119 citations · 139 across the 12 of their papers we have counts for
14 papers
Invariant Polydiagonal Subspaces of Matrices and Constraint Programming
John M. Neuberger, Nándor Sieben, James W. Swift
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a ma…
A Bifurcation Lemma for Invariant Subspaces
John M. Neuberger, Nándor Sieben, James W. Swift
The Bifurcation from a Simple Eigenvalue (BSE) Theorem is the foundation of steady-state bifurcation theory for one-parameter families of functions. When eigenvalues of multiplicit…
On Second-Order Cone Functions
Shafiu Jibrin, James W. Swift
We consider the second-order cone function (SOCF) defined by . Every SOCF is concave. We give necessary and sufficie…
Invariant Synchrony and Anti-Synchrony Subspaces of Weighted Networks
Eddie Nijholt, Nándor Sieben, James W. Swift
The internal state of a cell in a coupled cell network is often described by an element of a vector space. Synchrony or anti-synchrony occurs when some of the cells are in the same…
Invariant synchrony subspaces of sets of matrices
John M. Neuberger, Nandor Sieben, James W. Swift
A synchrony subspace of R^n is defined by setting certain components of the vectors equal according to an equivalence relation. Synchrony subspaces invariant under a given set of s…
Synchrony and Anti-Synchrony for Difference-Coupled Vector Fields on Graph Network Systems
John M. Neuberger, Nándor Sieben, James W. Swift
We define a graph network to be a coupled cell network where there are only one type of cell and one type of symmetric coupling between the cells. For a difference-coupled vector f…
Newton's Method and Symmetry for Semilinear Elliptic PDE on the Cube
John M. Neuberger, Nandor Sieben, James W. Swift
We seek discrete approximations to solutions of semilinear elliptic partial differential equations of the form , where is a one-parameter family o…
An MPI Implementation of a Self-Submitting Parallel Job Queue
John M. Neuberger, Nandor Sieben, James W. Swift
We present a simple and easy to apply methodology for using high-level self-submitting parallel job queues in an MPI environment. Using C++, we implemented a library of functions,…
Automated Bifurcation Analysis for Nonlinear Elliptic Partial Difference Equations on Graphs
John M. Neuberger, Nandor Sieben, James W. Swift
We seek solutions to the semilinear elliptic partial difference equation , where is the matrix corresponding to the Laplacian operator on a graph $…
Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region
John M. Neuberger, Nandor Sieben, James W. Swift
We apply the Gradient-Newton-Galerkin-Algorithm (GNGA) of Neuberger & Swift to find solutions to a semilinear elliptic Dirichlet problem on the region whose boundary is the Koch sn…
Computing Eigenfunctions on the Koch Snowflake: A New Grid and Symmetry
John M. Neuberger, Nandor Sieben, James W. Swift
In this paper we numerically solve the eigenvalue problem on the fractal region defined by the Koch Snowflake, with zero-Dirichlet or zero-Neumann boundary conditions…
Observing the Symmetry of Attractors
Jeffrey H. Schenker, James W. Swift
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used,…
Stability of periodic solutions in series arrays of Josephson junctions with internal Capacitance
Shinya Watanabe, James W. Swift
A mystery surrounds the stability properties of the splay-phase periodic solutions to a series array of N Josephson junction oscillators. Contrary to what one would expect from dyn…
Averaged equations for Josephson junction series arrays with LRC load
Kurt Wiesenfeld, James W. Swift
We derive the averaged equations describing a series array of Josephson junctions shunted by a parallel inductor-resistor-capacitor load. We assume that the junctions have negligab…