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The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
van der Pol oscillator hybrid dynamical system
2015/8/25
The forced van der Pol oscillator has been the focus of scientific scrutiny for almost a century, yet
its global bifurcation structure is still poorly understood. In this paper, we present a hybrid s...
The phase flow method
The phase flow method Ordinary differential equations Phase maps Phase flow Interpolation High-frequency wave propagation Geometrical optics Hamiltonian dynamics Ray equations Wave arrival times Eulerian and Lagrangian formulations
2015/7/14
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially ...
The Phase Flow Method
The phase flow method ordinary differential equations phase maps phase flow interpolation high-frequency wave propagation geometrical optics Hamiltonian dynamics ray equations wave arrival times Eulerian and Lagrangian formulations
2015/6/17
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially ...
On modeling and simulation of surfactants in diffuse interface flow
modeling and simulation surfactants interface flow
2011/9/29
An existing phase- eld model of two immiscible uids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and show that it is mathematically ill-p...