Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

MQFD: A Model for Synergizing TPM and QFD

This thesis presents the methodology of linking Total Productive Maintenance (TPM) and Quality Function Deployment (QFD). The Synergic power ofTPM and QFD led to the formation of a new maintenance model named Maintenance Quality Function Deployment (MQFD). This model was found so powerful that, it could overcome the drawbacks of TPM, by taking care of customer voices. Those voices of customers are used to develop the house of quality. The outputs of house of quality, which are in the form of technical languages, are submitted to the top management for making strategic decisions. The technical languages, which are concerned with enhancing maintenance quality, are strategically directed by the top management towards their adoption of eight TPM pillars. The TPM characteristics developed through the development of eight pillars are fed into the production system, where their implementation is focused towards increasing the values of the maintenance quality parameters, namely overall equipment efficiency (GEE), mean time between failures (MTBF), mean time to repair (MTIR), performance quality, availability and mean down time (MDT). The outputs from production system are required to be reflected in the form of business values namely improved maintenance quality, increased profit, upgraded core competence, and enhanced goodwill. A unique feature of the MQFD model is that it is not necessary to change or dismantle the existing process ofdeveloping house ofquality and TPM projects, which may already be under practice in the company concerned. Thus, the MQFD model enables the tactical marriage between QFD and TPM.First, the literature was reviewed. The results of this review indicated that no activities had so far been reported on integrating QFD in TPM and vice versa. During the second phase, a survey was conducted in six companies in which TPM had been implemented. The objective of this survey was to locate any traces of QFD implementation in TPM programme being implemented in these companies. This survey results indicated that no effort on integrating QFD in TPM had been made in these companies. After completing these two phases of activities, the MQFD model was designed. The details of this work are presented in this research work. Followed by this, the explorative studies on implementing this MQFD model in real time environments were conducted. In addition to that, an empirical study was carried out to examine the receptivity of MQFD model among the practitioners and multifarious organizational cultures. Finally, a sensitivity analysis was conducted to find the hierarchy of various factors influencing MQFD in a company. Throughout the research work, the theory and practice of MQFD were juxtaposed by presenting and publishing papers among scholarly communities and conducting case studies in real time scenario.

SPATIAL CLUSTERING ALGORITHMS-AN OVERVIEW.

An Overview of known spatial clustering algorithms The space of interest can be the two-dimensional abstraction of the surface of the earth or a man-made space like the layout of a VLSI design, a volume containing a model of the human brain, or another 3d-space representing the arrangement of chains of protein molecules. The data consists of geometric information and can be either discrete or continuous. The explicit location and extension of spatial objects define implicit relations of spatial neighborhood (such as topological, distance and direction relations) which are used by spatial data mining algorithms. Therefore, spatial data mining algorithms are required for spatial characterization and spatial trend analysis. Spatial data mining or knowledge discovery in spatial databases differs from regular data mining in analogous with the differences between non-spatial data and spatial data. The attributes of a spatial object stored in a database may be affected by the attributes of the spatial neighbors of that object. In addition, spatial location, and implicit information about the location of an object, may be exactly the information that can be extracted through spatial data mining

Some Aspects of Domain Specific Conceptual Modeling for Simulation of Logistic Terminal Operations

When simulation modeling is used for performance improvement studies of complex systems such as transport terminals, domain specific conceptual modeling constructs could be used by modelers to create structured models. A two stage procedure which includes identification of the problem characteristics/cluster - ‘knowledge acquisition’ and identification of standard models for the problem cluster – ‘model abstraction’ was found to be effective in creating structured models when applied to certain logistic terminal systems. In this paper we discuss some methods and examples related the knowledge acquisition and model abstraction stages for the development of three different types of model categories of terminal systems