Current Search: Research Repository (x) » Mathematics (x) » info:fedora/ir:thesisCModel (x)
Search results
Pages
 Title
 Acknowledging the Religious Beliefs Students Bring into the Science Classroom: Using the Bounded Nature of Science.
 Creator

Southerland, Sherry A., Scharmann, Lawrence Conrad
 Abstract/Description

Scientific knowledge often appears to contradict many students' religious beliefs. Indeed, the assumptions of science appear contradictory to the metaphysical claims of many religions. This conflict is most evident in discussions of biological evolution. Teachers, in attempts to limit the controversy, often avoid this topic or teach it superficially. Recently, there has been a political effort to "teach to the controversy" – which some see as a way of introducing religious explanations for...
Show moreScientific knowledge often appears to contradict many students' religious beliefs. Indeed, the assumptions of science appear contradictory to the metaphysical claims of many religions. This conflict is most evident in discussions of biological evolution. Teachers, in attempts to limit the controversy, often avoid this topic or teach it superficially. Recently, there has been a political effort to "teach to the controversy" – which some see as a way of introducing religious explanations for biological diversity into science classrooms. Many science educators reject this approach, insisting that we limit classroom discussions to science alone. This "science only" approach leaves the negotiation of alternative knowledge frameworks to students, who are often illprepared for such epistemological comparisons. To support students' understanding of science while maintaining their religious commitments, this article explores the utility of emphasizing the boundaries of scientific knowledge and the need to support students in their comparison of contradictory knowledge frameworks.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_ste_faculty_publications0013, 10.1080/07351690.2013.743778
 Format
 Citation
 Title
 An analysis of mushchimney structure.
 Creator

Yang, YoungKyun., Florida State University
 Abstract/Description

When a multicomponent liquid is cooled and solidified, commonly, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. When the fluid seeps through the dendrites, further freezing occurs which fills in pores of the matrix and reduces its...
Show moreWhen a multicomponent liquid is cooled and solidified, commonly, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. When the fluid seeps through the dendrites, further freezing occurs which fills in pores of the matrix and reduces its permeability to the liquid flow. In particular, if a binary alloy (for example, NH$\sb4$ClH$\sb2$O solution) is cooled at bottom and a dense component (for example, NH$\sb4$Cl) is solidified, buoyant material released during freezing in the pores returns to the melt only through thin, vertical, but widely separated, 'chimneys', the flow through the matrix between them being organized to supply these chimneys., We presented photos of a mushchimney system obtained from the ammonium chloride experiment, and we studied how convection with horizontal divergence affects the structure and flow of the mushchimney system. We use a simple ODE system in the mush derived by assuming that the temperature depends on vertical coordinate only. We find that the mass fraction of solid increases and the depth of a mush decreases when the strength of convection increases., We present an axisymmetric model containing only one chimney to analyze the structure of the mushchimney system. We find solutions of the temperature, the solid fraction, and the pressure in the chimney wall. In particular, the pressure expression shows that the fluid flow needs a huge pressure in order to pass through the chimney wall if its permeability is very small., We assume that a ratio of composition is large, which allows us to neglect the pressure contribution of the chimney wall. We use the knowledge of the variables in the mush, evaluated on the chimney wall, to find the fluid flow in the chimney and the radius of chimney. Our procedure employs the von KarmanPohlhausen technique for determining chimney flow (Roberts & Loper, 1983) and makes use of the fact that the radius of the chimney is much less than the thickness of the mush. We find a relation between a parameter measuring the ratio of viscous and buoyancy forces in the chimney and the vertical velocity component on the top of the mush, and estimate numerically the value of this velocity measuring the strength of convection. The results obtained show reasonably good agreement with theoretical and experimental works (Roberts & Loper (1983), Chen & Chen (1991), Tait & Jaupart (1992), Hellawell etc. (1993), Worster (1991)).
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9540067, 3088707, FSDT3088707, fsu:77509
 Format
 Document (PDF)
 Title
 An analytical approach to the thermal residual stress problem in fiberreinforced composites.
 Creator

Xie, Zhiyun., Florida State University
 Abstract/Description

A pair of two new tensors called Generalized Plane Strain (GPS) tensors S and D is proposed for the concentric cylindrical inclusion problem. GPS tensors take the fiber volume fraction explicitly into account. When the cylindrical matrix is of infinite radius, tensor S reduces to the appropriate Eshelby's tensor. The GPS tensors provide a convenient form of solution to a class of problems involving eigenstrain, e.g., strain due to thermal expansion, phase transformation, plastic and misfit...
Show moreA pair of two new tensors called Generalized Plane Strain (GPS) tensors S and D is proposed for the concentric cylindrical inclusion problem. GPS tensors take the fiber volume fraction explicitly into account. When the cylindrical matrix is of infinite radius, tensor S reduces to the appropriate Eshelby's tensor. The GPS tensors provide a convenient form of solution to a class of problems involving eigenstrain, e.g., strain due to thermal expansion, phase transformation, plastic and misfit strain. Explicit expressions to evaluate thermal residual stresses in the matrix and the fiber using GPS tensors are developed for metallic/intermetallic matrix composites. Results are compared with Eshelby's infinite domain solution and Finite Element solution for SCS6/Ti24Al11Nb composite. The method of superposition using GPS tensor is proposed for evaluating thermal residual stress distribution in a fiber reinforced composite with periodic arrays. The results compare very favorably with Finite Element solution. GPS tensors are also used in the evaluation of the effective material properties. We demonstrated the approach by studying two fiber reinforced composites, Graphite/Epoxy and Glass/Epoxy composites. A good agreement between analytical results using GPS tensor and experimental data was found. We also compared the results of using GPS tensor along with the original Eshelby's tensor and found that GPS tensor provides a better match with experimental data.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9526758, 3088646, FSDT3088646, fsu:77448
 Format
 Document (PDF)
 Title
 Analytical Results on the Role of Flexibility in Flapping Propulsion.
 Creator

Moore, Nicholas
 Abstract/Description

Wing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop smallamplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing's emergent pitching motions, along with...
Show moreWing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop smallamplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing's emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviours and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. The simple robust estimates afforded by our theory may prove valuable even in situations where details of the flapping motion and wing geometry differ.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_math_faculty_publications0002, 10.1017/jfm.2014.533
 Format
 Citation
 Title
 Bayesian nonparametric estimation via Gibbs sampling for coherent systems with redundancy.
 Creator

Lawson, Kevin Lee., Florida State University
 Abstract/Description

We consider a coherent system S consisting of m independent components for which we do not know the distributions of the components' lifelengths. If we know the structure function of the system, then we can estimate the distribution of the system lifelength by estimating the distributions of the lifelengths of the individual components. Suppose that we can collect data under the 'autopsy model', wherein a system is run until a failure occurs and then the status (functioning or dead) of each...
Show moreWe consider a coherent system S consisting of m independent components for which we do not know the distributions of the components' lifelengths. If we know the structure function of the system, then we can estimate the distribution of the system lifelength by estimating the distributions of the lifelengths of the individual components. Suppose that we can collect data under the 'autopsy model', wherein a system is run until a failure occurs and then the status (functioning or dead) of each component is obtained. This test is repeated n times. The autopsy statistics consist of the age of the system at the time of breakdown and the set of parts that are dead by the time of breakdown. Using the structure function and the recorded status of the components, we then classify the failure time of each component. We develop a nonparametric Bayesian estimate of the distributions of the component lifelengths and then use this to obtain an estimate of the distribution of the lifelength of the system. The procedure is applicable to machinetest settings wherein the machines have redundant designs. A parametric procedure is also given.
Show less  Date Issued
 1994, 1994
 Identifier
 AAI9502812, 3088467, FSDT3088467, fsu:77272
 Format
 Document (PDF)
 Title
 Boundaries of groups.
 Creator

Ruane, Kim E., Florida State University
 Abstract/Description

In recent years, the theory of infinite groups has been revolutionized by the introduction of geometric methods. In his foundational paper, "Hyperbolic Groups", Gromov outlines a geometric group theory which provides tools for studying a wide class of groups meant to generalize the classical groups coming from Riemannian geometry. In this setting, the metric geometry of the space is used to study the algebraic properties of the group. One aspect of the metric geometry is the behavior of...
Show moreIn recent years, the theory of infinite groups has been revolutionized by the introduction of geometric methods. In his foundational paper, "Hyperbolic Groups", Gromov outlines a geometric group theory which provides tools for studying a wide class of groups meant to generalize the classical groups coming from Riemannian geometry. In this setting, the metric geometry of the space is used to study the algebraic properties of the group. One aspect of the metric geometry is the behavior of geodesic rays in the space. A technique used for studying this behavior is to compactify the space by adding the endpoints of geodesic raysi.e. the boundary of the space., Several new theorems in group theory were proven only after the introduction of these geometric methodsfor instance, the Scott conjectureand many known theorems can be given new, elegant geometric proofs. With the success of this approach, Gromov wrote a second paper which gives certain minimum requirements for a theory including certain nonpositively curved groups., The first task is to define a notion of nonpositive curvature that will generalize the classical Riemannian notion. One proposed notion goes back to the work of Alexandroff and Topogonov wherein they compare the triangles in a given geometry to the triangles in Euclidean geometry and ask that those in the former be as least as thin as those in the latter. Then a class of nonpositively curved groups can be defined as those that act geometrically on one of these nonpositively curved spaces., My research has focused on studying the boundary of the nonpositively curved spaces which admit geometric actions by a group. The overriding question is a question in Gromov's second paper: If a group acts geometrically on two such spaces, then do they have homeomorphic boundaries?
Show less  Date Issued
 1996, 1996
 Identifier
 AAI9627212, 3088922, FSDT3088922, fsu:77721
 Format
 Document (PDF)
 Title
 The boundedness of a certain convolution operator.
 Creator

Rhee, Jungsoo., Florida State University
 Abstract/Description

Let M be a nonnegative measurable function on (0,$\infty)$ and let $\tilde{M}(x) = \vert x\vert\sp{{n\over p}{n\over q}n} M(\vert x\vert), x\in R\sp{n}.$ We can consider a convolution operator: for a suitable f,, (UNFORMATTED TABLE OR EQUATION FOLLOWS), (a) Suppose $1\le s\le\infty.$ Then $M\in L\sp{t}({dr\over r})$ implies that $T\sb{M}:L\sp{p}(R\sp{n})\to L\sp{q}(R\sp{n})$ is bounded for all $({1\over p},{1\over q})$ in the typediagram triangle with vertices $(1  {1\over s},0),\ (1,{1...
Show moreLet M be a nonnegative measurable function on (0,$\infty)$ and let $\tilde{M}(x) = \vert x\vert\sp{{n\over p}{n\over q}n} M(\vert x\vert), x\in R\sp{n}.$ We can consider a convolution operator: for a suitable f,, (UNFORMATTED TABLE OR EQUATION FOLLOWS), (a) Suppose $1\le s\le\infty.$ Then $M\in L\sp{t}({dr\over r})$ implies that $T\sb{M}:L\sp{p}(R\sp{n})\to L\sp{q}(R\sp{n})$ is bounded for all $({1\over p},{1\over q})$ in the typediagram triangle with vertices $(1  {1\over s},0),\ (1,{1\over s})\ {\rm and}\ (1  {1\over(n+1)s},{1\over(n+1)s})$ if and only if s = t., (b) Suppose $1  Date Issued
 1993, 1993
 Identifier
 AAI9334267, 3088175, FSDT3088175, fsu:76982
 Format
 Document (PDF)
 Title
 CANONICAL SYSTEMS OF TORI AND KLEIN BOTTLES IN NONORIENTABLE 3MANIFOLDS OF GENUS TWO.
 Creator

CARDONA, IVAN., Florida State University
 Abstract/Description

Let M be a closed nonorientable 3manifold with a Heegaard splitting of genus two. We show that, if M has a nonseparating essential Klein bottle, then there is a nonseparating essential Klein bottle (or torus) K such that the intersection of K and one of the handlebodies in the Heegaard splitting is an essential disk. Also, if every essential Klein bottle (or torus) is separating in M and if M has a nontrivial canonical system of 2sided tori and Klein bottles, then there is a canonical...
Show moreLet M be a closed nonorientable 3manifold with a Heegaard splitting of genus two. We show that, if M has a nonseparating essential Klein bottle, then there is a nonseparating essential Klein bottle (or torus) K such that the intersection of K and one of the handlebodies in the Heegaard splitting is an essential disk. Also, if every essential Klein bottle (or torus) is separating in M and if M has a nontrivial canonical system of 2sided tori and Klein bottles, then there is a canonical system such that the intersection of this system with one of the handlebodies in the Heegaard splitting consists of at most two essential disks. We use these results to give a complete list of all the nonorientable 3manifolds with a Heegaard splitting of genus two which are either not P('2)irreducible or contain an incompressible torus or Klein bottle.
Show less  Date Issued
 1987, 1987
 Identifier
 AAI8713306, 3086609, FSDT3086609, fsu:76084
 Format
 Document (PDF)
 Title
 A COMPARATIVE STUDY OF THE ABILITY OF FOURTH YEAR HIGH SCHOOL MATHEMATICSSTUDENTS TO USE THE PRINCIPLE OF MATHEMATICAL INDUCTION AND THE WELL ORDERING PRINCIPLE TO PROVE CONJECTURES.
 Creator

WARD, RONALD ALLISON., The Florida State University
 Date Issued
 1971, 1971
 Identifier
 AAI7210053, 2986635, FSDT2986635, fsu:71144
 Format
 Document (PDF)
 Title
 A COMPARISON OF TWO GUIDED DISCOVERY STRATEGIES AND AN EXPOSITORY STRATEGY FOR TEACHING COLLEGE FRESHMEN PROOF OF THEOREMS BASED UPON THE FIELDAXIOMS.
 Creator

ESPIGH, MERRILL ALVIN., The Florida State University
 Date Issued
 1974, 1974
 Identifier
 AAI7418071, 2987602, FSDT2987602, fsu:72109
 Format
 Document (PDF)
 Title
 A computational study of the effects of serotonin on the molluscan burster neuron R(15).
 Creator

Bertram, Richard., Florida State University
 Abstract/Description

A mathematical model is constructed which describes the bursting electrical behavior of neuron R$\sb{15},$ located in the abdominal ganglion of the marine mollusc Aplysia. This model, consisting of a system of ten coupled nonlinear ordinary differential equations, compares well with published experimental data and, unlike earlier models, incorporates ionic mechanisms now thought to be responsible for the bursting behavior of the neuron. Exogenous application of the neurotransmitter serotonin...
Show moreA mathematical model is constructed which describes the bursting electrical behavior of neuron R$\sb{15},$ located in the abdominal ganglion of the marine mollusc Aplysia. This model, consisting of a system of ten coupled nonlinear ordinary differential equations, compares well with published experimental data and, unlike earlier models, incorporates ionic mechanisms now thought to be responsible for the bursting behavior of the neuron. Exogenous application of the neurotransmitter serotonin is simulated by modifying the R$\sb{15}$ model. Numerical simulations show that the model reproduces the sequence of voltage waveform modulations observed experimentally as the concentration of applied serotonin is increased, thus supporting the validity of both the mathematical model and the proposed ionic modifications brought about by the application of serotonin. Finally, the bursting oscillation and the serotonininduced modulation of this oscillation are analyzed using techniques from Dynamical Systems Theory. This analysis yields insight into the changing system dynamics brought about by the application of serotonin and allows predictions to be made concerning the sensitivity of the system to brief synaptic perturbations and the way in which this sensitivity is modified by serotonin.
Show less  Date Issued
 1993, 1993
 Identifier
 AAI9321878, 3088083, FSDT3088083, fsu:76890
 Format
 Document (PDF)
 Title
 A computational study of turbulent jet flows and their instability waves.
 Creator

Thies, Andrew Timothy., Florida State University
 Abstract/Description

The nature of turbulent jet flows is considered. First, the effects of nozzle geometry are examined. A boundary element formulation, which may be used to analyze the stability of vortexsheet jets of arbitrary geometry, is developed. This formulation is applied to rectangular jets. It is found that rectangular jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics...
Show moreThe nature of turbulent jet flows is considered. First, the effects of nozzle geometry are examined. A boundary element formulation, which may be used to analyze the stability of vortexsheet jets of arbitrary geometry, is developed. This formulation is applied to rectangular jets. It is found that rectangular jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their eigenfunctions is proposed. It is found that the first and third modes of each family are corner modes. The fluctuations associated with these waves are localized near the corners of the jet. The second mode in each family, however, is a center mode with maximum fluctuations concentrated near the central portions of the jet. The center modes have the largest spatial growth rates. It is anticipated that as the instability waves propagate downstream the center modes would emerge as the dominant instabilities of the jet. Second, a K$\varepsilon$ turbulence model, which incorporates Pope's nonplaner correction and Sarkar's high convective Mach number correction, is proposed for the computation of timeaveraged turbulent jet flows. It is demonstrated that this model does contain the essential ingredients of turbulence physics for adequate jet mean flow prediction. However, the empirical constants that are generally used are found to be inappropriate for jets. A highorder parabolized approach to computing ideally expanded jet flows is presented. A new set of empirical constants is chosen, which better correlates the computations with measurements for a set of jets representative of a variety of nozzle configurations. It is demonstrated that, when the standard constants are replaced by the new ones, the model can offer good mean flow predictions for axisymmetric,, rectangular and elliptic jets with Mach numbers ranging from 0.4 to 2.0 and jet total temperature to ambient temperature ratios ranging from 1.0 to 4.0. Together, the two efforts lay much of the groundwork for a complete study of the effects of nozzle geometry on the mixing and noise generation in highspeed jet flows.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9526498, 3088592, FSDT3088592, fsu:77394
 Format
 Document (PDF)
 Title
 Confined supersonic mixing layers: A computational investigation of instability and mixing enhancement.
 Creator

Hu, Fang Qiang., Florida State University
 Abstract/Description

Hydrodynamic instability of a compressible shear mixing layer plays a very important role in controlling and promoting the mixing processes in supersonic combustion problems. At supersonic convective Mach numbers the natural mixing rates of the shear layer are observed to be very small. The current research interest is in the mixing enhancement. In the first part of the present study, the linear spatial instability problem of a supersonic shear mixing layer inside a rectangular channel is...
Show moreHydrodynamic instability of a compressible shear mixing layer plays a very important role in controlling and promoting the mixing processes in supersonic combustion problems. At supersonic convective Mach numbers the natural mixing rates of the shear layer are observed to be very small. The current research interest is in the mixing enhancement. In the first part of the present study, the linear spatial instability problem of a supersonic shear mixing layer inside a rectangular channel is solved. A systematic way of calculating and classifying all the normal modes is developed. It is demonstrated that a vortex sheet at high supersonic convective Mach number, neutrally stable when unconfined, becomes unstable when confined. Extensive numerical computations indicate that two classes of unstable waves, named as class A and class B supersonic instability waves, can be identified. In addition to unstable waves, two families of neutral waves, named as class C and class D neutral acoustic waves, can also be identified. The characteristics of the unstable waves as well as the neutral waves are determined. It is concluded that the new supersonic instabilities found in this study are the dominant instabilities of a confined mixing layer at high supersonic convective Mach numbers. As such they are very relevant to the supersonic combustion problem. The second part of the study explores the possibility of enhancing the rate of supersonic mixing by means of a periodic Mach wave system. The Mach wave system may be generated by small amplitude waviness of the confining channel walls. The stability of the periodic basic flow is analyzed numerically by the Floquet theory and the spectralcollocation method. The convergence of the numerical solutions is discussed. New secondary instabilities of the shear layer induced by the periodic Mach waves are found computationally. The, growth rate of the new instabilities is found to vary nearly linearly with the ratio of the wavy wall amplitude to the wave length. Therefore it is a potentially promising scheme for the enhancement of supersonic mixing.
Show less  Date Issued
 1990, 1990
 Identifier
 AAI9027799, 3162059, FSDT3162059, fsu:78257
 Format
 Document (PDF)
 Title
 Cosemisimple Hopf algebras.
 Creator

Eberwein, Martin., Florida State University
 Abstract/Description

Throughout, H is a finite dimensional Hopf algebra with antipode S over an algebraically closed field k satisfying (dimH)1 $\ne$ 0. G(H) denotes the group of grouplikes. A Hopf algebra is said to be involutory if the square of its antipode is the identity. We study the mathematics related to Kaplansky's 5$\sp{th}$ conjecture, (1), that if the Hopf algebra H or its dual H* is semisimple as an algebra, then H is involutory., Suppose that B is a sub Hopf algebra of H. We investigate the question...
Show moreThroughout, H is a finite dimensional Hopf algebra with antipode S over an algebraically closed field k satisfying (dimH)1 $\ne$ 0. G(H) denotes the group of grouplikes. A Hopf algebra is said to be involutory if the square of its antipode is the identity. We study the mathematics related to Kaplansky's 5$\sp{th}$ conjecture, (1), that if the Hopf algebra H or its dual H* is semisimple as an algebra, then H is involutory., Suppose that B is a sub Hopf algebra of H. We investigate the question under which assumptions B involutory implies H involutory. We succeed in showing that if H is cosemisimple and $rank\sb{B}H \leq$ 4, then H is semisimple and cosemisimple and $S\sp2$ = id., If char(k) $\not=$ 2, we establish a relationship between $S\sp2$ and grouplikes $g\in G$(H) acting on simple subcoalgebras. It is shown that if A is a simple subcoalgebra A of dimension $n\sp2$ and $g\in$ G(H) is a grouplike of order n such that gA = A then $S\sp2\vert\sb{A} = id\sb{A}$. This enables us to verify Kaplansky's conjecture for cosemisimple Hopf algebras all of whose simple subcoalgebras have dimension 1 or $q\sp2$ with q prime., The main part of our thesis concentrates on cosemisimple Hopf algebras all of whose simple subcoalgebras have dimension at most 9. It is shown that if A is a simple subcoalgebra A of dimension 9 and char(k) $\not=$ 2,3, then $S\sp2\vert\sb{A}$ has order 1, 2 or 3. If the characteristic of the field k is p $>$ dimH, then H is semisimple and cosemisimple. As a consequence, we are able to verify Kaplansky's conjecture for cosemisimple Hopf algebras with "small" simple subcoalgebras, if the characteristic of the field k is p $>$ (dimH)$\sp2$.
Show less  Date Issued
 1992, 1992
 Identifier
 AAI9234216, 3087892, FSDT3087892, fsu:76702
 Format
 Document (PDF)
 Title
 Domain decomposition algorithms and parallel computation techniques for the numerical solution of PDE's with applications to the finite element shallow water flow modeling.
 Creator

Cai, Yihong., Florida State University
 Abstract/Description

In this dissertation, we focus on (1) improving the efficiency of some iterative domain decomposition methods, (2) proposing and developing a novel domain decomposition algorithm, (3) applying these algorithms to the efficient numerical solution of the finite element discretization of the shallow water equations on a 2D limited area domain and (4) investigating parallel implementation issues., We have closely examined the iterative Schur domain decomposition method. A modified version of the...
Show moreIn this dissertation, we focus on (1) improving the efficiency of some iterative domain decomposition methods, (2) proposing and developing a novel domain decomposition algorithm, (3) applying these algorithms to the efficient numerical solution of the finite element discretization of the shallow water equations on a 2D limited area domain and (4) investigating parallel implementation issues., We have closely examined the iterative Schur domain decomposition method. A modified version of the rowsum preserving interface probing preconditioner is proposed to accelerate the convergence on the interfaces. The algorithm has been successfully applied to the finite element shallow water flow modeling., The modified interface matrix domain decomposition algorithm is proposed and developed to reduce computational complexity. The numerical results obtained by applying this algorithm to our problem improve upon those obtained by employing the traditional Schur domain decomposition algorithm., We then investigate parallel block preconditioning techniques in the framework of three frequently used and competitive nonsymmetric linear iterative solvers. Two types of existing domain decomposed (DD) preconditioners are employed and a novel one is proposed. The newly proposed third type of DD preconditioners turns out to be computationally the most efficient., Parallel implementation issues of domain decomposition algorithms are then discussed. Typical parallelization results on the CRAY YMP are presented and discussed., This dissertation also contains a relatively thorough review of two fast growing areas in computational sciences, namely, parallel scientific computing in general and iterative domain decomposition methods in particular as well as a discussion concerning possible future research directions.
Show less  Date Issued
 1994, 1994
 Identifier
 AAI9432613, 3088390, FSDT3088390, fsu:77195
 Format
 Document (PDF)
 Title
 Doublynullcobordant links.
 Creator

Sun, Biansheng., Florida State University
 Abstract/Description

Throughout, we work in the smooth category. We consider a special class of links and knots in $S\sp3$ which are transverse crosssections of trivial 2spheres in $S\sp4.$ They are called DoublyNullCobordant (DNC) links and DNC knots respectively. Closely related concepts are those of NullCobordant (NC) links and NC knots., We are interested in obtaining necessary conditions satisfied by DNC (NC) links and knots, and in constructing nontrivial links and knots which satisfy these conditions....
Show moreThroughout, we work in the smooth category. We consider a special class of links and knots in $S\sp3$ which are transverse crosssections of trivial 2spheres in $S\sp4.$ They are called DoublyNullCobordant (DNC) links and DNC knots respectively. Closely related concepts are those of NullCobordant (NC) links and NC knots., We are interested in obtaining necessary conditions satisfied by DNC (NC) links and knots, and in constructing nontrivial links and knots which satisfy these conditions., Based on analysis of various linking patterns of NC links, we are able to prove that any Hopf link of $\mu$ components is NC if and only if $\mu$ is odd. Another result obtained in this work is that there exists at least one pair of components of an NC link of an even number of components such that the linking number between these two components is zero. Various methods are employed in the geometric realizations of DNC links of a given number of components; we construct DNC links for any given number of components., The 2fold branched cyclic cover of $S\sp3$ branched along any link plays a fundamental role in detecting whether a given link is DNC or not since the cyclic branched cover embeds in $S\sp4$ if the given link is DNC. Considering the embedding problem of the cyclic branched cover leads to the hyperbolicity problem of the associated linking pairing on the homology of the cyclic branched cover. By investigating the torsion part of the first homology of the rfold cyclic branched cover of the 3sphere branched along a link, we are able to produce infinitely many NC links, none of which are DNC links. When specialized to knots, we also discover infinitely many NC knots, none of which are DNC., We also consider higher dimensional DNC links. We obtain a necessary condition for a higher dimensional link being DNC. Specifically, we prove that if L is a DNC (2m $$ 1)link of $\mu$ components with $m >$ 1, then L has a DNC Seifert matrix for any connected Seifert manifold of L.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9527942, 3088652, FSDT3088652, fsu:77454
 Format
 Document (PDF)
 Title
 THE EIGENVALUES OF THE SPHEROIDAL WAVE EQUATION AND THEIR BRANCH POINTS.
 Creator

GUERRIERI, BRUNO., Florida State University
 Abstract/Description

A comprehensive account is given of the behavior of the eigenvalues of the spheroidal wave equation as functions of the complex variable c('2). The convergence of their smallc('2) expansions is limited by an infinite sequence of rings of branch points of square root type at which adjacent eigenvalues of the same type become equal. Known asymptotic formulas are shown to account for how and where the eigenvalues become equal. These asymptotic series for the eigenvalues apply beyond the rings...
Show moreA comprehensive account is given of the behavior of the eigenvalues of the spheroidal wave equation as functions of the complex variable c('2). The convergence of their smallc('2) expansions is limited by an infinite sequence of rings of branch points of square root type at which adjacent eigenvalues of the same type become equal. Known asymptotic formulas are shown to account for how and where the eigenvalues become equal. These asymptotic series for the eigenvalues apply beyond the rings of branch points; we show how they can now be identified with specific eigenvalues.
Show less  Date Issued
 1982, 1982
 Identifier
 AAI8208739, 3085212, FSDT3085212, fsu:74707
 Format
 Document (PDF)
 Title
 Finite dimensional Hopf algebras.
 Creator

Williams, Roselyn Elaine., Florida State University
 Abstract/Description

Let k be an algebraically closed field of characteristic 0. This thesis develops techniques used to determine the structure of a finite dimensional Hopf algebra over k. The Hopf algebras of dimension $\leq$11 are classified., Let p be a prime number, r a positive integer, and n = p$\sp{\rm r}1$. Let GF(p$\sp{\rm r}$) be the Galois field of order p$\sp{\rm r}$. Let G = GF(p$\sp{\rm r}$) $\times$ $\sb\varphi$ GF(p$\sp{\rm r}$)$\sp\cdot$ be the semidirect product of GF(p$\sp{\rm r}$) and GF(p$...
Show moreLet k be an algebraically closed field of characteristic 0. This thesis develops techniques used to determine the structure of a finite dimensional Hopf algebra over k. The Hopf algebras of dimension $\leq$11 are classified., Let p be a prime number, r a positive integer, and n = p$\sp{\rm r}1$. Let GF(p$\sp{\rm r}$) be the Galois field of order p$\sp{\rm r}$. Let G = GF(p$\sp{\rm r}$) $\times$ $\sb\varphi$ GF(p$\sp{\rm r}$)$\sp\cdot$ be the semidirect product of GF(p$\sp{\rm r}$) and GF(p$\sp{\rm r}$)$\sp\cdot$ relative to the homomorphism $\varphi$:GF(p$\sp{\rm r}$)$\sp\cdot$ $\to$ AutGF(p$\sp{\rm r}$) defined by $\varphi$(x)(v) = xv for v$\in$ GF(p$\sp{\rm r}$) and x$\in$ GF(p$\sp{\rm r}$)$\sp\cdot$. A Hopf algebra H of dimension n$\sp2$(n + 1) is constructed which contains a Hopf subalgebra isomorphic to (kG)*. H is shown to be isomorphic to its linear dual.
Show less  Date Issued
 1988, 1988
 Identifier
 AAI8909946, 3161752, FSDT3161752, fsu:77951
 Format
 Document (PDF)
 Title
 FREENESS OF HOPF ALGEBRAS OVER GROUPLIKE SUBALGEBRAS.
 Creator

ZOELLER, MARTHA BETTINA., Florida State University
 Abstract/Description

Throughout, H is a Hopf algebra over a field k of characteristic p, G(H) is the group of grouplikes of H and L is any subgroup of G(H). We denote the antipode of H by S. We investigate the freeness of Hopf algebras as modules over their group algebras of grouplikes., In chapter II we consider semisimple group algebras kL. We prove that for finite dimensional H all nonzero objects in the category (' )(, ) of left (H,kL)Hopf modules are free kLmodules. We also prove this in the case when S('2...
Show moreThroughout, H is a Hopf algebra over a field k of characteristic p, G(H) is the group of grouplikes of H and L is any subgroup of G(H). We denote the antipode of H by S. We investigate the freeness of Hopf algebras as modules over their group algebras of grouplikes., In chapter II we consider semisimple group algebras kL. We prove that for finite dimensional H all nonzero objects in the category (' )(, ) of left (H,kL)Hopf modules are free kLmodules. We also prove this in the case when S('2) = id. Hence, for a finite dimensional H, the number of onedimensional ideals divides the dimension of H and the order of S divides 4(.)dimension of H., In chapter III we prove that a finite dimensional H is a free kmodule for any g (ELEM) G(H), even if p divides the order of g. Further we establish that a finite dimensional H is a free kLmodule if and only if H is a free kAmodule for any elementary abelian psubgroup A of L., In chapter IV we prove that a finite dimensional H over an algebraically closed field k of characteristic p is a free kLmodule, if H does not contain any simple subcoalgebra of dimension (lp)('2) for any natural number 1 (GREATERTHEQ) 2. Further we construct an example of an infinite dimensional H showing that not all objects in (' )(, ) are free kLmodules. Finally we show that any infinite dimensional H is a free kLmodule, if L is an infinite group which contains no nontrivial finite subgroup. Also, if the dimension of H equals the dimension of the coradical of H, then H is a free module over any of its semisimple group algebras k where g (ELEM) G(H).
Show less  Date Issued
 1985, 1985
 Identifier
 AAI8605802, 3086283, FSDT3086283, fsu:75766
 Format
 Document (PDF)
 Title
 Fundamental problems in computational acoustics.
 Creator

Dong, Zhong., Florida State University
 Abstract/Description

High order finite difference schemes are generally less dispersive, less dissipative and more isotropic than low order schemes. They are, therefore, better suited for the solution of wave propagation problems. High order schemes, however, support spurious numerical waves which have no relationship to the waves of the original partial differential equations. The large stencils associated with the high order schemes also make the implementation of boundary conditions more difficult. A number of...
Show moreHigh order finite difference schemes are generally less dispersive, less dissipative and more isotropic than low order schemes. They are, therefore, better suited for the solution of wave propagation problems. High order schemes, however, support spurious numerical waves which have no relationship to the waves of the original partial differential equations. The large stencils associated with the high order schemes also make the implementation of boundary conditions more difficult. A number of fundamental difficulties which occur when high order finite difference schemes are used to solve computational aeroacoustics and flow problems are investigated and resolved. The research work includes: (a) Development of an artificial selective damping technique for the elimination of spurious numerical waves; (b) Formation of a set of solid wall boundary conditions for high order finite difference schemes; (c) Design of a family of multidomain multipletimestep high order finite difference algorithms for the solution of acoustics and flow problems with large disparate length scales. A sequence of direct numerical simulations are performed to demonstrate the effectiveness of all the proposed methods.
Show less  Date Issued
 1994, 1994
 Identifier
 AAI9432616, 3088391, FSDT3088391, fsu:77196
 Format
 Document (PDF)