Contribution Of Vibrational Modes Research Articles

Determining the key vibrations for spin relaxation in ruffled Cu(ii) porphyrins via resonance Raman spectroscopy.

Pinpointing vibrational mode contributions to electron spin relaxation (T1) constitutes a key goal for developing molecular quantum bits (qubits) with long room-temperature coherence times. However, there remains no consensus to date as to the energy and symmetry of the relevant modes that drive relaxation. Here, we analyze a series of three geometrically-tunable S = ½ Cu(ii) porphyrins with varying degrees of ruffling distortion in the ground state. Theoretical calculations predict that increased distortion should activate low-energy ruffling modes (∼50 cm-1) for spin-phonon coupling, thereby causing faster spin relaxation in distorted porphyrins. However, experimental T1 times do not follow the degree of ruffling, with the highly distorted copper tetraisopropylporphyrin (CuTiPP) even displaying room-temperature coherence. Local mode fitting indicates that the true vibrations dominating T1 lie in the energy regime of bond stretches (∼200-300 cm-1), which are comparatively insensitive to the degree of ruffling. We employ resonance Raman (rR) spectroscopy to determine vibrational modes possessing both the correct energy and symmetry to drive spin-phonon coupling. The rR spectra uncover a set of mixed symmetric stretch vibrations from 200-250 cm-1 that explain the trends in temperature-dependent T1. These results indicate that molecular spin-phonon coupling models systematically overestimate the contribution of ultra-low-energy distortion modes to T1, pointing out a key deficiency of existing theory. Furthermore, this work highlights the untapped power of rR spectroscopy as a tool for building spin dynamics structure-property relationships in molecular quantum information science.

Dynamic characteristics and wind-induced vibration coefficients of purlin-sheet roofs

This paper presents the dynamic characteristics analysis of the purlin-sheet roofs by the random vibration theories. Results show that the natural vibration frequency of the purlin-sheet roof is low, while the frequencies and mode distributions are very intensive. The random vibration theory should be used for the dynamic characteristics of the roof structures due to complex vibration response. Among the first 20th vibration modes, the first vibration mode is mainly the deformations of purlins, while the rest modes are the overall deformations of the roof. In the following 30th modes, it mainly performs unilateral local deformations of the roof. The frequency distribution of the first 20th modes varies significantly while those of the following 30th modes are relatively sensitive. For different parts, the contributions of vibration modes on the vibration response are different. For the part far from the roof ridge, only considering the first 5th modes can reflect the wind-induced vibration response. For the part near the ridge, at least the first 12 modes should be considered, due to complex vibration response. The wind vibration coefficients of the upwind side are slightly higher than that of the leeward side. Finally, the corresponding wind vibration coefficient for the purlin-sheet roof is proposed.

Calculating vibrational mode contributions to sound absorption in excitable gas mixtures by decomposing multi-relaxation absorption spectroscopy

Sound relaxational absorption spectroscopy of excitable gas mixtures is potentially applied for gas composition detection. The relaxation of vibrational modes of gas molecules determines the sound relaxational absorption. However, to our knowledge, the contribution of each vibrational mode available in gas mixtures to sound multi-relaxation absorption has not been calculated in existing literature. In this paper, based on the decoupled expression of the effective isochoric molar heat for a gas mixture, a sound multi-relaxation absorption spectrum is decomposed into the sum of single-relaxation spectra. From this decomposable characteristic, the contribution of each vibrational mode available in the gaseous medium to the multi-relaxation absorption is obtained at room temperature. For various gas compositions including carbon dioxide, methane, nitrogen etc., the calculated contributions of vibrational modes are verified by the comparison with experiment data. We prove the following views with quantifiable outcomes that the primary molecular relaxation process associated with the lowest mode plays the major role in acoustic relaxational absorption of gas mixtures; the mode with lower vibrational frequency provides higher contribution to the primary relaxation process. This work could provide a deeper insight into the relationship between the sound relaxational absorption spectroscopy and gas molecules.

EO polymer at cryogenic temperatures

Electro-optic (EO) properties at 7 K of a guest–host type nonlinear poled polymer system consisting of AJLZ53 chromophores in an amorphous polycarbonate host are reported for the first time. A modified attenuated total reflection method that takes into account multilayer structure is used to accurately characterise linear and nonlinear optical properties. At the telecommunication wavelength of 1550 nm, <10% drop of the EO coefficient r 33 at 7 K is observed compared with that at 300 K, while n 3 r 33 only decreases <5% because of increased anisotropic indices of refraction at low temperatures. This decrease of the r 33 at 7 K indicates that the EO activity of nonlinear polymers at room temperatures is not of pure electronic origin because of vibrational mode contributions to the first-order hyperpolarisability.

Calculation of vibrational mode contributions to sound absorption in excitable gases by decomposing multi-relaxation absorption curve

Molecular vibrational relaxation is responsible for the sound relaxational absorption in most excitable gases. However, it is desirable to calculate the contribution of each vibrational mode to sound multi-relaxation absorption. In this paper, first, a sound multi-relaxation absorption curve is decomposed into the sum of single-relaxation curves; second, based on this decomposed characteristic, a model to quantitatively analyze the vibrational mode contributions to sound absorption is proposed. The simulation results quantitatively demonstrates that the primary relaxation process connected with the lowest mode is the decisive factor for sound relaxational absorption, and the mode with lower vibrational frequency supplies higher contribution to the primary relaxation process in pure polyatomic gases.

The dynamics of the non-heme iron in bacterial reaction centers from Rhodobacter sphaeroides

We investigate the dynamical properties of the non-heme iron (NHFe) in His-tagged photosynthetic bacterial reaction centers (RCs) isolated from Rhodobacter (Rb.) sphaeroides. Mössbauer spectroscopy and nuclear inelastic scattering of synchrotron radiation (NIS) were applied to monitor the arrangement and flexibility of the NHFe binding site. In His-tagged RCs, NHFe was stabilized only in a high spin ferrous state. Its hyperfine parameters (IS=1.06±0.01mm/s and QS=2.12±0.01mm/s), and Debye temperature (θD0~167K) are comparable to those detected for the high spin state of NHFe in non-His-tagged RCs. For the first time, pure vibrational modes characteristic of NHFe in a high spin ferrous state are revealed. The vibrational density of states (DOS) shows some maxima between 22 and 33meV, 33 and 42meV, and 53 and 60meV and a very sharp one at 44.5meV. In addition, we observe a large contribution of vibrational modes at low energies. This iron atom is directly connected to the protein matrix via all its ligands, and it is therefore extremely sensitive to the collective motions of the RC protein core. A comparison of the DOS spectra of His-tagged and non-His-tagged RCs from Rb. sphaeroides shows that in the latter case the spectrum was overlapped by the vibrations of the heme iron of residual cytochrome c2, and a low spin state of NHFe in addition to its high spin one. This enabled us to pin-point vibrations characteristic for the low spin state of NHFe.

809 流体励振による弦拘束された長方形板の振動実験

Experimental results are presented on flow-induced vibrations of a rectangular plate constrained by a stretched string. The plate is clamped at the bottom and deformed to curved configuration by a stretched string at tip ends. Vibration responses of plate are measured, with and without constraint by a stretched string. Changing the angle of the flow, strain of the plate is measured. Maximum strain is obtained when the wind is blown nearly parallel to the plate. Although the strain of the plate constrained by a stretched string is small, the amplitude has broadband spectrum. Chaotic responses are generated by the flow-induced vibrations. Dominant frequency components of the vibration responses correspond to the natural frequencies of the plate. Chaotic responses are examined by the Fourier spectra and the maximum Lyapunov exponents. Contributions of vibration modes to the chaotic responses are inspected by the principal components analysis.

Chaotic vibrations of a post-buckled L-shaped beam with an axial constraint

Analytical results are presented on chaotic vibrations of a post-buckled L-shaped beam with an axial constraint. The L-shaped beam is composed of two beams which are a horizontal beam and a vertical beam. The two beams are firmly connected with a right angle at each end. The beams joint with the right angle is attached to a linear spring. The other ends are firmly clamped for displacement. The L-shaped beam is compressed horizontally via the spring at the beams joint. The L-shaped beam deforms to a post-buckled configuration. Boundary conditions are required with geometrical continuity of displacements and dynamical equilibrium with axial force, bending moment, and share force, respectively. In the analysis, the mode shape function proposed by the senior author is introduced. The coefficients of the mode shape function are fixed to satisfy boundary conditions of displacements and linearized equilibrium conditions of force and moment. Assuming responses of the beam with the sum of the mode shape function, then applying the modified Galerkin procedure to the governing equations, a set of nonlinear ordinary differential equations is obtained in a multiple-degree-of-freedom system. Nonlinear responses of the beam are calculated under periodic lateral acceleration. Nonlinear frequency response curves are computed with the harmonic balance method in a wide range of excitation frequency. Chaotic vibrations are obtained with the numerical integration in a specific frequency region. The chaotic responses are investigated with the Fourier spectra, the Poincare projections, the maximum Lyapunov exponents and the Lyapunov dimension. Applying the procedure of the proper orthogonal decomposition to the chaotic responses, contribution of vibration modes to the chaotic responses is confirmed. The following results have been found: The chaotic responses are generated with the ultra-subharmonic resonant response of the two-third order corresponding to the lowest mode of vibration. The Lyapunov dimension shows that three modes of vibration contribute to the chaotic vibrations predominantly. The results of proper orthogonal decomposition confirm that the three modes contribute to the chaos, which are the first, second, and third modes of vibration. Moreover, the results of the proper orthogonal decomposition are evaluated with velocity which is equivalent to kinetic energy. Higher modes of vibration show larger contribution to the chaotic responses, even though the first mode of vibration has the largest contribution ratio.

A finite element approach to the inverse dynamics and vibrations of variable geometry trusses

This paper presents a novel numerical approach to solving the inverse dynamics of variable geometry trusses (VGTs) with elastic elements, allowing designers to accurately and efficiently determine motor action requirements, the time-dependent behavior of the structure, and the contribution of vibration modes to the motion. The dynamic equations have been simplified by assuming that movements of the structure are relatively slow, since VGTs are generally used in situations requiring high accuracy. Unlike existing techniques, the formulation is based on simple finite element models. The analysis is based on modal coordinates, and takes place in two stages: first, motor actions are calculated in a model with no actuator stiffness; then, small-amplitude, undamped vibrations are obtained in a model that includes actuator stiffness. The method is validated by simulating a pinned planar flexbeam and a three-dimensional VGT.

固定辺で面内弾性拘束を受ける長方形板のカオス振動実験(&lt;特集&gt;D&amp;D 2008)

Experimental results are presented on chaotic vibrations of a rectangular plate with an in-plane elastic constraint. Opposite edges of the plate are clamped and the other edges are simply supported. One of the clamped edges is connected with elastic springs and is movable to an in-plane direction. The simply-supported edges are composed with adhesive elastic thin films. Under the specified in-plane compressive force, the plate shows the type of a softening-and-hardening spring. Moreover, the plate has the condition of the two to three internal resonance between the second and third modes. Under periodic lateral excitation, non-periodic responses are obtained in specific frequency regions. The non-periodic responses are examined with the Fourier spectra, the Poincare projections and the maximum Lyapunov exponents. It is found that two types of chaotic responses are generated from the internal resonances dominated by the first mode and higher modes of vibration. Appying the Karhunen Loeve method, contributions of vibration modes on the chaotic responses are confirmed. The first mode contributes to the chaotic responses dominantly. The higher three modes including the second, third and fourth modes have 10 to 20 percent of contribution. As exciting amplitude increases, the lower frequency region of chaotic response with large amplitude shifts to the higher frequency range owing to the hardening nonlinearity of the plate, while the higher region of chaotic response with small amplitude shifts to the lower frequency range.

Experiments on Chaotic Vibrations of a Rectangular Plate under an In-Plane Elastic Constraint at Clamped Edges

Experimental results are presented on chaotic vibrations of a rectangular plate with in-plane elastic constraint. The plate has initial imperfection. Opposite edges of the plate are clamped and the other edges are simply supported. One side of clamped edges is connected to elastic springs and is movable to in-plane direction. The simply-supported edges are connected to the boundaries with adhesive flexible films. Loading in-plane compressive force to the plate, the plate shows pre-buckled configuration with the type of a softening-and-hardening spring. Under periodic lateral excitation, chaotic responses are obtained in specific frequency regions. Predominant chaotic responses are examined with the Fourier spectra, the Poincare projections and the maximum Lyapunov exponents. Furthermore, applying the Karhunen-Loeve method, contributions of vibration modes on the chaotic responses are confirmed. It is found that the chaotic responses are generated from the internal resonant vibrations with the first mode of vibration and higher modes of vibration. The chaotic responses are dominated by the lowest mode of vibration. The higher modes of vibration contribute from 11 to 20 percent to the chaos. As the exciting amplitude increases, the amplitude of the chaotic responses increases and frequency regions of the chaotic responses shift. In the larger amplitude of the response, the frequency region shifts to the higher range owing to the resonant response with the type of a hardening spring. In contrast, the frequency region shifts to the lower range when the amplitude of the chaotic response is smaller comparatively. The resonant response with the smaller amplitude corresponds to the type of a softening spring.

Electron–phonon coupling and vibrational modes contributing to linear electro‐optic effect of the efficient NLO chromophore 4‐(N,N‐dimethylamino)‐N‐methyl‐4′‐toluene sulfonate (DAST) from their vibrational spectra

AbstractThe optimized geometry and structural features of the most prospective electro‐optic crystal 4‐(N,N‐dimethylamino)‐N‐methyl‐4′‐toluene sulfonate (DAST), and the vibrational spectral investigations have been comprehensively described with the near infrared Fourier transform (NIR FT) Raman and Fourier transform infrared (FT‐IR) spectra supported by the density functional theoretical (DFT) computations to elucidate the contribution of vibrational modes to the linear electro‐optic (LEO) effect. Mulliken population analysis and natural bond orbital (NBO) analysis have also been carried out to analyze the effects of intramolecular charge transfer (ICT), intramolecular hydrogen bonding and hyperconjugative interactions on the geometries. The influence of CT interaction between the phenyl ring and the dimethylamino group of the nonlinear optical (NLO) chromophore on the endocyclic and exocyclic angles, and the electronic effects such as hyperconjugation and back‐donation on the methyl hydrogen atoms have been examined. The concurrent intense activation of Raman and IR activities of the effective conjugation vibrational coordinate, which significantly contributes to the LEO effect resulting from the strong electron–phonon (e/ph) coupling, has been analyzed in detail. The effects of frontier orbitals, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), transition of electron density (ED) transfer and the influence of planarity in the stilbazolium ring on the first hyperpolarizability are also discussed. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Modal-based model reduction and vibration control for uncertain piezoelectric flexible structures

In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial H2 norm of modes, which serves as a measure of the intensity of modes to system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible structures with piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by simultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.

146 ばね-質量系に弦で連結された座屈後片持ちはりのカオス振動実験

Experimental results are presented on chaotic vibrations of a post-buckled cantilevered beam connected to a spring-mass system by a string. The string is stretched between the beam end and leaf springs of spring-mass system on a base. Applying tensile force to the string, the beam is compressed, and then the beam is buckled to a post-buckled state. The axial force and the shearing force of the beam are varied due to the geometrical configuration of deflection of the beam and the displacement of the leaf spring. The beam is subjected to lateral periodic acceleration, chaotic responses are observed in typical frequency region. Predominant chaotic responses are examined by the Fourier spectrum, the Poincare map and the maximum Lyapnov exponents. Contributions of vibration modes to the chaotic responses are analyzed by the principal component analysis. Increasing the amount of the mass in the spring-mass system, the maximum Lyapnov exponents and the corresponding embedding dimension increase. The figure of the Poincare map looses the focus due to the increase of the maximum Lyapnov exponents.

604 初期軸圧縮変位を受ける両端固定偏平アーチのカオス振動におけるモード連成

Experimental and anlaytical results are presented on modal interaction in chaotic vibrations of a shallow clamped arch deformed by initial axial displacement. Chaotic responses due to internal responce and dynamic snap-through are observed in specific regions of the exciting frequency. The responses are examined by the Fourier spectra, Poincare projections and the maximum Lyapunov exponents comparing the analytical and experimental results. Contribution of each vibration mode to the chaotic vibration is then analyzed by the Karhumen-Loeve transformation. The chaotic vibration generated from internal resonance including super-harmonic resonance of second and third modes has relatively large contribution of higher vibration modes. Chaotic vibrations including dynamic snap-through generated from sub-harmonic resonance of the lowest vibration mode have relatively large contributions of asymmetric mode.

Magneto-optical studies of silver atoms in neon matrices

Abstract Absorption and magnetic circular dichroism measurements have been carried out on silver atoms trapped in neon matrices at cryogenic temperatures. By using the method of moments, it has been possible to show that the degeneracy of the 2 P excited state, obtained from the promotion of an electron from the Ag 5s to the 5p orbital, is lifted under the influence of simultaneous spin–orbit and vibrational coupling with the rare gas cage. From an analysis of the 2 P ← 2 S transition, the 2 P state spin–orbit coupling constant ( λ ) as well as the cubic ( E C ) and noncubic ( E NC ) rare gas cage vibrational mode contributions have been extracted. They are λ = 829 ± 52, E C = 340 ± 54 and E NC = 465 ± 74 cm −1 . The neon matrix has a profound influence on the silver atom spin–orbit coupling constant, increasing it from 614 cm −1 in the gas phase to 829 cm −1 . This large value is in line with the trend previously found for the other rare gas matrices: spin–orbit constant decrease with rare gas atomic mass increase. The trend is: 829 cm −1 (Ag/Ne), 783 cm −1 (Ag/Ar), 638 cm −1 (Ag/Kr), and 583 cm −1 (Ag/Xe). Calculations of the spin–orbit reduction factors using a “supermolecule” model involving the metal atom and the 12 surrounding rare gas atoms mimics the experimental results well, although the predicted value for Ag/Ne is smaller than the observed one by ∼15%. This discrepancy may arise from a slight collapsing of the rare gas cage onto the entrapped silver atom.

Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field [Eur. Phys. J. C 20 (2001) 723]. The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes [Eur. Phys. J. C 24 (2002) 653]. This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode [hep-th/0212226]. We argue that the obtained result is not a counterexample to the Mermin–Wagner–Hohenberg and Coleman theorems.

Oriented polyacetylene and copolymer systems: Polarized photoinduced infrared spectra

We report on the experimental polarized photoinduced infrared absorption spectra of oriented copolymers (CH) x - (polynorbornene) - (CH) x and oriented trans(CH) x. In these experiments the pump beam is polarized perpendicular and the probe beam is polarized parallel to the stretching axis, respectively. In this experiments among the three vibrational photoinduced bands observed in the PIA spectra we focus on the one peaked at 500–600 cm −1 which exhibits a more or less structured shape, sample dependent. Also, changes in the peak position of the low energy electronic band are observed in the different samples. Such a behavior can be interpreted in terms of the perturbation induced by the photogenerated charges on the lattice dynamics of the different conjugated segments. In order to calculate the band shapes, the photoinduced vibrational mode contributions of the different segments are weighted by the conjugation length dependent infrared dipole moments and by the bimodal distribution derived from the Raman spectra analysis of the same samples. Excellent agreement is found between the calculated and the experimentally recorded band shapes in the polarized photoinduced spectra of the different samples. In the framework of this model the changes of the low energy peak position are also qualitatively explained.

Contribution of concerted exchange to the entropy of self-diffusion in Si.

The concerted-exchange (CE) mechanism is at present the only viable candidate for atomic exchange that does not involve intrinsic lattice defects. In order to evaluate its contribution to self-diffusion in Si, we calculate the entropy associated with CE. We include full relaxation of the energy surface through an interatomic potential and take into account the dominant contributions of vibrational modes through the harmonic approximation. This gives an entropy of 6.3${\mathit{k}}_{\mathit{B}}$, which accounts for a large portion of the experimental result (7${\mathit{k}}_{\mathit{B}}$--9${\mathit{k}}_{\mathit{B}}$). We conclude that the CE mechanism is a significant contributor to self-diffusion in Si.

The thermodynamic functions and the regions of (P, T)-states of dense carbon and boron nitride modifications

Abstract For the first time the thermodynamic functions for boron nitride and carbon were defined in the temperature range 300 to 4000K by a computational procedure which was impossible in the previous empirical approach. This involved the application of the theoretical functions from Refs. 1, 2, and 3. There the temperature dependence of the heat capacity is characterized by a sum of two Debye functions that reflect the contribution of vibration modes of different characteristic temperature to the heat capacity. The above-mentioned theoretical functions make it possible to calculate the thermodynamic function without allowing for the anharmonic effect in the temperature range rather wider th-an the one wherein the initial experiments were conducted. It is sufficient for their computation to define Debye characteristic temperatures. One of the procedures of their calculation using experimental enthalpy data is described in Ref. 4. Besides, this work contains the majority of known experimental and theoreti...