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- Acoustic analogy (1)
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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
On The Use Of Quasi-Newton Methods For The Minimization Of Convex Quadratic Splines, William Howard Thomas Ii
On The Use Of Quasi-Newton Methods For The Minimization Of Convex Quadratic Splines, William Howard Thomas Ii
Mathematics & Statistics Theses & Dissertations
In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, the process terminates in a finite number of iterations. Numerical examples are provided.
The Computation Of Exact Green's Functions In Acoustic Analogy By A Spectral Collocation Boundary Element Method, Andrea D. Jones
The Computation Of Exact Green's Functions In Acoustic Analogy By A Spectral Collocation Boundary Element Method, Andrea D. Jones
Mathematics & Statistics Theses & Dissertations
Aircraft airframe noise pollution resulting from the take-off and landing of airplanes is a growing concern. Because of advances in numerical analysis and computer technology, most of the current noise prediction methods are computationally efficient. However, the ability to effectively apply an approach to complex airframe geometries continues to challenge researchers. The objective of this research is to develop and analyze a robust noise prediction method for dealing with geometrical modifications. This new approach for determining sound pressure involves computing exact, or tailored, Green's functions for use in acoustic analogy. The effects of sound propagation and scattering by solid surfaces …
Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba
Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba
Mathematics & Statistics Theses & Dissertations
The solution to the neutron Boltzmann equation is separated into a straightahead component dominating at high energies and an isotropic component dominating at low energies. The high-energy solution is calculated using HZETRN-05, and the low-energy isotropic component is modeled by two non-coupled integro-differential equations describing both forward and backward neutron propagation. Three different solution methods are then used to solve the equations. The collocation method employs linear I3-splines to transform each equation into a system of ODES; the resulting system is then solved exactly and evaluated using numerical integration techniques. Wilson's method uses a perturbational approach in which a fundamental …
A Technique For Solving The Singular Integral Equations Of Potential Theory, Brian George Burns
A Technique For Solving The Singular Integral Equations Of Potential Theory, Brian George Burns
Mathematics & Statistics Theses & Dissertations
The singular integral equations of Potential Theory are investigated using ideas from both classical and contemporary mathematics. The goal of this semi-analytic approach is to produce numerical schemes that are both general and computationally simple. Previous works based on classical methods have yielded solutions only for very special cases while contemporary methods such as finite differences, finite elements and boundary element techniques are computationally extensive. Since the two-dimensional integral equations of interest exhibit structural invariance under a wide class of conformal mappings initial emphasis is placed on circular domains. By Fourier expansion with respect to the angular variable, such two-dimensional …
Canonical Correlation And Correspondence Analysis Of Longitudinal Data, Jayesh Srivastava
Canonical Correlation And Correspondence Analysis Of Longitudinal Data, Jayesh Srivastava
Mathematics & Statistics Theses & Dissertations
Assessing the relationship between two sets of multivariate vectors is an important problem in statistics. Canonical correlation coefficients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. When the variables are qualitative (categorical), a technique called correspondence analysis (CA) is used. Canonical correspondence analysis (CCPA) is used to deal with the case when one set of variables is categorical and the other set is quantitative. By exploiting the interrelationships between these three techniques we first provide a theoretical basis for …
Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo
Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo
Mathematics & Statistics Theses & Dissertations
Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create …