On the nonlinear dynamics of trolling-mode AFM: Analytical solution using multiple time scales method

2018 ◽  
Vol 423 ◽  
pp. 263-286 ◽  
Author(s):  
Mohammadreza Sajjadi ◽  
Hossein Nejat Pishkenari ◽  
Gholamreza Vossoughi
Keyword(s):  
Nonlinear Dynamics ◽  
Analytical Solution ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multiple Time Scales Method

scholarly journals Recent advances in periodic vibrations of the middle ear with a floating mass transducer

Meccanica ◽  
2020 ◽  
Vol 55 (12) ◽  
pp. 2609-2621
Author(s):  
Rafal Rusinek ◽  
Andrzej Weremczuk
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Middle Ear ◽  
Nonlinear Model ◽  
Degree Of Freedom ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multiple Time Scales Method ◽  
Recent Advances ◽  
The Stability

AbstractThe paper investigates periodic solutions of a nonlinear model of the middle ear with a floating mass transducer. A multi degree of freedom model is used to obtain a solution near the first resonance. The model is solved analytically by means of the multiple time scales method. Next, the stability of obtained periodic solutions is analysed in order to identify the parameters of the floating mass transducer that affect the middle ear dynamics. Moreover, some parameters of the middle ear structure are investigated with respect to their impact on obtained periodic solutions.

Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yélomè Judicaël Fernando Kpomahou ◽  
Clément Hodévèwan Miwadinou ◽  
Richard Gilles Agbokpanzo ◽  
Laurent Amoussou Hinvi
Keyword(s):  
Nonlinear Dynamics ◽  
System Parameter ◽  
Nonlinear Ordinary Differential Equation ◽  
Van Der Pol Oscillator ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Bifurcation Diagrams ◽  
External Excitation ◽  
Van Der Pol ◽  
Multiple Time Scales Method

Abstract In this paper, nonlinear dynamics study of a RLC series circuit modeled by a generalized Van der Pol oscillator is investigated. After establishing a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. According to the external excitation strength, harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. Bifurcation diagrams displayed by the model for each system parameter are performed numerically through the fourth-order Runge–Kutta algorithm.

SOME REMARKS ON THE MULTIPLE TIME SCALES OF DIFFUSION IN MINERALS AND MELTS

2018 ◽  
Author(s):  
Yan Liang ◽  
◽  
Daniele J. Cherniak ◽  
Chenguang Sun
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Are We Doing ‘Systems’ Research? An Assessment of Methods for Climate Change Adaptation to Hydrohazards in a Complex World

2019 ◽  
Vol 11 (4) ◽  
pp. 1163 ◽  
Author(s):  
Melissa Bedinger ◽  
Lindsay Beevers ◽  
Lila Collet ◽  
Annie Visser
Keyword(s):  
Climate Change ◽  
Human Nature ◽  
Climate Change Adaptation ◽  
Time Scales ◽  
Spatial Scales ◽  
Local Context ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Systems Research

Climate change is a product of the Anthropocene, and the human–nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for ‘systems’ research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human–nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human–nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom–up and top–down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human–nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.

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