Mathematics Faculty Proceedings, Presentations, Speeches, LecturesCopyright (c) 2021 Nova Southeastern University All rights reserved.
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Recent documents in Mathematics Faculty Proceedings, Presentations, Speeches, Lecturesen-usFri, 15 Oct 2021 03:00:05 PDT3600A splitting approximation for the numerical solution of a self-adjoint quenching problem
https://nsuworks.nova.edu/cnso_math_facpres/433
https://nsuworks.nova.edu/cnso_math_facpres/433Wed, 13 Oct 2021 05:14:01 PDT
Ideal combustion processes are often modelled via nonlinear reaction-diffusion equations with singular forcing terms. Our preliminary work considers the numerical solution of such a partial differential equation problem, where a self-adjoint operator with variable diffusion coefficient is considered. Traditional Peaceman-Rachford-Strang splitting is used for time stepping of the semi-discrete system of equations obtained. Conditions are derived to ensure the monotonicity, positivity, and linear stability of the finite difference method. Simulation experiments are provided to validate our splitting approximation.
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Julienne KabreRadial Basis Functions Generated Finite-Difference Method for the Korteweg-de Vries Equation
https://nsuworks.nova.edu/cnso_math_facpres/432
https://nsuworks.nova.edu/cnso_math_facpres/432Wed, 13 Oct 2021 05:13:57 PDT
The Korteweg-de Vries equation (KDV) is a third order non-linear Partial Differential Equation(PDE) which solutions are traveling waves called solitons. A numerical method namely radial basis functions generated finite-difference (RBF-FD) integrating factor method was applied and the numerical solutions of the KDV equations were compared with the analytical solutions for 1, 2 and 3 solitons . Hyperviscosity was used for stability of the RBF-FD method in the case of irregular nodes.
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Julienne Kabre et al.A PETSC implementation of the energy-preserving scheme for the Poisson-Nernst-Planck Equations
https://nsuworks.nova.edu/cnso_math_facpres/431
https://nsuworks.nova.edu/cnso_math_facpres/431Wed, 13 Oct 2021 05:13:53 PDTJulienne KabreImproving accuracy of ECG monitoring using a wearable device
https://nsuworks.nova.edu/cnso_math_facpres/430
https://nsuworks.nova.edu/cnso_math_facpres/430Wed, 13 Oct 2021 05:13:49 PDTJulienne KabreEnergy-Conserving Numerical Scheme for the Poisson-Nerst-Plank Equations
https://nsuworks.nova.edu/cnso_math_facpres/429
https://nsuworks.nova.edu/cnso_math_facpres/429Wed, 13 Oct 2021 05:13:45 PDT
The Poisson-Nernst-Planck equations are a system of nonlinear partial differential equations that describe flow of charged particles in solution. In particular, we are interested in the transport of ions in the biological membrane proteins (ion channels). This work is about the design of numerical schemes that preserve exactly (up to round off error) a discretized form of the energy dynamics of the system. We will present a scheme that achieves the conservation of energy law, and the numerical results.
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Julienne KabreEnergy-Conserving Numerical Scheme for the Poisson-Nerst-Plank Equations
https://nsuworks.nova.edu/cnso_math_facpres/428
https://nsuworks.nova.edu/cnso_math_facpres/428Wed, 13 Oct 2021 05:13:41 PDT
Preliminary report. The Poisson-Nernst-Planck equations are a system of nonlinear partial differential equations that describe flow of charged particles in solution. In particular, we are interested in the transport of ions in the biological membrane proteins (ion channels). This work is about the design of numerical schemes that preserve exactly (up to roundoff error) a discretized form of the energy dynamics of the system. We will present a scheme that achieves the goal of preserving the energy dissipation law and some preliminary numerical results.
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Julienne KabreAn Energy-Dynamics-Preserving Discretization for the Poisson-Nernst-Planck Equations
https://nsuworks.nova.edu/cnso_math_facpres/427
https://nsuworks.nova.edu/cnso_math_facpres/427Wed, 13 Oct 2021 05:13:37 PDTJulienne KabreModelling diffusion through the finite composite medium of a dye sensitized solar cell
https://nsuworks.nova.edu/cnso_math_facpres/426
https://nsuworks.nova.edu/cnso_math_facpres/426Wed, 13 Oct 2021 05:13:33 PDTJulienne KabreAnalysis of EDS spectra of titanium dioxide coated TEC-8 conductive glass: Modeling diffusion in the photoanode of dye sensitized solar cells
https://nsuworks.nova.edu/cnso_math_facpres/425
https://nsuworks.nova.edu/cnso_math_facpres/425Wed, 13 Oct 2021 05:13:29 PDT
The photoanode of a dye sensitized solar cell (DSSC) is typically a mesoporous titanium dioxide thin film adhered to a conductive glass plate. In the case of TEC-8 glass, an approximately 700 nm film of tin oxide provides the conductivity of this substrate. During the calcining step of photoanode fabrication, tin diffuses into the other layers. SEM and Electron Dispersion Microscopy are used to analyze the spreading of tin through the photoanode. The transport of tin is described using Fick's Law of Diffusion through a semi-infinite medium with a fixed tin concentration at the interface. Preliminary data suggest that this diffusion follows the Arrhenius model for diffusion in solids. However a semi-infinite model may be needed for the finite TiO2 layer. At temperatures (400 to 600 C) and times (30 to 90 min) typically employed in the calcinations of titanium dioxide layers for dye sensitized solar cells, the variation of the tin thickness may be affecting the resistance of the photoanode.
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Julienne Cabel et al.Diffusion of tin from TEC-8 conductive glass into mesoporous titanium dioxide in dye sensitized solar cells
https://nsuworks.nova.edu/cnso_math_facpres/424
https://nsuworks.nova.edu/cnso_math_facpres/424Wed, 13 Oct 2021 05:13:25 PDT
The photoanode of a dye sensitized solar cell is typically a mesoporous titanium dioxide thin film adhered to a conductive glass plate. In the case of TEC-8 glass, an approximately 500 nm film of tin oxide provides the conductivity of this substrate. During the calcining step of photoanode fabrication, tin diffuses into the titanium dioxide layer. Scanning Electron Microscopy and Electron Dispersion Microscopy are used to analyze quantitatively the diffusion of tin through the photoanode. At temperatures (400 to 600 °C) and times (30 to 90 min) typically employed in the calcinations of titanium dioxide layers for dye sensitized solar cells, tin is observed to diffuse through several micrometers of the photoanode. The transport of tin is reasonably described using Fick's Law of Diffusion through a semi-infinite medium with a fixed tin concentration at the interface. Numerical modeling allows for extraction of mass transport parameters that will be important in assessing the degree to which tin diffusion influences the performance of dye sensitized solar cells.
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Julienne Cabell et al.Diffusion of tin from TEC-8 conductive glass into mesoporous titanium dioxide in dye sensitized solar cells
https://nsuworks.nova.edu/cnso_math_facpres/423
https://nsuworks.nova.edu/cnso_math_facpres/423Wed, 13 Oct 2021 05:13:21 PDTJulienne KabreAn energy-preserving scheme for the Poisson -Nernst-Planck equations
https://nsuworks.nova.edu/cnso_math_facpres/422
https://nsuworks.nova.edu/cnso_math_facpres/422Wed, 13 Oct 2021 05:13:18 PDTJulienne Kabre