Temporal homogenization of linear ODEs, with applications to parametric super-resonance and energy harvest

DOI10.1007/s00205-015-0932-4zbMath1338.34037arXiv1310.6460OpenAlexW3105687466MaRDI QIDQ261300

Molei Tao, Houman Owhadi

Publication date: 23 March 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6460

zbMATH Keywords

oscillators2-scale expansion approachlong-time approximationnon-homogeneous linear ODERLC circuits

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Multiple scale methods for ordinary differential equations (34E13)

Related Items

Parametric Resonance for Enhancing the Rate of Metastable Transition, Explicit high-order symplectic integrators for charged particles in general electromagnetic fields, Simply improved averaging for coupled oscillators and weakly nonlinear waves

Uses Software

• DLMF

Cites Work

• Averaging in vibration suppression by parametric stiffness excitation
• Subharmonic resonance in the nonlinear Mathieu equation
• Bifurcations in an autoparametric system in \(1:1\) internal resonance with parametric excitation
• The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential
• Approximate asymptotics for a nonlinear Mathieu equation using harmonic balance based averaging
• Effects of FGM materials on the parametric resonance of plate structures
• Parametric and autoparametric resonance
• Thermalization of fermionic quantum fields
• Multiple scale and singular perturbation methods
• Stability and asymptotic properties of a system of functional differential equations with nonconstant delays
• Extension of Floquet's theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows
• Unified Krylov–Bogoliubov–Mitropolskii method for solving nth order non-linear systems with slowly varying coefficients
• Control of a model of DNA division via parametric resonance
• Homogenization in a Periodic and Time-Dependent Potential
• The adiabatic invariant of the n -degree-of-freedom harmonic oscillator
• Parametric resonance of a spherical bubble
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Compactness of Floquet isospectral sets for the matrix Hill's equation
• Parametric Resonance in Wave Equations with a Time-Periodic Potential
• Autoparametric resonance of relaxation oscillations
• The Borg theorem for the vectorial Hill's equation
• Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case
• Magnus and Fer expansions for matrix differential equations: the convergence problem
• Multiscale Methods
• HANS BETHE'S CONTRIBUTIONS TO SOLID-STATE PHYSICS
• Exponential Operators and Parameter Differentiation in Quantum Physics
• On the exponential solution of differential equations for a linear operator
• Averaging methods in nonlinear dynamical systems
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