Search results for "Instability"
showing 10 items of 724 documents
Towards a quantitative comparison between global and local stability analysis
2017
A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed spher…
Mesoscopic Scale Structural Instability in Ferroelectrics
2009
First-principles statistics addressed to structural phase transitions and temperature development of ferroelectric response is derived within the framework of the Fokker-Planck (Smoluchowsky) equation as complementary to the Monte Carlo [R.D King-Smith., D Vanderbilt, Phys. Rev. B 49, 5828–5844 (1994)] and molecular dynamics [T. Nishimatsu, U. V Waghmare, Y. Kawazoe., D. Vanderbilt, arXiv:0804.1853v2] simulations. Illustrative example of is given for 5 × 5 × 5 BaTiO 3 supercell.
Experimental observation of incoherent modulation instability in standard optical fibers
2005
In this work, we demonstrate theoretically and experimentally that a partially temporally incoherent light can exhibit modulational instability when propagating in an optical fiber with instantaneous nonlinear Kerr response.
More on Transmission-Line Solitons
1996
The study of solitons on discrete lattices dates back to the early days of soliton theory (Frenkel and Kontorova 1939, Fermi et al. 1955) and is of great physical importance. Generally, the discrete nonlinear equations which model these lattices cannot be solved analytically. Consequently, one looks for possible pulse-soliton solutions in the continuum or long wavelength approximation, that is, solitons with a width much larger than the electrical length of a unit section of the electrical network, as described in Chap.3. When this approach is not workable, one has to use numerical approaches (Zabusky 1973, Eilbeck 1991) or simulations. Nevertheless, there exist some lattice models for whic…
Role of Polarization Mode Dispersion on Modulational Instability in Optical Fibers
2001
We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we give the explicit form of the effective matrix and numerically compute the maximal eigenvalue. In the anomalous dispersion regime, polarization dispersion widens the unstable bandwidth. Depending on the type of variations of the birefringence parameters, polariza…
Strong four-photon conversion regime of cross-phase-modulation-induced modulational instability
2000
We investigate theoretically and experimentally the strong conversion regime of parametric four-photon amplification or induced modulational instability in the normal dispersion regime of propagation in a highly birefringent fiber. Such optical mixing is observed by injecting a tunable linearly polarized (along the fast axis) anti-Stokes signal wave copropagating with a pump equisplitted between the fiber axes (i.e., linearly polarized at 45\ifmmode^\circ\else\textdegree\fi{}) which entail that the two pump modes experience cross-phase modulation. In agreement with a four-wave model developed to study the depleted regime of the mixing process, we observe that the strongest conversion occurs…
Multimode emission in inhomogeneously broadened ring lasers
2001
The threshold for multilongitudinal-mode emission in inhomogeneously broadened ring lasers is analytically investigated. In the homogeneous limit the multimode instability corresponds to the classical Risken–Nummedal–Graham–Haken instability. It is found that by increasing the inhomogeneous linewidth, the instability threshold is decreased and the growth of high-frequency side modes is favored. In the limit where the population-inversion decay rate γ‖ is much smaller than the polarization decay rate γ⊥ (class B lasers), analytical expressions for the instability threshold are found, which are then generalized to three-level lasers for a comparison with experimental results obtained with erb…
Generalized rate equations for multimode lasers
2003
Abstract A generalized rate equations model for class B lasers outside the uniform field limit is presented. This model allows to correctly describe the Risken–Nummedal–Graham–Haken instability and its associated multimode dynamics. When parameters suitable for fiber lasers – where the instability has been observed – are adopted, the computation time is shown to be greatly reduced with respect to the complete model based on the full set of Maxwell–Bloch (MB) equations.
Multimode instability in inhomogeneously broadened class-Bring lasers: Beyond the uniform-field limit
2001
The multimode emission threshold of class-$B$ ring lasers is analytically investigated taking into account the localized nature of the cavity losses and the inhomogeneous broadening of the amplifying medium. This analysis finds a relevant application to erbium-doped fiber lasers (EDFL's). The main conclusion is that the predictions of the simplest models are deeply modified both quantitatively and qualitatively. Thus, any attempt to interpret multimode emission in EDFL's must incorporate the two considered factors. Two main results are: (i) While in homogeneously broadened lasers instabilities are inhibited for values of the mirrors' reflectivity $\mathcal{R}l0.54ca,$ this limitation disapp…
KRYLOV-BOGOLIUBOV APPROACH TO NON-LINEAR HYSTERETIC INSTABILITY IN ROTORDYNAMICS
2012
The internal friction due to the shaft hysteresis or the shrink fitting release exerts a destabilizing effect on the overcritical rotor whirl, but may be counteracted by other external dissipative sources and/or by proper anisotropy of the support stiffness. The internal friction effect may be treated by either dry or viscous models, obtaining similar results in the hypothesis of small dissipation levels, provided that proper equivalence criteria are defined between the two approaches. The equivalence is here stated by imposing the same energy dissipation over a large number of shaft revolutions. Approximate closed-form autonomous solutions for a symmetric rotor arrangement subject to Coulo…