Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1502.06642

A statistical model for the excitation of cavities through apertures

Gabriele Gradoni·Thomas M. Antonsen·Steven M. Anlage·Edward Ott
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, a statistical model for the coupling of electromagnetic radiation into enclosures through apertures is presented. The model gives a unified picture bridging deterministic theories of aperture radiation, and statistical models necessary for capturing the properties of irregular shaped enclosures. A Monte Carlo technique based on random matrix theory is used to predict and study the power transmitted through the aperture into the enclosure. Universal behavior of the net power entering the aperture is found. Results are of interest for predicting the coupling of external radiation through openings in irregular enclosures and reverberation chambers.

Explore related subjects

nlin.CDphysics.class-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gabriele Gradoni, Thomas M. Antonsen, Steven M. Anlage, Edward Ott. 2015-02-23. A statistical model for the excitation of cavities through apertures. https://doi.org/10.1109/temc.2015.2421346

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Final state sensitivity and fractal basin boundaries from coupled Chialvo neurons

We investigate and quantify the basin geometry and extreme final state uncertainty of two identical electrically asymmetrically coupled Chialvo neurons. The system's diverse behaviors are presented, along with the mathematical reasoning behind its chaotic and nonchaotic dynamics as determined by the structure of the coupled equations. The system is found to be multistable with two qualitatively different attractors. Although each neuron is individually nonchaotic, the chaotic basin takes up the vast majority of the coupled system's state space, but the nonchaotic basin stretches to infinity due to chance synchronization. The boundary between the basins is found to be fractal, leading to extreme final state sensitivity. This uncertainty and its potential effect on the synchronization of biological neurons may have implications for understanding neuronal biology.

nlin.CD↗
arXiv2026

Jordan-Block Degeneracy and Cubic-Order Bifurcating Periodic Orbits in Minimum-Energy Optimal Control of Hamiltonian Equilibria

Equilibria of the Hamiltonian system associated with Pontryagin's minimum principle exhibit an exact doubling of the natural spectrum and, under a simple pairing condition, a Jordan block at every simple purely imaginary eigenvalue. Consequently, the classical Lyapunov Center Theorem does not apply to the augmented system, and no periodic orbit with nonzero optimal control bifurcates at linear order. We establish this mechanism in general and show that an optimal-control-induced periodic family emerges at cubic order in a Lindstedt--Poincaré expansion. The mechanism is illustrated in closed form for the pendulum and evaluated numerically for the planar $L_2$ equilibrium of Hill's restricted three-body problem, where the third-order approximation is validated against an independently computed family of periodic orbits.

nlin.CD↗
arXiv2026

Hypersensitivity and Turnpikes in Optimal Control of Inverted Pendulum: A Dynamical Systems Perspective

The hypersensitivity and turnpike phenomena in the optimal control of an inverted pendulum are investigated from a dynamical-systems perspective. We show that, for a fixed terminal time and a fixed terminal state optimal control problem, (1) the hypersensitivity originates from the fractal structure of the set of initial adjoint variables in the associated Hamiltonian dynamics, (2) the turnpike arises from slow dynamics in the vicinity of a degenerate center manifold, and (3) the escape channels are formed by normally hyperbolic invariant manifolds (NHIMs). As a consequence, small perturbations in the initial adjoint variables lead to qualitatively distinct extremal trajectories, resulting in severe numerical instability in trajectory optimization. Both the fractal structure and the invariant sets are characterized numerically and analytically.

nlin.CD↗