Electromagnetic Levitation: A Nonlinear Analysis Approach

1999 ◽  
Author(s):  
Bogdan O. Ciocirlan ◽  
Dan B. Marghitu ◽  
David G. Beale ◽  
Ruel A. Overfelt
Keyword(s):  
Nonlinear Dynamics ◽  
Time Evolution ◽  
Time Series Data ◽  
Electromagnetic Levitation ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Attractor Dimension ◽  
Molten Droplet ◽  
Levitated Droplet ◽  
Electromagnetically Levitated

Abstract In this paper, a nonlinear dynamics approach for analyzing the time evolution of an electromagnetically levitated droplet is proposed. The analysis was performed on the experimental data acquired from a levitation instrument developed by Space Power Institute at Auburn University. Several nonlinear dynamics tools were applied in order to reveal whether the time evolution of the droplet is deterministic (periodic, quasiperiodic or chaotic) or random. Quantities characterizing time series data such as the attractor dimension or the largest Lyapunov exponent were computed. It was mainly found that the underlying dynamics of the molten droplet is in fact chaotic.

The Dynamics of a Flexible Levitated Droplet

2001 ◽  
Author(s):  
Mihai Dupac ◽  
Dan B. Marghitu ◽  
David G. Beale
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Time Series Data ◽  
Simulated Data ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Dynamics Analysis ◽  
Attractor Dimension ◽  
Levitated Droplet

Abstract In this paper, a nonlinear dynamics analysis of the simulated data was considered to study the time evolution of an electro-magnetically levitated flexible droplet. The main goals of this work are to study the behavior of the levitated droplet and to investigate its stability. Quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent were computed.

Stability Analysis of a Levitated Droplet by Using Floquet Multipliers

2000 ◽  
Vol 122 (4) ◽  
pp. 399-408 ◽  
Author(s):  
Bogdan O. Ciocirlan ◽  
Dan B. Marghitu
Keyword(s):  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Time Series Data ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Attractor Dimension ◽  
Floquet Multipliers ◽  
Levitated Droplet ◽  
System Data ◽  
The Stability

In this paper, the analysis of the time evolution of a levitated droplet is proposed. The analysis is composed of two parts: in the first part, a nonlinear dynamics approach was considered to calculate quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent. The number of degrees of freedom in the system was also assessed. Based on the results obtained in the first part, Floquet theory was applied in the second part of the analysis to investigate the stability of the system. Data acquired from a levitation instrument developed by Space Power Institute at Auburn University was used to perform the analysis. [S0739-3717(00)01903-6]

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals Indication of Mental Health from Fingertip Pulse Waves and Its Application

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Mayumi Oyama-Higa ◽  
Fumitake Ou
Keyword(s):  
Mental Health ◽  
Real Time ◽  
Time Series Data ◽  
Biological Information ◽  
Autonomic Nerve ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Vascular Age ◽  
Pulse Waves ◽  
High Level

This article is a comprehensive review of recent studies of the authors on the indication of mental health from biological information contained in pulse waves. A series of studies discovered that the largest Lyapunov exponent (LLE) of the attractor, which is constructed for the time series data from pulse waves, can provide as an effective indicator of mental health. A low level of LLE indicates insufficiency of external adaptability, which is characteristic of dementia and depression sufferers. On the contrary, a continuous high level of LLE indicates excessive external adaptability, and people in this condition tend to resort to violence. With this discovery, real-time display of the LLE, combined with other physiological indexes such as the autonomic nerve balance (ANB), sample entropy, and vascular age, as a reference, can enable people to conduct self-check of mental status. To this end, software development was performed in order to enable users to conduct pulse wave measurement anywhere at any time and display the analytical results in real time during the measurement.

DETECTING NONLINEAR DETERMINISM IN VOICED SOUNDS OF JAPANESE VOWEL /a/

2000 ◽  
Vol 10 (08) ◽  
pp. 1973-1979 ◽  
Author(s):  
TAKAYA MIYANO ◽  
AKIRA NAGAMI ◽  
ISAO TOKUDA ◽  
KAZUYUKI AIHARA
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Time Series Analysis ◽  
Basis Function ◽  
Speech Signal ◽  
Time Series Data ◽  
Series Data ◽  
Radial Basis Function Networks ◽  
Data Points ◽  
Surrogate Method

Nonlinear determinism in voiced sounds of the Japanese vowel /a/ is tested by the time series analysis associated with the surrogate method. To capture nonlinear dynamics underlying the speech signal, we apply the generalized radial basis function networks as nonlinear predictors to the time series data. The optimized network parameters may show a trail of the nonlinear dynamics though not conspicuously. This may be due to paucity of data points.

scholarly journals Structured Inference for Recurrent Hidden Semi-markov Model

2018 ◽  
Author(s):  
Hao Liu ◽  
Lirong He ◽  
Haoli Bai ◽  
Bo Dai ◽  
Kun Bai ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Time Series Data ◽  
Markov Models ◽  
Series Data ◽  
Discrete Variables ◽  
Inference Procedure ◽  
Behavior Understanding ◽  
Proposed Model ◽  
Inference Network

Segmentation and labeling for high dimensional time series is an important yet challenging task in a number of applications, such as behavior understanding and medical diagnosis. Recent advances to model the nonlinear dynamics in such time series data, has suggested to involve recurrent neural networks into  Hidden Markov Models. However, this involvement has caused the inference procedure much more complicated, often leading to intractable inference, especially for the discrete variables of segmentation and labeling. To achieve both flexibility and tractability in modeling nonlinear dynamics of discrete variables, we present a structured and stochastic sequential neural network (SSNN), which composes with a generative network and an inference network. In detail, the generative network aims to not only capture the long-term dependencies but also model the uncertainty of the segmentation labels via semi-Markov models. More importantly, for efficient and accurate inference, the proposed bi-directional inference network reparameterizes the categorical segmentation with the Gumbel-Softmax approximation and resorts to the Stochastic Gradient Variational Bayes. We evaluate the proposed model in a number of tasks, including speech modeling, automatic segmentation and labeling in behavior understanding, and sequential multi-objects recognition. Experimental results have demonstrated that our proposed model can achieve significant improvement over the state-of-the-art methods.

scholarly journals Forecasting Development of Economic Processes using Adapted Nonlinear Dynamics Methods

2019 ◽  
Vol 9 (1) ◽  
pp. 3082-3085
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Chaotic Dynamics ◽  
Time Series Data ◽  
Data Preprocessing ◽  
Comprehensive Analysis ◽  
Series Data ◽  
The Future ◽  
The Many ◽  
Type Of Behavior

In this work authors propose using adapted nonlinear dynamics methods to prepare time series data for the forecast procedure in order to identify chaotic dynamics and to select forecast methods and models. Each step of the proposed set of methods for data preprocessing allows us to put forward proposals on certain properties of the studied time series. This, in turn, proves that to obtain reliable and reasonable conclusions about the type of behavior of the investigated system, the results of one of the many existing tests are not enough. Conducting a comprehensive analysis, will most correctly determine the type of behavior of the time series and its characteristics, which will make it possible to obtain a reliable forecast in the future.

scholarly journals Evaluating Emotional and Biological Sensitivity to Maternal Behavior Among Self-Injuring and Depressed Adolescent Girls Using Nonlinear Dynamics

2017 ◽  
Vol 5 (2) ◽  
pp. 272-285 ◽  
Author(s):  
Sheila E. Crowell ◽  
Jonathan E. Butner ◽  
Travis J. Wiltshire ◽  
Ascher K. Munion ◽  
Mona Yaptangco ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Adolescent Girls ◽  
Time Series Data ◽  
Behavioral Responses ◽  
High Sensitivity ◽  
Series Data ◽  
Physiological Reactivity ◽  
Psychophysiological Reactivity ◽  
Depressed Adolescent ◽  
And Control

High sensitivity and reactivity to behaviors of family members characterize several forms of psychopathology, including self-inflicted injury (SII). We examined mother-daughter behavioral and psychophysiological reactivity during a conflict discussion using nonlinear dynamics to assess asymmetrical associations within time-series data. Depressed, SII, and control adolescents and their mothers participated ( N = 76 dyads). We expected that (a) mothers’ evocative behaviors would affect behavioral and psychophysiological reactivity among depressed and, especially, SII adolescents, (b) adolescents’ behaviors would not evoke mothers’ behavioral or physiological reactivity, and (c) control teens and mothers would be less reactive, with no dynamic associations in either direction. Convergent cross-mapping with dewdrop regression, which identifies directional associations, indicated that mothers’ behaviors evoked behavioral responses among depressed and SII participants, but evoked psychophysiological reactivity for SII teens only. There were no effects of adolescents’ behavior on mothers’ reactivity. Results are interpreted based on sensitivity theories and directions for further research are outlined.

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