A mechanism for energy transfer leading to conformation change in networked nonlinear systems

Eisenhower, Bryan; Mezić, Igor

doi:10.1109/cdc.2007.4434507

Cited by 11 publications

(18 citation statements)

References 15 publications

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“…This salient feature of J suggests a directed transmission path of energy from high-frequency KMs to low ones. This is consistent with that in [84] that analyzes global dynamics occurring in nearly-integrable Hamiltonian systems. The The symbol T is the sampling period.…”

Section: Precursor Diagnostic To Coherent Swing Instabilitysupporting

confidence: 90%

Applied Koopman operator theory for power systems technology

Susuki

Mezić

Raak

et al. 2016

NOLTA

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Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this paper, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power systems technology. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models. Future problems of this research direction are identified in the last concluding part of this paper.

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Section: Precursor Diagnostic To Coherent Swing Instabilitysupporting

confidence: 90%

Applied Koopman operator theory for power systems technology

Susuki

Mezić

Raak

et al. 2016

NOLTA

Self Cite

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“…In particular, we point out for the loop system that incoherent bounded swings of generators lead to their coherent loss of synchronism, namely, global instability. This is motivated by [12], [13], [14] on dynamics of molecular conformation. Sec.…”

Section: Introductionmentioning

confidence: 99%

Global swing instability of multimachine power systems

Susuki

Mezić

Hikihara

2008

2008 47th IEEE Conference on Decision and Control

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This paper studies global instability in swing equations of multimachine power systems. Global instability is related to the undesirable phenomenon of power system, implying that most of all generators in a system coherently lose synchronism with the remaining generators of the system. By analyzing a power system with the loop transmission network, we analytically show that global instability can occur as a result of the interplay between network topology of the system and local dynamics of generators in the system. This suggests a possibility of control for global instability by varying network topology of the system.

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“…Previous studies, 8,9,11,24 mainly numerical, showed that this model exhibits an intriguing phenomenon of structured activations observed in many bio-molecules: While the system is robust to noise, it is sensitive to certain specific fine scale modes that can trigger the division. Figure 2 provides the numerical data for such claim.…”

Section: B Phenomenon Of Structured Activationsmentioning

confidence: 99%

“…24,38 Previous studies, 8,9,24 mainly numerical, showed that this model exhibits an intriguing phenomenon of structured activations observed in many bio-molecules: While the system is robust to noise, it is sensitive to certain specific fine scale modes that can trigger the division. Below, we will describe briefly the results of our analytical study on this intriguing phenomenon and our effort in the control of this DNA model via parametric resonance.…”

Section: Introductionmentioning

confidence: 99%

Control of a model of DNA division via parametric resonance

Koon

Owhadi

Tao

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the internal resonance, energy transfer, activation mechanism, and control of a model of DNA division via parametric resonance. While the system is robust to noise, this study shows that it is sensitive to specific fine scale modes and frequencies that could be targeted by low intensity electro-magnetic fields for triggering and controlling the division. The DNA model is a chain of pendula in a Morse potential. While the (possibly parametrically excited) system has a large number of degrees of freedom and a large number of intrinsic time scales, global and slow variables can be identified by (1) first reducing its dynamic to two modes exchanging energy between each other and (2) averaging the dynamic of the reduced system with respect to the phase of the fastest mode. Surprisingly, the global and slow dynamic of the system remains Hamiltonian (despite the parametric excitation) and the study of its associated effective potential shows how parametric excitation can turn the unstable open state into a stable one. Numerical experiments support the accuracy of the time-averaged reduced Hamiltonian in capturing the global and slow dynamic of the full system. In this paper, we study the internal resonance, energy transfer, activation mechanism, and control of a model of DNA division via parametric resonance. While DNA macro-molecules are robust to noise, our study shows that they are sensitive to specific fine scale modes and frequencies that could be targeted by low intensity electromagnetic fields for triggering and controlling the division. The suggested method of control is supported not only by the observation that DNA vibrations induced by electricfields or microwave absorption are an experimental reality but also by the fact that electric field-induced molecular vibrations have already been used as a noninvasive cell transfection protocol. Our study also raises the question on whether enzymes are using the proposed mechanism to initiate the opening of DNA strands. This question is to put into correspondence with increasing theoretical and experimental evidence that low-frequency vibrations do exist and play significant biological functions in proteins, DNA molecules, and other bio-macromolecules.

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A mechanism for energy transfer leading to conformation change in networked nonlinear systems

Cited by 11 publications

References 15 publications

Applied Koopman operator theory for power systems technology

Applied Koopman operator theory for power systems technology

Global swing instability of multimachine power systems

Control of a model of DNA division via parametric resonance

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