Analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables

A study is carried out on nonlinear multimodal galloping of suspended cables. A consistent model of a curved cable-beam, geometrically nonlinear and able to torque, recently formulated by the authors, is used. The model accounts for quasi-steady aerodynamic forces, including the effect of static swing of the cable and dynamic twist of the cross-section. Complementary solution methods are employed, namely, finite-difference and Galerkin spatial discretization, followed by numerical time-integration, or Galerkin spatial discretization in conjunction with Multiple Scale perturbation analysis. The different techniques are applied to a cable close to the first cross-over point, at which a number of internal resonances exist. Branches of periodic solutions and their stability are evaluated as functions of wind velocity. The existence of branches of quasi-periodic solutions, originating from narrow unstable intervals and propagating elsewhere, is also proved. Qualitative and quantitative results furnished by the different investigation tools are compared among them, and the importance of the various components of motion, accounted or neglected in the reduced models, is discussed.     

Non-linear responses of suspended cables to primary resonance excitations

We investigate the non-linear forced responses of shallow suspended cables. We consider the following cases: (1) primary resonance of a single in-plane mode and (2) primary resonance of a single out-of-plane mode. In both cases, we assume that the excited mode is not involved in an autoparametric resonance with any other mode. We analyze the system by following two approaches. In the first, we discretize the equations of motion using the Galerkin procedure and then apply the method of multiple scales to the resulting system of non-linear ordinary-differential equations to obtain approximate solutions (discretization approach). In the second, we apply the method of multiple scales directly to the non-linear integral-partial-differential equations of motion and associated boundary conditions to determine approximate solutions (direct approach). We then compare results obtained with both approaches and discuss the influence of the number of modes retained in the discretization procedure on the predicted solutions.     

Wide band polarizer with suspended germanium resonant grating

An ultra broad band polarizer that operates in the telecommunication wavelength band is proposed.This device,which consists of a single suspended germanium resonant grating layer,is designed using the inverse mathematical method and the rigorous vector diffraction theory.Calculated results indicate that the ultra broad band polarizer exhibits extremely high reflection(R > 99%) for TE polarization light and high transmission(T > 99%) for TM polarization at the wavelength range greater than 300 nm,and it has an extinction ratio of approximately 1 000 at the 1 550-nm central wavelength.The results of the rigorous coupled wave analysis indicate that the extremely wide band property of the TE polarization is caused by the excitation of strong modulation guided modes in the design wavelength range.     

Modeling interactions for resonant p-wave scattering

In view of recent experiments on ultracold polarized fermions, the zero-range potential approach is generalized to situations where two-body scattering is resonant in the p-wave channel. We introduce a modified scalar product which reveals a deep relation between the geometry of the Hilbert space and the interaction. This formulation is used to obtain a simple interpretation for the transfer rates between atomic and molecular states within a two branches picture of the many-body system close to resonance. At resonance, the energy of the dilute gas is found to vary linearly with density.     

Nonlinear mode coupling in doubly resonant frequency doublers

The concept of a doubly resonant frequency doubler can be used for a variety of experiments concerning both classical phenomena like efficient frequency doubling at low power levels and quantum effects like squeezed states of light or Quantum Non Demolition (QND) measurements. In many of these experiments the strength of the nonlinear coupling of fundamental and second-harmonic modes is of crucial importance. First we treat the general theory for the calculation of the coupling parameter, which depends not only on properties of the nonlinear material but also on resonator geometry and some optical phases. On this basis we discuss in detail the situation for two different monolithic resonator geometries, namely a linear (standing-wave) and a ring (travelling-wave) cavity. Finally we compare theoretical predictions for these resonators to the experimentally achieved results.     

Spectroscopic mode mapping of resonant plasmon nanoantennas

We present spatially resolved spectral mode mapping of resonant plasmon gap antennas using two-photon luminescence microspectroscopy. The obtained maps are in good agreement with 3D calculations of the antenna modes. The evolution of the modal field with wavelength, both in the gap and along the two coupled gold nanowires forming the antenna, is directly visualized. At resonance, the luminescence for the gap area is enhanced at least 80 times and a comparison with the antenna extremities shows a dynamical charge redistribution due to the near-field coupling between the two arms.     

New resonant backscattering mode in a small-size quantum interferometer

Giant conductance oscillations quasi-periodic in the gate voltage are observed in the open state of a small-size quantum interferometer (of effective radius r ≈ 100 nm) based on the high-mobility 2D electron gas of an AlGaAs/GaAs heterojunction. These oscillations presumably result from the multiparticle effects that occur in the interferometer arms and give rise to a strong backscattering and to conductance peaks, whose period corresponds to a one-electron change in the number of electrons in the arms.     

X-ray absorption measured in the resonant Auger scattering mode

We report both experimental and theoretical studies on x-ray absorption measured in the resonant Auger scattering mode of gas phase carbon monoxide near the O1s-->2pi region. Both experiment and theory display a crucial difference between the x-ray absorption profiles obtained in the conventional and resonant scattering modes. Lifetime vibrational interference is the main source of the difference. It is demonstrated that such interference, which arises from a coherent excitation to overlapping intermediate levels, ruins the idea for obtaining x-ray absorption spectra in a lifetime broadening free regime.     

The evolution of the resonant mode in plasma-maser interaction

We study the evolution of the resonant waves considering its interaction with the nonresonant waves and the plasma particles due to plasma-maser effect. The nonlinear dielectric function of the resonant wave is calculated and is found to consist of two parts: the direct and the polarization coupling terms. On the other hand, the nonlinear dielectric function of the nonresonant wave consists only of the direct coupling term. The significance of our results is discussed.     

Local run-up amplification by resonant wave interactions

Until now, the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the nonlinear shallow water equations are used to investigate the boundary value problem for plane and nontrivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the boundary value problem. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced run-up of nonleading waves. The evolution of energy reveals the existence of a quasiperiodic state for the case of sinusoidal waves. Dispersion is found to slightly reduce the value of maximum run-up but not to change the overall picture. Run-up amplification occurs for both leading elevation and depression waves.     

Multiple internal resonances and non-planar dynamics of shallow suspended cables to the harmonic excitations

In the present study, the nonlinear response of a shallow suspended cable with multiple internal resonances to the primary resonance excitation is investigated. The method of multiple scales is applied directly to the nonlinear equations of motion and associated boundary conditions to obtain the modulation equations and approximate solutions of the cable. Frequency–response curves and force–response curves are used to study the equilibrium solution and its stability. The effects of the excitation amplitude on the frequency–response curves of the cable are also analyzed. Moreover, the chaotic dynamics of the shallow suspended cable is investigated by means of numerical simulations.     

太赫兹频段开口环谐振器的可调谐振模式转换

在硅衬底上设计了一种单开口环谐振器,对其太赫兹频段内的透射性质进行了研究。假定通过光注入方式改变衬底硅的电导率,实现了谐振环的双谐振透射率可调。将砷化镓材料生长于该谐振环的开口处,通过光注入方式改变砷化镓材料的电导率,可以实现谐振环的双频LC共振和偶极子共振模式与单频闭合环共振模式之间的转换。这种通过光注入改变半导体材料电导率的方法,可以在不破坏原来谐振器件物理结构的前提下,实现谐振环谐振模式的可逆转换。     

太赫兹频段开口环谐振器的可调谐振模式转换

在硅衬底上设计了一种单开口环谐振器,对其太赫兹频段内的透射性质进行了研究。假定通过光注入方式改变衬底硅的电导率,实现了谐振环的双谐振透射率可调。将砷化镓材料生长于该谐振环的开口处,通过光注入方式改变砷化镓材料的电导率,可以实现谐振环的双频LC共振和偶极子共振模式与单频闭合环共振模式之间的转换。这种通过光注入改变半导体材料电导率的方法,可以在不破坏原来谐振器件物理结构的前提下,实现谐振环谐振模式的可逆转换。     

Superfluid transition in a rotating fermi gas with resonant interactions

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial trap with frequencies Omega perpendicular, Omega z. We predict the upper-critical angular velocity, omega c2(delta,T), as a function of temperature T and detuning delta across the BEC-BCS crossover. The suppression of superfluidity at omega c2 is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low T and Omega z < Omega perpendicular, in the BCS and crossover regimes of 0 less similar delta less similar delta c, omega c2 is implicitly given by [formula: see text], vanishing as omega c2 approximately Omega perpendicular(1 - delta/delta c)(1/2) near [formula: see text] (with Delta the BCS gap and gamma the resonance width), and extending the bulk result variant Planck's over 2pi omega c2 approximately 2Delta2/epsilonF to a trap. In the BEC regime of delta < 0 we find omega c2-->Omega perpendicular-, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.     

Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables

This paper presents space-time numerical simulation and validation of analytical predictions for the finite-amplitude forced dynamics of suspended cables. The main goal is to complement analytical and numerical solutions, accomplishing overall quantitative/qualitative comparisons of nonlinear response characteristics. By relying on an approximate, kinematically non-condensed, planar modeling, a simply supported horizontal cable subject to a primary external resonance and a 1:1, or 1:1 vs. 2:1, internal resonance is analyzed. To obtain analytical solution, a second-order multiple scales approach is applied to a complete eigenfunction-based series of nonlinear ordinary-differential equations of cable damped forced motion. Accounting for both quadratic/cubic geometric nonlinearities and multiple modal contributions, local scenarios of cable uncoupled/coupled responses and associated stability are predicted, based on chosen reduced-order models. As a cross-checking tool, numerical simulation of the associated nonlinear partial-differential equations describing the dynamics of the actual infinite-dimensional system is carried out using a finite difference technique employing a hybrid explicit-implicit integration scheme. Based on system control parameters and initial conditions, cable amplitude, displacement and tension responses are numerically assessed, thoroughly validating the analytically predicted solutions as regards the actual existence, the meaningful role and the predominating internal resonance of coexisting/competing dynamics. Some methodological aspects are noticed, along with a discussion on the kinematically approximate versus exact, as well as planar versus non-planar, cable modeling.     

Spin diffusion in trapped clouds of cold atoms with resonant interactions

We show that puzzling recent experimental results on spin diffusion in a strongly interacting atomic gas may be understood in terms of the predicted spin diffusion coefficient for a generic strongly interacting system. Three important features play a central role: (a)?Fick's law for diffusion must be modified to allow for the trapping potential; (b)?the diffusion coefficient is inhomogeneous, due to the density variations in the cloud; and (c)?the diffusion approximation fails in the outer parts of the cloud, where the mean free path is long.     

Coherence and clock shifts in ultracold fermi gases with resonant interactions

Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.