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Numerical Analysis and Computation Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Numerical Analysis and Computation
Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy
Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy
Applications and Applied Mathematics: An International Journal (AAM)
A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented …
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Mathematics & Statistics ETDs
The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
Mathematics & Statistics ETDs
In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …
A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu
A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu
Master's Theses
A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …
A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew
A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew
Electrical & Systems Engineering Publications and Presentations
Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the …
Effects Of Aperiodicity And Frustration On The Magnetic Properties Of Artificial Quasicrystals, Barry Farmer
Effects Of Aperiodicity And Frustration On The Magnetic Properties Of Artificial Quasicrystals, Barry Farmer
Theses and Dissertations--Physics and Astronomy
Quasicrystals have been shown to exhibit physical properties that are dramatically different from their periodic counterparts. A limited number of magnetic quasicrystals have been fabricated and measured, and they do not exhibit long-range magnetic order, which is in direct conflict with simulations that indicate such a state should be accessible. This dissertation adopts a metamaterials approach in which artificial quasicrystals are fabricated and studied with the specific goal of identifying how aperiodicity affects magnetic long-range order. Electron beam lithography techniques were used to pattern magnetic thin films into two types of aperiodic tilings, the Penrose P2, and Ammann-Beenker tilings. SQUID …
Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, Gregory Allen Riggs
Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, Gregory Allen Riggs
Graduate Theses, Dissertations, and Problem Reports
The application of bicoherence analysis to plasma research, particularly in non-linear, coupled-wave regimes, has thus far been significantly belied by poor resolution in time, and/or outright destruction of frequency information. Though the typical power spectrum cloaks the phase-coherency between frequencies, Fourier transforms of higher-order convolutions provide an n-dimensional spectrum which is adept at elucidating n-wave phase coherence. As such, this investigation focuses on the utility of the normalized bispectrum for detection of wave-wave coupling in general, with emphasis on distinct implications within the scope of non-linear plasma physics. Interpretations of bicoherent features are given for time series from …