4,063 research outputs found
Protein folding tames chaos
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
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
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
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
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
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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
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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