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.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Utilisation of Coir Geotextiles for Unpaved Roads and Embankments

The increasing tempo of construction activity the world over creates heavy pressure on existing land space. The quest for new and competent site often points to the needs for improving existing sites, which are otherwise deemed unsuitable for adopting conventional foundations. This is accomplished by ground improvement methods, which are employed to improve the quality of soil incompetent in their natural state. Among the construction activities, a well-connected road network is one of the basic infrastructure requirements, which play a vital role for the fast and comfortable movement of inter- regional traffic in countries like India.One of the innovative ground improvement techniques practised all over the world is the use of geosynthetics, which include geotextiles, geomembranes, geogrids, etc . They offer the advantages such as space saving, enviromnental sensitivity, material availability, technical superiority, higher cost savings, less construction time, etc . Because of its fundamental properties, such as tensile strength, filtering and water permeability, a geotextile inserted between the base material and sub grade can function as reinforcement, a filter medium, a separation layer and as a drainage medium. Though polymeric geotextiles are used in abundant quantities, the use of natural geotextiles (like coir, jute, etc.) has yet to get momentum. This is primarily due to the lack of research work on natural geotextilcs for ground improvement, particularly in the areas of un paved roads. Coir geotextiles are best suited for low cost applications because of its availability at low prices compared to its synthetic counterparts. The proper utilisation of coir geotextilcs in various applications demands large quantities of the product, which in turn can create a boom in the coir industry. The present study aims at exploring the possibilities of utilising coir geotextiles for unpaved roads and embankments.The properties of coir geotextiles used have been evaluated. The properties studied include mass per unit area, puncture resistance, tensile strength, secant modulus, etc . The interfacial friction between soils and three types of coir geotextiles used was also evaluated. It was found that though the parameters evaluated for coir geotextiles have low values compared to polymeric geotextiles, the former are sufficient for use in unpaved roads and embankments. The frictional characteristics of coir geotextile - soil interfaces are extremely good and satisfy the condition set by the International Geosynthetic Society for varied applications.The performance of coir geotextiles reinforced subgrade was studied by conducting California Bearing Ratio (CBR) tests. Studies were made with coir geotextiles placed at different levels and also in multiple layers. The results have shown that the coir geotextile enhances the subgrade strength. A regression analysis was perfonned and a mathematical model was developed to predict the CBR of the coir geotextile reinforced subgrade soil as a function of the soil properties, coir geotextile properties, and placement depth of reinforcement.The effects of coir geotextiles on bearing capacity were studied by perfonning plate load tests in a test tan1e This helped to understand the functioning of geotextile as reinforcement in unpaved roads and embankments. The perfonnance of different types of coir geotextiles with respect to the placement depth in dry and saturated conditions was studied. The results revealed that the bearing capacity of coir-reinforced soil is increasing irrespective of the type of coir geotextiles and saturation condition.The rut behaviour of unreinforced and coir reinforced unpaved road sections were compared by conducting model static load tests in a test tank and also under repetitive loads in a wheel track test facility. The results showed that coir geotextiles could fulfill the functions as reinforcement and as a separator, both under static and repetitive loads. The rut depth was very much reduced whik placing coir geotextiles in between sub grade and sub base.In order to study the use of Coir geotextiles in improving the settlement characteristics, two types of prefabricated COlf geotextile vertical drains were developed and their time - settlement behaviour were studied. Three different dispositions were tried. It was found that the coir geotextile drains were very effective in reducing consolidation time due to radial drainage. The circular drains in triangular disposition gave maximum beneficial effect.In long run, the degradation of coir geotextile is expected, which results in a soil - fibre matrix. Hence, studies pertaining to strength and compressibility characteristics of soil - coir fibre composites were conducted. Experiments were done using coir fibres having different aspect ratios and in different proportions. The results revealed that the strength of the soil was increased by 150% to 200% when mixed with 2% of fibre having approximately 12mm length, at all compaction conditions. Also, the coefficient of consolidation increased and compression index decreased with the addition of coir fibre.Typical design charts were prepared for the design of coir geotextile reinforced unpaved roads. Some illustrative examples are also given. The results demonstrated that a considerable saving in subase / base thickness can he achieved with the use of eoir geotextiles, which in turn, would save large quantities of natural aggregates.

Investment analysis of chemical projects and development of standerdised mathematical co-relation for cost estimation of pressure vessels in chemical industry

The present study is intended to provide a new scientific approach to the solution of the worlds cost engineering problems encountered in the chemical industries in our nation. The problem is that of cost estimation of equipments especially of pressure vessels when setting up chemical industries .The present study attempts to develop a model for such cost estimation. This in turn is hoped would go a long way to solve this and related problems in forecasting the cost of setting up chemical plants.

An Improved Color Video Super-Resolution Using Kernel Regression and Fuzzy Enhancement

An improved color video super-resolution technique using kernel regression and fuzzy enhancement is presented in this paper. A high resolution frame is computed from a set of low resolution video frames by kernel regression using an adaptive Gaussian kernel. A fuzzy smoothing filter is proposed to enhance the regression output. The proposed technique is a low cost software solution to resolution enhancement of color video in multimedia applications. The performance of the proposed technique is evaluated using several color videos and it is found to be better than other techniques in producing high quality high resolution color videos

Mathematical Morphology on Hypergraphs Using Vertex-Hyperedge Correspondence

The focus of this paper is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyperedge set of a hypergraph , by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of . This paper also studies the concept of morphological adjunction on hypergraphs for which both the input and the output are hypergraphs

Using Neural Network Classifier Support Vector Machine Regression for the prediction of Melting Point of Drug – like compounds

In our study we use a kernel based classification technique, Support Vector Machine Regression for predicting the Melting Point of Drug – like compounds in terms of Topological Descriptors, Topological Charge Indices, Connectivity Indices and 2D Auto Correlations. The Machine Learning model was designed, trained and tested using a dataset of 100 compounds and it was found that an SVMReg model with RBF Kernel could predict the Melting Point with a mean absolute error 15.5854 and Root Mean Squared Error 19.7576

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education