Thin tubes in mathematical physics, global analysis and spectral geometry

A thin tube is an $n$-dimensional space which is very thin in $n-1$ directions, compared to the remaining direction, for example the $\epsilon$-neighborhood of a curve or an embedded graph in $\R^n$ for small $\epsilon$. The Laplacian on thin tubes and related operators have been studied in various contexts, with different goals but overlapping techniques. In this survey we explain some of these contexts, methods and results, hoping to encourage more interaction between the disciplines mentioned in the title.Comment: 29 pages, 4 figures. To appear in 'Analysis on Graphs and its Applications', Proceedings of the Newton Institute Program 2007, in the series 'Proceedings of Symposia in Pure Mathematics' by the AM

Mathematical and numerical methods for inverse problems using fundamental solutions techniques

Fundação para a Ciência e a Tecnologia - SFRH/BD/27914/200

The Photometric Effect of Macroscopic Surface Roughness on Sediment Surfaces

The focus of this work was on explaining the effect of macroscopic surface roughness on the reflected light from a soil surface. These questions extend from deciding how to best describe roughness mathematically, to figuring out how to quantify its effect on the spectral reflectance from a soil’s surface. In this document, I provide a background of the fundamental literature in the fields of remote sensing and computer vision that have been instrumental in my research. I then outline the software and hardware tools that I have developed to quantify roughness. This includes a detailed outline of a custom LiDAR operating mode for the GRIT-T goniometer system that was developed and characterized over the course of this research, as well as proposed methods for using convergent images acquired by our goniometer system’s camera to derive useful structure from motion point clouds. These tools and concepts are then used in two experiments that aim to explain the relationship between soil surface roughness and spectral BRF phenomena. In the first experiment, clay sediment samples were gradually pulverized into a smooth powderized state and in steps of reduced surface roughness. Results show that variance in the continuum spectra as a function of viewing angle increased with the roughness of the sediment surface. This result suggests that inter-facet multiple scattering caused a variance in absorption band centering and depth due to an increased path length traveled through the medium. In the second experiment, we examine the performance of the Hapke photometric roughness correction for sand sediment surfaces of controlled sample density. We find that the correction factor potentially underpredicts the effect of shadowing in the forward scattering direction. The percentage difference between forward-modeled BRF measurements and empirically measured BRF measurements is constant across wavelength, suggesting that a factor can be empirically derived. Future results should also investigate the scale at which the photometric correction factor should be applied. Finally, I also outline a structure from motion processing chain aimed at deriving meaningful metrics of vegetation structure. Results show that correlations between these metrics and observed directional reflectance phenomena of chordgrass are strong for peak growing state plants. We observe good agreement between destructive LAI metrics and contact-based LAI metrics

Interval simplex splines for scientific databases

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1995.Includes bibliographical references (p. 130-138).by Jingfang Zhou.Ph.D

Sensory processing and world modeling for an active ranging device

In this project, we studied world modeling and sensory processing for laser range data. World Model data representation and operation were defined. Sensory processing algorithms for point processing and linear feature detection were designed and implemented. The interface between world modeling and sensory processing in the Servo and Primitive levels was investigated and implemented. In the primitive level, linear features detectors for edges were also implemented, analyzed and compared. The existing world model representations is surveyed. Also presented is the design and implementation of the Y-frame model, a hierarchical world model. The interfaces between the world model module and the sensory processing module are discussed as well as the linear feature detectors that were designed and implemented

Numerical and experimental modelling of microwave applicators

This thesis presents a time domain finite element method for the solution of microwave heating problems. This is the first time that this particular technique has been applied to microwave heating. It is found that the standard frequency domain finite element method is unsuitable for analysing multimode applicators containing food-like materials due to a severe ill-conditioning of the matrix equations. The field distribution in multimode applicators loaded with low loss materials is found to be very sensitive to small frequency changes. Several solutions at different frequencies are therefore required to characterise the behaviour of the loaded applicator. The time domain finite element method is capable of producing multiple solutions at different frequencies when used with Gaussian pulse excitation; it is therefore ideally suited to the analysis of multimode applicators. A brief survey of the methods available for the solution of the linear equations is provided. The performance of these techniques with both the frequency domain and time domain finite element methods is then studied. Single mode applicators are also analysed and it is found that the frequency domain method is superior in these cases. Comparisons are given between the calculated results and experimental data for both single mode and multimode systems. The importance of experimental verification being stressed. The choice of element type is an important consideration for the finite element method. Three basic types of element are considered; nodal, Whitney edge elements and linear edge elements. Comparisons of the errors with these elements show that Whitney elements produce a consistently lower error when post-processing is used to smooth the solution. The coupled thermal-electromagnetic problem is investigated with many difficulties being identified for the application to multimode cavity problems

Process planning for robotic wire ARC additive manufacturing

Robotic Wire Arc Additive Manufacturing (WAAM) refers to a class of additive manufacturing processes that builds parts from 3D CAD models by joining materials layerupon- layer, as opposed to conventional subtractive manufacturing technologies. Over the past half century, a significant amount of work has been done to develop the capability to produce parts from weld deposits through the additive approach. However, a fully automated CAD-topart additive manufacturing (AM) system that incorporates an arc welding process has yet to be developed. The missing link is an automated process planning methodology that can generate robotic welding paths directly from CAD models based on various process models. The development of such a highly integrated process planning method for WAAM is the focus of this thesis

Learning Algorithms for Fat Quantification and Tumor Characterization

Obesity is one of the most prevalent health conditions. About 30% of the world\u27s and over 70% of the United States\u27 adult populations are either overweight or obese, causing an increased risk for cardiovascular diseases, diabetes, and certain types of cancer. Among all cancers, lung cancer is the leading cause of death, whereas pancreatic cancer has the poorest prognosis among all major cancers. Early diagnosis of these cancers can save lives. This dissertation contributes towards the development of computer-aided diagnosis tools in order to aid clinicians in establishing the quantitative relationship between obesity and cancers. With respect to obesity and metabolism, in the first part of the dissertation, we specifically focus on the segmentation and quantification of white and brown adipose tissue. For cancer diagnosis, we perform analysis on two important cases: lung cancer and Intraductal Papillary Mucinous Neoplasm (IPMN), a precursor to pancreatic cancer. This dissertation proposes an automatic body region detection method trained with only a single example. Then a new fat quantification approach is proposed which is based on geometric and appearance characteristics. For the segmentation of brown fat, a PET-guided CT co-segmentation method is presented. With different variants of Convolutional Neural Networks (CNN), supervised learning strategies are proposed for the automatic diagnosis of lung nodules and IPMN. In order to address the unavailability of a large number of labeled examples required for training, unsupervised learning approaches for cancer diagnosis without explicit labeling are proposed. We evaluate our proposed approaches (both supervised and unsupervised) on two different tumor diagnosis challenges: lung and pancreas with 1018 CT and 171 MRI scans respectively. The proposed segmentation, quantification and diagnosis approaches explore the important adiposity-cancer association and help pave the way towards improved diagnostic decision making in routine clinical practice

A Contribution to the Modeling of Metal Plasticity and Fracture: From Continuum to Discrete Descriptions

The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill-Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified two dimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures