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Multiple Time Scale Methods and Gyrotrons
1987Abstract : Objectives were to complete a study of one-dimensional electrostatic plasmas using the discrete Hamiltonian method, and to construct a model of ridged high harmonic gyrtron oscillators using standard gyrotron modeling techniques. Ridged gyrotrons appear ideal for the future application of the multiple time scale, discrete Hamiltonian method.
Peter Vitello, Curtic R. Menyuk
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Continuation of Approximate Transformation Groups via Multiple Time Scales Method
Nonlinear Dynamics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baikov, V. A., Ibragimov, N. H.
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Multiple time scale methods for adiabatic systems
American Journal of Physics, 1992The method of multiple time scales is applied to adiabatic systems. Adiabatic theorems for both classical and quantum systems are derived and expressions for Berry’s phase and its classical counterpart are obtained within the framework of a consistent approximation scheme.
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THE KBM DERIVATIVE EXPANSION METHOD IS EQUIVALENT TO THE MULTIPLE-TIME-SCALES METHOD
Journal of Sound and Vibration, 1997Summary: Several perturbation methods are commonly used to predict the free and forced response of weakly non-linear oscillators. The Krylov-Bogoliubov-Mitropolsky (KBM) and multiple-time-scales (MTS) methods use expansions of dependent variables, ordinary time derivatives, and some system parameters to convert the equations of motion into a set of ...
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On the Equivalence of Normal Form Theory and Multiple Time Scale Method
Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2007Multiple time scales technique has long been an important method for the analysis of weakly nonlinear systems. In this technique, a set of multiple time scales are introduced that serve as the independent variables. The evolution of state variables at slower time scales is then determined so as to make the expansions for solutions in a perturbation ...
Fengxia Wang, Anil K. Bajaj
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A reduction method for multiple time scale stochastic reaction networks
Journal of Mathematical Chemistry, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lee, Chang Hyeong, Lui, Roger
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Journal of Applied Mechanics, 1983
An incremental harmonic balance method with multiple time scales is presented in this paper. As a general and systematic computer method, it is capable of treating aperiodic “steady-state” vibrations such as combination resonance, etc. Moreover, this method is not subjected to the limitation of weak nonlinearity.
Lau, SL, Cheung, YK, Wu, SY
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An incremental harmonic balance method with multiple time scales is presented in this paper. As a general and systematic computer method, it is capable of treating aperiodic “steady-state” vibrations such as combination resonance, etc. Moreover, this method is not subjected to the limitation of weak nonlinearity.
Lau, SL, Cheung, YK, Wu, SY
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Analysis of Multiscale Methods for Stochastic Dynamical Systems with Multiple Time Scales
Multiscale Modeling & Simulation, 2010We prove the convergence of a class of numerical schemes for stochastic dynamical systems with well-separated time scales. A sharp error estimate for the schemes is provided. The optimality of the convergence rate is illustrated through examples.
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Multiple Time Scale Numerical Methods for the Inverted Pendulum Problem
2005In this article, we study a class of numerical ODE schemes that use a time filtering strategy and operate in two time scales. The algorithms follow the framework of the heterogeneous multiscale methods (HMM) [1]. We apply the methods to compute the averaged path of the inverted pendulum under a highly oscillatory vertical forcing on the pivot.
Richard Sharp +2 more
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Multiple-time-scaling lattice Boltzmann method for the convection diffusion equation
Physical Review E, 2019A multiple-time-scaling (MTS) strategy that decouples the time discretization in different domains and enables flexible time-step coarsening, refinement, and stretching in the lattice Boltzmann method (LBM) for the convection diffusion equation is developed.
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