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 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
 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
 The Influence of RET's on Elementary and Secondary Teachers' Views of Scientific Inquiry.
 Creator

Bahbah, Sibel, Golden, Barry W. (Barry Wade), Roseler, Katrina, Enderle, Patrick, Saka, Yavuz, Southerland, Sherry A.
 Abstract/Description

This study explores inservice elementary and secondary science teachers' conceptions of the Nature of Scientific Inquiry and the influence participation in two different Research Experience for Teacher (RET) had on these conceptions. Participant teachers attended one of two six week RET programs in which they worked with scientists to engage in scientific inquiry. Before and after the RETs, teachers completed the Views of Scientific Inquiry (VOSI) questionnaire. Teachers' answers were...
Show moreThis study explores inservice elementary and secondary science teachers' conceptions of the Nature of Scientific Inquiry and the influence participation in two different Research Experience for Teacher (RET) had on these conceptions. Participant teachers attended one of two six week RET programs in which they worked with scientists to engage in scientific inquiry. Before and after the RETs, teachers completed the Views of Scientific Inquiry (VOSI) questionnaire. Teachers' answers were analyzed to determine the degree of sophistication of their understanding of five facets of scientific inquiry. Both elementary and secondary teacher participants showed improvement in their understanding of nature of scientific inquiry as a result of program participation, and both programs were successful in supporting the development of inquiry conceptions, although secondary science teachers started and finished the RET's with a more sophisticated understandings of scientific inquiry. Areas of improvement for elementary teachers included the role of questions in science and the role subjectivity and creativity play in the processes of science, and for secondary teachers growth was seen in the role of questions, the relationship of data and evidence, the distinction of experiments and other means of investigations, and the varied methods of science. Implications of these results are discussed.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_ste_faculty_publications0014, 10.5539/ies.v6n1p117
 Format
 Citation
 Title
 Understanding the Induction of a Science Teacher: The Interaction of Identity and Context.
 Creator

Saka, Yavuz, Southerland, Sherry A., Kittleson, Julie, Hunter, Todd
 Abstract/Description

The demanding first years of teaching are a time when many teachers leave the teaching profession or discard the reformminded practice emphasized in teacher preparation. If we are to lessen teacher attrition and more effectively support teachers during their development, a better understanding of what occurs during their induction into the profession is needed. The question that drove this research was what factors influence how a beginning science teacher negotiates entry into teaching?...
Show moreThe demanding first years of teaching are a time when many teachers leave the teaching profession or discard the reformminded practice emphasized in teacher preparation. If we are to lessen teacher attrition and more effectively support teachers during their development, a better understanding of what occurs during their induction into the profession is needed. The question that drove this research was what factors influence how a beginning science teacher negotiates entry into teaching? Specifically, we sought to understand how a beginning science teacher's identities interact with the teaching context, how this interactions shapes his use of reform minded teaching practice, and how the negotiation of identity, context and practice influence a novice teacher's employment decisions. The study involved two years of data collection; data included classroom and school observations, questionnaires, interviews, and teaching artifacts (such as lesson plans and assessments). The results demonstrate how conflicts in identities, institutional expectations, and personal dispositions of this novice influenced his transition in becoming a member of his school community. Implications of these interactions for teacher preparation and support are provided.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_ste_faculty_publications0012, 10.1007/s1116501293105
 Format
 Citation
 Title
 A longitudinal study on predictors of early calculation development among young children at risk for learning difficulties.
 Creator

Peng, Peng, Namkung, Jessica M, Fuchs, Douglas, Fuchs, Lynn S, Patton, Samuel, Yen, Loulee, Compton, Donald L, Zhang, Wenjuan, Miller, Amanda, Hamlett, Carol
 Abstract/Description

The purpose of this study was to explore domaingeneral cognitive skills, domainspecific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young children with learning difficulties. Participants were 176 children identified with reading and mathematics difficulties at the beginning of first grade. Data were collected on working memory, language, nonverbal reasoning, processing speed, decoding, numerical...
Show moreThe purpose of this study was to explore domaingeneral cognitive skills, domainspecific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young children with learning difficulties. Participants were 176 children identified with reading and mathematics difficulties at the beginning of first grade. Data were collected on working memory, language, nonverbal reasoning, processing speed, decoding, numerical competence, incoming calculations, socioeconomic status, and gender at the beginning of first grade and on calculation performance at four time points: the beginning of first grade, the end of first grade, the end of second grade, and the end of third grade. Latent growth modeling analysis showed that numerical competence, incoming calculation, processing speed, and decoding skills significantly explained the variance in calculation performance at the beginning of first grade. Numerical competence and processing speed significantly explained the variance in calculation performance at the end of third grade. However, numerical competence was the only significant predictor of calculation development from the beginning of first grade to the end of third grade. Implications of these findings for early calculation instructions among young atrisk children are discussed.
Show less  Date Issued
 20161201
 Identifier
 FSU_pmch_27572520, 10.1016/j.jecp.2016.07.017, PMC5052117, 27572520, 27572520, S00220965(16)301059
 Format
 Citation
 Title
 ON THE RAUTOMORPHISMS OF R(X).
 Creator

DOWLEN, MARY MARGARET., Florida State University
 Abstract/Description

Throughout, R is a commutative ring with identity and X is an indeterminate over R. We consider R{X}, the polynomial ring in one indeterminate over R, and G(R), the group of Rautomorphisms of R{X}. In particular, we consider the subring of R{X} left fixed by the group G(R), denoted by R{X}('G(R)). Let B(R) be the subgroup of G(R) such that (sigma) (ELEM) B(R) if and only if (sigma)(X) = a + bX, b a unit of R. If R is reduced, then G(R) = B(R); otherwise, B(R) (LHOOK) G(R). We prove in...
Show moreThroughout, R is a commutative ring with identity and X is an indeterminate over R. We consider R{X}, the polynomial ring in one indeterminate over R, and G(R), the group of Rautomorphisms of R{X}. In particular, we consider the subring of R{X} left fixed by the group G(R), denoted by R{X}('G(R)). Let B(R) be the subgroup of G(R) such that (sigma) (ELEM) B(R) if and only if (sigma)(X) = a + bX, b a unit of R. If R is reduced, then G(R) = B(R); otherwise, B(R) (LHOOK) G(R). We prove in Chapter I that R{X}('G(R)) = R{X}('B(R))., In Chapter I we also prove that for R to be properly contained in R{X}('G(R)), it is necessary that R/M is a finite field for some maximal ideal M of R. Hence, if R is a quasilocal ring with maximal ideal M and R/M is infinite, then R{X}('G(R)) = R., Let R be a quasilocal ring with maximal ideal M such that R/M is isomorphic to the Galois field with p('s) elements, where p is a prime integer and s (ELEM) Z('+). In Chapter II, we show that, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI), where, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI), In particular, we determine Z(,n){X}('G(Zn)) for n (ELEM) Z('+). Moreover, we prove that R{X}('G(R)) contains a nonconstant monic polynomial if and only if R is a 0dimensional SFTring., In Chapter III, we investigate R{X}('G(R)) for a von Neumann regular ring R. We obtain equivalent conditions for R{X}('G(R)) to contain a nonconstant monic polynomial; one of these is that {card(R/M)} is bounded for all maximal ideals M of R. Moreover, we prove that R is properly contained in R{X}('G(R)) if and only if R has a direct summand S such that S{X}('G(S)) contains a nonconstant monic polynomial. Finally, in Chapter III we construct a von Neumann regular ring B such that B/M is finite for infinitely many maximal ideals M of B, but B{X}('G(B)) = B., In Chapter IV, we show that for any commutative ring R with identity, R{X}('G(R)) contains a nonconstant monic polynomial if and only if R is 0dimensional, card(R/M) < N for some N (ELEM) Z('+) and for all maximal ideals M of R, and nilpotent elements have bounded order of nilpotency.
Show less  Date Issued
 1982, 1982
 Identifier
 AAI8218637, 3085307, FSDT3085307, fsu:74802
 Format
 Document (PDF)
 Title
 A Spectral Element Method to Price Single and MultiAsset European Options.
 Creator

Zhu, Wuming, Kopriva, David A., Huﬀer, Fred, Case, Bettye Anne, Kercheval, Alec N., Okten, Giray, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

We develop a spectral element method to price European options under the BlackScholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre polynomial expansions to approximate the option price represented pointwise on a GaussLobatto mesh within each element. This piecewise polynomial approximation allows an exact representation of the nonsmooth initial condition. For options with one asset under...
Show moreWe develop a spectral element method to price European options under the BlackScholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre polynomial expansions to approximate the option price represented pointwise on a GaussLobatto mesh within each element. This piecewise polynomial approximation allows an exact representation of the nonsmooth initial condition. For options with one asset under the jump diffusion model, the convolution integral is approximated by high order GaussLobatto quadratures. A second order implicit/explicit (IMEX) approximation is used to integrate in time, with the convolution integral integrated explicitly. The use of the IMEX approximation in time means that only a block diagonal, rather than full, system of equations needs to be solved at each time step. For options with two variables, i.e., two assets under the BlackScholes model or one asset under the stochastic volatility model, the domain is subdivided into quadrilateral elements. Within each element, the expansion basis functions are chosen to be tensor products of the Legendre polynomials. Three iterative methods are investigated to solve the system of equations at each time step with the corresponding second order time integration schemes, i.e., IMEX and CrankNicholson. Also, the boundary conditions are carefully studied for the stochastic volatility model. The method is spectrally accurate (exponentially convergent) in space and second order accurate in time for European options under all the three models. Spectral accuracy is observed in not only the solution, but also in the Greeks.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0513
 Format
 Thesis
 Title
 Modeling the Folding Pattern of the Cerebral Cortex.
 Creator

Striegel, Deborah A., Hurdal, Monica K., Steinbock, Oliver, Quine, Jack, Sumners, DeWitt, Bertram, Richard, Department of Mathematics, Florida State University
 Abstract/Description

The mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions and one recent model is the intermediate progenitor model. The intermediate progenitor (IP) model describes a local chemicallydriven scenario, where an increase in intermediate progenitor cells in the subventricular zone (an area surrounding the lateral ventricles) correlates to gyral formation. This dissertation presents...
Show moreThe mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions and one recent model is the intermediate progenitor model. The intermediate progenitor (IP) model describes a local chemicallydriven scenario, where an increase in intermediate progenitor cells in the subventricular zone (an area surrounding the lateral ventricles) correlates to gyral formation. This dissertation presents the Global Intermediate Progenitor (GIP) model, a theoretical biological model that uses features of the IP model and further captures global characteristics of cortical pattern formation. To illustrate how global features can effect the development of certain patterns, a mathematical model that incorporates a Turing system is used to examine pattern formation on a prolate spheroidal surface. Pattern formation in a biological system can be studied with a Turing reactiondiffusion system which utilizes characteristics of domain size and shape to predict which pattern will form. The GIP model approximates the shape of the lateral ventricle with a prolate spheroid. This representation allows the capture of a key shape feature, lateral ventricular eccentricity, in terms of the focal distance of the prolate spheroid. A formula relating domain scale and focal distance of a prolate spheroidal surface to specific prolate spheroidal harmonics is developed. This formula allows the prediction of pattern formation with solutions in the form of prolate spheroidal harmonics based on the size and shape of the prolate spheroidal surface. By utilizing this formula a direct correlation between the size and shape of the lateral ventricle, which drives the shape of the ventricular zone, and cerebral cortical folding pattern formation is found. This correlation is illustrated in two different applications: (i) how the location and directionality of the initial cortical folds change with respect to evolutionary development and (ii) how the initial folds change with respect to certain diseases, such as Microcephalia Vera and Megalencephaly Polymicrogyria Polydactyly with Hydrocephalus. The significance of the model, presented in this dissertation, is that it elucidates the consistency of cortical patterns among healthy individuals within a species and addresses interspecies variability based on global characteristics. This model provides a critical piece to the puzzle of cortical pattern formation.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd0394
 Format
 Thesis
 Title
 Peridynamic Multiscale Models for the Mechanics of Materials: Constitutive Relations, Upscaling from Atomistic Systems, and Interface Problems.
 Creator

Seleson, Pablo D, Gunzburger, Max, Rikvold, Per Arne, ElAzab, Anter, Peterson, Janet, Shanbhag, Sachin, Lehoucq, Richard B., Parks, Michael L., Department of Scientific...
Show moreSeleson, Pablo D, Gunzburger, Max, Rikvold, Per Arne, ElAzab, Anter, Peterson, Janet, Shanbhag, Sachin, Lehoucq, Richard B., Parks, Michael L., Department of Scientific Computing, Florida State University
Show less  Abstract/Description

This dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the statebased peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models,...
Show moreThis dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the statebased peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models, establishing a hierarchy that reveals that some models are special cases of others. Furthermore, this allows for the modulation of the strength of non local interactions, even for a fixed radius of interactions between material points in the peridynamics model. The multiscale aspect of peridynamics is demonstrated through its connections to molecular dynamics. Using higherorder gradient models, it is shown that peridynamics can be viewed as an upscaling of molecular dynamics, preserving the relevant dynamics under appropriate choices of length scales. The statebased peridynamic model is shown to be appropriate for the description of multiscale and multimodel systems. A formulation for nonlocal interface problems involving scalar fields is presented, and derivations of non local transmission conditions are derived. Specializations that describe local, non local, and local/non local transmission conditions are considered. Moreover, the convergence of the non local transmission conditions to their classical local counterparts is shown. In all cases, results are illustrated by numerical experiments.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0273
 Format
 Thesis
 Title
 QuasiMonte Carlo and Genetic Algorithms with Applications to Endogenous Mortgage Rate Computation.
 Creator

Shah, Manan, Okten, Giray, Goncharov, Yevgeny, Srinivasan, Ashok, Bellenot, Steve, Case, Bettye Anne, Kercheval, Alec, Kopriva, David, Nichols, Warren, Department of Mathematics...
Show moreShah, Manan, Okten, Giray, Goncharov, Yevgeny, Srinivasan, Ashok, Bellenot, Steve, Case, Bettye Anne, Kercheval, Alec, Kopriva, David, Nichols, Warren, Department of Mathematics, Florida State University
Show less  Abstract/Description

In this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digitpermutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions...
Show moreIn this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digitpermutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions for the test problems considered. Next, we use randomized quasiMonte Carlo methods to numerically solve a onefactor mortgage model expressed as a stochastic fixedpoint problem. Finally, we show that this mortgage model coincides with and is computationally faster than Citigroup's MOATS model, which is based on a binomial tree approach.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0297
 Format
 Thesis
 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
 On the motion of a rigid cylinder parallel to its axis in a rotating electrically conducting fluid.
 Creator

Ruan, Kezhi., Florida State University
 Abstract/Description

In an effort to understand better the flow in the core of the Earth, we investigate the steady rise of an infinitely long vertical rigid cylinder parallel to its axis in a rotating electrically conducting fluid in the presence of uniform prescribed transverse magnetic field. The rotation and magneticfield vectors have arbitrary orientation. We suppose the circular cylinder is forced to rise with a constant speed and investigate the structure of the flow and calculate the drag on the cylinder...
Show moreIn an effort to understand better the flow in the core of the Earth, we investigate the steady rise of an infinitely long vertical rigid cylinder parallel to its axis in a rotating electrically conducting fluid in the presence of uniform prescribed transverse magnetic field. The rotation and magneticfield vectors have arbitrary orientation. We suppose the circular cylinder is forced to rise with a constant speed and investigate the structure of the flow and calculate the drag on the cylinder. The flow structure is found by solving a twodimensional (independent of the axial coordinate) mixed boundary value problem. Approximate analytic solutions for velocity field and perturbed magnetic field are obtained. The buoyancy driven rise speed of the cylinder is calculated. The results are consistent with the those derived from Moore and Saffman (1969) and given by Hasimoto (1960) as limiting cases. The numerical value of dimensional rise speed obtained is in good agreement with the typically quoted rise speed in geophysics.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9525925, 3088642, FSDT3088642, fsu:77444
 Format
 Document (PDF)
 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
 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
 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
 Variance Gamma Pricing of American Futures Options.
 Creator

Yoo, Eunjoo, Nolder, Craig A., Huﬀer, Fred, Case, Bettye Anne, Kercheval, Alec N., Quine, Jack, Department of Mathematics, Florida State University
 Abstract/Description

In financial markets under uncertainty, the classical BlackScholes model cannot explain the empirical facts such as fat tails observed in the probability density. To overcome this drawback, during the last decade, Lévy process and stochastic volatility models were introduced to financial modeling. Today crude oil futures markets are highly volatile. It is the purpose of this dissertation to develop a mathematical framework in which American options on crude oil futures contracts are priced...
Show moreIn financial markets under uncertainty, the classical BlackScholes model cannot explain the empirical facts such as fat tails observed in the probability density. To overcome this drawback, during the last decade, Lévy process and stochastic volatility models were introduced to financial modeling. Today crude oil futures markets are highly volatile. It is the purpose of this dissertation to develop a mathematical framework in which American options on crude oil futures contracts are priced more effectively than by current methods. In this work, we use the Variance Gamma process to model the futures price process. To generate the underlying process, we use a random tress method so that we evaluate the option prices at each tree node. Through fifty replications of a random tree, the averaged value is taken as a true option price. Pricing performance using this method is accessed using American options on crude oil commodity contracts from December 2003 to November 2004. In comparison with the Variance Gamma model, we price using the BlackScholes model as well. Over the entire sample period, a positive skewness and high kurtosis, especially in the shortterm options, are observed. In terms of pricing errors, the Variance Gamma process performs better than the BlackScholes model for the American options on crude oil commodities.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0691
 Format
 Thesis
 Title
 A Comparison Study of Principal Component Analysis and Nonlinear Principal Component Analysis.
 Creator

Wu, Rui, Magnan, Jerry F., Bellenot, Steven, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

In the field of data analysis, it is important to reduce the dimensionality of data, because it will help to understand the data, extract new knowledge from the data, and decrease the computational cost. Principal Component Analysis (PCA) [1, 7, 19] has been applied in various areas as a method of dimensionality reduction. Nonlinear Principal Component Analysis (NLPCA) [1, 7, 19] was originally introduced as a nonlinear generalization of PCA. Both of the methods were tested on various...
Show moreIn the field of data analysis, it is important to reduce the dimensionality of data, because it will help to understand the data, extract new knowledge from the data, and decrease the computational cost. Principal Component Analysis (PCA) [1, 7, 19] has been applied in various areas as a method of dimensionality reduction. Nonlinear Principal Component Analysis (NLPCA) [1, 7, 19] was originally introduced as a nonlinear generalization of PCA. Both of the methods were tested on various artificial and natural datasets sampled from: "F(x) = sin(x) + x", the Lorenz Attractor, and sunspot data. The results from the experiments have been analyzed and compared. Generally speaking, NLPCA can explain more variance than a neural network PCA (NN PCA) in lower dimensions. However, as a result of increasing the dimension, the NLPCA approximation will eventually loss its advantage. Finally, we introduce a new combination of NN PCA and NLPCA, and analyze and compare its performance.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd0704
 Format
 Thesis
 Title
 Numerical Methods for Portfolio Risk Estimation.
 Creator

Zhang, Jianke, Kercheval, Alec, Huﬀer, Fred, Gallivan, Kyle, Beaumont, Paul, Nichols, Warren, Department of Mathematics, Florida State University
 Abstract/Description

In portfolio risk management, a global covariance matrix forecast often needs to be adjusted by changing diagonal blocks corresponding to specific submarkets. Unless certain constraints are obeyed, this can result in the loss of positive definiteness of the global matrix. Imposing the proper constraints while minimizing the disturbance of offdiagonal blocks leads to a nonconvex optimization problem in numerical linear algebra called the Weighted Orthogonal Procrustes Problem. We analyze...
Show moreIn portfolio risk management, a global covariance matrix forecast often needs to be adjusted by changing diagonal blocks corresponding to specific submarkets. Unless certain constraints are obeyed, this can result in the loss of positive definiteness of the global matrix. Imposing the proper constraints while minimizing the disturbance of offdiagonal blocks leads to a nonconvex optimization problem in numerical linear algebra called the Weighted Orthogonal Procrustes Problem. We analyze and compare two local minimizing algorithms and offer an algorithm for global minimization. Our methods are faster and more effective than current numerical methods for covariance matrix revision.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd0542
 Format
 Thesis
 Title
 MANIFOLD FACTORS THAT ARE THE CELLLIKE IMAGE OF A MANIFOLD.
 Creator

KUTTER, MARY YEILDING., Florida State University
 Abstract/Description

F. Waldhausen defines a kfold end structure on a space X to be an ordered ktuple of continuous maps xj :X(>)R('+), 1 (LESSTHEQ) j (LESSTHEQ) k (where R('+) is the euclidean half line) yielding a map x:X(>)(R)('k). The pairs (X,x) are made into the category E('k) of spaces with kfold end structure. Attachments and expansions in E('k) are defined by induction on k, where elementary attachments and expansions in E('0) have their usual meaning. For Z (epsilon) E('k), the category E('k)/Z...
Show moreF. Waldhausen defines a kfold end structure on a space X to be an ordered ktuple of continuous maps xj :X(>)R('+), 1 (LESSTHEQ) j (LESSTHEQ) k (where R('+) is the euclidean half line) yielding a map x:X(>)(R)('k). The pairs (X,x) are made into the category E('k) of spaces with kfold end structure. Attachments and expansions in E('k) are defined by induction on k, where elementary attachments and expansions in E('0) have their usual meaning. For Z (epsilon) E('k), the category E('k)/Z consists of pairs (X,i) where i:Z(>)X is an inclusion in E('k) such that there exists an attachment from i(z) to X. And E('k)//Z is the category whose objects are triples (X,i,r) with (X,i) (epsilon) E('k)/z and r:X(>)Z a retraction. An infinite complex over Z is a sequence of inclusions in E('k)//Z, X = {X(,1))(Y,y) in E('k) can be madebounded with respect to equivalent kfold end structures x',y' onX,Y respectively. When X (epsilon) S(,1)(R('k)), that fact can be used to extendthe guaranteed deformation X(SQUIGARR)R('k) in E('k) to a proper deformation(')X(SQUIGARR)D('k) where, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI), is the associated compactification of X. It is shown that after embedding (')X in R('n) for n large enough, and choosing a regular neighborhood (')N of (')X, that ((')N,D('k)) is a proper unknotted ball pair. The result proves, when R('k) is given the natural product kfold end structure, Waldhausen's group S(,1)(R('k)) = 0. An exact sequence established by M. Petty is applied to show S(,0)(R('k)) is also trivial. As a consequence, we show that when X is a generalized qmanifold (q (GREATERTHEQ) 5) with singular set S(X) a polyhedron, XxR a piecewiselinear (q+1)manifold, then X is the celllike image of a manifold.
Show less  Date Issued
 1982, 1982
 Identifier
 AAI8306166, 3085519, FSDT3085519, fsu:75011
 Format
 Document (PDF)
 Title
 A NUMERICAL AND ANALYTICAL STUDY OF DRAG ON A SPHERE IN OSEEN'S APPROXIMATION.
 Creator

LEE, SANG MYUNG., Florida State University
 Abstract/Description

We have investigated the properties of the drag coefficient C(,D) of a sphere according to Oseen's linearization of the equations of viscous incompressible flow. We have treated C(,D) as a complex function of complex Reynolds number with an aim of determining its asymptotic behavior as R(>)(INFIN). C(,D) has a doubly infinite array of simple poles in the left half complex Rplane, each of which lies close to one of the zeros of the spherical Bessel Function K(,m+1/2)(R), for some positive...
Show moreWe have investigated the properties of the drag coefficient C(,D) of a sphere according to Oseen's linearization of the equations of viscous incompressible flow. We have treated C(,D) as a complex function of complex Reynolds number with an aim of determining its asymptotic behavior as R(>)(INFIN). C(,D) has a doubly infinite array of simple poles in the left half complex Rplane, each of which lies close to one of the zeros of the spherical Bessel Function K(,m+1/2)(R), for some positive integer m. These zeros of K(,m+1/2)(R) are the poles of the heat transfer coefficient C(,H)(R) that arises from a simple problem studied by Illingworth (1963). Wu's (1956) analysis of a shortwave scattering problem shows that C(,H)(R) has, for large R, an asymptotic expansion in powers of R('2/3). Numerical computations showed that the same form of expansion works well for C(,D)(R). However, the asymptotic behavior of C(,D)(R) is represented better still by including, in the expansion, an additional term that decays more slowly than R('2/3). The coefficients of this(' )presumed expansion have been estimated by fitting values of C(,D)(R) in the interval 5 < R < 21., The(' )smallReynoldsnumber series for C(,D)(R) has also been extended to 66 terms in double precision. The validity and effectiveness of the techniques used by Van Dyke in extending and improving this series, which is known to be valid only within (VBAR)R(VBAR) = 1.04543, have been examined.
Show less  Date Issued
 1984, 1984
 Identifier
 AAI8501833, 3085973, FSDT3085973, fsu:75459
 Format
 Document (PDF)
 Title
 A STUDY OF STRONG SRINGS AND PRUEFER VMULTIPLICATION DOMAINS.
 Creator

MALIK, SAROJ BALA., The Florida State University
 Abstract/Description

In this work two types of rings have been studied, strong Srings and Prufer vmultiplication domains. Let R be a Prufer domain then R{X} is a strong Sring. For an integrally closed domain R, each tideal is a finite type videal if and only if each prime tideal is a finite type videal. The semigroup ring R{X;S} is a Prufer vmultiplication domain if and only if R and K{X;S} are. A PVMD is an Sdomain.
 Date Issued
 1979, 1979
 Identifier
 AAI8017668, 2989587, FSDT2989587, fsu:74094
 Format
 Document (PDF)