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Full-Text Articles in Physical Sciences and Mathematics
Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman
Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …
Transients In The Synchronization Of Asymmetrically Coupled Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J.J.P. Veerman
Transients In The Synchronization Of Asymmetrically Coupled Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J.J.P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.
On The Coupling Of Dpg And Bem, Thomas Führer, Norbert Heuer, Michael Karkulik
On The Coupling Of Dpg And Bem, Thomas Führer, Norbert Heuer, Michael Karkulik
Mathematics and Statistics Faculty Publications and Presentations
We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of standard Galerkin boundary elements. An essential feature of our method is that, despite the use of boundary integral equations, optimal test functions have to be computed only locally. We apply our findings to a standard transmission problem in full space and present numerical experiments to validate our theory.
Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman
Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves …
A Second Elasticity Element Using The Matrix Bubble, Jay Gopalakrishnan, Johnny Guzmán
A Second Elasticity Element Using The Matrix Bubble, Jay Gopalakrishnan, Johnny Guzmán
Mathematics and Statistics Faculty Publications and Presentations
We presented a family of finite elements that use a polynomial space augmented by certain matrix bubbles in Cockburn et al. (2010) A new elasticity element made for enforcing weak stress symmetry. Math. Comput., 79, 1331–1349 . In this sequel we exhibit a second family of elements that use the same matrix bubble. This second element uses a stress space smaller than the first while maintaining the same space for rotations (which are the Lagrange multipliers corresponding to a weak symmetry constraint). The space of displacements is of one degree less than the first method. The analysis, while similar to …
On The Spectra Of Certain Directed Paths, Carlos Martins Da Fonseca, J. J. P. Veerman
On The Spectra Of Certain Directed Paths, Carlos Martins Da Fonseca, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We describe the eigenpairs of special kinds of tridiagonal matrices related to problems on traffic on a one-lane road. Some numerical examples are provided.
Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees …
Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We introduce a method that gives exactly incompressible velocity approximations to Stokes ow in three space dimensions. The method is designed by extending the ideas in Part I (http://archives.pdx.edu/ds/psu/10914) of this series, where the Stokes system in two space dimensions was considered. Thus we hybridize a vorticity-velocity formulation to obtain a new mixed method coupling approximations of tangential velocity and pressure on mesh faces. Once this relatively small tangential velocity-pressure system is solved, it is possible to recover a globally divergence-free numerical approximation of the fluid velocity, an approximation of the vorticity whose tangential component is continuous across …