+publisher:"University of Arizona" +contributor:("Greenlee, W. M.")

University of Arizona

1. RUSSELL, DAVID MARTIN. THE CALCULATION OF LOWER BOUNDS TO ATOMIC ENERGIES.

Degree: 1983, University of Arizona

► The goal of this dissertation has been to develop a method that enables one to calculate accurate, rigorous lower bounds to the eigenvalues of the… (more)

▼ The goal of this dissertation has been to develop a method that enables one to calculate accurate, rigorous lower bounds to the eigenvalues of the standard nonrelativistic spin-free Hamiltonian for an atom with N electrons. Lower bounds are necessary in order to complement upper bounds obtained from the Hartree-Fock and Rayleigh-Ritz techniques. Without accurate lower bounds, it is impossible to estimate the error of the approximate values of the energies. By combining two heretofore distinct methods and using the symmetry properties of the Hamiltonian, this goal has been achieved. The first of the two methods is the method of intermediate problems. By beginning with an appropriately chosen "base operator" H⁰, one forms a sequence of intermediate Hamiltonians Hᵏ, k = 1,2,..., whose corresponding eigenvalues form a sequence of lower bounds to the eigenvalues of the original Hamiltonian H. Complications which occurred in this method due to the stability of essential spectra under compact perturbations were later surmounted with the use of abstract separation of variables by D. W. Fox. The second technique, the effective field method, provides a lower bound operator to the interelectron repulsion term in H that is of the form of a sum of separable potentials. This latter technique reduces the eigenvalue problem for H⁰ to a sum of single particle operators. With the use of a special potential, the Hulthen potential, one may construct an explicitly solvable base problem from the effective field method, if one uses the method of intermediate problems to calculate lower bounds to non-S states. This base problem is then suitable as a starting point for the method of intermediate problems with the Fox modifications. The eigenvalues of the new base problem are already comparable to the celebrated Thomas-Fermi energies. The final part of the dissertation provides a practical procedure for determining the physically realizable spectra of the intermediate operators. This is accomplished by restricting the Hamiltonian to subspaces of proper physical symmetry so that the resulting lower bounds will be to eigenvalues of physical significance. Advisors/Committee Members: Greenlee, W. M (advisor).

Subjects/Keywords: Atomic orbitals – Mathematical models.; Hamiltonian systems.

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APA (6^th Edition):

RUSSELL, D. M. (1983). THE CALCULATION OF LOWER BOUNDS TO ATOMIC ENERGIES. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/187605

Chicago Manual of Style (16^th Edition):

RUSSELL, DAVID MARTIN. “THE CALCULATION OF LOWER BOUNDS TO ATOMIC ENERGIES. ” 1983. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/187605.

MLA Handbook (7^th Edition):

RUSSELL, DAVID MARTIN. “THE CALCULATION OF LOWER BOUNDS TO ATOMIC ENERGIES. ” 1983. Web. 22 Jan 2021.

Vancouver:

RUSSELL DM. THE CALCULATION OF LOWER BOUNDS TO ATOMIC ENERGIES. [Internet] [Doctoral dissertation]. University of Arizona; 1983. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/187605.

Council of Science Editors:

RUSSELL DM. THE CALCULATION OF LOWER BOUNDS TO ATOMIC ENERGIES. [Doctoral Dissertation]. University of Arizona; 1983. Available from: http://hdl.handle.net/10150/187605

University of Arizona

2. Elfendahl, Michael Preston. Investigation of the convergence properties of an iterative image restoration algorithm.

Degree: 1994, University of Arizona

URL: http://hdl.handle.net/10150/186848

► Iterative algorithms for image restoration which include the use of prior knowledge of the solution in their design have proven useful in super resolution imaging.… (more)

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APA (6^th Edition):

Elfendahl, M. P. (1994). Investigation of the convergence properties of an iterative image restoration algorithm. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/186848

Chicago Manual of Style (16^th Edition):

Elfendahl, Michael Preston. “Investigation of the convergence properties of an iterative image restoration algorithm. ” 1994. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/186848.

MLA Handbook (7^th Edition):

Elfendahl, Michael Preston. “Investigation of the convergence properties of an iterative image restoration algorithm. ” 1994. Web. 22 Jan 2021.

Vancouver:

Elfendahl MP. Investigation of the convergence properties of an iterative image restoration algorithm. [Internet] [Doctoral dissertation]. University of Arizona; 1994. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/186848.

Council of Science Editors:

Elfendahl MP. Investigation of the convergence properties of an iterative image restoration algorithm. [Doctoral Dissertation]. University of Arizona; 1994. Available from: http://hdl.handle.net/10150/186848

University of Arizona

3. Halpern, David Carlos Mohrer Judice. The squeezing of red blood cells through tubes and channels of near-critical dimensions.

Degree: 1989, University of Arizona

URL: http://hdl.handle.net/10150/184839

► The aim of this dissertation is to develop theoretical models for the motion of rigid and flexible particles through very tight spaces. The geometries of… (more)

▼ The aim of this dissertation is to develop theoretical models for the motion of rigid and flexible particles through very tight spaces. The geometries of conduits which will be investigated are cylindrical tubes, parallel plane walls and rectangular channels. This work is motivated by an interest in the flow and deformation of single red blood cells in very narrow capillaries, in spleen and in bone marrow. Mammalian red cells are highly flexible, but their deformations satisfy two significant constraints. They must deform at constant volume, because the contents of the cell are incompressible, and also at nearly constant surface area, because the red cell membrane strongly resists dilation. Consequently, there exists a minimal tube diameter below which passage of intact cells is not possible. A cell in a tube with this diameter has its critical shape: a cylinder with hemispherical ends. The motion of red cells is analysed using lubrication theory. When the tube diameter is slightly larger than the minimal value, the cell shape is close to its shape in the critical case. However, the rear end of the cell becomes flattened and then concave with a relatively small further increase in the diameter. The changes in cell shape and the resulting rheological parameters are analysed using matched asymptotic expansions for the high-velocity limit and using numerical solutions. A rapid decrease in the apparent viscosity of red cell suspensions with increasing tube diameter is predicted over the range of diameters considered. The red cell velocity is found to exceed the mean bulk velocity by an amount which increases with increasing tube diameter. The same type of analysis is applied to the flow and deformation of red blood cells between two parallel plates with near-minimal spacings. First, the critical shape of the particle and the minimum gap width are determined using calculus of variations. In this case, it is a disk with a rounded edge. The flow in the plasma layers between the cell and the plates is described using lubrication theory. Approximate solutions can be obtained using a locally two-dimensional analysis at each point of the rim of the cell. Cell shapes, pressure distributions, membrane stresses and particle velocities are deduced as functions of geometrical parameters. One significant finding is that the gap width between the cell and the wall decreases with distance from the axis of symmetry parallel to the flow direction. The red cell velocity may be smaller or larger than the mean fluid velocity far from the cell, depending on the spacing of the plates, with equality when the width of the red cell is about ninety percent of the spacing between plates. The same procedure is also applied to rectangular channels. Advisors/Committee Members: Secomb, T. W (advisor), Gross, J. F. (committeemember), Greenlee, W. M. (committeemember), Lomen, D. O. (committeemember).

Subjects/Keywords: Cells – Motility – Mathematical models.; Erythrocytes – Deformability.

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APA (6^th Edition):

Halpern, D. C. M. J. (1989). The squeezing of red blood cells through tubes and channels of near-critical dimensions. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184839

Chicago Manual of Style (16^th Edition):

Halpern, David Carlos Mohrer Judice. “The squeezing of red blood cells through tubes and channels of near-critical dimensions. ” 1989. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/184839.

MLA Handbook (7^th Edition):

Halpern, David Carlos Mohrer Judice. “The squeezing of red blood cells through tubes and channels of near-critical dimensions. ” 1989. Web. 22 Jan 2021.

Vancouver:

Halpern DCMJ. The squeezing of red blood cells through tubes and channels of near-critical dimensions. [Internet] [Doctoral dissertation]. University of Arizona; 1989. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/184839.

Council of Science Editors:

Halpern DCMJ. The squeezing of red blood cells through tubes and channels of near-critical dimensions. [Doctoral Dissertation]. University of Arizona; 1989. Available from: http://hdl.handle.net/10150/184839

University of Arizona

4. Amoozegar-Fard, Azizolah. Salt and water movement in soils following heavy applications of feedlot waste .

Degree: 1977, University of Arizona

URL: http://hdl.handle.net/10150/191041

► The movement of salts in soils following application of feedlot wastes was studied experimentally and theoretically. The objectives of the study were (1) to evaluate… (more)

▼ The movement of salts in soils following application of feedlot wastes was studied experimentally and theoretically. The objectives of the study were (1) to evaluate the movement of salts in the soil following heavy application of animal wastes as related to the aggregate sizes of manure and water management practices and (2) to develop a mathematical model to predict the movement of salts within the soil and manure mixture. In the experimental study, air dried manure was formed into three distinct sizes, small (to pass 40 mesh sieve), medium (0.9 am in diameter, 1.2 cm in length), and large (1.8 cm in diameter, 1.8 cm in length). Soil columns of 15 cm inside diameter were packed with 30 cm of a soil-manure mixture over a 10 cm depth of soil. The manure application rate was equivalent to 100 metric tons/ha calculated on the basis of the cross-sectional area of the column. A total of five pore volumes of water was passed through the soil under continuous and intermittent water applications. The leachates were collected in 1/2 pore volume increments and the volume, EC, and pH determined immediately. Within 48 hours of the sampling, the leachates were analyzed for Na, K, Ca, Mg, Cl, and five trace elements (Fe, Mn, Zn, Cu, and Ni). The EC of the leachate for the first 1/2 pore volume was significantly (1% level) highest for the small-sized aggregates and the lowest for the large aggregate treatments under both moisture regimes. During the second increment, the order was reversed. In the later water applications, the EC for small aggregates was higher than the other sizes. There were no significant differences between the EC of the leachate from medium and large aggregate treatments during the later periods under either water treatments. Under both moisture regimes, the amount of Na removed from small aggregates decreased more rapidly than the other sizes. More than 90% of the total Na added to the system by manure was removed from the small aggregate treatment. In contrast, the highest amount of K removed (895 mg from small-sized aggregates under continuous leaching' represents about 35% of the total amount present In the manure applied. More Ca was removed from the small-sized aggregate treatments under both moisture regimes than was added by manure application. As for Mg the pattern of the removal was similar to that of Ca. No Cl was detected in the leachate after the fifth 1/2 pore volume was displaced. A mathematical model was developed to predict the movement of readily soluble ions such as Na, K, and Cl from different aggregate sizes of manure. The theoretical curves were compared with earlier experimental data and the parameters appearing in the mathematical equation were estimated. The results for Cl, Na, and K are presented graphically, and the estimated parameters as well as the values of the square roots of the sum of the squares between the theoretical and experimental values as percentage of the sum of the experimental values (SSR) are reported. From the low value of SSR's, it is evident that the model can… Advisors/Committee Members: Warrick, Arthur W. (committeemember), Matlock, W. G. (committeemember), Lomen, D. O. (committeemember), Greenlee, W. M. (committeemember).

Subjects/Keywords: Hydrology.; Soil percolation.; Feedlots – Waste disposal.; Soils, Salts in.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Amoozegar-Fard, A. (1977). Salt and water movement in soils following heavy applications of feedlot waste . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/191041

Chicago Manual of Style (16^th Edition):

Amoozegar-Fard, Azizolah. “Salt and water movement in soils following heavy applications of feedlot waste .” 1977. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/191041.

MLA Handbook (7^th Edition):

Amoozegar-Fard, Azizolah. “Salt and water movement in soils following heavy applications of feedlot waste .” 1977. Web. 22 Jan 2021.

Vancouver:

Amoozegar-Fard A. Salt and water movement in soils following heavy applications of feedlot waste . [Internet] [Doctoral dissertation]. University of Arizona; 1977. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/191041.

Council of Science Editors:

Amoozegar-Fard A. Salt and water movement in soils following heavy applications of feedlot waste . [Doctoral Dissertation]. University of Arizona; 1977. Available from: http://hdl.handle.net/10150/191041

University of Arizona

5. Modisett, Matthew Clayton. A characterization of the circularity of certain balanced incomplete block designs.

Degree: 1988, University of Arizona

URL: http://hdl.handle.net/10150/184393

► When defining a structure to fulfill a set of axioms that are similar to those prescribed by Euclid, one must select a set of points… (more)

▼ When defining a structure to fulfill a set of axioms that are similar to those prescribed by Euclid, one must select a set of points and then define what is meant by a line and what is meant by a circle. When properly defined these labels will have properties which are similar to their counterparts in the (complex) plane, the lines and circles which Euclid undoubtedly had in mind. In this manner, the geometer may employ his intuition from the complex plane to prove theorems about other systems. Most "finite geometries" have clearly defined notions of points and lines but fail to define circles. The two notable exceptions are the circles in a finite affine plane and the circles in a Mobius plane. Using the geometry of Euclid as motivation, we strive to develop structures with both lines and circles. The only successful example other than the complex plane is the affine plane over a finite field, where all of Euclid's geometry holds except for any assertions involving order or continuity. To complement the prolific work concerning finite geometries and their lines, we provide a general definition of a circle, or more correctly, of a collection of circles and present some preliminary results concerning the construction of such structures. Our definition includes the circles of an affine plane over a finite field and the circles in a Mobius plane as special cases. We develop a necessary and sufficient condition for circularity, present computational techniques for determining circularity and give varying constructions. We devote a chapter to the use of circular designs in coding theory. It is proven that these structures are not useful in the theory of error-correcting codes, since more efficient codes are known, for example the Reed-Muller codes. However, the theory developed in the earlier chapters does have applications to Cryptology. We present five encryption methods utilizing circular structures. Advisors/Committee Members: Clay, James R (advisor), Benson, Clark (committeemember), Brillhart, John (committeemember), Gay, David (committeemember), Greenlee, W. M. (committeemember).

Subjects/Keywords: Incomplete block designs.; Combinatorial designs and configurations.; Circle.

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APA (6^th Edition):

Modisett, M. C. (1988). A characterization of the circularity of certain balanced incomplete block designs. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184393

Chicago Manual of Style (16^th Edition):

Modisett, Matthew Clayton. “A characterization of the circularity of certain balanced incomplete block designs. ” 1988. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/184393.

MLA Handbook (7^th Edition):

Modisett, Matthew Clayton. “A characterization of the circularity of certain balanced incomplete block designs. ” 1988. Web. 22 Jan 2021.

Vancouver:

Modisett MC. A characterization of the circularity of certain balanced incomplete block designs. [Internet] [Doctoral dissertation]. University of Arizona; 1988. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/184393.

Council of Science Editors:

Modisett MC. A characterization of the circularity of certain balanced incomplete block designs. [Doctoral Dissertation]. University of Arizona; 1988. Available from: http://hdl.handle.net/10150/184393

University of Arizona

6. Elele, Nwabuisi N. O. Mathematical modeling of multistep chemical combustion: The hydrogen-oxygen system.

Degree: 1988, University of Arizona

URL: http://hdl.handle.net/10150/184573

► A model of premixed lean Hydrogen-Oxygen flame is studied by singular perturbation techniques based on high activation energy. The model is built from four reaction… (more)

Subjects/Keywords: Combustion – Mathematical models.; Fire – Mathematical models.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Elele, N. N. O. (1988). Mathematical modeling of multistep chemical combustion: The hydrogen-oxygen system. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184573

Chicago Manual of Style (16^th Edition):

Elele, Nwabuisi N O. “Mathematical modeling of multistep chemical combustion: The hydrogen-oxygen system. ” 1988. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/184573.

MLA Handbook (7^th Edition):

Elele, Nwabuisi N O. “Mathematical modeling of multistep chemical combustion: The hydrogen-oxygen system. ” 1988. Web. 22 Jan 2021.

Vancouver:

Elele NNO. Mathematical modeling of multistep chemical combustion: The hydrogen-oxygen system. [Internet] [Doctoral dissertation]. University of Arizona; 1988. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/184573.

Council of Science Editors:

Elele NNO. Mathematical modeling of multistep chemical combustion: The hydrogen-oxygen system. [Doctoral Dissertation]. University of Arizona; 1988. Available from: http://hdl.handle.net/10150/184573

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