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Papers by Sylvester Thompson Jr

Research paper thumbnail of Extending Open Architecture (OA) to the physical layer

Public reporting burden for this collection of information is estimated to average 1 hour per res... more Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to

Research paper thumbnail of A delay differential model of ENSO variability: parametric instability and the distribution of extremes

Nonlinear Processes in Geophysics, 2008

We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) var... more We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform stability analyses of the model in the three-dimensional space of its physically relevant parameters. Our results illustrate the role of these three parameters: strength of seasonal forcing b, atmosphere-ocean coupling κ, and propagation period τ of oceanic waves across the Tropical Pacific. Two regimes of variability, stable and unstable, are separated by a sharp neutral curve in the (b, τ) plane at constant κ. The detailed structure of the neutral curve becomes very irregular and possibly fractal, while individual trajectories within the unstable region become highly complex and possibly chaotic, as the atmosphere-ocean coupling κ increases. In the unstable regime, spontaneous transitions occur in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values, for purely periodic, seasonal forcing. The model reproduces the Devil's bleachers characterizing other ENSO models, such as nonlinear, coupled systems of partial differential equations; some of the features of this behavior have been documented in general circulation models, as well as in observations. We expect, therefore, similar behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.

Research paper thumbnail of Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared-memory parallel computer

Journal of Computational and Applied Mathematics, 1991

Experiments with an ordinary differential equation solver in the parallel solution of method of l... more Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared-memory parallel computer, Journal of Computational and Applied Mathematics 38 (1991) 231-253. We consider method of lines solutions of partial differential equations on shared-memory parallel computers. Solutions using the ordinary differential equation solver SDRIV3 (which is similar to the well-known LSODE solver) are considered. It is shown that portions of the solver may be implemented in parallel. In particular, formation of the Jacobian matrix and the linear algebra required to solve the corrector equations are natural candidates for parallel implementation since these portions dominate the cost ,of solving large systems of equations. A variant of Gaussian elimination is described which allows efficient parallel solution of systems of

Research paper thumbnail of On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems

Journal of Computational and Applied Mathematics, 1989

We discuss how rootfinding, which is built into some ODE software, can be used to generate Poinca... more We discuss how rootfinding, which is built into some ODE software, can be used to generate Poincare sections. An interactive program is also described.

Research paper thumbnail of Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials

Communications in Nonlinear Science and Numerical Simulation, 2012

ABSTRACT In this article we propose a numerical scheme to solve the pantograph equation. The meth... more ABSTRACT In this article we propose a numerical scheme to solve the pantograph equation. The method consists of expanding the required approximate solution as the elements of the shifted Chebyshev polynomials. The Chebyshev pantograph operational matrix is introduced. The operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.

Research paper thumbnail of Extreme Lengths for Chords of an Ellipse

The Electronic Journal of Mathematics and Technology

The problem originated in a Chinese university entrance practice problem. We extend the original ... more The problem originated in a Chinese university entrance practice problem. We extend the original circle case to more challenging ones for ellipses. It is evident that technological tools provide us crucial intuitions before attempting for more rigorous analytical solutions. We use GinMA [2] and ClassPad Manager [1] for simulating where the possible solutions maybe in 2D. Next, we introduce two analytical methods, one is applying the Lagrange multiplier method that involves two parameters, and the other is applying the trigonometry method using one parameter. Finally, with the help of Maple [3] as a computational engine, we verify our results using mentioned two methods indeed coincide with each other and are consistent with our geometry conjectures. The content is accessible to those who have completed the calculus courses.

Research paper thumbnail of Extending Open Architecture (OA) to the physical layer

Public reporting burden for this collection of information is estimated to average 1 hour per res... more Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to

Research paper thumbnail of A delay differential model of ENSO variability: parametric instability and the distribution of extremes

Nonlinear Processes in Geophysics, 2008

We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) var... more We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform stability analyses of the model in the three-dimensional space of its physically relevant parameters. Our results illustrate the role of these three parameters: strength of seasonal forcing b, atmosphere-ocean coupling κ, and propagation period τ of oceanic waves across the Tropical Pacific. Two regimes of variability, stable and unstable, are separated by a sharp neutral curve in the (b, τ) plane at constant κ. The detailed structure of the neutral curve becomes very irregular and possibly fractal, while individual trajectories within the unstable region become highly complex and possibly chaotic, as the atmosphere-ocean coupling κ increases. In the unstable regime, spontaneous transitions occur in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values, for purely periodic, seasonal forcing. The model reproduces the Devil's bleachers characterizing other ENSO models, such as nonlinear, coupled systems of partial differential equations; some of the features of this behavior have been documented in general circulation models, as well as in observations. We expect, therefore, similar behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.

Research paper thumbnail of Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared-memory parallel computer

Journal of Computational and Applied Mathematics, 1991

Experiments with an ordinary differential equation solver in the parallel solution of method of l... more Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared-memory parallel computer, Journal of Computational and Applied Mathematics 38 (1991) 231-253. We consider method of lines solutions of partial differential equations on shared-memory parallel computers. Solutions using the ordinary differential equation solver SDRIV3 (which is similar to the well-known LSODE solver) are considered. It is shown that portions of the solver may be implemented in parallel. In particular, formation of the Jacobian matrix and the linear algebra required to solve the corrector equations are natural candidates for parallel implementation since these portions dominate the cost ,of solving large systems of equations. A variant of Gaussian elimination is described which allows efficient parallel solution of systems of

Research paper thumbnail of On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems

Journal of Computational and Applied Mathematics, 1989

We discuss how rootfinding, which is built into some ODE software, can be used to generate Poinca... more We discuss how rootfinding, which is built into some ODE software, can be used to generate Poincare sections. An interactive program is also described.

Research paper thumbnail of Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials

Communications in Nonlinear Science and Numerical Simulation, 2012

ABSTRACT In this article we propose a numerical scheme to solve the pantograph equation. The meth... more ABSTRACT In this article we propose a numerical scheme to solve the pantograph equation. The method consists of expanding the required approximate solution as the elements of the shifted Chebyshev polynomials. The Chebyshev pantograph operational matrix is introduced. The operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.

Research paper thumbnail of Extreme Lengths for Chords of an Ellipse

The Electronic Journal of Mathematics and Technology

The problem originated in a Chinese university entrance practice problem. We extend the original ... more The problem originated in a Chinese university entrance practice problem. We extend the original circle case to more challenging ones for ellipses. It is evident that technological tools provide us crucial intuitions before attempting for more rigorous analytical solutions. We use GinMA [2] and ClassPad Manager [1] for simulating where the possible solutions maybe in 2D. Next, we introduce two analytical methods, one is applying the Lagrange multiplier method that involves two parameters, and the other is applying the trigonometry method using one parameter. Finally, with the help of Maple [3] as a computational engine, we verify our results using mentioned two methods indeed coincide with each other and are consistent with our geometry conjectures. The content is accessible to those who have completed the calculus courses.