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Articles 1 - 10 of 10
Full-Text Articles in Applied Mathematics
Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook
Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook
Electronic Theses and Dissertations
This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared …
Spreading Speeds Along Shifting Resource Gradients In Reaction-Diffusion Models And Lattice Differential Equations., Jin Shang
Electronic Theses and Dissertations
A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c*(∞) and c*(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When …
Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh
Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh
Electronic Theses and Dissertations
Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …
An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger
An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger
Electronic Theses and Dissertations
Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.
Mathematical Hybrid Models For Image Segmentation., Carlos M. Paniagua Mejia
Mathematical Hybrid Models For Image Segmentation., Carlos M. Paniagua Mejia
Electronic Theses and Dissertations
Two hybrid image segmentation models that are able to process a wide variety of images are proposed. The models take advantage of global (region) and local (edge) data of the image to be segmented. The first one is a region-based PDE model that incorporates a combination of global and local statistics. The influence of each statistic is controlled using weights obtained via an asymptotically stable exponential function. Through incorporation of edge information, the second model extends the capabilities of a strictly region-based variational formulation, making it able to process more general images. Several examples are provided showing the improvements of …
Consensus Model Of Families Of Images Using Tensor-Based Fourier Analysis, Joel A. Shelton
Consensus Model Of Families Of Images Using Tensor-Based Fourier Analysis, Joel A. Shelton
Electronic Theses and Dissertations
A consensus model is a statistical approach that uses a family of signals or in our case, a family of images to generate a predictive model. In this thesis, we consider a family of images that are represented as tensors. In particular, our images are (2,0)-tensors. The consensus model is produced by utilizing the quantum Fourier transform of a family of images as tensors to transform images to images. We write a quantum Fourier transform in the numerical computation library for Python, known as Theano to produce the consensus spectrum. From the consensus spectrum, we produce the consensus model via …
Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku
Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku
Electronic Theses and Dissertations
The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …
Blow-Up Solution And Blow-Up Rate Of Bose-Einstein Condensates With Rotational Term, Nyla Basharat
Blow-Up Solution And Blow-Up Rate Of Bose-Einstein Condensates With Rotational Term, Nyla Basharat
Electronic Theses and Dissertations
In this thesis, we discuss the Gross Pitaevskii Equation (GPE) with harmonic potential and with an angular momentum rotational term in space R^2, which describes the model for Bose-Einstein Condensation. Local Well-Posedness of the equation and the conservation identities for mass, energy and angular momentum are presented. Using the virial identities, we derive the condition for blow-up solution in finite time. Then a threshold of L^2 norm of wave function is obtained for global existence, of GPE in term of ground state solution. This method allows us to obtain our main result ``Sharp sufficient condition for global …
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
Electronic Theses and Dissertations
This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton's Universal Gravitation constant also known as "Big G". This tool set is especially applicable to Bose--Einstein--condensed systems present in NASA's Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrödinger or Gross--Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of the optical …
Geometric-Based Algorithm For A Full Row-Rank System Matrix Along Multiple Directions In Dt, Igor Lutsenko
Geometric-Based Algorithm For A Full Row-Rank System Matrix Along Multiple Directions In Dt, Igor Lutsenko
Electronic Theses and Dissertations
Discrete tomography (DT) is an image reconstruction procedure that deals with computational synthesis of a cross-sectional image of an object from either transmission or reflection data collected by penetrating an object with X-rays from a small number of different directions, and whose range of the underlying function is discrete. Image reconstruction using algebraic approach is time consuming and the computation cost depends on the size of the system matrix. More scanning directions provide an increase in the reconstructed image quality, however they increase the size of the system matrix dramatically. Deletion of linearly dependent rows of this matrix is necessary …