Near-resonant Region Research Articles

Effect of Mathieu instability on motion response of Spar hull with heave damping plate

The use of Spar hulls in floating solutions for offshore oil and gas application is well established. However, the studies on hydrodynamic responses in near-resonant region of loading, especially in harsh met-ocean conditions are limited. The phenomenon of Mathieu instability and reducing its effect on hydrodynamic response using heave damping plate configurations has been investigated using experimental studies and numerical simulation. This near-resonant-coupled response has been investigated in this study by tuning the pitch and heave natural frequency of the Spar such that the ratio becomes half. This may lead to increased response due to Mathieu instability and hence this study will provide insight into the response characteristics. The experimental investigations were conducted in a laboratory wave basin using a scale model (1:150) Spar hull with four different configurations of heave damping plate in regular waves. The hydrodynamic response of the proposed configurations was measured and simulated for different wave periods and heights. The Spar hull models were moored using catenary mooring line. The responses of the system are presented in the form of response amplitude operators (RAOs). Numerical simulation of the hydrodynamic response has been carried out by solving pitch/heave-coupled non-linear response equation. The results obtained from experimental studies are compared with numerical results and are found to be in good agreement. The increased pitch response coupled with the heave response for all four configurations are investigated and it is observed that the Spar with heave damping plates near the water line shows reduction in response. Mathieu stability diagrams are prepared for all four Spar configurations.

An experimental investigation into topographic resonance in a baroclinic rotating annulus

This paper documents an experimental investigation in which a differentially-heated rotating annulus experiment was used to investigate the effects of topography on fluid flow under conditions similar to the atmospheric and oceanic circulation on Earth and other planets. In particular, the relationship between the effects of topographic resonance and the existence and mechanism for generation of low-frequency variability (LFV) were studied, motivated by outstanding questions in works such as Jin and Ghil (J. Atmos. Sci., 1990, 47) and Read and Risch (Geophys. Astrophys. Fluid Dyn., 2011, 105). Whilst employing sinusoidal wavenumber-3 topography a new regime was encountered within a region of stationary wavenumber-3 structural vacillation. Denoted as the “stationary-transition” regime, it featured periodic oscillations between a dominant stationary wavenumber-3 flow and axisymmetric or chaotic flow. Further investigation found that the “stationary-transition” regime appeared to be a near-resonant region where nonlinear topographic resonant instability led to a 23–42 “day” oscillatory behaviour. Within the regime, a Hopf bifurcation sequence was discovered, and the nonlinear instabilities were found to have terms in both wave-zonal flow and wave–wave interactions, including a notable resonant wave-triad. This report summarises the nature of the “stationary-transition” regime, and also makes comparisons with similar regimes of LFV found in other experimental studies, as well as intraseasonal oscillations in the atmosphere.

Effect of pump-1 laser on Autler–Townes splitting in photoelectron spectrum of K2 molecule**Project supported by the National Natural Science Foundation of China (Grant Nos. 41104094 and 11174119), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20114324120002), the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 12C0370), and the Scientific Research Foundation

We theoretically investigate the Autler–Townes (AT) splitting in the photoelectron spectrum of four-level ladder K2 molecule driven by a pump 1-pump 2-probe pulse via employing the time-dependent wave packet approach. The effects of the pump-1 laser intensity and wavelength on AT splitting are studied for the first time. The magnitude of AT splitting increases with increasing the pump-1 laser intensity. The triple splitting with asymmetric profile occurs due to the nonresonant excitation. The triple structure is transformed into a double structure (near-resonant region), and then becomes a peak (far-off resonant region) progressively as the pump-1 laser is detuned from the resonance wavelength, which can be explained in terms of the asymmetric excitation/population of dressed states. The splitting between adjacent peaks and the splitting between the two sideband peaks in the triplet do not change with the pump-1 pulse wavelength. The three peaks shift toward lower energy with the same shift 1/4*Δ1 as the pump-1 wavelength changes in near-resonant region. The asymptotic behaviors of AT splitting with the pump-1 laser intensity are interesting in the threshold points of the near-resonant region and the far-off resonant region.

Near-resonant second-order nonlinear susceptibility in c-axis oriented ZnO nanorods

Near-resonant second-harmonic generation (SHG) in c-axis oriented ZnO nanorods is studied under the femtosecond laser with wavelength from 780 nm to 810 nm. A highly efficient SHG is obtained, which is attributed to the d131 component of the second-order nonlinear susceptibility. The largest d131 value is estimated to be 10.2 pm/V at the pumping wavelength of 800 nm, which indicates a large SHG response of the c-axis oriented ZnO nanorods in the near-resonant region. Theoretical calculation based on finite-difference time-domain simulation suggests a four-fold local-field enhancement of the SHG.

Exit Routes from the Transition State: Angular Momentum Constraints on the Formation of Products

We have analyzed experimental data from a number of exothermic processes in which molecules in well-defined initial states are deactivated by inelastic, dissociative, or reactive collisions. Further, we analyze deactivation processes that do not occur in molecules despite their containing high levels of excitation. Significant common elements are found among these forms of deactivation. The initial step consists of transition to a product state involving minimum rotation state change (Delta j) consistent with energy conservation. Frequently, this process is near-energy-resonant. More critically, it may frequently require substantial angular momentum (AM) change. Analysis of experimental data indicates that constraints act upon on the formation of products in processes that involve release of excess energy. These constraints are associated with the magnitude of AM that must be generated for the initial transition to occur and this AM "load" increases with the amount of energy to be released. In general, the probability of generating rotational AM falls rapidly as Delta j increases, and this effectively limits the size of energy gap that may be bridged by a given reactant pair and at some point the constraint is sufficient to constitute a barrier that prevents the process from taking place. The choice of reactant species strongly affects the probability of each process that increases (i) when molecules efficiently interconvert momentum and (ii) when many product states are available in the critical near-resonant region. These factors increase the proportion of initial trajectories that possess the energy and momentum necessary to open a "product" channel. Evidence is presented showing that AM load-reduction strategies lead to marked enhancement of rates of collision-induced processes, suggesting that reduction of constraints in the exit channels from the transition state may constitute a previously unrecognized form of catalysis.

Structure-fluid interaction model of tuned liquid dampers

A Lagrangian displacement-based fluid element has been developed to model large amplitude free surface motion of nearly incompressible viscous fluids in a tank of rectangular cross-section under dynamic excitation for tuned liquid damper applications. The penalty method is employed to enforce the nearly incompressible characteristic of fluids considering the non-linear effect of finite distortion of zero-shear and low-viscous fluid elements. The effectiveness of the proposed model was verified by experimental results from the literature. The results show that the proposed non-linear fluid element can predict non-linear behaviours of large amplitude sloshing due to dynamic excitation, especially at near-resonant region. The proposed fluid element can be conveniently incorporated into any existing general-purpose finite element program to serve as an effective tool for the analysis and design of tuned liquid dampers. Copyright © 1999 John Wiley & Sons, Ltd.

Theoretical mean wave resistance of precursor solition generation in two-layer flow

Theoretical mean wave resistance and regional division of the energy of single-layer flow over topography is studied at the near-resonant region in the weakly nonlinear, long wave limit. The theoretical mean wave resistance is determined in terms of the 1st and 2nd conservation laws of the fKdV equation. It is proved by the asymptotic mean method that the theoretical mean wave resistance depends only on the intensity and moving velocity of the topography. The theoretical results of this paper are in good agreement with numerical calculations. Comparisons between the theoretical and numerical results showed that the theory of the present paper holds for any small compact topography.

Theoretical mean wave resistance of precursor soliton generation of single-layer flow

Theoretical mean wave resistance and regional division of the energy of single-layer flow over topography is studied at the near-resonant region in the weakly nonlinear, long wave limit. The theoretical mean wave resistance is determined in terms of the 1st and 2nd conservation laws of the fKdV equation. It is proved by the asymptotic mean method that the theoretical mean wave resistance depends only on the intensity and moving velocity of the topography. The theoretical results of this paper are in good agreement with numerical calculations. Comparisons between the theoretical and numerical results showed that the theory of the present paper holds for any small compact topography.

RECENT PROGRESS IN POLYDIACETYLENE MATERIAL RESEARCH FOR NONLINEAR OPTICS

In order to enhance the third-order nonlinear optical susceptibilities (χ(3) s ) of polydiacetylenes, polydiacetylenes with π-conjugation between polymer backbone and acetylenic substituents were synthesized. In the case of hexatriyne monomer, solid-state polymerization proceeded via 1, 4-addition to give polydiacetylene with directly bound ethynyl substituents. Also 1, 4-addition polymerization took place in the case of octatetrayne and dodecahexayne monomers and gave polydiacetylenes with butadiynyl and octatetraynyl substituents, respectively. These butadiynyl and octatetraynyl moieties of the latter two polymers could thermally be polymerized furthermore. Especially, in the case of dodecahexayne, formation of an interesting ladder polymer with π-conjugation between two polydiacetylene backbones were confirmed by the solid-state NMR. The effective χ(3)(−3ω; ω, ω, ω) value in three-photon resonant region of the π-conjugation system of polydiacetylenes with butadiynyl substituents was elucidated to be about 10−9 esu. The ratio of χ(3) to absorption at the THG wavelength in near-resonant region was found to be larger than that in resonant region. Aiming at obtaining sharp excitonic absorption of polydiacetylenes, polydiacetylene microcrystals with controlled molecular weight distribution, i.e., uniform electronic structure in the polymer backbones, were also examined.

Photon-emission spectra of the H2+ molecular ion in an intense laser field.

Photon-emission spectra of the ${\mathrm{H}}_{2}^{+}$ molecular ion in an intense, linearly polarized laser field (wavelength \ensuremath{\lambda}=1064 nm and intensities ${10}^{13}$\ensuremath{\le}I\ensuremath{\le}${10}^{14}$ W/${\mathrm{cm}}^{2}$) have been calculated using an exact method and compared to two-level models. The exact calculation requires solving a three-dimensional time-dependent Schr\odinger equation which allows a full treatment of all the electronic states of ${\mathrm{H}}_{2}^{+}$ as a function of the internuclear separation R. Three separate excitation regions can be defined which are associated with the 1${\mathrm{\ensuremath{\sigma}}}_{\mathit{g}\mathrm{\ensuremath{-}}}$1${\mathrm{\ensuremath{\sigma}}}_{\mathit{u}}$ charge-resonant (CR) transition of the ${\mathrm{H}}_{2}^{+}$ molecular ion: (1) for small R, the multiphoton excitation region; (2) for intermediate R, the near-resonant excitation region; and (3) for large R, the strong-coupling region. Two- and three-level models are used for the description of these excitations of the CR states. We will show in this work that (a) in the multiphoton excitation region, an approximate solution of the laser-driven CR states is given by WKB solutions of a Mathieu equation; (b) in the near-resonant region, Rabi or Mollow triplets are obtained for all the harmonics; and (c) in the strong-coupling region, an analytic two-level solution for the CR state excitation reproduces well the exact results. The effects of ground-continuum coupling and ionization is shown to be important for laser intensities I\ensuremath{\ge}${10}^{14}$ W/${\mathrm{cm}}^{2}$.

Nonlinear optics in polydiacetylene single crystals: Anisotropy, spectral response and thermo-optic effect

Polydiacetylenes are well known for their fast and large third order nonlinear optical response. The nonlinear optical properties of various kinds of Polydiacetylene single crystals and films were investigated by degenerate four-wave mixing. With the DFWM-technique it is possible to measure different tensor-components of χ (3) in the strongly anisotropic crystal systems. The spectral dispersion of χ (3) bbbb was studied in the resonant as well as in the nonresonant region and compared with theoretical predictions. Special attention was paid to the NLO-signal dependence on the incident power: The results show, that a thermo-optic effect and higher-order NLO-effects must be considered in all these experiments, even in the near-resonant region and at low powers.

Linear and Nonlinear Optical Properties of Processable Polymeric Materials

ABSTRACTLinear and nonlinear optical (NLO) polymeric materials with good processabilities are discussed. An azo-dye substituted copolymer (3RNO2, nitro-terminated diazo dye) are investigated. The polymer film was found to be transparent and attenuation loss was less than 2 dB/cm. The χ(3) of 3RNo2 reaches 5×10−11 esu in the near-resonant region. With polymers where the dye molecules are introduced into the polymer backbone (a main chain polymer), a χ(3) larger than 10−11 esu is obtained even in a monoazo dye introduced polymer. A new molecular crystal, symmetrically substituted benzylidene-aniline compound, SBAC for short, are also successfully polymerized (introduced into a polymer main chain) and their χ(3) values are revealed to be around 1010 esu in the near-resonant wavelength region. The optical transmission of these polymers is also investigated and revealed to be around 2 dB/cm. With poly(arylene vinylene), a certain population of χ-conjugation length will induce enhancement of the resonant χ(3) of the polymers. The polymer can be used to fabricate channel waveguides with the photo-bleaching technique.

Near-resonant holography

Experimental results of a new technique for measuring species concentration by using two-wavelength holography are described. The refractive-index difference between two pulsed dye-laser wavelengths tuned to the nearresonant region of atomic sodium is recorded on a hologram. For small wavelength differences, the nonresonance aberrations are subtracted out.