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.

Dynamics of laser produced silver plasma under film deposition conditions studied using optical emission spectroscopy

Laser produced plasma from silver is generated using a Q-switched Nd:YAG laser. Optical emission spectroscopy is used to carry out time of flight (TOF) analysis of atomic particles. An anomalous double peak profile in the TOF distribution is observed at low pressure. A collection of slower species emerge at reduced pressure below 4 X lO-3 mbar and this species has a greater velocity spread. At high pressure the plasma expansion follows the shockwave model with cylindrical symmetry whereas at reduced pressure it shows unsteady adiabatic expansion (UAE). During UAE the species show a parabolic increases in the expansion time with radial distance whereas during shock wave expansion the exponent is less than one. The angular distribution of the ablated species in the plume is obtained from the measurement of optical density of thin films deposited on to glass substrates kept perpendicular to the plume. There is a sharp variation in the film thickness away from the film centre due to asymmetries in the plume.

Emission characteristics and dynamics of C2 from laser produced graphite plasma

The emission features of laser ablated graphite plume generated in a helium ambient atmosphere have been investigated with time and space resolved plasma diagnostic technique. Time resolved optical emission spectroscopy is employed to reveal the velocity distribution of different species ejected during ablation. At lower values of laser fluences only a slowly propagating component of C2 is seen. At high fluences emission from C2 shows a twin peak distribution in time. The formation of an emission peak with diminished time delay giving an energetic peak at higher laser fluences is attributed to many body recombination. It is also observed that these double peaks get modified into triple peak time of flight distribution at distances greater than 16 mm from the target. The occurrence of multiple peaks in the C2 emission is mainly due to the delays caused from the different formation mechanism of C2 species. The velocity distribution of the faster peak exhibits an oscillating character with distance from the target surface.

Performance characteristics of positive and negative delayed feedback on chaotic dynamics of directly modulated InGaAsP semiconductor lasers

The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.

Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal

The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.

Chaotic Dynamics of Semiconductor Laser with Current Modulation and optoelectronic feedback

Chaotic dynamics of directly modulated semiconductor lasers have been studied extensively over the last two decades because of their application in secure optical communication. However, chaos is generally suppressed in such systems when the nonlinear gain reduction factor is above 0.01 which is very much smaller than the reported values in semiconductors like InGaAsP. In this paper we show that by giving an optoelectronic feedback with appropriate delay one can increase the range of the values of the gain reduction factor for which chaos can be observed. Numerical studies show that negative feedback is more efficient in producing chaotic dynamics.

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

Effect of ambient gas on the expansion dynamics of plasma plume formed by laser blow off of thin film

A study has been carried out to understand the influence of ambient gases on the dynamics of laser-blow-off plumes of multi-layered LiF–C thin film. Plume images at various time intervals ranging from 100 to 3000 ns have been recorded using an intensified CCD camera. Enhancement in the plume intensity and change in size and shape occurs on introducing ambient gases and these changes are highly dependent on the nature and composition of the ambient gas used. Velocity of the plume was found to be higher in helium ambient whereas intensity enhancement is greater in argon environment. The plume shapes have maximum size at 10−2 and 10−1 Torr of Ar and He pressures, respectively. As the background pressure increases further (>10−2 Torr: depending on the nature of gas), the plume gets compressed/focused in the lateral direction. Internal structure formation and turbulences are observed at higher pressures (>10−1 Torr) in both ambient gases.

Dynamics of Rifting Along the Southwest Continental margin of India Through Coherence and Process oriented Analysis of Gravity Data

Department of Marine Geology and Geophysics,Cochin University of Science and Technology

Dynamics of coupled Josephson junctions under the influence of applied fields

We investigate the effect of the phase difference of appliedfields on the dynamics of mutually coupledJosephsonjunctions. A phase difference between the appliedfields desynchronizes the system. It is found that though the amplitudes of the output voltage values are uncorrelated, a phase correlation is found to exist for small values of applied phase difference. The dynamics of the system is found to change from chaotic to periodic for certain values of phase difference. We report that by keeping the value of phase difference as π, the system continues to be in periodic motion for a wide range of values of system parameters. This result may find applications in devices like voltage standards, detectors, SQUIDS, etc., where chaos is least desired.

Application of Imaging to Study the Evolution and Dynamics of Laser Produced Plasma from Solid and Thin Film Li Targets

The present thesis report the results obtained from the studies carried out on the laser blow off plasma (LBO) from LiF-C (Lithium Fluoride with Carbon) thin film target, which is of particular importance in Tokamak plasma diagnostics. Keeping in view of its significance, plasma generated by the irradiation of thin film target by nanosecond laser pulses from an Nd:YAG laser over the thin film target has been characterized by fast photography using intensified CCD. In comparison to other diagnostic techniques, imaging studies provide better understanding of plasma geometry (size, shape, divergence etc) and structural formations inside the plume during different stages of expansion.

Dynamics of Deforestation and Socio-Economic profile of Tribal Women Folk in Kerala- A study of Attappady is

This thesis Entitled Dynamics of deforestation and Socio-Economic profile of tribal women flok in kerala -A study of Attappady. The study was based on both primary and secondary data. Primary data were collected through a sample survey conducted in three panchayaths .The thesis is organized in eight chapters. The first chapter provides the background to the study. Second chapter reviews the literature. Third chapter provides the profile of the study area and general conditions. Fourth chapter consists of the life cycle structure of the tribal woman. Fifth chapter covers the socio-economic conditions of the tribal women in the study area. Sixth chapter consists of relationship between tribal women and forest and the degradation of the forest. Seventh chapter provides the documentation of the development programmes implemented in Attappady and their importance to the tribals. Last chapter consists of summary and conclusions of the study, suggestions and recommendations of the study.

Dynamics of some Environmentally Significant Pesticides in a Tropical Waterway - A Toxicological Approach

Industrial pollutants, consisting of heavy metals, petroleum residues, petrochemicals, and a wide spectrum of pesticides, enter the marine environment on a massive scale and pose a very serious threat to all forms of aquatic life. Although, earlier, efforts were directed towards the identification of pollutants and their major sources, because of a growing apprehension about the potential harm that pesticides can inflict upon various aquatic fauna and flora, research on fundamental and applied aspects of pesticides in the aquatic environment has mushroomed to a point where it has become difficult to even keep track of the current advances and developments. The Cochin Estuarine System (CES), adjoining the Greater Cochin area, receives considerable amounts of domestic sewage, urban wastes, agricultural runoff as well as effluent from the industrial units spread all along its shores. Since preliminary investigations revealed that the most prominent of organic pollutants discharged to these estuarine waters were the pesticides, the present study was designed to analyse the temporal and spatial distribution profile of some of the more toxic, persistent pesticides ——— organochlorines such as DDT and their metabolites; HCH-isomers; a cyclodiene compound," Endosulfan and a widely distributed, easily degradable, organophosphorus compound, Malathion, besides investigating their sorptional and toxicological characteristics. Although, there were indications of widespread contamination of various regions of the CBS with DDT, HCH-isomers etc., due to inadequacies of the monitoring programmes and due to a glaring void of baseline data the causative factors could not identified authentically. Therefore, seasonal and spatial distributions of some of the more commonly used pesticides in the CES were monitored systematically, (employing Gas Chromatographic techniques) and the results are analysed.

Studies on the Dynamics of Cochin Estuary

The thesis entitled Studies on the Dynamics of Cochin Estuary. This thesis is addressed to an investigation on the tidal, seasonal and spatial variations of the hydrographic parameters, circulation and mixing processes of the Cochin estuary. The present programme of study is aimed at obtaining a comprehensive picture of the tidal characteristics, hydrography, circulation and mixing present in this estuarine system during different seasons. The studies have been carried out through field collection of data on salinity, temperature and water currents to get a picture of their spatial and temporal variations. The hydrographic data have been analysed in relation to tide, rainfall and river discharges. From the findings it is seen that at the Cochin inlet, the estuarine features vary annually. During July and August, the estuary is characterised as almost saltwedge type; during June, September, October, December and January it shows appreciabie stratification, and during the rest of the months the estuary shows almost well mixed nature. Seasonal variations are well reflected in water temperature in the Cochin estuary, where the temperature reaches its maximum during the dry pre monsoon period with very weak thermal gradients indicating strong vertical mixing

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.