Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Studies on Two-Photon Absorption of Aniline Using Thermal Lens Effect

Two-photon absorption spectrum of aniline is recorded using thermal lens effect with optical parametric oscillator as the pump source. Studies show that the two-photon absorption spectrum observed corresponds to I Al -. I B2 transition of aniline.

Sedimentological and Geotechnical Studies of Coastal Sediments of Central Kerala.

All over the world, several Quaternary proxy data have been used to reconstruct past sea levels, mainly radiocarbon or OSL dating of exposures of marine facies or shore line indicators (e.g. Carr et al., 2010) as well as paleoenvironmental indicators in lagoon or estuary sediments (e.g. Baxter and Meadows, 1999). Estuaries and deltas develop at river mouths during transgressive and regressive phases, respectively (Boyd et al., 1992). In particular, the postglacial Holocene sea-level rise has contributed importantly to the estuary-to-delta transition (Hori et al. 2004). By analyzing radiocarbon ages of the basal or near-basal sediments of the world’s deltas, Stanley and Warne (1994) showed that delta initiation occurred on a worldwide scale after about 8500–6500 years BP and concluded that the initiation was controlled principally by the declining rate of the Holocene sea-level rise. Worldwide there were different regional sea-level changes since the last glacial maximum (LGM) (Irion et al., 2012). Along the northern Canadian coast, for example, sea level has been falling throughout the Holocene due to the glacial rebound of the crust after the last glaciation (Peltier, 1988). This is comparable to the development in Scandinavia (Steffen and Kaufmann, 2005) where sea level drops today. From about Virginia/USA to Mexico there is a constant sea-level rise similar to the Holocene sea-level development of the southern North Sea (e.g. Vink et al., 2007). From the border of Ceará/Rio Grande do Norte down to Patagonia, indicators of Holocene sea level point to a level that was up to 5 m higher than today's mean sea level (Angulo et al., 1999; Martin et al., 2003; Caldas et al., 2006a, b)

Influence of a Salt Water Regulator on the Survival Response of Salmonella Paratyphi in Vembanadu Lake: India

Contamination of environmental water by pathogenic microorganisms and subsequent infections originated from such sources during different contact and non- contact recreational activities are a major public health problem worldwide particularly in developing countries. The main pathogen frequently associated with enteric infection in developing countries are Salmonella enterica serovar typhi and paratyphi. Although the natural habitat of Salmonella is the gastrointestinal tract of animals, it find its way into natural water through faecal contamination and are frequently identified from various aquatic environments (Baudart et al., 2000; Dionisio et al., 2000; Martinez -Urtaza et al., 2004., Abhirosh et al., 2008). Typhoid fever caused by S. enterica serotype typhi and paratyphi are a common infectious disease occurring in all the parts of the world with its highest endemicity in certain parts of Asia, Africa, Latin America and in the Indian subcontinent with an estimated incidence of 33 million cases each year with significant morbidity and mortality (Threlfall, 2002). In most cases the disease is transmitted by polluted water (Girard et al., 2006) because of the poor hygienic conditions, inadequate clean water supplies and sewage treatment facilities. However in developed countries the disease is mainly associated with food (Bell et al., 2002) especially shellfish (Heinitz et al., 2000

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis