Phase effects in passive nonlinear resonators

Vorontsov, Mikhail A.; Shishakov, К. V.

doi:10.1070/qe1991v021n01abeh003726

Cited by 4 publications

(4 citation statements)

References 4 publications

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“…Such a behaviour is exhibited by the solutions to the oscillation equations in the adiabatically-stratified part of the solar convective envelope, owing to their high-frequency asymptotic properties (the wave propagation here is close to that of purely acoustic waves). Specifically, the near-harmonic behavior is exhibited with best accuracy by eigenfunction ψp(τ ) defined as (see Vorontsov 1991, and Paper I)…”

Section: The Group Velocitymentioning

confidence: 99%

Helioseismic measurements in the solar envelope using group velocities of surface waves

Vorontsov

Батурин

Ayukov

et al. 2014

Monthly Notices of the Royal Astronomical Society

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At intermediate and high degree l, solar p-and f modes can be considered as surface waves. Using variational principle, we derive an integral expression for the group velocities of the surface waves in terms of adiabatic eigenfunctions of normal modes, and address the benefits of using group-velocity measurements as a supplementary diagnostic tool in solar seismology. The principal advantage of using group velocities, when compared with direct analysis of the oscillation frequencies, comes from their smaller sensitivity to the uncertainties in the near-photospheric layers. We address some numerical examples where group velocities are used to reveal inconsistencies between the solar models and the seismic data. Further, we implement the group-velocity measurements to the calibration of the specific entropy, helium abundance Y and heavy-element abundance Z in the adiabatically-stratified part of the solar convective envelope, using different recent versions of the equation of state. The results are in close agreement with our earlier measurements based on more sophisticated analysis of the solar oscillation frequencies , MNRAS 430, 1636. These results bring further support to the downward revision of the solar heavy-element abundances in recent spectroscopic measurements.

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Section: The Group Velocitymentioning

confidence: 99%

Helioseismic measurements in the solar envelope using group velocities of surface waves

Vorontsov

Батурин

Ayukov

et al. 2014

Monthly Notices of the Royal Astronomical Society

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“…Nevertheless, it is a first approximation. A generalization at second order has been developed for both high (Vorontsov 1991) and low degree modes (Lopes & Turck-Chieze 1994) that find better evidence about the role of the sub surface layers and of the gravity in the core when one can only measure low degree modes; this will be used soon for solar-like stars.…”

Section: The Solar Acoustic Modesmentioning

confidence: 99%

Solar-stellar astrophysics and dark matter

Turck‐Chièze¹,

Lopes²

2012

Res. Astron. Astrophys.

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In this review, we recall how stars contribute to the search for dark matter and the specific role of the Sun. We describe a more complete picture of the solar interior that emerges from neutrino detections, gravity and acoustic mode measurements of the Solar and Heliospheric Observatory (SOHO) satellite, becoming a reference for the most common stars in the Universe. The Sun is a unique star in that we can observe directly the effect of dark matter. The absence of a signature related to Weakly Interacting Massive Particles (WIMPs) in its core disfavors a WIMP mass range below 12 GeV. We give arguments to continue this search on the Sun and other promising cases. We also examine another dark matter candidate, the sterile neutrino, and infer the limitations of the classical structural equations. Open questions on the young Sun, when planets formed, and on its present internal dynamics are finally discussed. Future directions are proposed for the next decade: a better description of the solar core, a generalization to stars coming from seismic missions and a better understanding of the dynamics of our galaxy which are all crucial keys for understanding dark matter.

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“…In the one-pass resonator model the phase modulation dynamics u = u(t; K) = u(x, y, t; K) is described by the quasilinear diffusion equation [2] ∂ t u + u − D∆u = K(x, y) (1 + γ cos(u + ϕ)) .…”

Section: Introductionmentioning

confidence: 99%

Distortion-suppression optimization for a class of nonlinear optical systems with feedback

Pulin¹,

Razgulin²

2006

Comput Math Model

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We consider the initial boundary-value problem for the quasilinear diffusion equation ∂tu + u − D∆u = K(x, y)`1 + γ(u + ϕ(x, y))´describing the dynamics of optical systems with controlled feedback wave intensity modulation K(x, y) in the presence of incoming-wave phase perturbations ϕ(x, y). The control problem for the parameter K(x, y) is formulated with the objective of smoothing out the spatial nonhomogeneities of the total output phase u(x, y, T ) + ϕ(x, y). We prove existence and uniqueness theorems for the generalized solutions of the direct and conjugate problems, solvability theorems for the optimization problems, and Frechet-differentiability of the objective functional. A formula for the functional gradient is derived and the efficiency of the gradient projection method is demonstrated numerically.

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Phase effects in passive nonlinear resonators

Cited by 4 publications

References 4 publications

Helioseismic measurements in the solar envelope using group velocities of surface waves

Helioseismic measurements in the solar envelope using group velocities of surface waves

Solar-stellar astrophysics and dark matter

Distortion-suppression optimization for a class of nonlinear optical systems with feedback

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