4,063 research outputs found

    Protein folding tames chaos

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    Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderliness and relative energies of folded, misfolded and unfolded protein states. Finally, we exploit chaos for protein flexibility analysis and develop a robust chaotic algorithm for the prediction of Debye-Waller factors, or temperature factors, of protein structures

    Synchronization of many nano-mechanical resonators coupled via a common cavity field

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    Using amplitude equations, we show that groups of identical nano-mechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the square sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behaviour which, when analyzed using amplitude equations, can be shown to exhibit multi-stability. In contrast groups of sufficiently dissimilar nano-mechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.Comment: 23 pages, 11 figure

    Entrainment and stimulated emission of auto-oscillators in an acoustic cavity

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    We report theory, measurements and numerical simulations on nonlinear piezoelectric ultrasonic devices with stable limit cycles. The devices are shown to exhibit behavior familiar from the theory of coupled auto-oscillators. Frequency of auto-oscillation is affected by the presence of an acoustic cavity as these spontaneously emitting devices adjust their frequency to the spectrum of the acoustic cavity. Also, the auto-oscillation is shown to be entrained by an applied field; the oscillator synchronizes to an incident wave at a frequency close to the natural frequency of the limit cycle. It is further shown that synchronization occurs here with a phase that can, depending on details, correspond to stimulated emission: the power emission from the oscillator is augmented by the incident field. These behaviors are essential to eventual design of an ultrasonic system that would consist of a number of such devices entrained to their mutual field, a system that would be an analog to a laser. A prototype laser is constructed

    Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system

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    We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The considered system includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and time-convolutionless generator as well as Nakajima-Zwanzig memory kernel. This non-perturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that depending on the state of the environment the operator structures of the two set of equations of motion can exhibit important differences.Comment: 12 pages, no figure

    Mode competition in a system of two parametrically driven pendulums with nonlinear coupling

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    This paper is part three in a series on the dynamics of two coupled, parametrically driven pendulums. In the previous parts Banning and van der Weele (1995) and Banning et al. (1997) studied the case of linear coupling; the present paper deals with the changes brought on by the inclusion of a nonlinear (third-order) term in the coupling. Special attention will be given to the phenomenon of mode competition.\ud \ud The nonlinear coupling is seen to introduce a new kind of threshold into the system, namely a lower limit to the frequency at which certain motions can exist. Another consequence is that the mode interaction between 1¿ and 2ß (two of the normal motions of the system) is less degenerate, causing the intermediary mixed motion known as MP to manifest itself more strongly

    Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

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    In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in Physics Please Lakshmanan for figures (e-mail: [email protected]
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