Spatially incoherent modulational instability in a non local medium

We investigate one-dimensional transverse modulational instability in a non local medium excited with a spatially incoherent source. Employing undoped nematic liquid crystals in a planar pre-tilted configuration, we investigate the role of the spectral broadening induced by incoherence in conjunction with the spatially non local molecular reorientation. The phenomenon is modeled using the Wigner transform.Comment: 13 pages with 4 figures included. To be published in Laser Physics Letter

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyse a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite's temperature is analysed by qualitative, perturbation and numerical methods, which show that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.Comment: 13 pages, 4 figures (5 EPS files

Breakdown of Conformal Invariance at Strongly Random Critical Points

We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a strongly random critical point. The average correlation functions of this system demonstrate a breakdown of conformal invariance, while the typical correlation functions demonstrate a breakdown of scale invariance. The breakdown of conformal invariance is due to the vanishing of the correlation functions at the infinite disorder fixed point, causing the critical correlation functions to be controlled by a dangerously irrelevant operator describing the approach to the fixed point. We relate the computation of average correlation functions to a problem of persistence in the RG flow.Comment: 9 page

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I : theoretical formulation and model validation

This paper is first of the two papers dealingwith analytical investigation of resonant multimodal dynamics due to 2:1 internal resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small sagged cables - which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to inclined sagged configurations - are presented. A multidimensional Galerkin expansion of the solution ofnonplanar/planar motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance is accomplished by the method of multiple scales. On accounting for higher-order effectsof quadratic/cubic nonlinearities, approximate closed form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful effects due to kinematic condensation

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Dynamics of a suspended nanowire driven by an ac Josephson current in an inhomogeneous magnetic field

We consider a voltage-biased nanoelectromechanical Josephson junction, where a suspended nanowire forms a superconducting weak-link, in an inhomogeneous magnetic field. We show that a nonlinear coupling between the Josephson current and the magnetic field generates a Laplace force that induces a whirling motion of the nanowire. By performing an analytical and a numerical analysis, we demonstrate that at resonance, the amplitude-phase dynamics of the whirling movement present different regimes depending on the degree of inhomogeneity of the magnetic field: time independent, periodic and chaotic. Transitions between these regimes are also discussed.Comment: 7 pages, 5 figure

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II : internal resonance activation, reduced-order models and nonlinear normal modes

Resonant multi-modal dynamics due to planar 2:1 internal resonances in the nonlinear, finite-amplitude, free vibrations of horizontal/inclined cables are parametrically investigated based on the second-order multiple scales solution in Part I [1]. The already validated kinematically non-condensed cable model accounts for the effects of both non-linear dynamic extensibility and system asymmetry due to inclined sagged configurations. Actual activation of 2:1 resonances is discussed, enlightening on a remarkable qualitative difference of horizontal/inclined cables as regards non-linear orthogonality properties of normal modes. Based on the analysis of modal contribution and solution convergence of various resonant cables, hints are obtained on proper reduced-order model selections from the asymptotic solution accounting for higher-order effects of quadratic nonlinearities. The dependence of resonant dynamics on coupled vibration amplitudes, and the significant effects of cable sag, inclination and extensibility on system non-linear behavior are highlighted, along with meaningful contributions of longitudinal dynamics. The spatio-temporal variation of non-linear dynamic configurations and dynamic tensions associated with 2:1 resonant non-linear normal modes is illustrated. Overall, the analytical predictions are validated by finite difference-based numerical investigations of the original partial-differential equations of motion

Higher-order corrections to the relativistic perihelion advance and the mass of binary pulsars

We study the general relativistic orbital equation and using a straightforward perturbation method and a mathematical device first introduced by d'Alembert, we work out approximate expressions of a bound planetary orbit in the form of trigonometrical polynomials and the first three terms of the power series development of the perihelion advance. The results are applied to a more precise determination of the total mass of the double pulsar J0737-3039.Comment: 8 pages. Accepted for publication in "Astrophysics & Space Science

Duality in Perturbation Theory and the Quantum Adiabatic Approximation

Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is identified. It is then shown that the dual to the Dyson series in quantum mechanics is given by a recent devised series having the adiabatic approximation as leading order. A simple application of this result is given by rederiving a theorem for strongly perturbed quantum systems.Comment: 9 pages, revtex. Improved english and presentation. Final version accepted for publication by Physical Review