Stabilization Schemes for Convection Dominated Scalar Problems with Different Time Discretizations in Time dependent Domains

Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering systems e.g., aircrafts and bridges as well as to the analysis of several biological phenomena e.g., blood ow in arteries. However, developing numerical scheme for such problems is still very challenging even when the deformation of the boundary of domain is prescribed a priori. Possibility of excessive mesh distortion is one of the major challenge when solving such problems with numerical methods using boundary tted meshes. The arbitrary Lagrangian- Eulerian (ALE) approach is a way to overcome this difficulty. Numerical simulations of convection-dominated problems have for long been the subject to many researchers. Galerkin formulations, which yield the best approximations for differential equations with high diffusivity, tend to induce spurious oscillations in the numerical solution of convection dominated equations. Though such spurious oscillations can be avoided by adaptive meshing, which is computationally very expensive on ne grids. Alternatively, stabilization methods can be used to suppress the spurious oscillations. In this work, the considered equation is designed within the framework of ALE formulation. In the first part, Streamline Upwind Petrov-Galerkin (SUPG) finite element method with conservative ALE formulation is proposed. Further, the first order backward Euler and the second order Crank-Nicolson methods are used for the temporal discretization. It is shown that the stability of the semi-discrete (continuous in time) ALE-SUPG equation is independent of the mesh velocity, whereas the stability of the fully discrete problem is unconditionally stable for implicit Euler method and is only conditionally stable for Crank-Nicolson time discretization. Numerical results are presented to support the stability estimates and to show the influence of the SUPG stabilization parameter in a time-dependent domain. In the second part of this work, SUPG stabilization method with non-conservative ALE formulation is proposed. The implicit Euler, Crank-Nicolson and backward difference methods are used for the temporal discretization. At the discrete level in time, the ALE map influences the stability of the corresponding discrete scheme with different time discretizations, and it leads to schemes where conservative and non-conservative formulations are no longer equivalent. The stability of the fully discrete scheme, irrespective of the temporal discretization, is only conditionally stable. It is observed from numerical results that the Crank-Nicolson scheme induces high oscillations in the numerical solution compare to the implicit Euler and the backward difference time discretiza-tions. Moreover, the backward difference scheme is more sensitive to the stabilization parameter k than the other time discretizations. Further, the difference between the solutions obtained with the conservative and non-conservative ALE forms is significant when the deformation of domain is large, whereas it is negligible in domains with small deformation. Finally, the local projection stabilization (LPS) and the higher order dG time stepping scheme are studied for convection dominated problems. The analysis is based on the quadrature formula for approximating the integrals in time. We considered the exact integration in time, which is impractical to implement and the Radau quadrature in time, which can be used in practice. The stability and error estimates are shown for the mathematical basis of considered numerical scheme with both time integration methods. The numerical analysis reveals that the proposed stabilized scheme with exact integration in time is unconditionally stable, whereas Radau quadrature in time is conditionally stable with time-step restriction depending on the ALE map. The theoretical estimates are illustrated with appropriate numerical examples with distinct features. The second order dG(1) time discretization is unconditionally stable while Crank-Nicolson gives the conditional stable estimates only. The convergence order for dG(1) is two which supports the error estimate

Shape Characterization of Granular Particles using Image Based Techniques

Granular soils with different sizes and shapes are often used in many civil engineering structures. In different contexts, several researchers have emphasized that shape of particles play a pivotal role in influencing several engineering properties such as maximum and minimum packing densities, shear strength, permeability and compressibility. However, the complexities involved in obtaining the geometrical parameters necessary to adequately compute particle shape have hampered the clear understanding of the contribution of particle shape to such properties. Researchers have attempted to characterize the shape of the particles by many conventional and advanced image based methods in the past. However, these methods suffer from many criticisms; conventional methods of shape characterization include ocular inspection of particles based on visual reference charts, which are more prone to user dependent interpretations. The recently developed image based methods deviate from the conventional and most well accepted definitions formulated by researchers in the past due to the difficulties involved in automating them. The aim of this thesis is to address this shortcoming by developing a robust methodology for accurate and precise determination of particle shape in accordance with the most widely accepted formulae in literature, which can replace the existing methods based on manual measurements, approximate visual charts and non-robust imaging techniques. For this purpose, several computational algorithms are written and implemented in MATLAB and operations are performed on particle images. These methods are developed to precisely characterize the particles shape parameters observed at three levels of scales, which are adequate for complete shape characterization. According to Barrett (1980) the particle shape features can be observed independently at three different scales, viz. macro-scale, meso-scale and micro-scale, the shape parameters such as form, roundness and surface texture falls into these three scales respectively. The macro-scale component of form (sphericity) is quantified as per the formula used in the visual chart proposed by Krumbein & Sloss (1951). In light of its continuing popularity and wide usage, the roundness concept proposed by Wadell (1932) is chosen to be the appropriate parameter for meso-scale shape representation. The micro-scale component of surface texture or roughness is measured by the conventional and widely used root mean square definition, by incorporating the use of digital filtering techniques. The distinct concept of angularity as proposed by Lees (1964) is used for effective shape representation of crushed particles. Kinematic behaviour of particles such as sliding, rolling and interlocking are dependent on the geometrical features observed at meso-scale present along their boundaries, which consequently govern the material strength and deformation characteristics. Based on precise identification of such features (concavo-convex regions along particle boundary), a new classification chart is proposed in this thesis to comprehend the kinematics of particles. The effects of critical parameters such as scale, resolution and user defined cutoff values on the quantification of shape parameters are analyzed and eliminated. The proposed methodology is compared with standard visual charts provided by earlier researchers and is demonstrated on real soil particles falling across a wide range of sizes and shapes. Finally, the role of particle shape in governing packing behaviour of aggregates is quantified based on the precise particle shape characterization

Unraveling the Evolutionary Advantages of Crosstalk Between Two-Component Signalling Systems of M tuberculosis

M. tuberculosis (Mtb) senses and responds to changes in its environment primar-ily through two-component signalling systems (TCSs). Each TCS contains a trans-membrane histidine kinase (HK ) protein and a cytoplasmic response regulator (RR) protein. HK detects a stimulus and gets phosphorylated. It then binds and transfers the phosphoryl group to the RR of the same TCS. Activated RR then triggers gene ex-pression, including upregulation of the HK and RR involved, eliciting responses that are essential for the bacterium to adapt. Though di erent TCSs detect distinct stimuli, the binding regions of the HK s and RRs share signi cant similarity. This raises the possibil-ity of crosstalk, where HK s dissipate signals to RRs that do not belong to the same TCS. Studies have argued that such dissipation of signals impairs the fitness of the organism, as it decreases the output levels as well as triggers unwanted responses. In contrast, a recent experimental study has discovered that TCSs of Mtb share extensive crosstalk, violating the widely accepted specificity paradigm. In this study, we have attempted to unravel the evolutionary underpinnings of this extensive crosstalk observed in Mtb. We hypothesised that such crosstalk may be advantageous in programmed environments, where there are well-defined sequences of stimuli. In such situations, crosstalk can up-regulate HK s and RRs of non-cognate TCSs. This up-regulation primes the latter TCSs for upcoming signals, increasing their sensitivity. We constructed a mechanistic model of the functioning of TCSs and a fitness variable to qualitatively measure the response of a TCS to a signal, to test the hypothesis. We performed population genetics simulations of the evolution of phenotypes of different crosstalk patterns. We found that in a random environment, the phenotype without any crosstalk is selected over time, which is in agreement with prevalent arguments in favour of specificity of TCSs. But when the environment is programmed, the phenotype with a crosstalk pattern mirroring the pattern of stimuli dominates the population. Finally, we found evidence for the evolutionary preference to preserve crosstalk in gene sequences of HK s and RRs encoded in Mtb. We found that the binding domains of HK s and RRs, which were predicted to share crosstalk, are under greater pressure to be similar than those domains which do not crosstalk. Our study thus provides a plausible explanation of the unexpected presence of crosstalk in Mtb. Since these cross-interactions aid the pathogen to adapt in the host, inhibitors of such interactions are likely to have therapeutic potential

Characterization of Flow Induced Noise Received by an Array Placed at Stagnation Point of an Underwater Axisymmetric Body

Given the interest on underwater axisymmetric cylindrical bodies for the development of high-speed underwater weapons, characterization of the boundary layer flow-induced noise received by a Sound NAvigation and Ranging (SONAR) is very important to improve sonar detection ranges. The debate on generating mechanisms of the flow induced noise received at the stagnation point is still on as there is no experimental evidence conclusively suggesting whether it is a near-field or far-field phenomenon, thereby introducing an element of uncertainty in the prediction models. Further, the models developed thus far were based on low Reynolds numbers involving flows in water tunnels and buoyant vehicles. Therefore, the main focus of the thesis is to measure the flow induced noise using a sonar fitted at the most forward stagnation point of an underwater axisymmetric body as realistically as possible and predict the same theoretically for identifying a suitable flow noise model for future use by designers. In order to meet the stated goal, two exclusive experiments were conducted at sea using an underwater autonomous high-speed axisymmetric vehicle fitted with a planar hydrophone array (8X8) in its nose cone which measured the flow noise signature. Two different sets of existing models are used in characterizing the flow noise received by the array, while the first set comprises of models developed based on the Turbulent Boundary Layer induced noise and other is based on the transition zone radiated noise model. Through this study, it was found that the transition zone radiated noise model is in close agreement with the measured data

Design of Quality Assuring Mechanisms with Learning for Strategic Crowds

In this thesis, we address several generic problems concerned with procurement of tasks from a crowd that consists of strategic workers with uncertainty in their qualities. These problems assume importance as the quality of services in a service marketplace is known to degrade when there is (unchecked) information asymmetry pertaining to quality. Moreover, crowdsourcing is increasingly being used for a wide variety of tasks these days since it offers high levels of flexibility to workers as well as employers. We seek to address the issue of quality uncertainty in crowdsourcing through mechanism design and machine learning. As the interactions in web-based crowdsourcing platform are logged, the data captured could be used to learn unknown parameters such as qualities of individual crowd workers. Further, many of these platforms invite bids by crowd workers for available tasks but the strategic workers may not bid truthfully. This warrants the use of mechanism design to induce truthful bidding. There ensues a complex interplay between machine learning and mechanism design, leading to interesting technical challenges. We resolve some generic challenges in the context of the following problems. Design of a quality eliciting mechanism with interdependent values We consider an expert sourcing problem, where a planner seeks opinions from a pool of experts. Execution of the task at an assured quality level in a cost effective manner turns out to be a mechanism design problem when the individual qualities are private information of the experts. Also, the task execution problem involves interdependent values, where truthfulness and efficiency cannot be achieved in an unrestricted setting due to an impossibility result. We propose a novel mechanism that exploits the special structure of the problem and guarantees allocative efficiency, ex-post incentive compatibility and strict budget balance for the mechanism, and ex-post individual rationality for the experts. Design of an optimal dimensional crowdsourcing auction We study the problem faced by an auctioneer who gains stochastic rewards by procuring multiple units of a service from a pool of heterogeneous strategic workers. The reward obtained depends on the inherent quality of the worker; the worker’s quality is fixed but unknown. The costs and capacities are private information of the workers. The auctioneer is required to elicit costs and capacities (making the mechanism design dimensional) and further, has to learn the qualities of the workers as well, to enable utility maximization. To solve this problem, we design a dimensional multi-armed bandit auction that maximizes the expected utility of the auctioneer subject to incentive compatibility and individual rationality while simultaneously learning the unknown qualities of the agents. Design of a multi-parameter learning mechanism for crowdsourcing We investigate the problem of allocating divisible jobs, arriving online, to workers in a crowd-sourcing platform. Each job is split into a certain number of tasks that are then allocated to workers. These tasks have to meet several constraints that depend on the worker performance. The performance of each worker in turn is characterized by several intrinsic stochastic parameters. In particular, we study a problem where each arriving job has to be completed within a deadline and each task has to be completed, honouring a lower bound on quality. The job completion time and quality of each worker are stochastic with fixed but unknown means. We propose a learning mechanism to elicit the costs truthfully while simultaneously learning the stochastic parameters. Our proposed mechanism is dominant strategy incentive compatible and ex-post individually rational with asymptotically optimal regret performance

A Ghost Fluid Method for Modelling Liquid Jet Atomization

Liquid jet atomisation has a wide variety of application in areas such as injectors in automobile and launch vehicle combustors, spray painting, ink jet printing etc. Understanding physical mechanisms involved in the primary regime of atomisation in combustors is extremely challenging due to the lack of experimental techniques that can reliably provide measurements of gas and liquid velocity fields in this region. Experimental studies have so far been mostly restricted to conditions at atmospheric conditions rather than technically relevant operating pressures. We present a computational fluid dynamics based modelling approach that can capture the evolution of the flow field in the dense primary atomization region of the spray as part of the present thesis work. A fully compressible 3D flow solver is coupled with an interface tracking solver based on level set method. A generalised mathematical formulation for thermodynamic models is implemented in flow solver enabling easy switching between various equations of states. Solvers are parallelised to run on large number of processors and are shown to have good scalability. A modification to the level set method which greatly reduces mass conservation inaccuracies when compared with existing state-of-art baseline schemes has been developed during this work. The Ghost uid Method is used for applying matching conditions at the Interface. The liquid and gas phases are modelled using the perfect gas and Tait equations of state respectively. Several validation studies have been carried out to ensure quantitative accuracy of the solver implemented. Results from canonical Rayleigh Taylor instability simulations shows good agreement with reported results in literature. Finally, results for unsteady evolution of a water-air jet at a liquid to gas density ratio of 10 are shown. Physical mechanisms causing the initial droplet formation are discussed in detail. Droplet feedback is identified as one of the important mechanisms in triggering liquid core instabilities. Comparisons between droplet size distributions obtained from computations are carried out. Vorticity dynamics is used to understand hole and ligament formation from liquid core. Effect of numerical droplets on the simulation results is also looked at in detail

Efficient Whole Program Path Tracing

Obtaining an accurate whole program path (WPP) that captures a program’s runtime behaviour in terms of a control-flow trace has a number of well-known benefits, including opportunities for code optimization, bug detection, program analysis refinement, etc. Existing techniques to compute WPPs perform sub-optimal instrumentation resulting in significant space and time overheads. Our goal in this thesis is to minimize these overheads without losing precision. To do so, we design a novel and scalable whole program analysis to determine instrumentation points used to obtain WPPs. Our approach is divided into three components: (a) an efficient summarization technique for inter-procedural path reconstruction, (b) specialized data structures called conflict sets that serve to effectively distinguish between pairs of paths, and (c) an instrumentation algorithm that computes the minimum number of edges to describe a path based on these conflict sets. We show that the overall problem is a variant of the minimum hitting set problem, which is NP-hard, and employ various sound approximation strategies to yield a practical solution. We have implemented our approach and performed elaborate experimentation on Java programs from the DaCapo benchmark suite to demonstrate the efficacy of our approach across multiple dimensions. On average, our approach necessitates instrumenting only 9% of the total number of CFG edges in the program. The average runtime overhead incurred by our approach to collect WPPs is 1.97x, which is only 26% greater than the overhead induced by only instrumenting edges guaranteed to exist in an optimal solution. Furthermore, compared to the state-of-the-art, we observe a reduction in runtime overhead by an average and maximum factor of 2.8 and 5.4, respectively

Studies on Silicone Rubber Insulators used for High Voltage Transmission

Recently high temperature vulcanized (HTV) silicone rubber (SIR) / polymeric/composite insulators are gaining wider acceptance as overhead transmission line insulators for extra high voltage (EHV) and ultra-high voltage (UHV) systems due to some promising features like hydrophobicity recovery, light weight, ease of handling and installation, better pollution ashover performance, admirable resistance against vandalism etc. Since polymeric insula-tors are of recent origin, their long-term eld performance is yet to be understood. Owing to their organic nature, and exposure to environmental stresses like pollution, temperature, UV radiation, humidity, fog, rain etc., the insulator performance degrades over a period. The sheds/petticoats of the insulators become wettable leading to frequent ashover in humid and contaminated environment. Hence, long term reliability of the composite insulators is of foremost concern to the power utilities. The available literature on the long term eld performance of these insulators for di erent climatic conditions and under multiple environ-mental stresses for both the HTV SIR and Liquid Silicone Rubber (LSR) is scant. Also there is no reference standard for evaluation of these insulators for pollution/contamination test methods in the laboratory. However currently, CIGRE Work Group is working towards the standardization of the test methods for arti cial pollution tests for polymeric insulators. The thesis addresses some of the issues in detail. In the first part of the thesis, a new and simple pre-treatment methodology to achieve uniform contamination layer on inherently hydrophobic HTV SIR Insulator samples is presented for laboratory pollution performance evaluation. The surface water level di usion in the dipping period is found to make the insulator surface temporarily hydrophilic. Then the uniform contamination layer is applied by dipping the sample immediately in the pollution slurry. Exhaustive experiments were conducted on full scale SIR insulators as well as SIR slabs to investigate the hydrophilicity appearance on the SIR surface. A specially fabricated arrangement for assessment of Wettability Class (WC) is made as per IEC stds. The results of WC measurement and wet ashover studies support the temporary reduction in hydrophobicity of SIR due to dipping phase in the proposed pre-treatment methodology. The next part of the thesis presents the results for the effeect of long term thermal aging experimentation conducted on HTV SIR with difffeerent degrees of pollution (medium, heavy), the effeect of arid desert climate on polymeric insulators is studied. The experimental set-up consists of controlled HVAC source, temperature controlled furnace with a provision for high voltage (HV) and Leakage Current (LC) monitoring, a Digital Storage Oscilloscope (DSO), compact DAQ-9201 of National Instruments operated in LabVIEW platform etc. Two types of HTV SIR Insulators are considered for the study. Flat slabs as well as full-scale insulator samples of creepage length 725 mm are stressed simultaneously to simulate the in-service condition. The experimentation is conducted for about 575 hours with application of 21.0 kVrms at 60oC. The results of the hydrophobicity recovery for thermally aged contaminated polymeric insulators are reported. Besides, monitoring electrical and mechanical proper-ties, changes in material properties of SIR are also analyzed using Physiochemical analysis techniques like Fourier transform infrared (FTIR) spectroscopy, X-Ray Photoelectron Spectroscopy (XPS), Scanning Electron Microscopy (SEM), Thermo-Gravimetric Analysis (TGA), Differential Scanning Calorimetry (DSC). Some of the key findings of the study are increased surface oxidation, surface roughness and mechanical stress due to thermal aging of polymeric insulators. Experimental investigations show that the characteristics of power frequency component of leakage current can be linked with thermal aging of SIR. Further, a unique climatic aging experimental facility is established to evaluate the long-term reliability of SIR under environmental stresses like UV, Humidity, temperature and applied electric stress. The investigations are conducted on two different types of HTV SIR and LSR at samples as well as full-scale insulator samples. The experimentation is conducted for 500 hours with 10.0 kVrms at 50oC, with 85% humidity and 1 W/m2 UV ir-radiation which is in accordance with the aging cycle specified in IEC standard. The results of the comparative studies conducted for the electrical, mechanical and material properties indicate leakage current pulses, brittleness, Salt deposition for multistress aged samples. In summary, an attempt has been made to contribute a pollution methodology with sim-ple pre-treatment technique for inherently hydrophobic HTV SIR surface to achieve better uniformity of contamination layer. Also, electro-thermal and multiple stresses investigations were conducted for long term performance on polymeric insulators

Sputter Deposited ZrC and NbC Thin Films – Studies on Microstructure, Texture and Hardness

Transition metal carbides have great industrial importance with a wide area of applications. Unlike many ceramic materials which can be produced from raw materials found in nature, the refractory carbides generally do not exist in the natural state. Synthesis of these carbides is costly and exacting. Sputtered coatings of the refractory metal carbides are of great interest for applications where hard wear-resistant materials are desired. Understanding how the experimental conditions affect the microstructure and properties in reactive sputtering deposition process is still an area of intense research activity. Reactively sputtered zirconium carbide thin films were grown on (100) silicon substrate and the influence of substrate temperature on the properties of the films were investigated. The substrate temperature was varied from ambient to 500°C and partial pressures of the sputter gas and reactive gas (argon and methane) were optimised to obtain crystalline films. Structural characteristics showed that the films exhibit nanocomposite structure consisting of ZrC nanocrystallites embedded in amorphous carbon typically at lower growth temperature (TS < 300°C), and at higher growth temperatures film were highly textured. In addition, Films deposited at 325 °C showed a distinct increase in FWHM which had considerable effect on the mechanical properties of the film. Maximum hardness of 24.8 GPa was seen at 325ºC. The changes in atomic bonding structures, their relative fractions with respect to substrate temperature were discussed. We also report superhard nanocrystalline nanocomposite NbC thin film deposited on Si (100) under 500˚C growth temperature via reactive magnetron sputtering. The pronounced nano hardness and modulus value of 42 GPa and 267 GPa at 40/60 C/Nb ratio were found to be strongly dependent on the grain size and higher percentage of carbide content. HRTEM studies further confirm the formation of nanocomposite structure with nanocrystalline grains embedded in amorphous matrix. The influence of vapour incidence angle (α= 0˚ to 75˚) on optimized ZrC and NbC thin films were investigated by depositing films in Oblique angle deposition geometry (OAD). The anisotropic growth rate of crystallographic planes and the mechanism of development of micro structural features in OAD of carbide films have been investigated. XRD and pole figure measurements indicated that the films grown at higher growth temperatures (800°C) exhibited higher degree of preferred orientation coupled with larger crystallite size whereas the films deposited at room temperature displayed random polycrystalline nature. The strong increase in porosity with increase in deposition angle with distinctly separated nanometer sized columns resulted in lowering of hardness and reduced modulus value. The film with zero incidence angle exhibited a maximum hardness and reduced modulus of 28 GPa and 223 GPa respectively. On the other hand, NbC films deposited with OAD, remained to be polycrystalline in nature with less intense peaks and also exhibited loss of preferential orientation indicating lower crystal quality with increase in vapor deposition angle. It is apparent that variation in crystallographic texture coupled with sculptured nanostructures are solely material dependent properties. Nano metric modulated ZrC/NbC superlattice multilayer structure performance has been evaluated for structural stability and hardness enhancement. Multilayers present superlattice effect in XRD patterns, which are attributed to the precise periodical stacking of crystalline monolayers also confirmed by cross section FESEM. X-ray photoelectron spectroscopy depth profile analysis was performed to get information on chemical composition of modulated layers and also to get an insight on the interface region. Hardness and modulus value of 43.2 GPa and 272 GPa was observed which is higher than individual monolayers response to mechanical loading. The enhanced hardness is possibly due to the inhibition of dislocation motion along the interface and also due to strain effects at the interface

Active Power Flow Tracing for Preventive Control in Deregulated Power Systems

Modern day power systems present an open access environment, inspiring participation from small scale and large power suppliers. With multiple players in the system driven by the market, proper monitoring and control of system becomes a major concern. This transformation is accompanied by dynamic consumption patterns and rising power demands. The expanding network encompassing EHV/AC network, HVDC and FACTS devices, along with increased penetration of renewable sources, viz. solar and wind energy at medium and low voltage levels, adds to the problem. Independent System Operators (ISO) are entrusted with ensuring smooth operation, and employing proper preventive measures to eliminate a possible cascade tripping leading to a partial or large-scale blackout. To aid the operator in the process of ensuring secure operation of the grid, there are many tools that provide required information and guidance. Power flow tracing is one such tool that aids the operator in congestion management, transmission pricing, transaction evaluation, loss allocation and reactive power optimization. In this thesis, a novel active power flow tracing approach is proposed that takes into account, the real-time operating conditions and network topology. It provides the decomposition of active power flow in a line into respective components injected by various generators in the system. It also provides the contribution of the generators to various loads in the system. The approach is simple and computationally fast, making it an ideal tool to aid preventive control decisions. Based on the proposed active power flow tracing, a congestion management approach is developed. The approach indicates the least number of generators that need to be coordinated for generation rescheduling, so as to alleviate overloading in affected transmission lines and transformers. The approach also takes into consideration the operating constraints on the system, while computing the optimal rescheduling amongst selected generators using LP technique. The thesis also presents a real power loss allocation approach based on the proposed power flow tracing. Loss allocation is an important part of tariff design as the cost associated with losses amounts to a sizable fraction of total revenue collected from the loads. The approach provides information as to how losses are distributed among loads and how much each generator is providing for the loss share of each load. The approaches developed in the thesis are illustrated on a sample 10-bus equivalent system, IEEE 30-bus, and IEEE 39-bus systems. Results for typical case studies are presented for practical systems of 72-bus equivalent and 203-bus equivalent of Indian Southern grid