Fractional Reaction-Diffusion Equations

In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.     

An analytic approach to the connection between stellar structure parameters and the neutrino emission rate in a simple stellar model

In order to obtain the internal structure of a main-sequence star such as the Sun usually one has to solve the detailed structure equations numerically. This paper is an attempt to construct analytic models for the stellar nuclear energy generation. We give closed-form analytic results for the stellar luminosity and stellar neutrino emission rate when the radial matter density of the spherical star under consideration is linear. For the numerical estimation of the neutrino flux of a specified stellar nuclear reaction we take into account parameters of the standard solar model. The present paper gives for the first time the connection between stellar structure parameters and neutrino fluxes in an analytic stellar model.     

A Comparative Evaluation of the Geotechnical Index Properties of Clayey Sediments along the West Coast of India

Sediment core samples collected during geotechnical surveys along the West Coast of India in the near shore areas of Arabian Sea have generated data on the geotechnical index properties of clayey sediments up to nearly 5 m depth below seafloor. A comparative study of three sectors within themselves is attempted before carrying out a final evaluation between the sectors. Cohesive clayey sediments of Gujarat sector are comparable though widely variant in a few aspects; in the Maharashtra-Goa-Karnataka sector though, plasticity levels and clay type vary, and activity and consistency levels are quite similar. Though broadly comparable, the clayey sediments of Kerala-Tamilnadu sector have quite diverse characteristics that fail to conform to any particular pattern as each area has an exclusive set of geotechnical properties.     

A Comparative Evaluation of the Geotechnical Index Properties of Clayey Sediments along the West Coast of India

Sediment core samples collected during geotechnical surveys along the West Coast of India in the near shore areas of Arabian Sea have generated data on the geotechnical index properties of clayey sediments up to nearly 5 m depth below seafloor. A comparative study of three sectors within themselves is attempted before carrying out a final evaluation between the sectors. Cohesive clayey sediments of Gujarat sector are comparable though widely variant in a few aspects; in the Maharashtra-Goa-Karnataka sector though, plasticity levels and clay type vary, and activity and consistency levels are quite similar. Though broadly comparable, the clayey sediments of Kerala-Tamilnadu sector have quite diverse characteristics that fail to conform to any particular pattern as each area has an exclusive set of geotechnical properties.     

Review of mathematical techniques applicable in astrophysical reaction rate theory

An overview is presented on statistical techniques for the analytic evaluation of integrals for non-resonant, non-resonant depleted, non-resonant cut-off, non-resonant sccreened, and resonant thermonuclear reaction rates. The techniques are based on statistical distribution theory and the theory of Meijer's G-function and Fox's H-function. The implementation of Meijer's G-function in Mathematica constituts an additional utility for analytic manipulations and numerical computation of thermonuclear reaction rate integrals. Recent results in the astrophysical literature related to the use of analytic thermonuclear reaction rates are incorporated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Weathering Controlled Landslide in Deccan Traps: Insight from Mahabaleshwar,Maharashtra

Landslide is one of the devastating natural phenomenon that threatens human life and property. Every year a number of persons lost their lives due to the landslides. Therefore, a better understanding and characterization of landslide is very essential for adopting mitigation strategies to contain the adversities of this natural hazard. Information on landslides from different climatic setup are very essential for better understanding of the influence of weathering, rainfall, or topography on landslide generation. Weathering is one of the important causative factor for landslide generation in the moderate topography or inactive mountainous terrain. The Western Ghats including the Deccan Traps, an inactive mountain range, receives torrential rainfall. Intense rainfall in these areas enhances the weathering processes and fabricates thick soil covers. Mahabaleshwar area, Maharashtra was chosen as a case study, where high elevated part is covered by lateritic layer and each lava flow unit is separated by a thin weathered bed of red bole. The area experiences series of landslides during the summer monsoon months. Mainly two types of landslides have been identified in the area confined with the red bole bed and powdery lateritic soil. The first type of landslides occur at higher elevations (≥1200m) where horizontal beds of permeable laterites underlined by impermeable thick basalt beds. The rain water infiltrates down and spread laterally within the permeable lateritic beds. It finally spouts at lower plateau elevations and triggers mainly debris flows. The other category of landslides occurs where the weathered red bole bed separates two successive lava flows. The percolating water from the secondary porosities (joints and inter connected vugs) comes out from the contact zones of basalt and red bole bed in the form of seepages. It erodes the red bole bed and as a result the overlying masses hang and consequently lead to rock fall. The Chemical Index of Alteration (CIA) of the representative samples from landslide locations indicates significant weathering. The CIA values for the fine lateritic soil are up to 98% whereas for the red bole bed it varies from 77 to 85%. This suggests a high chemical weathering and higher erodibility. The association of active landslide locations with the red bole bed and fine lateritic soil suggests a close relation between weathering and landslide occurrences in the area.     

Analytic stellar structure

This paper continues to elaborate on analytic methods to construct models for the internal structure of solar-type stars. Since a detailed stellar model is desired, a nonlinear analytic density distribution in terms of a two-parameter family of models has been assumed. Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized stellar fusion reactor. The results show once more that methods of differential and integral calculus provide a laboratory for the application of special functions of mathematical physics in stellar structure.Paper presented at the Second International Conference on Industrial and Applied Mathematics, July 8–12 1991, Washington D.C., U.S.A.     

Geotechnical Surveys Indicate Potential Offshore Port Facilities off Subarnarekha Outflow Sector,Orissa, India

Deficiency in major port facilities off Orissa prompted the State Government to promote development of a port facility in the Subarnarekha river outflow sector utilizing the inland water network of Orissa coast canal and Contai canal. Marine and Coastal Surveys Division of Geological Survey of India carried out geotechnical feasibility surveys to explore possibilities of setting up a port facility in this sector. Bathymetry reveals smooth, parallel isobaths signifying gentle slopes with varying gradients. The East-West profile delineates a natural channel that could be dredged into a navigational channel. Sediments are dominantly sandy silt marginally varying either into silty sand or clayey silt. Geotechnical characteristics suggest a stable substratum ideal for developing the offshore port facility. Side-scan sonar surveys reveal a seafloor bereft of any hazardous rocks or reefs. The surveys espouse immense potential for developing this sector into an offshore port facility.     

Analytic results for screened non-resonant nuclear reaction rates

This paper deals with the closed-form representation of the non-resonant nuclear reaction rate taking into account electron screening effects for the reacting particles. The basic physical principles concerning nuclear reactions in dense astrophysical plasmas are applied to derive the representation of the screened nuclear reaction rate integral. Taking advantage of the theory of Meijer'sG-function it is shown that both the reaction rate integrals with and without screening corrections can be represented in closed form. Mathematical approximations for the reaction rate integral, till now considered as inevitable in the literature, are avoided and exact computable representations given.     

A note on the linear stellar model

For a purely gaseous self-gravitating stellar configuration with linear matter density distribution the total power generated by nuclear reactions is considered. The analytic connection between physical parameters of the macroscopic and microscopic levels of the stellar equilibrium configuration is revealed.