Non-fundamental Modes Research Articles

A novel design method for wave-induced fatigue of flood gates

This paper presents a novel design method to predict fatigue of flood gates due to dynamic wave loading. The accumulation of fatigue damage is predicted probabilistically over the entire lifetime of the structure rather than with a set of normative events. Load events are defined using a joint probability distribution of historical wind and water level data. The random phase-amplitude model is employed to obtain realisations of the wave state for every combination of environmental conditions. Linear wave theory and pressure-impulse theory are used to predict both quasi-steady and highly dynamic wave pressures. The stress response of the structure is predicted with a hybrid semi-analytical and finite element model. By applying a mode matching technique the fluid-structure interaction is solved in a computationally efficient manner. This facilitates the large number of simulations required for a comprehensive fatigue analysis without making concessions in the physical modelling. The fatigue damage is then evaluated with the linear Palmgren-Miner method by applying a rainflow algorithm. A Monte Carlo analysis is performed to estimate the expected fatigue lifetime of the structure. The modular structure of the model routine allows for easy adaptation to other situations where fatigue due to hydrodynamic loading is of interest. The design method is applied to a case study of a flood gate with an overhang inspired by the situation at the Afsluitdijk. Non-fundamental modes are taken into account without simplification of the fluid-structure interaction process and found to be governing for the fatigue damage for the studied case. Moreover, the interference of vibrations due to consecutive wave impacts is shown to have a significant influence on the outcome of the fatigue assessment. For the case study, the design method leads to a 10-20% reduction of the governing fatigue damage compared to a method commonly used in practice. At specific locations on the flood gate fatigue damage is found to be underestimated by current design methods. The presented design method is therefore found to be a significant improvement.

Extremely Low-Profile Monopolar Microstrip Antenna with Wide Bandwidth.

In this paper, we propose a new monopolar microstrip antenna for a high-speed moving swarm sensor network. The proposed antenna shows an extremely thin substrate thickness supported with an omni-directional radiation pattern and wide operation frequency bandwidth. First, to achieve the low-profile monopolar microstrip antenna, the symmetrical center feeding network and the gap-coupled six arrayed patches which form a hexagonal microstrip radiator were utilized. The partially loaded ground-slots under the top patches were employed to improve the radiation performance and adjust the impedance bandwidth. Second, to obtain the broad bandwidth of the low-profile monopolar microstrip antenna, the degenerated non-fundamental TM02 modes, that is, even and odd TM02 modes, were carefully analyzed. To verify the feasibility of the degenerated TM02 mode operation, the parametric study of the proposed antenna was theoretically investigated and implemented with the optimized parameter dimensions. Finally, the fabricated antenna showed a 0.254 mm-thick substrate and demonstrates 1.5-wavelength resonant monopolar radiation with broad impedance bandwidth of 855 MHz and its factional bandwidth of 15.24% at the resonant frequency of 5.57 GHz.

Application of the augmented block Householder Arnoldi method to the calculation of non-fundamental modes of the diffusion equation

The determination of non-fundamental modes of the diffusion equation is required for computing CANDU reactor power distribution from analysis of in-core detector readings. They are also important for understanding subcritical mode instabilities occurring in boiling water reactors. The legacy method for computing these modes is the Hotelling deflation technique based on bi-harmonic decontamination. However, the Hotelling technique becomes unstable as the number of modes increase or as their eigenvalues become closer. Effective and fast alternatives are provided with Implicit Arnoldi Restarted Methods (IRAM). Among them, we investigated the Krylov–Schur method available in the SLEPc library, and we are proposing a custom implementation of the augmented block Householder Arnoldi (ABHA) method, similar to the Open Source implementation of Prof. James Baglama. In our work, the ABHA method is applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas-Schneider methods or with the mesh-centered finite difference method.

Raman Scattering on the Effective Soft Mode for Lithium Niobate Crystals

The evolution of Raman spectra in a wide range of temperatures that includes the ferroelectric transition point in lithium niobate single crystals is studied for polarization geometry X(ZZ)Y. In this geometry, the soft mode responsible for the phase transition distinguished by 1A1(TO)-type symmetry should appear in the spectra. Experimental studies show that the 1A1(TO) mode interacts resonantly with nonfundamental modes in the low-frequency region of the spectrum. Near the ferroelectric phase transition point, an isofrequency opalescence effect is observed that consists of an abrupt increase in Raman signal intensity at fixed frequencies near the excitation line.

A Krylov–Schur solution of the eigenvalue problem for the neutron diffusion equation discretized with the Raviart–Thomas method

ABSTRACTMixed-dual formulations of the finite element method were successfully applied to the neutron diffusion equation, such as the Raviart–Thomas method in Cartesian geometry and the Raviart–Thomas–Schneider in hexagonal geometry. Both methods obtain system matrices which are suitable for solving the eigenvalue problem with the preconditioned power method. This method is very fast and optimized, but only for the calculation of the fundamental mode. However, the determination of non-fundamental modes is important for modal analysis, instabilities, and fluctuations of nuclear reactors. So, effective and fast methods are required for solving eigenvalue problems. The most effective methods are those based on Krylov subspaces projection combined with restart, such as Krylov–Schur. In this work, a Krylov–Schur method has been applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas–Schneider methods.

Structure and Spectroscopy of C2HNO Isomers.

Formyl cyanide has been detected toward Sgr B2 making this chemical and its potential isomers of astrophysical interest. We calculated the precise energies of the five most stable structural isomers of formyl cyanide and found that formyl isocyanide and 2H-azirin-2-one are less stable than formyl cyanide by 55 and 125 kJ/mol, respectively. We present our ab initio coupled cluster predictions of the spectroscopic parameters relevant to their gas-phase rotational and vibrational spectroscopy. Parameters include ground vibrational state rotational constants, centrifugal distortion parameters, equilibrium electric dipole moments, and nuclear quadrupole coupling constants. Anharmonic vibrational frequencies together with infrared intensities of fundamental and nonfundamental modes were also calculated. The broader potential energy surface, including transition states and the minima they connect, were explored for these isomers at the B3LYP/aug-cc-pVTZ level of theory. Formyl cyanide can dissociate in an exothermic reaction to form HCN and CO or in an endothermic reaction to form HNC and CO. The activation energies for both processes are close to 260 kJ/mol. The activation barrier for conversion of formyl cyanide into formyl isocyanide is ∼180 kJ/mol. The energetic barrier for the exothermic decomposition of formyl isocyanide into HNC and CO is ∼210 kJ/mol. The barrier for transformation of formyl isocyanide into formyl cyanide is ∼130 kJ/mol. Formyl isocyanide seems to be a stable chemical and could potentially survive in a dense molecular cloud if formed. These data are useful for future identification of members of this family of molecules in a laboratory or in space.

Influence of Non-fundamental Modes on Mid-infrared Spectra: Anharmonic DFT Study of Aliphatic Ethers.

Fundamental and non-fundamental vibrational modes, first overtones, and binary combination modes of selected aliphatic ethers (di-n-propylether, di-iso-propylether, n-butylmethyl ether, n-butylethyl ether, di-n-butyl ether, tert-buytlmethyl ether, and tert-amylmethyl ether) were modeled in a fully anharmonic generalized second-order vibrational perturbation theory (GVPT2) approach on the DFT-B2PLYP/SNST level. The modeling procedure of theoretical line shapes took into account conformational isomers of studied molecules. The calculated spectra of the above ethers were compared to the corresponding experimental spectra in the infrared (IR) region (4000-560 cm-1) of the absorption index k(ν) derived from the neat liquid thin-film transmission data. It was found that IR spectra of aliphatic ethers are heavily influenced by the bands originating from non-fundamental modes, particularly from the combination modes in the C-H stretching region (3200-2800 cm-1). Because of the effects of vibrational resonances, the intensities of overtones and combination bands originating from methyl and methylene deformation modes increase sufficiently to influence the experimental line shape in this region. Less significant contributions from non-fundamental vibrational modes were noticed in the lower IR region (1600-560 cm-1), particularly in the vicinity of the C-O stretching band. The 2700-1600 cm-1 region, which is rich in weak bands due to non-fundamental vibrations, was reproduced accurately as well. It was concluded that a fully anharmonic approach allows significantly more accurate reproduction of the complex IR line shapes, particularly in the C-H stretching region of aliphatic ethers. On the basis of the achieved agreement between the experimental and calculated spectra, it may be concluded that the anharmonic GVPT2 method can adequately reproduce the anharmonic effects and vibrational resonances in particular, influencing the IR spectra of aliphatic ethers. The results obtained in this study show that the non-fundamental modes may play a significant role in shaping the IR spectra of aliphatic ethers and similar molecules in the neat liquid phase.

Ultrafast annular-magnetic-field-driven vortex-core reversals

By micromagnetic numerical simulations, we investigate the dynamics of vortex-core reversal in a soft magnetic nanodisk under the excitation of annular, perpendicular, resonant magnetic fields. The non-fundamental radial modes of the nanodisk are characterized into alternating radial-phase-regions for which two adjacent regions across a node point are in antiphase. We show that radial spin-waves excited by fields applied in the in-phase regions are in phase, and therefore generate strong magnetization oscillations resulting from constructive spin-wave interference. Such annular magnetic fields can substantially speed up the vortex-core reversal and lower the threshold field amplitude in comparison with the global field. Our work provides an efficient mechanism for spin-wave excitation and ultrafast vortex-core switching.

Computational and quantum chemical study on high-frequency dielectric function of tert-butylmethyl ether in mid-infrared and near-infrared regions

Complex dielectric function of tert-butylmethyl ether (TBME) was determined and analyzed in a broad spectral region covering mid-infrared (MIR) and near-infrared (NIR) regions (6500–560cm−1). Spectra of the complex electric permittivity and complex molecular polarizability have been derived from complex refractive index spectra. The molar vibrational polarization (Pvib) corresponding to individual modes has been estimated based on the data derived from fitting damped harmonic oscillator model to the experimental complex permittivity spectrum. Factors determining the dielectric functions due to vibrational resonance absorptions corresponding to fundamental and non-fundamental (overtones and combination modes) modes were taken into account. Direct comparison of contributions to total Pvib value stemming from corresponding fundamental and non-fundamental modes has been carried out and discussed for the first time. In order to identify overtones and binary combination modes, quantum chemical calculation of the vibrational spectrum of tert-butylmethyl ether was performed for MIR and NIR regions. Fully anharmonic approach by means of generalized second-order vibrational perturbation theory (GVPT2) was applied on DFT-B2PLYP/SNST level. An accurate reproduction of experimental data was achieved with subsequent assignment of fundamental and non-fundamental bands, which enabled detailed discussion of relations between dielectric contributions of fundamental and non-fundamental modes of tert-butylmethyl ether.

Anharmonicity Effects in the Vibrational CD Spectra of Propylene Oxide

This study reports the first vibrational circular dichroism (VCD) spectra of propylene oxide isolated in an argon matrix. The narrow bandwidth achieved, in addition to the rich VCD features, allows a thorough analysis of the spectra and detailed comparison with the calculated harmonic and anharmonic IR and VCD spectra. Several bands in the fingerprint region are identified as nonfundamental modes based on the harmonic calculation, and three of them feature significant VCD intensity. Anharmonic VCD intensity calculations were carried out using a newly developed methodology based on the second-order level of vibrational perturbation theory. All new bands observed can be undoubtedly assigned to combination or overtone modes except the band at 1486.4 cm–1, which is tentatively identified to contain contributions from an overtone and a combination mode. The study also reveals that the current theoretical approach for anharmonic contributions to VCD spectra needs to be further improved when there is an accident...

Modal filtering for midinfrared nulling interferometry using single mode silver halide fibers

We demonstrate the modal filtering properties of newly developed single mode silver halide fibers for use at midinfrared wavelengths, centered at 10.5 microm. The goal was to achieve a suppression of nonfundamental modes greater than a factor of 300 to enable the detection and characterization of Earthlike exoplanets with a space-based nulling interferometer. Fiber segments of 4.5 cm, 10.5 cm, 15 cm, and 20 cm lengths were tested. We find that the performance of the fiber was limited not by the modal filtering properties of the core but by the unsuppressed cladding modes present at the output of the fiber. In 10.5 cm and longer sections, this effect can be alleviated by properly aperturing the output. Exclusive of coupling losses, the fiber segments of 10.5-20 cm length can provide power suppression of undesirable components of the input field by a factor of 15,000 at least. The demonstrated performance thus far surpasses our requirements, such that even very short sections of fiber provide adequate modal filtering for exoplanet characterization.

Behaviour of forbidden modes in the impedance characterization and modeling of piezoelectric microcantilevers

A systematic impedance analysis of the resonance response obtained from commercial piezoelectric scanning force microscopy (SFM) cantilevers, comprising both experimental and simulation work, has been carried out. A finite element model (FEM) has been developed and fitted using experimental data, from which valuable conclusions have been reached. Although non-fundamental modes are less used in sensing applications, they have been emphasized in this work. Two main arguments justify a deeper study of these higher order modes. First, an SFM cantilever acting as a gravimetric sensor and driven at a non-fundamental resonance frequency shows a real potential to enhance its mass detection sensitivity when compared with its performance in the usual driving scheme at the fundamental frequency. Secondly, the characterization of some non-fundamental modes, torsionally shaped, reveals an unexpected behaviour that should be known and understood previously to any gravimetric sensor design using torsional modes. Results show that modes of torsional nature cannot be detected electrically because they are not even excited by the applied ac field. Moreover, torsional modes, successfully excited by an external harmonic mechanical stimulus, cannot be detected electrically either. An explanation to this phenomenon, based on the redistribution and cancellation of surface reaction charges, is given in detail and supported by simulation results.

Vibrational studies of the solid imidazole and pyridine adducts of metal(II) saccharinates I. The OH/OD and NH/ND stretching regions of the cobalt(II) and nickel(II) complexes

FT-IR spectra of both protiated and deuterated analogues of the complexes [M(HIm) 4 (H 2 O) 2 ](sac) 2 and [M(H 2 O) 4 (py) 2 ](sac) 2 ·4H 2 O (M=Co, Ni) in the region of the water stretching modes, at room temperature down to the liquid-nitrogen boiling temperature, are recorded and discussed. The regions of the NH/ND stretchings in the spectra of the imidazole saccharinates are also studied. The appearance of the bands that are mainly due to the OH, OD, NH and ND stretchings is discussed in connection with the crystallographic data. The appearance of the NH stretching region in the spectra of the studied imidazole adducts is partly explained as a result of Evans-type Fermi resonance of the NH stretchings with non-fundamental modes. In spite of the existence of single type of asymmetrically bonded water molecules in the structures of the studied imidazole complexes, an unexpected ratio 1:2 of the integral intensities of the two isotopically isolated ν (OD) stretchings in their spectra was found.

Fundamental, overtone and combination vibrations in condensed methanol studied with low-energy electron-energy-loss spectroscopy

Abstract High-resolution electron-energy-loss spectroscopy, within the incident electron energy range 1 to 20 eV, was performed for solid methanol condensed at 15 K on a polycrystalline platinum substrate. Besides the most prominent energy loss peaks, which correspond to the fundamental vibrations, we observe several medium and small energy loss features that are ascribed to overtone and combination bands of some fundamentals. The effects of the film thickness and electron impact energy are shown for the fundamental as well as for the overtone and combination vibrations. The incident energy at which resonance enhancement occurs for the fundamentals favors the observation of the non-fundamental modes within and beyond the normal infrared frequency range. The first overtone of the CO stretching mode is found at 255 meV. The combination of the CH3 rocking vibration with the OH in-plane bending or the CH3 asymmetric bending mode is located at 320 meV. The series of additional energy loss bands, appearing beyond the normal infrared region (

The influence of nonfundamental pump modes in erbium-doped fiber amplifiers

Abstract This work analyzes how the characteristics of an erbium-doped fiber amplifier (EDFA) depends on the mode distribution of 800-nm pump light. The analysis is performed by using a large-signal model of an optimally pumped erbium-doped fiber amplifier. Special attention is given to the gain degradation, and noise figures of the amplifier for co- and counterpropagating pump light.

Infrared studies of the conformation in salicylaldehyde, methylsalicylate and ethylsalicylate

Infrared spectral data are reported in the region 4000-200 cm −1 for salicylaldehyde (S. A.), methylsalicylate (M.S.) and ethylsalicylate (E.S.) in the solid, liquid and vapour phases. They indicate that these compounds exist as equilibrium mixtures of conformers through rotations around two or three axes with HO- cis and HO- trans as major ones in the case of M.S. and E.S. and as the only pair in the case of S.A. Vibrational frequency assignment of the fundamental and non-fundamental modes are made. Determination of Δ H values have been carried out and are used as a measure of the relative stabilities of the conformers in each system. In the vapour and liquid phases the HO- cis conformer was found to be the most stable one.

Resonance Raman spectra of octaethylporphyrinato-Ni(II) and m e s o-deuterated and 15N substituted derivatives. I. Observation and assignments of nonfundamental Raman lines

High resolution resonance Raman spectra of octaethylporphyrinato-Ni(II) [Ni (OEP)], its meso-deuterated and 15N substituted derivatives were measured. With excitation near the O–1 transition, about 90 nonfundamental modes and previously unrecognized fundamental modes were observed for each derivative. The analysis of the nonfundamental Raman lines allowed the determination of all the fundamental frequencies in the A1g, B1g, A2g, and B2g species of D4h symmetry. Experimental classification of depolarized Raman lines to the B1g and B2g species was worked out. Combinations of B1g and B2g modes give rise to anomalously-polarized Raman lines while combinations of B1g modes and of B2g modes give rise to polarized lines. The Raman lines of the B1g species of Ni(OEP) with D4h symmetry are correlated with those in the Ag species of H2(OEP) with D2h symmetry while the B2g species of D4h is correlated with the B1g species of D2h. The experimental frequencies of fundamental modes thus determined satisfied the product rule for the isotopic substitution.