Bayesian Analysis for a Theory of Random Consumer Demand: The Case of Indivisible Goods

McCausland (2004a) describes a new theory of random consumer demand. Theoretically consistent random demand can be represented by a \"regular\" \"L-utility\" function on the consumption set X. The present paper is about Bayesian inference for regular L-utility functions. We express prior and posterior uncertainty in terms of distributions over the indefinite-dimensional parameter set of a flexible functional form. We propose a class of proper priors on the parameter set. The priors are flexible, in the sense that they put positive probability in the neighborhood of any L-utility function that is regular on a large subset bar(X) of X; and regular, in the sense that they assign zero probability to the set of L-utility functions that are irregular on bar(X). We propose methods of Bayesian inference for an environment with indivisible goods, leaving the more difficult case of indefinitely divisible goods for another paper. We analyse individual choice data from a consumer experiment described in Harbaugh et al. (2001).

Factor Analysis of a Large DSGE Model

We study the workings of the factor analysis of high-dimensional data using artificial series generated from a large, multi-sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allow us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the theoretical and finite sample properties of the principal components estimates of the factor space, investigate the substantive reason(s) for the good performance of di¤usion index forecasts, and assess the quality of the factor analysis of highly dissagregated data. In all our exercises, we explain the precise relationship between the factors and the basic macroeconomic shocks postulated by the model.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Field Equilibrium Finite Elements for Structural Analysis

Many finite elements used in structural analysis possess deficiencies like shear locking, incompressibility locking, poor stress predictions within the element domain, violent stress oscillation, poor convergence etc. An approach that can probably overcome many of these problems would be to consider elements in which the assumed displacement functions satisfy the equations of stress field equilibrium. In this method, the finite element will not only have nodal equilibrium of forces, but also have inner stress field equilibrium. The displacement interpolation functions inside each individual element are truncated polynomial solutions of differential equations. Such elements are likely to give better solutions than the existing elements.In this thesis, a new family of finite elements in which the assumed displacement function satisfies the differential equations of stress field equilibrium is proposed. A general procedure for constructing the displacement functions and use of these functions in the generation of elemental stiffness matrices has been developed. The approach to develop field equilibrium elements is quite general and various elements to analyse different types of structures can be formulated from corresponding stress field equilibrium equations. Using this procedure, a nine node quadrilateral element SFCNQ for plane stress analysis, a sixteen node solid element SFCSS for three dimensional stress analysis and a four node quadrilateral element SFCFP for plate bending problems have been formulated.For implementing these elements, computer programs based on modular concepts have been developed. Numerical investigations on the performance of these elements have been carried out through standard test problems for validation purpose. Comparisons involving theoretical closed form solutions as well as results obtained with existing finite elements have also been made. It is found that the new elements perform well in all the situations considered. Solutions in all the cases converge correctly to the exact values. In many cases, convergence is faster when compared with other existing finite elements. The behaviour of field consistent elements would definitely generate a great deal of interest amongst the users of the finite elements.

Thermo-Structural Analysis of 3D Composites

Three dimensional (3D) composites are strong contenders for the structural applications in situations like aerospace,aircraft and automotive industries where multidirectional thermal and mechanical stresses exist. The presence of reinforcement along the thickness direction in 3D composites,increases the through the thickness stiffness and strength properties.The 3D preforms can be manufactured with numerous complex architecture variations to meet the needs of specific applications.For hot structure applications Carbon-Carbon(C-C) composites are generally used,whose property variation with respect to temperature is essential for carrying out the design of hot structures.The thermomechanical behavior of 3D composites is not fully understood and reported.The methodology to find the thermomechanical properties using analytical modelling of 3D woven,3D 4-axes braided and 3D 5-axes braided composites from Representative Unit Cells(RUC's) based on constitutive equations for 3D composites has been dealt in the present study.High Temperature Unidirectional (UD) Carbon-Carbon material properties have been evaluated using analytical methods,viz.,Composite cylinder assemblage Model and Method of Cells based on experiments carried out on Carbon-Carbon fabric composite for a temparature range of 300 degreeK to 2800degreeK.These properties have been used for evaluating the 3D composite properties.From among the existing methods of solution sequences for 3D composites,"3D composite Strength Model" has been identified as the most suitable method.For thegeneration of material properies of RUC's od 3D composites,software has been developed using MATLAB.Correlaton of the analytically determined properties with test results available in literature has been established.Parametric studies on the variation of all the thermomechanical constants for different 3D performs of Carbon-Carbon material have been studied and selection criteria have been formulated for their applications for the hot structures.Procedure for the structural design of hot structures made of 3D Carbon-Carbon composites has been established through the numerical investigations on a Nosecap.Nonlinear transient thermal and nonlinear transient thermo-structural analysis on the Nosecap have been carried out using finite element software NASTRAN.Failure indices have been established for the identified performs,identification of suitable 3D composite based on parametric studies on strength properties and recommendation of this material for Nosecap of RLV based on structural performance have been carried out in this Study.Based on the 3D failure theory the best perform for the Nosecap has been identified as 4-axis 15degree braided composite.

Consequence modelling,vulnerability assessment and fuzzy fault tree analysis of hazardous storages in an industrial area

The hazards associated with major accident hazard (MAH) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identitication and quantification of the hazards associated with chemical industries. This research work presents the results of a consequence analysis carried out to assess the damage potential of the hazardous material storages in an industrial area of central Kerala, India. A survey carried out in the major accident hazard (MAH) units in the industrial belt revealed that the major hazardous chemicals stored by the various industrial units are ammonia, chlorine, benzene, naphtha, cyclohexane, cyclohexanone and LPG. The damage potential of the above chemicals is assessed using consequence modelling. Modelling of pool fires for naphtha, cyclohexane, cyclohexanone, benzene and ammonia are carried out using TNO model. Vapor cloud explosion (VCE) modelling of LPG, cyclohexane and benzene are carried out using TNT equivalent model. Boiling liquid expanding vapor explosion (BLEVE) modelling of LPG is also carried out. Dispersion modelling of toxic chemicals like chlorine, ammonia and benzene is carried out using the ALOHA air quality model. Threat zones for different hazardous storages are estimated based on the consequence modelling. The distance covered by the threat zone was found to be maximum for chlorine release from a chlor-alkali industry located in the area. The results of consequence modelling are useful for the estimation of individual risk and societal risk in the above industrial area.Vulnerability assessment is carried out using probit functions for toxic, thermal and pressure loads. Individual and societal risks are also estimated at different locations. Mapping of threat zones due to different incident outcome cases from different MAH industries is done with the help of Are GIS.Fault Tree Analysis (FTA) is an established technique for hazard evaluation. This technique has the advantage of being both qualitative and quantitative, if the probabilities and frequencies of the basic events are known. However it is often difficult to estimate precisely the failure probability of the components due to insufficient data or vague characteristics of the basic event. It has been reported that availability of the failure probability data pertaining to local conditions is surprisingly limited in India. This thesis outlines the generation of failure probability values of the basic events that lead to the release of chlorine from the storage and filling facility of a major chlor-alkali industry located in the area using expert elicitation and proven fuzzy logic. Sensitivity analysis has been done to evaluate the percentage contribution of each basic event that could lead to chlorine release. Two dimensional fuzzy fault tree analysis (TDFFTA) has been proposed for balancing the hesitation factor invo1ved in expert elicitation .

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Two-dimensional clusters of liquid 4He

The binding energies of two-dimensional clusters (puddles) of¿4He are calculated in the framework of the diffusion Monte Carlo method. The results are well fitted by a mass formula in powers of x=N-1/2, where N is the number of particles. The analysis of the mass formula allows for the extraction of the line tension, which turns out to be 0.121 K/Å. Sizes and density profiles of the puddles are also reported.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Design and Finite Element Analysis of Hybrid Stepper Motor for Spacecraft Applications

This paper presents the design and analysis of a 400-step hybrid stepper motor for spacecraft applications. The design of the hybrid stepper motor for achieving a specific performance requires the choice of appropriate tooth geometry. In this paper, a detailed account of the results of two-dimensional finite-element (FE) analysis conducted with different tooth shapes such as square and trapezoidal, is presented. The use of % more corresponding increase in detent torque and distorted static torque profile. For the requirements of maximum torque density, less-detent torque, and better positional accuracy and smooth static torque profile, different pitch slotting with equal tooth width has to be provided. From the various FE models subjected to analysis trapezoidal teeth configuration with unequal tooth pitch on the stator and rotor is found to be the best configuration and is selected for fabrication. The designed motor is fabricated and the experimental results is compared with the FE results

Statistical evaluation of texture analysis from the biocrystallization method

The consumers are becoming more concerned about food quality, especially regarding how, when and where the foods are produced (Haglund et al., 1999; Kahl et al., 2004; Alföldi, et al., 2006). Therefore, during recent years there has been a growing interest in the methods for food quality assessment, especially in the picture-development methods as a complement to traditional chemical analysis of single compounds (Kahl et al., 2006). The biocrystallization as one of the picture-developing method is based on the crystallographic phenomenon that when crystallizing aqueous solutions of dihydrate CuCl2 with adding of organic solutions, originating, e.g., from crop samples, biocrystallograms are generated with reproducible crystal patterns (Kleber & Steinike-Hartung, 1959). Its output is a crystal pattern on glass plates from which different variables (numbers) can be calculated by using image analysis. However, there is a lack of a standardized evaluation method to quantify the morphological features of the biocrystallogram image. Therefore, the main sakes of this research are (1) to optimize an existing statistical model in order to describe all the effects that contribute to the experiment, (2) to investigate the effect of image parameters on the texture analysis of the biocrystallogram images, i.e., region of interest (ROI), color transformation and histogram matching on samples from the project 020E170/F financed by the Federal Ministry of Food, Agriculture and Consumer Protection(BMELV).The samples are wheat and carrots from controlled field and farm trials, (3) to consider the strongest effect of texture parameter with the visual evaluation criteria that have been developed by a group of researcher (University of Kassel, Germany; Louis Bolk Institute (LBI), Netherlands and Biodynamic Research Association Denmark (BRAD), Denmark) in order to clarify how the relation of the texture parameter and visual characteristics on an image is. The refined statistical model was accomplished by using a lme model with repeated measurements via crossed effects, programmed in R (version 2.1.0). The validity of the F and P values is checked against the SAS program. While getting from the ANOVA the same F values, the P values are bigger in R because of the more conservative approach. The refined model is calculating more significant P values. The optimization of the image analysis is dealing with the following parameters: ROI(Region of Interest which is the area around the geometrical center), color transformation (calculation of the 1 dimensional gray level value out of the three dimensional color information of the scanned picture, which is necessary for the texture analysis), histogram matching (normalization of the histogram of the picture to enhance the contrast and to minimize the errors from lighting conditions). The samples were wheat from DOC trial with 4 field replicates for the years 2003 and 2005, “market samples”(organic and conventional neighbors with the same variety) for 2004 and 2005, carrot where the samples were obtained from the University of Kassel (2 varieties, 2 nitrogen treatments) for the years 2004, 2005, 2006 and “market samples” of carrot for the years 2004 and 2005. The criterion for the optimization was repeatability of the differentiation of the samples over the different harvest(years). For different samples different ROIs were found, which reflect the different pictures. The best color transformation that shows efficiently differentiation is relied on gray scale, i.e., equal color transformation. The second dimension of the color transformation only appeared in some years for the effect of color wavelength(hue) for carrot treated with different nitrate fertilizer levels. The best histogram matching is the Gaussian distribution. The approach was to find a connection between the variables from textural image analysis with the different visual criteria. The relation between the texture parameters and visual evaluation criteria was limited to the carrot samples, especially, as it could be well differentiated by the texture analysis. It was possible to connect groups of variables of the texture analysis with groups of criteria from the visual evaluation. These selected variables were able to differentiate the samples but not able to classify the samples according to the treatment. Contrarily, in case of visual criteria which describe the picture as a whole there is a classification in 80% of the sample cases possible. Herewith, it clearly can find the limits of the single variable approach of the image analysis (texture analysis).