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Application of automatic differentiation to trajectory optimization via direct multiple shootingGarza, David Marcelo 28 August 2008 (has links)
Not available / text

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A second order ADI method for 2D parabolic equations with mixed derivativeZhang, Chun Yang January 2012 (has links)
University of Macau / Faculty of Science and Technology / Department of Mathematics

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Computer analysis of equations using Mathematica.Jugoo, Vikash R. January 2001 (has links)
In this thesis we analyse particular differential equations that arise in physical situations.
This is achieved with the aid of the computer software package called
Mathematica. We first describe the basic features of Mathematica highlighting its
capabilities in performing calculations in mathematics. Then we consider a first order
Newtonian equation representing the trajectory of a particle around a spherical
object. Mathematica is used to solve the Newtonian equation both analytically and
numerically. Graphical plots of the trajectories of the planetary bodies Mercury,
Earth and Jupiter are presented. We attempt a similar analysis for the corresponding
relativistic equation governing the orbits of gravitational objects. Only numerical
results are possible in this case. We also perform a perturbative analysis of the relativistic
equation and determine the amount of perihelion shift. The second equation
considered is the EmdenFowler equation of order two which arises in many physical
problems, including certain inhomogeneous cosmological applications. The analytical
features of this equation are investigated using Mathematica and the Lie analysis
of differential equations. Different cases of the related autonomous form of the
EmdenFowler equation are investigated and graphically represented. Thereafter, we
generate a number of profiles of the energy density and the pressure for a particular
solution which demonstrates that a numerical approach for studying inhomogeneity,
in cosmological models in general relativity, is feasible. / Thesis (M.Sc.)University of Natal, Durban, 2001.

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Finite Element Modeling of Dislocation Multiplication in Silicon Carbide Crystals Grown by Physical Vapor Transport MethodUnknown Date (has links)
Silicon carbide as a representative wide bandgap semiconductor has recently received wide attention due to its excellent physical, thermal and especially electrical properties. It becomes a promising material for electronic and optoelectronic device under hightemperature, highpower and highfrequency and intense radiation conditions. During the Silicon Carbide crystal grown by the physical vapor transport process, the temperature gradients induce thermal stresses which is a major cause of the dislocations multiplication. Although large dimension crystal with low dislocation density is required for satisfying the fast development of electronic and optoelectronic device, high dislocation densities always appear in large dimension crystal. Therefore, reducing dislocation density is one of the primary tasks of process optimization. This dissertation aims at developing a transient finite element model based on the AlexanderHaasen model for computing the dislocation densities in a crystal during its growing process. Different key growth parameters such as temperature gradient, crystal size will be used to investigate their influence on dislocation multiplications. The acceptable and optimal crystal diameter and temperature gradient to produce the lowest dislocation density in SiC crystal can be obtained through a thorough numerical investigation using this developed finite element model. The results reveal that the dislocation density multiplication in SiC crystal are easily affected by the crystal diameter and the temperature gradient. Generally, during the iterative calculation for SiC growth, the dislocation density multiples very rapidly in the early growth phase and then turns to a relatively slow multiplication or no multiplication at all. The results also show that larger size and higher temperature gradient causes the dislocation density enters rapid multiplication phase sooner and the final dislocation density in the crystal is higher. / Includes bibliography. / Dissertation (Ph.D.)Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection

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Algorithms for image segmentation in fermentation.Mkolesia, Andrew Chikondi. January 2011 (has links)
M. Tech. Mathematical Technology. / Aims of this research project is to mathematically analyse froth patterns and build a database of the images at different stages of the fermentation process, so that a decisionmaking procedure can be developed, which enables a computer to react according to what has been observed. This would allow aroundtheclock observation which is not possible with humans. In addition, mechanised decisionmaking would minimize errors usually associated with human actions. Different mathematical algorithms for image processing will be considered and compared. These algorithms have been designed for different image processing situations. In this dissertation the algorithms will be applied to froth images in particular and will be used to simulate the human eye for decisionmaking in the fermentation process. The preamble of the study will be to consider algorithms for the detection of edges and then analyse these edges. MATLAB will be used to do the preprocessing of the images and to write and test any new algorithms designed for this project.

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