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Linear differential equations with periodic coefficients
01 Jan 1975-
About: The article was published on 1975-01-01 and is currently open access. It has received 918 citations till now. The article focuses on the topics: Linear differential equation & Stochastic partial differential equation.
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TL;DR: Magnusson expansion as discussed by the authors provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory (TEPT).
1,013 citations
Cites background from "Linear differential equations with ..."
...Thus the piece exp(tF ) in (125) may be considered as an exact solution of the system (30) previously moved to a representation where the coefficient matrix is the constant matrix F [242]....
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...in [242]), the following result has been proved in [43]: if the analytic matrix function Yt(ε) has an eigenvalue ρ0(ε0) of multiplicity l > 1 for a certain ε0 such that: (a) there is a curve in the ε-plane joining ε = 0 with ε = ε0, and (b) the number of equal terms in log ρ1(ε0), log ρ2(ε0), ....
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TL;DR: In this article, a review of the past and recent developments in system identification of nonlinear dynamical structures is presented, highlighting their assets and limitations and identifying future directions in this research area.
1,000 citations
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19 May 2005TL;DR: In this article, the authors present a detailed review of liquid sloshing dynamics in rigid containers, including linear forced and non-linear interaction under external and parametric excitations.
Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.
920 citations
TL;DR: It is found that cycling is unlikely to reduce either the evolution or the spread of antibiotic resistance, and alternative drug-use strategies such as mixing are predicted to be more effective.
Abstract: Hospital-acquired infections caused by antibiotic-resistant bacteria pose a grave and growing threat to public health. Antimicrobial cycling, in which two or more antibiotic classes are alternated on a time scale of months to years, seems to be a leading candidate in the search for treatment strategies that can slow the evolution and spread of antibiotic resistance in hospitals. We develop a mathematical model of antimicrobial cycling in a hospital setting and use this model to explore the efficacy of cycling programs. We find that cycling is unlikely to reduce either the evolution or the spread of antibiotic resistance. Alternative drug-use strategies such as mixing, in which each treated patient receives one of several drug classes used simultaneously in the hospital, are predicted to be more effective. A simple ecological explanation underlies these results. Heterogeneous antibiotic use slows the spread of resistance. However, at the scale relevant to bacterial populations, mixing imposes greater heterogeneity than does cycling. As a consequence, cycling is unlikely to be effective and may even hinder resistance control. These results may explain the limited success reported thus far from clinical trials of antimicrobial cycling.
322 citations
Cites background from "Linear differential equations with ..."
...where [ ] is the dominant eigenvalue of the full-cycle growth matrix [the monodromy matrix in Floquet theory (39)] given by eM2teM1t....
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TL;DR: In this article, a WKB formalism for constructing normal modes of short-wavelength ideal hydromagnetic, pressure-driven instabilities (ballooning modes) in general toroidal magnetic containment devices with sheared magnetic fields is developed.
Abstract: A WKB formalism for constructing normal modes of short‐wavelength ideal hydromagnetic, pressure‐driven instabilities (ballooning modes) in general toroidal magnetic containment devices with sheared magnetic fields is developed. No incompressibility approximation is made. A dispersion relation is obtained from the eigenvalues of a fourth‐order system of ordinary differential equations to be solved by integrating along a line of force. Higher‐order calculations are performed to find the amplitude equation and the phase change at a caustic. These conform to typical WKB results. In axisymmetric systems, the ray equations are integrable, and semiclassical quantization leads to a growth rate spectrum consisting of an infinity of discrete eigenvalues, bounded above by an accumulation point. However, each eigenvalue is infinitely degenerate. In the nonaxisymmetric case, the rays are unbounded in a four‐dimensional phase space, and semiclassical quantization breaks down, leading to broadening of the discrete eigenvalues and the accumulation point of the axisymmetric unstable spectrum into continuum bands. Analysis of a model problem indicates that the broadening of the discrete eigenvalues is numerically very small, the dominant effect being broadening of the accumulation point.
282 citations