Randy C. Paffenroth

ELEMENTAL PERIODIC ORBITS ASSOCIATED WITH THE LIBRATION POINTS IN THE CIRCULAR RESTRICTED 3-BODY PROBLEM

We present an overview of detailed computational results for families of periodic orbits that emanate from the five libration points in the Circular Restricted 3-Body Problem, as well as for various secondary bifurcating families. Our extensive overview covers all values of the mass-ratio parameter, and includes many known families that have been studied in the past. The numerical continuation and bifurcation algorithms employed in our study are based on boundary value techniques, as implemented in the numerical continuation and bifurcation software AUTO.

Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem

We show how to compute families of periodic solutions of conservative systems with two-point boundary value problem continuation software. The computations include detection of bifurcations and corresponding branch switching. A simple example is used to illustrate the main idea. Thereafter we compute families of periodic solutions of the circular restricted 3-body problem. We also continue the figure-8 orbit recently discovered by Chenciner and Montgomery, and numerically computed by Simo, as the mass of one of the bodies is allowed to vary. In particular, we show how the invariances (phase-shift, scaling law, and x, y, z translations and rotations) can be dealt with. Our numerical results show, among other things, that there exists a continuous path of periodic solutions from the figure-8 orbit to a periodic solution of the restricted 3-body problem.

Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations

We present a new class of integral equations for the solution of problems of scattering of electromagnetic fields by perfectly conducting bodies. Like the classical Combined Field Integral Equation (CFIE), our formulation results from a representation of the scattered field as a combination of magnetic- and electric-dipole distributions on the surface of the scatterer. In contrast with the classical equations, however, the electric-dipole operator we use contains a regularizing operator; we call the resulting equations Regularized Combined Field Integral Equations (CFIE-R). Unlike the CFIE, the CFIE-R are Fredholm equations which, we show, are uniquely solvable; our selection of coupling parameters, further, yields CFIE-R operators with excellent spectral distributions-with closely clustered eigenvalues-so that small numbers of iterations suffice to solve the corresponding equations by means of Krylov subspace iterative solvers such as GMRES. The regularizing operators are constructed on the basis of the single layer operator, and can thus be incorporated easily within any existing surface integral equation implementation for the solution of the classical CFIE. We present one such methodology: a high-order Nystrom approach based on use of partitions of unity and trapezoidal-rule integration. A variety of numerical results demonstrate very significant gains in computational costs that can result from the new formulations, for a given accuracy, over those arising from previous approaches.

Calculation of the Stability Index in Parameter-Dependent Calculus of Variations Problems: Buckling of a Twisted Elastic Strut

We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler--Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting conjugate points, with local minima corresponding to equilibria with no conjugate points. These conjugate points are arclength values

Space-Time Signal Processing for Distributed Pattern Detection in Sensor Networks

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Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

at which a second ODE (the Jacobi equation) has a solution vanishing at 0 and

Space-time signal processing for distributed pattern detection in sensor networks

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INTERACTIVE COMPUTATION, PARAMETER CONTINUATION, AND VISUALIZATION

.Finding conjugate points normally involves the numerical solution of a set of initial value problems for the Jacobi equation. For problems involving a parameter

Out-of-sequence measurement updates for multi-hypothesis tracking algorithms

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Multi-objective reinforcement learning-based deep neural networks for cognitive space communications

, such as the force or twist angle in the elastic strut, this computation must be repeated for every value of