44,381 research outputs found
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Ultra-Strong Optomechanics Incorporating the Dynamical Casimir Effect
We propose a superconducting circuit comprising a dc-SQUID with mechanically
compliant arm embedded in a coplanar microwave cavity that realizes an
optomechanical system with a degenerate or non-degenerate parametric
interaction generated via the dynamical Casimir effect. For experimentally
feasible parameters, this setup is capable of reaching the single-photon,
ultra-strong coupling regime, while simultaneously possessing a parametric
coupling strength approaching the renormalized cavity frequency. This opens up
the possibility of observing the interplay between these two fundamental
nonlinearities at the single-photon level.Comment: 7 pages, 1 figure, 1 tabl
Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty
Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncertainty and bound the variation in the magnitude of the input-output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers
Molecular cavity optomechanics: a theory of plasmon-enhanced Raman scattering
The conventional explanation of plasmon-enhanced Raman scattering attributes
the enhancement to the antenna effect focusing the electromagnetic field into
sub-wavelength volumes. Here we introduce a new model that additionally
accounts for the dynamical and coherent nature of the plasmon-molecule
interaction and thereby reveals an enhancement mechanism not contemplated
before: dynamical backaction amplification of molecular vibrations. We first
map the problem onto the canonical model of cavity optomechanics, in which the
molecular vibration and the plasmon are \textit{parametrically coupled}. The
optomechanical coupling rate, from which we derive the Raman cross section, is
computed from the molecules Raman activities and the plasmonic field
distribution. When the plasmon decay rate is comparable or smaller than the
vibrational frequency and the excitation laser is blue-detuned from the plasmon
onto the vibrational sideband, the resulting delayed feedback force can lead to
efficient parametric amplification of molecular vibrations. The optomechanical
theory provides a quantitative framework for the calculation of enhanced
cross-sections, recovers known results, and enables the design of novel systems
that leverage dynamical backaction to achieve additional, mode-selective
enhancement. It yields a new understanding of plasmon-enhanced Raman scattering
and opens a route to molecular quantum optomechanics.Comment: Extensively revised and improved version thanks to the hard work and
constructive comments of a careful Referee. Includes Supplemental Materia
Nonlinear time-series analysis revisited
In 1980 and 1981, two pioneering papers laid the foundation for what became
known as nonlinear time-series analysis: the analysis of observed
data---typically univariate---via dynamical systems theory. Based on the
concept of state-space reconstruction, this set of methods allows us to compute
characteristic quantities such as Lyapunov exponents and fractal dimensions, to
predict the future course of the time series, and even to reconstruct the
equations of motion in some cases. In practice, however, there are a number of
issues that restrict the power of this approach: whether the signal accurately
and thoroughly samples the dynamics, for instance, and whether it contains
noise. Moreover, the numerical algorithms that we use to instantiate these
ideas are not perfect; they involve approximations, scale parameters, and
finite-precision arithmetic, among other things. Even so, nonlinear time-series
analysis has been used to great advantage on thousands of real and synthetic
data sets from a wide variety of systems ranging from roulette wheels to lasers
to the human heart. Even in cases where the data do not meet the mathematical
or algorithmic requirements to assure full topological conjugacy, the results
of nonlinear time-series analysis can be helpful in understanding,
characterizing, and predicting dynamical systems
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