through the Cenozoic.

    • A balanced cross section across the Himalayan foreland belt, the Punjab and Himachal foothills: A reinterpretation of structural styles and evolution

      Dilip K Mukhopadhyay Premanand Mishra

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      The Siwaliks in the foothills of the Himalayas, containing molasse sediments derived from the rising mountain front, represent a foreland fold-thrust belt which was deformed during the continued northward convergence of the Indian plate following the continent-continent collision. In this contribution we present balanced and restored cross sections along a line from Adampur through Jawalamukhi to Palampur in the foothills of the Punjab and Himachal Himalayas using published surface/subsurface data. The cross section incorporates all the rock units of the Sub-Himalaya Zone as well as that of the northern Lesser Himalaya Zone. The structural geometry of the fold-thrust belt in this section is largely controlled by three buried thrusts within the Sundernagar Formation of the Lesser Himalaya Zone. Two of these buried thrusts splay from the basal detachment and delineate a buried horse. Three thrusts towards foreland, including the Main Frontal Thrust (inferred to be a blind thrust in this sector), splay from these buried thrusts. In the hinterland, an anticlinal fault-bend fold was breached by a sequence of break-back thrusts, one of which is the Main Boundary Thrust. A foreland propagating thrust system is inadequate to explain the evolution of the fold-thrust-belt in this section. We show that a “synchronous thrusting” model in whichin-sequence initiation of thrusts at depth combined with continued motion on all the thrusts leading toout-of-sequence imbrication at the upper structural levels better explains the evolution of the fold-thrust belt in the Jawalamukhi section. The estimated shortening between the two chosen pin lines is about 36% (about 72 km).

    • Strain variation in fold-and-thrust belts: Implications for construction of retrodeformable models

      Malay Mukul

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      Deformation in fold-and-thrust belts such as the Himalayas can be represented by the displacement vector field. The strain component of the displacement vector field across the fold-and-thrust belt varies from near zero in external thrust sheets to a significant part of the field in internal thrust sheets. In addition, strain exhibits three-dimensional patterns in parts of internal sheets, near fault zones, and in the overturned limbs of fault-related folds due to superposition of penetrative-strain producing deformation events. This paper examines superposition of these strain producing deformation events in some detail and points out situations in fold-and-thrust belts wherein the finite strain becomes three-dimensional. This suggests that the plane-strain assumption used in the construction of retrodeformable models of fold-and-thrust belt evolution breaks down in these situations and the models lose their validity. Therefore, current techniques used for construction of retrodeformable models in fold-and-thrust belts need to be modified and three-dimensional models which include three-dimensional finite and incremental strain data need to be constructed for an accurate study of the evolution of geometry and kinematics in fold-and-thrust belts.

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