Current Search: Hussaini, M. Yousuff (x)
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 Title
 Optimal Unified Combination Rule In Application Of Dempstershafer Theory To Lung Cancer Radiotherapy Dose Response Outcome Analysis.
 Creator

He, Yanyan, Hussaini, M. Yousuff, Gong, Yutao U. T., Xiao, Ying
 Abstract/Description

Our previous study demonstrated the application of the DempsterShafer theory of evidence to dose/volume/outcome data analysis. Specifically, it provided Yager's rule to fuse data from different institutions pertaining to radiotherapy pneumonitis versus mean lung dose. The present work is a followon study that employs the optimal unified combination rule, which optimizes data similarity among independent sources. Specifically, we construct belief and plausibility functions on the lung cancer...
Show moreOur previous study demonstrated the application of the DempsterShafer theory of evidence to dose/volume/outcome data analysis. Specifically, it provided Yager's rule to fuse data from different institutions pertaining to radiotherapy pneumonitis versus mean lung dose. The present work is a followon study that employs the optimal unified combination rule, which optimizes data similarity among independent sources. Specifically, we construct belief and plausibility functions on the lung cancer radiotherapy dose outcome datasets, and then apply the optimal unified combination rule to obtain combined belief and plausibility, which bound the probabilities of pneumonitis incidence. To estimate the incidence of pneumonitis at any value of mean lung dose, we use the LymanKutcherBurman (LKB) model to fit the combined belief and plausibility curves. The results show that the optimal unified combination rule yields a narrower uncertainty range (as represented by the beliefplausibility range) than Yager's rule, which is also theoretically proven.
Show less  Date Issued
 2016
 Identifier
 FSU_libsubv1_wos_000368341200002, 10.1120/jacmp.v17i1.5737
 Format
 Citation
 Title
 Supersonic Jet Noise and Its Reduction Using Microjet Injection.
 Creator

Greska, Brenton J., Krothapalli, Anjaneyulu, Hussaini, M. Yousuﬀ, Alvi, Farrukh, Hollis, Pat, Seiner, John M., Department of Mechanical Engineering, Florida State University
 Abstract/Description

A twopart experimental study was conducted in order to investigate and then reduce the noise generated by hightemperature supersonic jets. The first part of the study focused on the noise generated by supersonic jets at Mach numbers ranging from 1.2 to 2.2 and temperatures ranging from 290 K to 1366 K. Through the use of a newly defined Mach number, it was found that the jet noise in the peak radiation direction is a function of the velocity to the eighth power for subsonic jets. For...
Show moreA twopart experimental study was conducted in order to investigate and then reduce the noise generated by hightemperature supersonic jets. The first part of the study focused on the noise generated by supersonic jets at Mach numbers ranging from 1.2 to 2.2 and temperatures ranging from 290 K to 1366 K. Through the use of a newly defined Mach number, it was found that the jet noise in the peak radiation direction is a function of the velocity to the eighth power for subsonic jets. For supersonic jets, the noise is a function of the velocity cubed. In the normal direction, the jet noise demonstrates a dependence on the velocity to the sixth and fourth powers. Based on these results, a simple scheme was developed for predicting the directivity of the jet noise in the aft quadrant. A universality of the frequency spectra was also observed in the peak radiation and normal directions. The second part of the study was focused on the use of microjet injection as a means of supersonic jet noise reduction. It was determined that the primary effect of microjet injection is the reduction of Mach wave radition due to the generation of strong streamwise vortices in the shear layer of the jet. However, through the use of waterbased microjets additional reductions in the turbulence levels were obtained. It was found that the effectiveness of the microjets in the peak radiation direction is dependent on the momentum ratio between the microjets and the main jet. The results from two fullscale jet engine tests were used to validate the results that were obtained in the laboratory.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3966
 Format
 Thesis
 Title
 Discontinuous Galerkin Spectral Element Approximations on Moving Meshes for Wave Scattering from Reflective Moving Boundaries.
 Creator

AcostaMinoli, Cesar Augusto, Kopriva, David, Srivastava, Anuj, Hussaini, M. Yousuﬀ, Sussman, Mark, Ewald, Brian, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation develops and evaluates a high order method to compute wave scattering from moving boundaries. Specifically, we derive and evaluate a Discontinuous Galerkin Spectral elements method (DGSEM) with Arbitrary Lagrangian Eulerian (ALE) mapping to compute conservation laws on moving meshes and numerical boundary conditions for Maxwell's equations, the linear Euler equations and the nonlinear Euler gasdynamics equations to calculate the numerical flux on reflective moving...
Show moreThis dissertation develops and evaluates a high order method to compute wave scattering from moving boundaries. Specifically, we derive and evaluate a Discontinuous Galerkin Spectral elements method (DGSEM) with Arbitrary Lagrangian Eulerian (ALE) mapping to compute conservation laws on moving meshes and numerical boundary conditions for Maxwell's equations, the linear Euler equations and the nonlinear Euler gasdynamics equations to calculate the numerical flux on reflective moving boundaries. We use one of a family of explicit time integrators such as AdamsBashforth or low storage explicit RungeKutta. The approximations preserve the discrete metric identities and the Discrete Geometric Conservation Law (DGCL) by construction. We present timestep refinement studies with moving meshes to validate the moving mesh approximations. The test problems include propagation of an electromagnetic gaussian plane wave, a cylindrical pressure wave propagating in a subsonic flow, and a vortex convecting in a uniform inviscid subsonic flow. Each problem is computed on a timedeforming mesh with three methods used to calculate the mesh velocities: From exact differentiation, from the integration of an acceleration equation, and from numerical differentiation of the mesh position. In addition, we also present four numerical examples using Maxwell's equations, one example using the linear Euler equations and one more example using nonlinear Euler equations to validate these approximations. These are: reflection of light from a constantly moving mirror, reflection of light from a constantly moving cylinder, reflection of light from a vibrating mirror, reflection of sound in linear acoustics and dipole sound generation by an oscillating cylinder in an inviscid flow.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0111
 Format
 Thesis
 Title
 Singleand MultipleObjective Stochastic Programming Models with Applications to Aerodynamics.
 Creator

Croicu, AnaMaria, Hussaini, M. Yousuﬀ, Srivastava, Anuj, Kopriva, David, Wang, Qi, Department of Mathematics, Florida State University
 Abstract/Description

Deterministic design assumes that there is no uncertainty in the modeling parameters, and as a consequence, there is no variability in the simulation outputs. Therefore, deterministic optimal designs that are obtained without taking into account uncertainty are usually unreliable. This is the case with transonic shape optimization, where the randomness in the cruise Mach number might have significant impact on the optimal geometric design. In this context, a stochastic search turns out to be...
Show moreDeterministic design assumes that there is no uncertainty in the modeling parameters, and as a consequence, there is no variability in the simulation outputs. Therefore, deterministic optimal designs that are obtained without taking into account uncertainty are usually unreliable. This is the case with transonic shape optimization, where the randomness in the cruise Mach number might have significant impact on the optimal geometric design. In this context, a stochastic search turns out to be more appropriate. Approaches to stochastic optimization have followed a variety of modeling philosophies, but little has been done to systematically compare different models. The goal of this thesis is to present a comparison between two stochastic optimization algorithms, with the emphasis on applications, especially on the airfoil shape optimization. Singleobjective and multiobjective optimization programs are analyzed as well. The relationship between the expected minimum value (EMV) criterion and the minimum expected value (MEV) criterion is explored, and it is shown that, under favorable conditions, a better optimal point could be obtained via the EMV approach. Unfortunately, the advantages of using the EMV approach are far outweighed by the prohibitive exorbitant computational cost.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3027
 Format
 Thesis
 Title
 An Experimental Study of a Pulsed Jet Ejector.
 Creator

Choutapalli, Isaac M., Krothapalli, Anjaneyulu, Hussaini, Yousuﬀ, Shih, Chiang, Hollis, Patrick, Department of Mechanical Engineering, Florida State University
 Abstract/Description

The additional thrust required to accelerate a Short/Vertical TakeOff and Landing (S/VTOL) aircraft to flying speed within short distances can be obtained by channeling the engine exhaust through a thrust augmenting ejector. In order to have a viable ejectoraugmented poweredlift for these types of aircraft, two most prevailing challenges need to be addressed  they are high performance and compactness of the ejector. Toward this end, an experimental investigation was carried out using a...
Show moreThe additional thrust required to accelerate a Short/Vertical TakeOff and Landing (S/VTOL) aircraft to flying speed within short distances can be obtained by channeling the engine exhaust through a thrust augmenting ejector. In order to have a viable ejectoraugmented poweredlift for these types of aircraft, two most prevailing challenges need to be addressed  they are high performance and compactness of the ejector. Toward this end, an experimental investigation was carried out using a pulsed jet as the driving source for the ejector configuration. The objectives of the investigation were threefold: first, to demonstrate that a suitably sized ejector with the pulsed jet as the driving source can give substantially higher levels of thrust augmentation (total thrust/primary nozzle thrust) than the steady jet driven ejector of comparable dimensions; second, to identify the characteristics of the pulsed flow that could be helpful in determining the optimal ejector flow conditions for maximizing thrust augmentation. And third, to understand the flow physics behind the thrust augmentation mechanism of the pulsed jet ejector. The first objective was addressed by carrying out direct thrust measurements on the free steady jet, free pulsed jet and the pulsed jet ejector configurations. Within the range of parameters investigated, it has been demonstrated conclusively that for an incompressible pulsed jet (Mj = 0.30) operating at a Strouhal number of around 0.1, thrust augmentation values as high as 1.9 can be obtained with a compact ejector (L/D ~ 3) at an area ratio (ejector inlet area / primary nozzle exit area) of about 11.0. The second objective was addressed by studying the detailed spatiotemporal evolution of the free pulsed jet flow field using phaselocked Particle Image Velocimetry (PIV). The investigation suggests that maximum jet entrainment is achieved when the primary jet Strouhal number is within a range of 0.2 to 0.25. The results further show that the entrainment is mainly dependant on the strength as well as the number of vortex rings present in the flow field. These characteristics helped to define the optimal flow conditions under which maximum mass flow rate into the ejector (and hence maximum ejector thrust augmentation) could be achieved. The results indicate that the thrust augmentation ratio can be improved to about 2.3 with the pulsed jet operating at an optimum Strouhal number of 0.24. Finally, the third objective was addressed by investigating the flow field characteristics of the pulsed jet ejector using phaselocked PIV. Experiments were carried out at three different area ratios that help to define the conditions for maximum thrust augmentation. The results show that in the presence of the ejector duct, the pulsed jet primary vortex induces a secondary vortex on the wall and the strength of the induced vortex depended strongly on the proximity of the ejector wall. At the optimal location where maximum thrust augmentation was observed, the strength of the induced vortex was found to be highest. This pair of the primary and induced vortex establishes an axial pressure gradient within the duct, that convects downstream thus causing an enhanced mass flow rate into the ejector and hence resulting in higher thrust augmentation.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd3634
 Format
 Thesis
 Title
 NonIntrusive Methods for Probablistic Uncertainty Quantification and Global Sensitivity Analysis in Nonlinea Stochastic Phenomena.
 Creator

Liu, Yaning, Hussaini, M. Yousuff, Okten, Giray, Srivastava, Anuj, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

The objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement nonintrusive methods that do not require modification of the programming code of the underlying deterministic model. To avoid the curse of dimensionality, two methods, namely sampling methods and high dimensional model representation are employed to propagate uncertainty and compute global sensitivity indices...
Show moreThe objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement nonintrusive methods that do not require modification of the programming code of the underlying deterministic model. To avoid the curse of dimensionality, two methods, namely sampling methods and high dimensional model representation are employed to propagate uncertainty and compute global sensitivity indices. Variancebased global sensitivity analysis identifies significant and insignificant model parameters. It also provides basis for reducing a model's stochastic dimension by freezing identified insignificant model parameters at their nominal values. The dimensionreduced model can then be analyzed efficiently. We use uncertainty quantification and global sensitivity analysis in three applications. The first application is to the Rothermel wildland surface fire spread model, which consists of around 80 nonlinear algebraic equations and 24 parameters. We find the reduced models for the selected model outputs and apply efficient sampling methods to quantify the uncertainty. High dimensional model representation is also applied for the Rothermel model for comparison. The second application is to a recently developed biological model that describes inflammatory host response to a bacterial infection. The model involves four nonlinear coupled ordinary differential equations and the dimension of the stochastic space is 16. We compute global sensitivity indices for all parameters and build a dimensionreduced model. The sensitivity results, combined with experiments, can improve the validity of the model. The third application quantifies the uncertainty of weather derivative models and investigates model robustness based on global sensitivity analysis. Three commonly used weather derivative models for the daily average temperature are considered. The one which is least influenced by an increase of parametric uncertainty level is identified as robust. In summary, the following contributions are made in this dissertation: 1. The optimization of sensitivity derivative enhanced sampling that guarantees variance reduction and improved estimation of stochastic moments. 2. The combination of optimized sensitivity derivative enhanced sampling with randomized quasiMonte Carlo sampling, and adaptive Monte Carlo sampling, to achieve higher convergence rates. 3. The construction of cutHDMR component functions based on Gauss quadrature points which results in a more accurate surrogate model, derivation of an integral form of low order partial variances based on cutHDMR, and efficient computation of global sensitivity analysis based on cutHDMR. 4. The application of efficient sampling methods, RSHDMR and cutHDMR for the quantification of Rothermel's wildland fire surface spread model. 5. The uncertainty quantification and global sensitivity analysis of a newly developed immune response model with parametric uncertainty. 6. The uncertainty quantification of weather derivative models and the analysis of model robustness based on global sensitivity analysis.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8681
 Format
 Thesis
 Title
 Uncertainty Quantification and Data Fusion Based on DempsterShafer Theory.
 Creator

He, Yanyan, Hussaini, M. Yousuff, Oates, William S., Kopriva, David A., Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

Quantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently nondeterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most welldeveloped nonadditivemeasure theory  the DempsterShafer theory of evidence  is explored for uncertainty quantification and propagation. For ''uncertainty quantification," we propose the MinMax method to construct belief functions to represent uncertainty in...
Show moreQuantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently nondeterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most welldeveloped nonadditivemeasure theory  the DempsterShafer theory of evidence  is explored for uncertainty quantification and propagation. For ''uncertainty quantification," we propose the MinMax method to construct belief functions to represent uncertainty in the information (data set) involving the inseparably mixed type of uncertainties. Using the principle of minimum uncertainty and the concepts of entropy and specificity, the MinMax method specifies a partition of a finite interval on the real line and assigns belief masses to the uniform subintervals. The method is illustrated in a simple example and applied to the total uncertainty quantification in flight plan of two actual flights. For ''uncertainty propagation," we construct belief/probability density functions for the output or the statistics of the output given the belief/probability density functions for the uncertain input variables. Different approaches are introduced for aleatory uncertainty propagation, epistemic uncertainty propagation, and mixed type of uncertainty propagation. The impact of the uncertain input parameters on the model output is studied using these approaches in a simple example of aerodynamic flow: quasionedimensional nozzle flow. In the situation that multiple models are available for the same quantity of interest, the combination rules in the DempsterShafer theory can be utilized to integrate the predictions from the different models. In the present work, we propose a robust and comprehensive procedure to combine multiple bodies of evidence. It is robust in that it can combine multiple bodies of evidence, consistent or otherwise. It is comprehensive in the sense that it examines the bodies of evidence strongly conflicted with others, reconstructs the basic belief mass functions by discounting, and then fuses all the bodies of evidence using an optimally parametrized combination rule. The proposed combination procedure is applied to radiotherapy dose response outcome analysis.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8563
 Format
 Thesis
 Title
 Next Generation Active Materials and Structures for Autonomous Systems.
 Creator

Hays, Michael R., Oates, William, Hussaini, M. Yousuff, Alvi, Farrukh, Hellstrom, Eric, Department of Mechanical Engineering, Florida State University
 Abstract/Description

No abstract at this time.
 Date Issued
 2013
 Identifier
 FSU_migr_etd7413
 Format
 Thesis
 Title
 Computational MultiPhysics Modeling of Adaptive Materials.
 Creator

Cheng, Liang, Oates, William S., Hussaini, M. Yousuﬀ, Hellstrom, Eric, Taira, Kunihiko, Department of Mechanical Engineering, Florida State University
 Abstract/Description

Adaptive materials are typically known as materials that convert one form of energy into another. Wellknown examples include ferroic materials (ferroelectric, ferromagnetic, shape memory alloys), dielectric elastomer, and azobenzene liquid crystal polymer networks. Many of these materials possess the ability to convert electric/magnetic, thermal, or chemical energy into mechanical energy and vice versa. Whereas these materials have been studied extensively, the underlying multiphysics...
Show moreAdaptive materials are typically known as materials that convert one form of energy into another. Wellknown examples include ferroic materials (ferroelectric, ferromagnetic, shape memory alloys), dielectric elastomer, and azobenzene liquid crystal polymer networks. Many of these materials possess the ability to convert electric/magnetic, thermal, or chemical energy into mechanical energy and vice versa. Whereas these materials have been studied extensively, the underlying multiphysics coupling and micro to nanostructure interactions still provide a fertile research area to understand and optimize such materials. This dissertation is focused on the analysis and modeling of specific adaptive materials with particular emphasis on complex electromagnetic interactions and chemical flux in solid materials. We study two kinds of new adaptive materials 1) selfassembling protein nanofibers and 2) photomechanical azobenzene liquid crystal network (azoLCN) films. The formation and evolution of protein nanofibers are quantified using a new phase field modeling framework and are compared to transmission electron microscopy (TEM) measurements and timedependent growth measurements given in the literature. Calculations based on the theoretical framework are implemented numerically using a nonlinear finite element phase field modeling approach that couples AllenCahn and CahnHilliard equations. These results provide a new modeling tool that couples underlying monomer structure with selfassembling nanofiber behavior. In contrast, the azoLCN films also have been studied to understand the photochemical coupling on macroscale deformation. The photoinduced strain of azoLCN films are examined using a large deformation photomechanical shell model to quantify the effect of polarized light interactions with the material. The model comparisons of static deformation illustrate differences in internal photostrain and deformation as a function of composition and external mechanical constraints. Preliminary numerical analysis and comparison with data are presented using the finite element method. This preliminary work has motivated the need for a higher accuracy computational approach to resolve the aforementioned protein selfhealing, photostriction, and more complicated multiphysics conditions. Toward this end, a general fieldcoupled framework for modeling a broad range of adaptive materials is initiated. The aim is to enhance our fundamental knowledge of the fieldcoupled microstructure of solid materials. Both electromagnetic field propagation and microstructure evolution are investigated with particular interest in understanding photomechanical behavior of azoLCNs. Correspondingly, the Maxwell's equations and AllenCahn equation are coupled to simulate the evolution of microstructure under the exposure of electromagnetic waves. The interactions between field and microstructure are effectively quantified within the proposed fieldcoupled system. This numerical framework can be applied to a variety of adaptive materials including azoLCNs as well as other light coupled materials. To further advance our study of adaptive materials and fieldcoupled behavior, the Discontinuous Galerkin Spectral Element Method (DGSEM) is applied. The DGSEM is an excellent numerical method for wave propagation, fluid dynamics, and phase evolution problems due to its higher accuracy and treatment of discontinuities. The DGSEM allows for the discontinuity between the element boundaries using what is known as a Riemann flux condition, the high order polynomials of spectral methods provide high accuracy with less computational penalties. These two characteristics are particularly useful in the computation of the microstructure of adaptive materials due to the complex microstructure and electromagnetic waves of light. We apply the DGSEM to solve the reflection and transmission of electromagnetic waves along the interface of dissimilar materials, transduction of azobenzene liquid crystal isomers, and the respective fieldcoupled characteristics. The numerical solutions shown in this dissertation illustrate the application of DGSEM on complex photomechanically coupled azobenzene liquid crystals. Although the proposed fieldcoupled theory and associated DGSEM algorithm are applicable to model various adaptive microstructures, we utilize this advanced framework to help understand the transcistrans photoisomerization of azobenzene liquid crystal and its interactions with the electromagnetic fields. The numerical solutions disclose the complicated evolution of photoresponsive liquid crystals and attenuation of optical waves and present transient results on a twodimensional domain. An auxiliary differential equation method is introduced to model the attenuated light propagating through the linear dispersive liquid crystal. The transcis, cistrans, and transcistrans transduction are simulated using a vector order phase field method and the DGSEM numerical method. Particularly, the thermodynamic path during different photoisomerization processes is studied by comparing the ratio between polarization and the Landau coefficients. In the fully fieldcoupled implementation for the light and azobenzene liquid crystals, we are able to quantify timedependent behavior associated with electric fields and liquid crystal orientation, which provide useful information for future materials development and engineering applications.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd6895
 Format
 Thesis
 Title
 Massively Parallel Algorithms for CFD Simulation and Optimization on Heterogeneous ManyCore Architectures.
 Creator

Duffy, Austen C., Sussman, Mark, Hussaini, M. Yousuﬀ, Van Engelen, Robert, Cogan, Nick, Gallivan, Kyle, Department of Mathematics, Florida State University
 Abstract/Description

In this dissertation we provide new numerical algorithms for use in conjunction with simulation based design codes. These algorithms are designed and best suited to run on emerging heterogenous computing architectures which contain a combination of traditional multicore processors and new programmable manycore graphics processing units (GPUs). We have developed the following numerical algorithms (i) a new Multidirectional Search (MDS) method for PDE constrained optimization that utilizes a...
Show moreIn this dissertation we provide new numerical algorithms for use in conjunction with simulation based design codes. These algorithms are designed and best suited to run on emerging heterogenous computing architectures which contain a combination of traditional multicore processors and new programmable manycore graphics processing units (GPUs). We have developed the following numerical algorithms (i) a new Multidirectional Search (MDS) method for PDE constrained optimization that utilizes a Multigrid (MG) strategy to accelerate convergence, this algorithm is well suited for use on GPU clusters due to its parallel nature and is more scalable than adjoint methods (ii) a new GPU accelerated point implicit solver for the NASA FUN3D code (unstructured NavierStokes) that is written in the Compute Unified Device Architecture (CUDA) language, and which employs a novel GPU sharing model, (iii) novel GPU accelerated smoothers (developed using PGI Fortran with accelerator compiler directives) used to accelerate the multigrid preconditioned conjugate gradient method (MGPCG) on a single rectangular grid, and (iv) an improved pressure projection solver for adaptive meshes that is based on the MGPCG method which requires fewer grid point calculations and has potential for better scalability on hetergeneous clusters. It is shown that a multigrid  multidirectional search (MGMDS) method can run up to 5.5X faster than the MDS method when used on a one dimensional data assimilation problem. It is also shown that the new GPU accelerated point implicit solver of FUN3D is up to 5.5X times faster than the CPU version and that the solver can perform up to 40% faster on a single GPU being shared by four CPU cores. It is found that GPU accelerated smoothers for the MGPCG method on uniform grids can run over 2X faster than the nonaccelerated versions for 2D problems, and that the new MGPCG pressure projection solver for adaptive grids is up to 4X faster than the previous MG algorithm.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0651
 Format
 Thesis
 Title
 Active Flow Control and Global Stability Analysis of Separated Flow over a NACA 0012 Airfoil.
 Creator

Munday, Phillip M. (Phillip Michael), Taira, Kunihiko, Hussaini, M. Yousuff, Alvi, Farrukh S., Cattafesta, Louis N., Lin, Shangchao, Florida State University, College of...
Show moreMunday, Phillip M. (Phillip Michael), Taira, Kunihiko, Hussaini, M. Yousuff, Alvi, Farrukh S., Cattafesta, Louis N., Lin, Shangchao, Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

The objective of this computational study is to examine and quantify the influence of fundamental flow control inputs in suppressing flow separation over a canonical airfoil. Most flow control studies to this date have relied on the development of actuator technology, and described the control input based on specific actuators. Taking advantage of a computational framework, we generalize the inputs to fundamental perturbations without restricting inputs to a particular actuator. Utilizing...
Show moreThe objective of this computational study is to examine and quantify the influence of fundamental flow control inputs in suppressing flow separation over a canonical airfoil. Most flow control studies to this date have relied on the development of actuator technology, and described the control input based on specific actuators. Taking advantage of a computational framework, we generalize the inputs to fundamental perturbations without restricting inputs to a particular actuator. Utilizing this viewpoint, generalized control inputs aim to aid in the quantification and support the design of separation control techniques. This study in particular independently introduces wallnormal momentum and angular momentum to the separated flow using swirling jets through model boundary conditions. The response of the flow field and the surface vorticity fluxes to various combinations of actuation inputs are examined in detail. By closely studying different variables, the influence of the wallnormal and angular momentum injections on separated flow is identified. As an example, openloop control of fully separated, incompressible flow over a NACA 0012 airfoil at α = 6° and $9° with Re = 23,000 is examined with largeeddy simulations. For the shallow angle of attack α = 6°, the small recirculation region is primarily affected by wallnormal momentum injection. For a larger separation region at α = 9°, it is observed that the addition of angular momentum input to wallnormal momentum injection enhances the suppression of flow separation. Reducing the size of the separated flow region significantly impacts the forces, and in particular reduces drag and increases lift on the airfoil. It was found that the influence of flow control on the small recirculation region (α = 6°) can be sufficiently quantified with the traditional coefficient of momentum. At α = 9°, the effects of wallnormal and angular momentum inputs are captured by modifying the standard definition of the coefficient of momentum, which successfully characterizes suppression of separation and lift enhancement. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the nondimensional swirl number. With the modified coefficient of momentum, this single value is able to categorize controlled flows into separated, transitional, and attached flows. With inadequate control input (separated flow regime), lift decreased compared to the baseline flow. Increasing the modified coefficient of momentum, flow transitions from separated to attached and accordingly results in improved aerodynamic forces. Modifying the spanwise spacing, it is shown that the minimum modified coefficient of momentum input required to begin transitioning the flow is dependent on actuator spacing. The growth (or decay) of perturbations can facilitate or inhibit the influence of flow control inputs. Biglobal stability analysis is considered to further analyze the behavior of control inputs on separated flow over a symmetric airfoil. Assuming a spanwise periodic waveform for the perturbations, the eigenvalues and eigenvectors about a base flow are solved to understand the influence of spanwise variation on the development of the flow. Two algorithms are developed and validated to solve for the eigenvalues of the flow: an algebraic eigenvalue solver (matrix based) and a timestepping algorithm. The matrix based approach is formulated without ever storing the matrices, creating a computationally memory efficient algorithm. Based on the matrix based solver, eigenvalues and eigenvectors are identified for flow over a NACA 0015 airfoil at Re = 200, $600, and $1,000. All three cases contain similar modes, although the growth rate of the leading eigenvalue is decreased with increasing Reynolds number. Three distinct types of modes are found, wake mode, steady mode, and modes of the continuous branch. While this method is limited in the range of Reynolds numbers, these results are used to validate the timestepper approach. Increasing the Reynolds number to Re = 23,000 over a NACA 0012 airfoil, the timestepper method is implemented due to rising computational cost of the matrixbased method. Stability analysis about the timeaveraged flow is performed for spanwise wavenumbers of β = 1$, $10π, and $20π, which the latter two wavenumbers are representative of the spanwise spacing between the actuators. The largest spanwise wavelength (β = 1$) contained unstable modes that ranged from low to high frequency, and a particular unstable lowfrequency mode corresponding to a frequency observed in the lift forces of the baseline largeeddy simulation. For the larger spanwise wavenumbers, β = 10π ($L_z/c = 0.2$) and $20π ($L_z/c = 0.1$), lowfrequency modes were damped and only modes with $f > 5$ were unstable. These results help us gain further insight into the influence of the flow control inputs. Flow control is not implemented in a manner to directly excite specific modes, but does dictate the spanwise wavelengths that can be generated. Comparing the unstable eigenmodes at these two spacings, the larger spanwise spacing ($\beta = 10\pi$) had a greater growth rate for the majority of the unstable modes. The smaller spanwise spacing ($\beta = 20\pi$) has only a single unstable mode with a growth rate an order of magnitude smaller than $\beta = 10\pi$. With the aid of the increased growth rate, perturbations to the flow with a wider spacing become more effective by interacting with natural modes of the flow. Taking advantage of these natural modes allows for decreased input for the wider spanwise spacing. In conclusion, it was shown that the influence of wallnormal and angular momentum inputs on fully separated flow can adequately be described by the modified coefficient of momentum. Through further analysis and the development of a biglobal stability solver, spanwise spacing effects observed in the flow control study can be explained. The findings from this study should aid in the development of more intelligently designed flow control strategies and provide guidance in the selection of flow control actuators.
Show less  Date Issued
 2017
 Identifier
 FSU_2017SP_Munday_fsu_0071E_13086
 Format
 Thesis
 Title
 Active Control of HighSpeed Free Jets Using HighFrequency Excitation.
 Creator

Upadhyay, Puja, Alvi, Farrukh S., Hussaini, M. Yousuff, Kumar, Rajan, Clark, Jonathan E., Gustavsson, Jonas, Florida State University, College of Engineering, Department of...
Show moreUpadhyay, Puja, Alvi, Farrukh S., Hussaini, M. Yousuff, Kumar, Rajan, Clark, Jonathan E., Gustavsson, Jonas, Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

Control of aerodynamic noise generated by highperformance jet engines continues to remain a serious problem for the aviation community. Intense low frequency noise produced by largescale coherent structures is known to dominate acoustic radiation in the aft angles. A tremendous amount of research effort has been dedicated towards the investigation of many passive and active flow control strategies to attenuate jet noise, while keeping performance penalties to a minimum. Unsteady excitation,...
Show moreControl of aerodynamic noise generated by highperformance jet engines continues to remain a serious problem for the aviation community. Intense low frequency noise produced by largescale coherent structures is known to dominate acoustic radiation in the aft angles. A tremendous amount of research effort has been dedicated towards the investigation of many passive and active flow control strategies to attenuate jet noise, while keeping performance penalties to a minimum. Unsteady excitation, an active control technique, seeks to modify acoustic sources in the jet by leveraging the naturallyoccurring flow instabilities in the shear layer. While excitation at a lower range of frequencies that scale with the dynamics of largescale structures, has been attempted by a number of studies, effects at higher excitation frequencies remain severely unexplored. One of the major limitations stems from the lack of appropriate flow control devices that have sufficient dynamic response and/or control authority to be useful in turbulent flows, especially at higher speeds. To this end, the current study seeks to fulfill two main objectives. First, the design and characterization of two highfrequency fluidic actuators ($25$ and $60$ kHz) are undertaken, where the target frequencies are guided by the dynamics of highspeed free jets. Second, the influence of highfrequency forcing on the aeroacoustics of highspeed jets is explored in some detail by implementing the nominally 25 kHz actuator on a Mach 0.9 ($Re_D = 5\times10^5$) free jet flow field. Subsequently, these findings are directly compared to the results of steady microjet injection experiments performed in the same rig and to prior jet noise control studies, where available. Finally, limited acoustic measurements were also performed by implementing the nominally 25 kHz actuators on jets at higher Mach numbers, including shock containing jets, and elevated temperatures. Using lumped element modeling as an initial guide, the current work expands on the previous development of lowfrequency (28 kHz) Resonance Enhanced Microactuators (REM) to design actuators that are capable of producing high amplitude pulses at much higher frequencies. Extensive benchtop characterization, using acoustic measurements as well as optical diagnostics using a high resolution microschlieren setup, is employed to characterize the flow properties and dynamic response of these actuators. The actuators produced highamplitude output a range of frequencies, $20.327.8$ kHz and $54.878.2$ kHz, respectively. In addition to providing information on the actuator flow physics and performances at various operating conditions, the benchtop study serves to develop relatively easytointegrate, highfrequency actuators for active control of highspeed jets for noise reduction. Following actuator characterization studies, the nominally 25 kHz ($St_{DF} \approx 2.2$) actuators are implemented on a Mach 0.9 free jet flow field. Eight actuators are azimuthally distributed at the nozzle exit to excite the initial shear layer at frequencies that are approximately an order of magnitude higher compared to the \textit{jet preferred frequency}, $St_P \approx 0.20.3$. The influence of control on the mean and turbulent characteristics of the jet, especially the developing shear layer, is examined in great detail using planar and stereoscopic Particle Image Velocimetry (PIV). Examination of crossstream velocity profiles revealed that actuation leads to strong, spatially coherent streamwise vortex pairs which in turn significantly modify the mean flow field, resulting in a prominently undulated shear layer. These vortices grow as they convect downstream, enhancing local entrainment and significantly thickening the initial shear layer. Azimuthal inhomogeneity introduced in the jet shear layer is also evident in the simultaneous redistribution and reduction of peak turbulent fluctuations in the crossplane near the nozzle exit. Further downstream, control results in a global suppression of turbulence intensities for all axial locations, also evidenced by a longer potential core and overall reduced jet spreading. The resulting impact on the noise signature is estimated via farfield acoustic measurements. Noise reduction was observed at low to moderate frequencies for all observation angles. Direct comparison of these results with that of steady microjet injection revealed some notable differences in the initial development of streamwise vorticity and the redistribution of peak turbulence in the azimuthal direction. However, despite significant differences in the near nozzle aerodynamics, the downstream evolution of the jet appeared to approach near similar conditions with both highfrequency and steady microjet injection. Moreover, the impact on farfield noise was also comparable between the two injection methods as well as with others reported in the literature. Finally, for jets at higher Mach numbers and elevated temperatures, the effect of control was observed to vary with jet conditions. While the impact of the two control mechanisms were fairly comparable on nonshock containing jets, highfrequency forcing was observed to produce significantly larger reductions in screech and broadband shockassociated noise (BBSN) at select underexpanded jet conditions. The observed variations in control effects at different jet conditions call for further investigation.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Upadhyay_fsu_0071E_14154
 Format
 Thesis
 Title
 Uncertainty Analysis of Multifunctional Constitutive Relations and Adaptive Structures.
 Creator

Miles, Paul R., Oates, William, Hussaini, M. Yousuff, Zeng, Changchun (Chad), Taira, Kunihiko, Lin, Shangchao, Smith, Ralph C., Florida State University, College of Engineering,...
Show moreMiles, Paul R., Oates, William, Hussaini, M. Yousuff, Zeng, Changchun (Chad), Taira, Kunihiko, Lin, Shangchao, Smith, Ralph C., Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

Practically all engineering applications require knowledge of uncertainty. Accurately quantifying uncertainty within engineering problems supports model development, potentially leading to identification of key risk factors or cost reductions. Often the full problem requires modeling behavior of materials or structures from the quantum scale all the way up to the macroscopic scale. Predicting such behavior can be extremely complex, and uncertainty in modeling is often increased due to...
Show morePractically all engineering applications require knowledge of uncertainty. Accurately quantifying uncertainty within engineering problems supports model development, potentially leading to identification of key risk factors or cost reductions. Often the full problem requires modeling behavior of materials or structures from the quantum scale all the way up to the macroscopic scale. Predicting such behavior can be extremely complex, and uncertainty in modeling is often increased due to necessary assumptions. We plan to demonstrate the benefits of performing uncertainty analysis on engineering problems, specifically in the development of constitutive relations and structural analysis of smart materials and adaptive structures. This will be highlighted by a discussion of ferroelectric materials and their domain structure interaction, as well as dielectric elastomers’ viscoelastic and electrostrictive properties.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Miles_fsu_0071E_14033
 Format
 Thesis
 Title
 SpaceTime Spectral Element Methods in Fluid Dynamics and Materials Science.
 Creator

Pei, Chaoxu, Sussman, Mark, Hussaini, M. Yousuff, Dewar, William K., Cogan, Nicholas G., Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of...
Show morePei, Chaoxu, Sussman, Mark, Hussaini, M. Yousuff, Dewar, William K., Cogan, Nicholas G., Wang, Xiaoming, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

In this manuscript, we propose spacetime spectral element methods to solve problems arising from fluid dynamics and materials science. Many engineering applications require one to solve complex problems, such as flows containing multiscale structure in either space or time or both. It is straightforward that highorder methods are always more accurate and efficient than loworder ones for solving smooth problems. For example, spectral element methods can achieve a given level of accuracy...
Show moreIn this manuscript, we propose spacetime spectral element methods to solve problems arising from fluid dynamics and materials science. Many engineering applications require one to solve complex problems, such as flows containing multiscale structure in either space or time or both. It is straightforward that highorder methods are always more accurate and efficient than loworder ones for solving smooth problems. For example, spectral element methods can achieve a given level of accuracy with significantly fewer degrees of freedom compared to methods with algebraic convergence rates, e.g., finite difference methods. However, when it comes to complex problems, a high order method should be augmented with, e.g., a level set method or an artificial viscosity method, in order to address the issues caused by either sharp interfaces or shocks in the solution. Complex problems considered in this work are problems with solutions exhibiting multiple scales, i.e., the Stefan problem, nonlinear hyperbolic problems, and problems with smooth solutions but forces exhibiting disparate temporal scales, such as advection, diffusion and reaction processes. Correspondingly, two families of spacetime spectral element methods are introduced in order to achieve spectral accuracy in both space and time. The first category of spacetime methods are the fully implicit spacetime discontinuous Galerkin spectral element methods. In the fully implicit spacetime methods, time is treated as an additional dimension, and the model equation is rewritten into a spacetime formulation. The other category of spacetime methods are specialized for problems exhibiting multiple time scales: multiimplicit spacetime spectral element methods are developed. The method of lines approach is employed in the multiimplicit spacetime methods. The model is first discretized by a discontinuous spectral element method in space, and the resulting ordinary differential equations are then solved by a new multiimplicit spectral deferred correction method. A novel fully implicit spacetime discontinuous Galerkin (DG) spectral element method is presented to solve the Stefan problem in an Eulerian coordinate system. This method employs a level set procedure to describe the timeevolving interface. To deal with the prior unknown interface, a backward transformation and a forward transformation are introduced in the spacetime mesh. By combining an Eulerian description with a Lagrangian description, the issue of dealing with the implicitly defined arbitrary shaped spacetime elements is avoided. The backward transformation maps the unknown timevarying interface in the fixed frame of reference to a known stationary interface in the moving frame of reference. In the moving frame of reference, the transformed governing equations, written in the spacetime framework, are discretized by a DG spectral element method in each spacetime slab. The forward transformation is used to update the level set function and then to project the solution in each phase onto the new corresponding timedependent domain. Two options for calculating the interface velocity are presented, and both options exhibit spectral accuracy. Benchmark tests in one spatial dimension indicate that the method converges with spectral accuracy in both space and time for the temperature distribution and the interface velocity. The interrelation between the interface position and the temperature makes the Stefan problem a nonlinear problem; a Picard iteration algorithm is introduced in order to solve the nonlinear algebraic system of equations and it is found that just a few iterations lead to convergence. We also apply the fully implicit spacetime DG spectral element method to solve nonlinear hyperbolic problems. The spacetime method is combined with two different approaches for treating problems with discontinuous solutions: (i) spacetime dependent artificial viscosity is introduced in order to capture discontinuities/shocks, and (ii) the sharp discontinuity is tracked with spacetime spectral accuracy, as it moves through the grid. To capture the discontinuity whose location is initially unknown, an artificial viscosity term is strategically introduced, and the amount of artificial viscosity varies in time within a given spacetime slab. It is found that spectral accuracy is recovered everywhere except in the "troublesome element(s)'' where the unresolved steep/sharp gradient exists. When the location of a discontinuity is initially known, a spacetime spectrally accurate tracking method has been developed so that the spectral accuracy of the position of the discontinuity and the solution on either side of the discontinuity is preserved. A Picard iteration method is employed to handle nonlinear terms. Within each Picard iteration, a linear system of equations is solved, which is derived from the spacetime DG spectral element discretization. Spectral accuracy in both space and time is first demonstrated for the Burgers' equation with a smooth solution. For tests with discontinuities, the present spacetime method enables better accuracy at capturing the shock strength in the element containing shock when higher order polynomials in both space and time are used. Moreover, the spectral accuracy of the shock speed and location is demonstrated for the solution of the inviscid Burgers' equation obtained by the shock tracking method, and the sensitivity of the number of Picard iterations to the temporal order is discussed. The dynamics of many physical and biological systems involve two or more processes with a wide difference of characteristic time scales, e.g., problems with advection, diffusion and reaction processes. The computational cost of solving a coupled nonlinear system of equations is expensive for a fully implicit (i.e., "monolithic") spacetime method. Thus, we develop another type of a spacetime spectral element method, which is referred to as the multiimplicit spacetime spectral element method. Rather than coupling space and time together, the method of lines is used to separate the discretization of space and time. The model is first discretized by a discontinuous spectral element method in space and the resulting ordinary differential equations are then solved by a new multiimplicit spectral deferred correction method. The present multiimplicit spectral deferred correction method treats processes with disparate temporal scales independently, but couples them iteratively by a series of deferred correction steps. Compared to lower order operator splitting methods, the splitting error in the multiimplicit spectral deferred correction method is eliminated by exploiting an iterative coupling strategy in the deferred correction procedure. For the spectral element discretization in space, two advective flux reconstructions are proposed: extended elementwise flux reconstruction and nonextended elementwise flux reconstruction. A loworder Istable building block time integration scheme is introduced as an explicit treatment for the hyperbolic terms in order to obtain a stable and efficient building block for the spectrally accurate spacetime scheme along with these two advective flux reconstructions. In other words, we compare the extended elementwise reconstruction with Istable building block scheme with the nonextended elementwise reconstruction with Istable building block scheme. Both options exhibit spectral accuracy in space and time. However, the solutions obtained by extended elementwise flux reconstruction are more accurate than those yielded by nonextended elementwise flux reconstruction with the same number of degrees of freedom. The spectral convergence in both space and time is demonstrated for advectiondiffusionreaction problems. Two different coupling strategies in the multiimplicit spectral deferred correction method are also investigated and both options exhibit spectral accuracy in space and time.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Pei_fsu_0071E_13972
 Format
 Thesis
 Title
 Mathematical Modeling and Sensitivity Analysis for Biological Systems.
 Creator

Aggarwal, Manu, Cogan, Nicholas G., Hussaini, M. Yousuff, Chicken, Eric, Jain, Harsh Vardhan, Bertram, R. (Richard), Mio, Washington, Florida State University, College of Arts...
Show moreAggarwal, Manu, Cogan, Nicholas G., Hussaini, M. Yousuff, Chicken, Eric, Jain, Harsh Vardhan, Bertram, R. (Richard), Mio, Washington, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

In this work, we propose a framework to develop testable hypotheses for the effects of changes in the experimental conditions on the dynamics of a biological system using mathematical models. We discuss the uncertainties present in this process and show how information from different experiment regimes can be used to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. To determine the significance of variation in the parameters due to varying...
Show moreIn this work, we propose a framework to develop testable hypotheses for the effects of changes in the experimental conditions on the dynamics of a biological system using mathematical models. We discuss the uncertainties present in this process and show how information from different experiment regimes can be used to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. To determine the significance of variation in the parameters due to varying experimental conditions, we propose using sensitivity analysis. Using our framework, we hypothesize that the experimentally observed decrease in the survivability of bacterial populations of Xylella fastidiosa (causal agent of Pierce’s Disease) upon addition of zinc, might be because of starvation of the bacteria in the biofilm due to an inhibition of the diffusion of the nutrients through the extracellular matrix of the biofilm. We also show how sensitivity is related to uncertainty and identifiability; and how it can be used to drive analysis of dynamical systems, illustrating it by analyzing a model which simulates bursting oscillations in pancreatic βcells. For sensitivity analysis, we use Sobol’ indices for which we provide algorithmic improvements towards computational efficiency. We also provide insights into the interpretation of Sobol’ indices, and consequently, define a notion of the importance of parameters in the context of inherently flexible biological systems.
Show less  Date Issued
 2019
 Identifier
 2019_Spring_Aggarwal_fsu_0071E_15070
 Format
 Thesis
 Title
 Numerical Optimization Methods on Riemannian Manifolds.
 Creator

Qi, Chunhong, Gallivan, Kyle A., Absil, PierreAntoine, Duke, Dennis, Erlebacher, Gordon, Hussaini, M. Yousuﬀ, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation considers the generalization of two wellknown unconstrained optimization algorithms for Rn to solve optimization problems whose constraints can be characterized as a Riemannian manifold. Efficiency and effectiveness are obtained compared to more traditional approaches to Riemannian optimization by applying the concepts of retraction and vector transport. We present a theory of building vector transports on submanifolds of Rn and use the theory to assess convergence...
Show moreThis dissertation considers the generalization of two wellknown unconstrained optimization algorithms for Rn to solve optimization problems whose constraints can be characterized as a Riemannian manifold. Efficiency and effectiveness are obtained compared to more traditional approaches to Riemannian optimization by applying the concepts of retraction and vector transport. We present a theory of building vector transports on submanifolds of Rn and use the theory to assess convergence conditions and computational efficiency of the Riemannian optimization algorithms. We generalize the BFGS method which is an highly effective quasiNewton method for unconstrained optimization on Rn. The Riemannian version, RBFGS, is developed and its convergence and efficiency analyzed. Conditions that ensure superlinear convergence are given. We also consider the Euclidean Adaptive Regularization using Cubics method (ARC) for unconstrained optimization on Rn. ARC is similar to trust region methods in that it uses a local model to determine the modification to the current estimate of the optimal solution. Rather than a quadratic local model and constraints as in a trust region method, ARC uses a parameterized local cubic model. We present a generalization, the Riemannian Adaptive Regularization using Cubics method (RARC), along with global and local convergence theory. The efficiency and effectiveness of the RARC and RBFGS methods are investigated and their performance compared to the predictions made by the convergence theory via a series of optimization problems on various manifolds.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd2263
 Format
 Thesis
 Title
 Probabilistic Uncertainty Analysis and Its Applications in Option Models.
 Creator

Namihira, Motoi J., Kopriva, David A., Srivastava, Anuj, Ewald, Brian, Hussaini, M. Yousuﬀ, Nichols, Warren, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

In this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst case or scenario analysis, Monte Carlo, and provide an in depth review of Polynomial Chaos in both one and multiple dimensions. We develop a numerically stable method of generating orthogonal polynomials that is used in the practical construction of the...
Show moreIn this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst case or scenario analysis, Monte Carlo, and provide an in depth review of Polynomial Chaos in both one and multiple dimensions. We develop a numerically stable method of generating orthogonal polynomials that is used in the practical construction of the Polynomial Chaos basis functions. We also develop a semi analytic density transform method that is 200 times faster and 1000 times more accurate than the Monte Carlo based kernel density method. Finally, we analyze the European and American put option models assuming a distribution for the volatility that is historically observed. We find that the sensitivity to uncertainty in volatility is greatest for the price of ATM puts, and tapers as one moves away from the strike. The Delta, however, exhibits the least sensitivity when ATM and is most sensitive when moderately ITM. The price uncertainty for ITM American puts is less than the price uncertainty of equivalent European puts. For OTM options, the price uncertainty is similar between American and European puts. The uncertainty in the Delta of ITM American puts is greater than the uncertainty of equivalent European puts. For OTM puts, the uncertainty in Delta is similar between American and European puts. For the American put, uncertainty in volatility introduces uncertainty in the location of the optimal exercise boundary, thereby making optimal exercise decisions more difficult.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7525
 Format
 Thesis
 Title
 Discontinuous Galerkin Spectral Element Approximations for the Reflection and Transmission of Waves from Moving Material Interfaces.
 Creator

Winters, Andrew R., Kopriva, David, Piekarewicz, Jorge, Hussaini, M. Yousuff, Gallivan, Kyle, Cogan, Nick, Case, Bettye Anne, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation develops and evaluates a computationally efficient and highorder numerical method to compute wave reflection and transmission from moving material boundaries. We use a discontinuous Galerkin spectral element approximation with an arbitrary LagrangianEulerian mapping and derive the exact upwind numerical fluxes to model the physics of wave reflection and transmission at jumps in material properties. Spectral accuracy is obtained by placing moving material interfaces at...
Show moreThis dissertation develops and evaluates a computationally efficient and highorder numerical method to compute wave reflection and transmission from moving material boundaries. We use a discontinuous Galerkin spectral element approximation with an arbitrary LagrangianEulerian mapping and derive the exact upwind numerical fluxes to model the physics of wave reflection and transmission at jumps in material properties. Spectral accuracy is obtained by placing moving material interfaces at element boundaries and solving the appropriate Riemann problem. We also derive and evaluate an explicit local time stepping (LTS) integration for the DGSEM on moving meshes. The LTS procedure is derived from AdamsBashforth multirate time integration methods. We present speedup and memory estimates, which show that the explicit LTS integration scales well with problem size. The LTS time integrator is also highly parallelizable. The manuscript also gathers, derives and analyzes several analytical solutions for the problem of wave reflection and transmission from a plane moving material interface. We present timestep refinement studies and numerical examples to show the approximations for wave reflection and transmission at dielectric and acoustic interfaces are spectrally accurate in space and have design temporal accuracy. The numerical tests also validate theoretical estimates that the LTS procedure can reduce computational cost by as much as an order of magnitude for time accurate problems. Finally, we investigate the parallel speedup of the LTS integrator and compare it to a standard, lowstorage RungeKutta method.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8916
 Format
 Thesis
 Title
 Investigating Persistent Infections Using Mathematical Modeling and Analyses.
 Creator

Jarrett, Angela Michelle, Cogan, Nicholas G., Hussaini, M. Yousuff, Bass, Hank W., Bertram, R. (Richard), Case, Bettye Anne, Hurdal, Monica K., Florida State University, College...
Show moreJarrett, Angela Michelle, Cogan, Nicholas G., Hussaini, M. Yousuff, Bass, Hank W., Bertram, R. (Richard), Case, Bettye Anne, Hurdal, Monica K., Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

While the immune system is extraordinarily complex and powerful, and medical advancements are more spectacular than ever, in recent history we have seen the unfortunate failure of both processes (immune system and drugs) in the increasing levels of persistent infections. This work is an example of a collaborative effort to study multiple forms of persistent infections using mathematical tools and analyses. We will discuss the biological backgrounds for the immune system's components and...
Show moreWhile the immune system is extraordinarily complex and powerful, and medical advancements are more spectacular than ever, in recent history we have seen the unfortunate failure of both processes (immune system and drugs) in the increasing levels of persistent infections. This work is an example of a collaborative effort to study multiple forms of persistent infections using mathematical tools and analyses. We will discuss the biological backgrounds for the immune system's components and functions, the bacterial and viral resistance mechanisms for methicillinresistant Staphylococcus aureus and the human immunodeficiency virus, respectively, and some of the current methods for treating these diseases. Then, using ordinary and partial differential equations we present the results of models that were created to study specific infections—namely, methicillinresistant Staphylococcus aureus osteomyelitis, Staphylococcus aureus nasal carriage, and human immunodeficiency virus prophylactic gel. These models are shown to be in good agreement with the biology by looking at, when possible, their analytical solutions and numerical results when compared to experimental evidence. We further explore these models using several different computational analyses that can be classified as at least one of the following methods: uncertainty quantification, sensitivity analysis, and data assimilation. We give an overview of each of these topics and delve into the technicalities and caveats of each of the analyses we apply. We show that all of the methods presented, individually and in concert, are valuable tools for not only revealing details about the model structure and verifying model robustness, but they can also bring to light elements of the biological phenomena that the model represents. While considering all these details, throughout the manuscript we consider the philosophical perspective of biological modeling and modeling in general.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Jarrett_fsu_0071E_13046
 Format
 Thesis
 Title
 On the Stability and Control of a Trailing Vortex.
 Creator

Edstrand, Adam, Cattafesta, Louis N., Hussaini, M. Yousuff, Schmid, Peter J., Taira, Kunihiko, Oates, William S., Florida State University, College of Engineering, Department of...
Show moreEdstrand, Adam, Cattafesta, Louis N., Hussaini, M. Yousuff, Schmid, Peter J., Taira, Kunihiko, Oates, William S., Florida State University, College of Engineering, Department of Mechanical Engineering
Show less  Abstract/Description

Trailing vortices are both a fundamental and practical problem of fluid mechanics. Fundamentally, they provide a canonical vortex flow that is pervasive in finite aspect ratio lifting bodies, practically producing many adverse effects across aeronautical and maritime applications. These adverse effects coupled with the broad range of applicability make their active control desirable; however, they remain robust to control efforts. Experimental baseline results provided an explanation of...
Show moreTrailing vortices are both a fundamental and practical problem of fluid mechanics. Fundamentally, they provide a canonical vortex flow that is pervasive in finite aspect ratio lifting bodies, practically producing many adverse effects across aeronautical and maritime applications. These adverse effects coupled with the broad range of applicability make their active control desirable; however, they remain robust to control efforts. Experimental baseline results provided an explanation of vortex wandering, the sidetoside motion often attributed to windtunnel unsteadiness or a vortex instability. We extracted the wandering motion and found striking similarities with the eigenmodes, growth rates, and frequencies from a stability analysis of the Batchelor vortex. After concluding that wandering is a result of a vortex instability, we applied control to the trailing vortex flow field through blowing from a slot at the wingtip. We experimentally obtained modest reductions in the metrics, but found the parameter space for optimization unwieldy. With the ultimate goal of designing control, we performed a physicsbased stability analysis in the wake of a NACA0012 wing with an aspect ratio of 1.25 positioned at a geometric angle of attack of 5 degrees. Numerically computing the base flow at a chord Reynolds number of 1000, we perform a parallel temporal and spatial stability analysis three chords downstream of the trailing edge finding seven instabilities: three temporal, four spatial. The three temporal contain a wake instability, a vortex instability, and a mixed instability, which is a higherorder wake instability. The primary instability localized to the wake results from the twodimensional wake, while the secondary instability is the mixed instability, containing higherorder spanwise structures in the wake. These instabilities imply that although it may be intuitive to place control at the wingtip, these results show that control may be more effective at the trailing edge, which would excite these instabilities that result with the eventual break up of the vortex. Further, by performing a wavepacket analysis, we found the wave packets contained directivity, coming inward toward the vortex above and below the wing, and traveling outward in the spanwise directions. We conjecture that this directivity can be translated to receptivity, with freestream disturbances above and below the wing being more receptive than spanwise disturbances. With this, we provide two methods for instability excitation: utilizing control devices on the wing to excite nearfield instabilities directly and utilizing freestream disturbances to such as a speaker to excite nearfield instabilities through receptivity.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Edstrand_fsu_0071E_13141
 Format
 Thesis
 Title
 Random Sobol' Sensitivity Analysis and Model Robustness.
 Creator

Mandel, David, Ökten, Giray, Hussaini, M. Yousuff, Huffer, Fred W. (Fred William), Kercheval, Alec N., Fahim, Arash, Florida State University, College of Arts and Sciences,...
Show moreMandel, David, Ökten, Giray, Hussaini, M. Yousuff, Huffer, Fred W. (Fred William), Kercheval, Alec N., Fahim, Arash, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

This work develops both the theoretical foundation and the practical application of random Sobol' analysis with two goals. The first is to provide a more general and accommodating approach to global sensitivity analysis, in which the parameter distribution themselves contain uncertainty, and hence the sensitivity results are random quantities as well. The framework for this approach is motivated by empirical evidence of such behavior, and examples of this behavior in interest rate and...
Show moreThis work develops both the theoretical foundation and the practical application of random Sobol' analysis with two goals. The first is to provide a more general and accommodating approach to global sensitivity analysis, in which the parameter distribution themselves contain uncertainty, and hence the sensitivity results are random quantities as well. The framework for this approach is motivated by empirical evidence of such behavior, and examples of this behavior in interest rate and temperature modeling are provided. The second goal is to compare competing models on their robustness, a notion developed and defined to provide a quantitative solution to model selection based on model uncertainty and sensitivity
Show less  Date Issued
 2017
 Identifier
 FSU_2017SP_Mandel_fsu_0071E_13682
 Format
 Thesis