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.

An analogue of the logistic map in two dimensions

This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.

Effects of the Piscicides, Mahua Oil Cake and Croton Seed on the Prawn Culture System

Department of Marine Biology, Microbiology and Biochemistry

Rotational analysis of the C1Π-X1 Σ+ system of indium monofluoride

Indium monofluoride was excited in a high-frequency discharge and the C-X system was photographed at a reciprocal dispersion of 0.3 AA mm-1 using a plane-grating spectrograph. Rotational analyses of the 0,0 1,0 2,2 3,3 4,4 2,4 3,5 4,6 and 5,7 bands have been carried out and the following molecular constants have been evaluated. Be'=0.2670(+or-3) cm-1, Be"=0.2628(+or-4) cm-1, alpha e'=0.0050(+or-4) cm-1, alpha e"=0.0020(+or-1) cm-1, De'=3.65(+or-5)*10-7 cm-1, De"=2.5(+or-3)*10-7 cm-1, beta e'=0.5(+or-2)*10-7 cm-1, beta e"=0.2(+or-1)*10-7 cm-1, re'=1.9672(+or-3) AA, re"=1.9853(+or-2) AA. The re" value agrees with the microwave absorption value 1.9854 AA.

Geodynamics of the Andaman - Sumatra - Java Trench - Arc System Based on Gravity and Seismotectonic Study

This work aims to study the variation in subduction zone geometry along and across the arc and the fault pattern within the subducting plate. Depth of penetration as well as the dip of the Benioff zone varies considerably along the arc which corresponds to the curvature of the fold- thrust belt which varies from concave to convex in different sectors of the arc. The entire arc is divided into 27 segments and depth sections thus prepared are utilized to investigate the average dip of the Benioff zone in the different parts of the entire arc, penetration depth of the subducting lithosphere, the subduction zone geometry underlying the trench, the arctrench gap, etc.The study also describes how different seismogenic sources are identified in the region, estimation of moment release rate and deformation pattern. The region is divided into broad seismogenic belts. Based on these previous studies and seismicity Pattern, we identified several broad distinct seismogenic belts/sources. These are l) the Outer arc region consisting of Andaman-Nicobar islands 2) the back-arc Andaman Sea 3)The Sumatran fault zone(SFZ)4)Java onshore region termed as Jave Fault Zone(JFZ)5)Sumatran fore arc silver plate consisting of Mentawai fault(MFZ)6) The offshore java fore arc region 7)The Sunda Strait region.As the Seismicity is variable,it is difficult to demarcate individual seismogenic sources.Hence, we employed a moving window method having a window length of 3—4° and with 50% overlapping starting from one end to the other. We succeeded in defining 4 sources each in the Andaman fore arc and Back arc region, 9 such sources (moving windows) in the Sumatran Fault zone (SFZ), 9 sources in the offshore SFZ region and 7 sources in the offshore Java region. Because of the low seismicity along JFZ, it is separated into three seismogenic sources namely West Java, Central Java and East Java. The Sunda strait is considered as a single seismogenic source.The deformation rates for each of the seismogenic zones have been computed. A detailed error analysis of velocity tensors using Monte—Carlo simulation method has been carried out in order to obtain uncertainties. The eigen values and the respective eigen vectors of the velocity tensor are computed to analyze the actual deformation pattem for different zones. The results obtained have been discussed in the light of regional tectonics, and their implications in terms of geodynamics have been enumerated.ln the light of recent major earthquakes (26th December 2004 and 28th March 2005 events) and the ongoing seismic activity, we have recalculated the variation in the crustal deformation rates prior and after these earthquakes in Andaman—Sumatra region including the data up to 2005 and the significant results has been presented.ln this chapter, the down going lithosphere along the subduction zone is modeled using the free air gravity data by taking into consideration the thickness of the crustal layer, the thickness of the subducting slab, sediment thickness, presence of volcanism, the proximity of the continental crust etc. Here a systematic and detailed gravity interpretation constrained by seismicity and seismic data in the Andaman arc and the Andaman Sea region in order to delineate the crustal structure and density heterogeneities a Io nagnd across the arc and its correlation with the seismogenic behaviour is presented.

Criminal justice system in pondicherry - a comparative critical study of the past and the presen

The Union Territory of Pondicherry prior to its merger with the Indian Union was a French Colony. The erstwhile territory of Pondicherry along with its hamlets, namely, KARAIKKAL, MAHE and YANAM was administered by the French Regime. Before it was established by French in 1 6 74 A.D. it was part of Vijayanagara Empire. Prior to this, Pondicherry was a part of the Kingdom of Chola and Pallava Kings. During French Regime, the laws which were in force in France in relation to administration of civil and criminal justice were extended to the erstwhile Territory of Pondicherry. Thus while Pondicherry stood influenced by the Inquisitorial system since the beginning of the 18th century, the neighboring states forming part of the Indian Union since Independence came under the Influence of the British system, viz. accusatorial system. The territory of Pondicherry, for administrative reasons, came to be merged with the Indian Union in the early 60's. Following the merger, the Indian administration sought to extent its own laws from time to time replacing erstwhile French Laws, however, subject to certain savings. Thus the transitional period witnessed consequential changes in the administration of the territory, including the sphere of judicial system. Since I 963, the Union Territory of Pondicherry was brought under the spell of the Indian Legal System The people in Pondicherry ' thus have had the benefit of experiencing both the svstems. Their experiences will be of much help to those who undertake comparative studies in law. The plus and minus points of the respective systems help one to develop a detachment that helps independent evaluation of the svstents. The result of these studies could be relevant in revitalising our criminal systems.The present system is evaluated in the light of the past system. New dimensions are added by way' of an empirical study also.

A study of the co-operative banking system in kerala

The co-operative credit structure in a state set up consists of 3 tiers — Primary Societies at the base, District Co-operative Banks at the middle and State Cooperative Bank at the top. But, some societies at the primary level are governed by, in addition to Co-operative Societies Act, the Banking Regulation Act. Thus they are under dual control. In addition, they are working under the direct purview of Reserve Bank of India. The scope of this study is restricted to such Primary Societies, District Co-operative Banks and State Co-operative Bank. For the evaluation of the working of Co-operative Banks, the board of directors and staff were interviewed with the help of pre-constructed and pre-tested interview schedules. However, the share holders and customers were not interviewed mainly because almost all respondents were reluctant to provide copies of an exhaustive list of share holders and non-share holder customers, for the purpose of maintaining secrecy. This being an individual work, it was found physically and financially very difficult to extend the study so as to cover the share holders and non-share holder customers. Limitations of time were also responsible for restricting this study. The period of study was restricted to 1980-'81 to 1983-'84 as the data relating to earlier periods were firstly not available from all banks and secondly the prior data was considered out of date for the purpose of the study.

Effects Of The Piscicides, Mahua Oil Cake And Croton Seed On The Prawn Culture System

The present research programme envisages a comparative study of the effects of two piscicides of plant origin, viz., mahua oil cake, a derivative from the plant fig Iatifolia and croton seed, a product from the plant Croton tiglium. Although some reports on the effects of mahua oil cake and croton seed on fresh water pond culture systems are available, information on their effect on brackishwater culture systems are rather scanty This was the guiding principle for launching the present study It is hoped that the findings will enable aquaculturists to make use of the piscicides in a more rational and efficient way, and will go a long way towards realising the maximum return liom culture systems without hampering the environment. The thesis is presented in seven chapters such as Introduction, Review of literature, Materials and Methods, Results, Discussion, Summary and Bibliography

Spatio-temporal variation of microphytoplankton in the upwelling system of the south-eastern Arabian Sea during the summer monsoon of 2009

The phytoplankton standing crop was assessed in detail along the South Eastern Arabian Sea (SEAS) during the different phases of coastal upwelling in 2009.During phase 1 intense upwelling was observed along the southern transects (8◦N and 8.5◦N). The maximum chlorophyll a concentration (22.7 mg m −3) was observed in the coastal waters off Thiruvananthapuram (8.5◦N). Further north there was no signature of upwelling, with extensive Trichodesmium erythraeum blooms. Diatoms dominated in these upwelling regions with the centric diatom Chaetoceros curvisetus being the dominant species along the 8◦N transect. Along the 8.5◦N transect pennate diatoms like Nitzschia seriata and Pseudo-nitzschia sp. dominated. During phase 2, upwelling of varying intensity was observed throughout the study area with maximum chlorophyll a concentrations along the 9◦N transect (25 mg m−3) with Chaetoceros curvisetus as the dominant phytoplankton. Along the 8.5◦N transect pennate diatoms during phase 1 were replaced by centric diatoms like Chaetoceros sp. The presence of solitary pennate diatoms Amphora sp. and Navicula sp. were significant in the waters off Kochi. Upwelling was waning during phase 3 and was confined to the coastal waters of the southern transects with the highest chlorophyll a concentration of 11.2 mg m−3. Along with diatoms, dinoflagellate cell densities increased in phases 2 and 3. In the northern transects (9◦N and 10◦N) the proportion of dinoflagellates was comparatively higher and was represented mainly by Protoperidinium spp., Ceratium spp. and Dinophysis spp.

Geochemical metal fractionation profile of the core sediment in the Cochin estuarine system

Geochemical composition is a set of data for predicting the climatic condition existing in an ecosystem. Both the surficial and core sediment geochemistry are helpful in monitoring, assessing and evaluating the marine environment. The aim of the research work is to assess the relationship between the biogeochemical constituents in the Cochin Estuarine System (CES), their modifications after a long period of anoxia and also to identify the various processes which control the sediment composition in this region, through a multivariate statistical approach. Therefore the study of present core sediment geochemistry has a critical role in unraveling the benchmark of their characterization. Sediment cores from four prominent zones of CES were examined for various biogeochemical aspects. The results have served as rejuvenating records for the prediction of core sediment status prevailing in the CES