Current Search: Numerical analysis (x)
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- Title
- Tidal and low frequency flushing of a coastal lagoon using a flexible grid model.
- Creator
- Smith, Ned P.
- Date Issued
- 1996
- PURL
- http://purl.flvc.org/FCLA/DT/3172979
- Subject Headings
- Tides, Lagoons, Estuaries, Inlets, Numerical grid generation (Numerical analysis)
- Format
- Document (PDF)
- Title
- PARAMETERIZATION OF INVARIANT CIRCLES IN MAPS.
- Creator
- Blessing, David Charles, James, J. D. James, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
We explore a novel method of approximating contractible invariant circles in maps. The process begins by leveraging improvements on Birkhoff's Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration scheme to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this...
Show moreWe explore a novel method of approximating contractible invariant circles in maps. The process begins by leveraging improvements on Birkhoff's Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration scheme to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this approximation in hand, we explore the phase space near the approximate invariant circle with a form numerical continuation where the rotation number is perturbed and the process is repeated. Then, we turn our attention to a completely different problem which can be approached in a similar way to the numerical continuation, finding a Siegel disk boundary in a holomorphic map. Given a holomorphic map which leads to a formally solvable cohomological equation near the origin, we use a numerical continuation style process to approximate an invariant circle in the Siegel disk near the origin. Using an iterative scheme, we then enlarge the invariant circle so that it approximates the boundary of the Siegel disk.
Show less - Date Issued
- 2024
- PURL
- http://purl.flvc.org/fau/fd/FA00014464
- Subject Headings
- Dynamical systems, Nonlinearity (Mathematics), Numerical analysis, Parameterization
- Format
- Document (PDF)
- Title
- Hybrid stress analysis using digitized photoelastic data and numerical methods.
- Creator
- Mahfuz, Hassan, Florida Atlantic University, Case, Robert O., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
-
Equations of stress-difference elasticity, derived from the equations of equilibrium and compatibility for a two-dimensional stress field, are solved for arbitrarily digitized, singly and multiply connected domains. Photoelastic data determined experimentally along the boundary provide the boundary values for the solution of the three elliptic partial differential equations by the finite difference method. A computerized method is developed to generate grid mesh, weighting functions and nodal...
Show moreEquations of stress-difference elasticity, derived from the equations of equilibrium and compatibility for a two-dimensional stress field, are solved for arbitrarily digitized, singly and multiply connected domains. Photoelastic data determined experimentally along the boundary provide the boundary values for the solution of the three elliptic partial differential equations by the finite difference method. A computerized method is developed to generate grid mesh, weighting functions and nodal connectivity within the digitized boundary for the solution of these partial differential equations. A method is introduced to digitize the photoelastic fringes, namely isochromatics and isoclinics, and to estimate the values of sigma1 - sigma2, sigma x - sigma y and tau xy at each nodal point by an interpolation technique. Interpolated values of the stress parameters are used to improve the initial estimate and hence the convergence of the iterative solution of the system of equations. Superfluous boundary conditions are added from the digitized photoelastic data for further speeding up the rate of convergence. The boundary of the domain and the photoelastic fringes are digitized by physically traversing the cursor along the boundary, and the digitized information is scanned horizontally and vertically to generate internal and boundary nodal points. A linear search determines the nodal connectivity and isolates the boundary points for the input of the boundary values. A similar scanning method estimates the photoelastic parameters at each nodal point and also finds the points closest to the tint of passage of each photoelastic fringe. Stress values at these close points are determined without interpolation and are subsequently used as superfluous boundary conditions in the iteration scheme. Successive over-relaxation is applied to the classical Gauss-Seidel method for final enhancement of the convergence of the iteration process. The iteration scheme starts with an accelerating factor other than unity and estimates the spectral radius of the iteration matrix from the two vector norms. This information is used to estimate a temporary value of the optimum relaxation parameter, omega[opt], which is used for a fixed number of iterations to approximate a better value of the accelerating factor. The process is continued until two successive estimates differ by a given tolerance or the stopping criteria are reached. Detailed techniques of developing the code for mesh generation, photoelastic data collection and boundary value interpolation to solve the elliptic boundary value problems are presented. Three separate examples with varying stress gradients and fringe patterns are presented to test the validity of the code and the overall method. Results are compared with the analytical and experimental solutions, and the significant improvement in the rate of convergence is demonstrated.
Show less - Date Issued
- 1989
- PURL
- http://purl.flvc.org/fcla/dt/11934
- Subject Headings
- Strains and stresses, Photoelasticity, Numerical analysis--Data processing
- Format
- Document (PDF)
- Title
- Studies of composite multihull ship structures using fluid structure interaction.
- Creator
- Ma, Siyuan, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
-
Studies of composite multihull structure under wave loads, extreme loads, and blast loads have been conducted using finite element and computational fluid dynamics (CPF) tools. A comprehensive finite element tool for structural analysis of composite multi-hull structures is developed. Two-way fluid structure interaction (FSI) is implemented by coupling finite element analysis (FEA) and CFD. FEA models have been developed using sandwich construction having composite face sheets and a foam core...
Show moreStudies of composite multihull structure under wave loads, extreme loads, and blast loads have been conducted using finite element and computational fluid dynamics (CPF) tools. A comprehensive finite element tool for structural analysis of composite multi-hull structures is developed. Two-way fluid structure interaction (FSI) is implemented by coupling finite element analysis (FEA) and CFD. FEA models have been developed using sandwich construction having composite face sheets and a foam core. Fluid domain was modeled using the CFD code, CFX and a wave motion was simulated based on Sea State 5... In addition to hydrodynamic loads, the simulation of composite ship under extreme loads is performed. Stress analysis was performed and dynamic response of the hull was determined in time domain. In the final analysis, an underwater explosion model was developed to study the composite hull resistance to blast load.
Show less - Date Issued
- 2012
- PURL
- http://purl.flvc.org/FAU/3355625
- Subject Headings
- Computational fluid dynamics, Numerical analysis, Engineering mathematics, Naval architecture, Structural analysis (Engineering)
- Format
- Document (PDF)
- Title
- Statistics preserving spatial interpolation methods for missing precipitation data.
- Creator
- El Sharif, Husayn., College of Engineering and Computer Science, Department of Civil, Environmental and Geomatics Engineering
- Abstract/Description
-
Deterministic and stochastic weighting methods are commonly used methods for estimating missing precipitation rain gauge data based on values recorded at neighboring gauges. However, these spatial interpolation methods seldom check for their ability to preserve site and regional statistics. Such statistics and primarily defined by spatial correlations and other site-to-site statistics in a region. Preservation of site and regional statistics represents a means of assessing the validity of...
Show moreDeterministic and stochastic weighting methods are commonly used methods for estimating missing precipitation rain gauge data based on values recorded at neighboring gauges. However, these spatial interpolation methods seldom check for their ability to preserve site and regional statistics. Such statistics and primarily defined by spatial correlations and other site-to-site statistics in a region. Preservation of site and regional statistics represents a means of assessing the validity of missing precipitation estimates at a site. This study evaluates the efficacy of traditional interpolation methods for estimation of missing data in preserving site and regional statistics. New optimal spatial interpolation methods intended to preserve these statistics are also proposed and evaluated in this study. Rain gauge sites in the state of Kentucky are used as a case study, and several error and performance measures are used to evaluate the trade-offs in accuracy of estimation and preservation of site and regional statistics.
Show less - Date Issued
- 2012
- PURL
- http://purl.flvc.org/FAU/3355568
- Subject Headings
- Numerical analysis, Meteorology, Statistical methods, Spatial analysis (Statistics), Data processing, Atmospheric physics, Statistical methods, Geographic information systems, Mathematical models
- Format
- Document (PDF)
- Title
- Shamir's secret sharing scheme using floating point arithmetic.
- Creator
- Finamore, Timothy., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Implementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and...
Show moreImplementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and propose improvements to attain these properties. Experiments indicate that property 2 of a perfect secret sharing scheme, "Any k-1 or fewer participants obtain no information regarding the shared secret", is compromised when Shamir's secret sharing scheme is implemented with floating point arithmetic. These experimental results also provide information regarding possible solutions and adjustments. One of which being, selecting randomly generated points from a smaller interval in one of the proposed schemes of this thesis. Further experimental results indicate improvement using the scheme outlined. Possible attacks are run to test the desirable properties of the different schemes and reinforce the improvements observed in prior experiments.
Show less - Date Issued
- 2012
- PURL
- http://purl.flvc.org/FAU/3342048
- Subject Headings
- Signal processing, Digital techniques, Mathematics, Data encryption (Computer science), Computer file sharing, Security measures, Computer algorithms, Numerical analysis, Data processing
- Format
- Document (PDF)
- Title
- Stability analysis for singularly perturbed systems with time-delays.
- Creator
- Yang, Yang, Wang, Yuan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Singularly perturbed systems with or without delays commonly appear in mathematical modeling of physical and chemical processes, engineering applications, and increasingly, in mathematical biology. There has been intensive work for singularly perturbed systems, yet most of the work so far focused on systems without delays. In this thesis, we provide a new set of tools for the stability analysis for singularly perturbed control systems with time delays.
- Date Issued
- 2015
- PURL
- http://purl.flvc.org/fau/fd/FA00004423, http://purl.flvc.org/fau/fd/FA00004423
- Subject Headings
- Biology -- Mathematical models, Biomathematics, Differentiable dynamical systems, Differential equations, Partial -- Numerical solutions, Global analysis (Mathematics), Lyapunov functions, Nonlinear theories
- Format
- Document (PDF)