Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.     

The harmonic force field and ground-state average structure of allene

Existing spectroscopic data for allene-H₄, -D₄, and -1,1-D₂ are improved and augmented by gas-phase Raman and solid-phase infrared studies. A number of ¹³C vibration frequencies are identified in natural abundance by each technique. A total of 58 input data enable 22 of the 23 force field parameters to be determined, the ¹³C frequency shift data removing the ambiguity of choice between two sets of A₁ and B₂ species force constants. The remaining interaction force constant is constrained to the predicted ab initio value of Botschwina and Pulay. The force field is used to determine the ground-state average (r_z) structure of allene. Observed trends in the H-D isotopic effects on the r_z structures of ethylene, allene, and ketene are in accordance with those expected.     

Application of optimization methods to vibration control of stretched strings

In this paper, non-linear programming techniques are applied to the problem of controlling the vibration pattern of a stretched string. First, the problem of finding the magnitudes of two control forces applied at two points l₁ and l₂ on the string to reduce the energy of vibration over the interval (l₁, l₂) relative to the energy outside the interval (l₁, l₂) is considered. For this problem the relative merits of various methods of non-linear programming are compared. The more complicated problem of finding the positions and magnitudes of two control forces to obtain the desired energy pattern is then solved by using the slack unconstrained minimization technique with the Fletcher-Powell search. In the discussion of the results it is shown that the position of the control force is very important in controlling the energy pattern of the string.     

EVALUATION OF VIBRATION AND SHOCK ATTENUATION PERFORMANCE OF A SUSPENSION SEAT WITH A SEMI-ACTIVE MAGNETORHEOLOGICAL FLUID DAMPER

The potential benefits of a semi-active magnetorheological (MR) damper in reducing the incidence and severity of end-stop impacts of a low natural frequency suspension seat are investigated. The MR damper considered is a commercially developed product, referred to as “Motion Master semi-active damping system” and manufactured by Lord Corporation. The end-stop impact and vibration attenuation performance of a seat equipped with such a damper are evaluated and compared with those of the same seat incorporating a conventional damper. The evaluation is performed on a servo-hydraulic vibration exciter by subjecting the seat-damper combinations to a transient excitation with dominant frequency close to that of the seat and continuous random excitation class EM1 applicable to earth-moving machinery, and a more severe excitation realized by amplifying the EM1 excitation by 150%. Tests are performed for medium and firm settings of the MR damper and for seat height positions corresponding to mid-ride and ±2·54 and ±5·08 cm relative to mid-ride. The results indicate that significantly higher levels of transient excitation are necessary to induce end-stop impacts for the seat equipped with the MR damper, particularly when set for firm damping, the difference with the conventional damper being more pronounced for seat positions closer to the end-stops. Under the EM1 excitation, the results indicate that under conditions which would otherwise favour the occurrence of end-stop impacts for a seat equipped with a conventional damper, the use of the MR damper can result in considerably less severe impacts and correspondingly lower vibration exposure levels, particularly when positioned closer to its compression or rebound limit stop.     

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of “edge functions” that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1−c/a), and the notch angle is defined as (360°−α). For a very small notch angle (1° or less), the notch may be regarded as a “sharp radial crack.” Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°−α), depths (1−c/a), and thickness ratios (a/h for plates and h/a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r(θ), several of which are described for future investigations and close extensions of this work.     

Direct energy flow measurement in magneto-sensitive vibration isolator systems

The effectiveness of highly nonlinear, frequency, amplitude and magnetic field dependent magneto-sensitive natural rubber components applied in a vibration isolation system is experimentally investigated by measuring the energy flow into the foundation. The energy flow, including both force and velocity of the foundation, is a suitable measure of the effectiveness of a real vibration isolation system where the foundation is not perfectly rigid. The vibration isolation system in this study consists of a solid aluminium mass supported on four magneto-sensitive rubber components and is excited by an electro-dynamic shaker while applying various excitation signals, amplitudes and positions in the frequency range of 20–200 Hz and using magneto-sensitive components at zero-field and at magnetic saturation. The energy flow through the magneto-sensitive rubber isolators is directly measured by inserting a force transducer below each isolator and an accelerometer on the foundation close to each isolator. This investigation provides novel practical insights into the potential of using magneto-sensitive material isolators in noise and vibration control, including their advantages compared to traditional vibration isolators. Finally, nonlinear features of magneto-sensitive components are experimentally verified.     

EVALUATION OF WHOLE-BODY VIBRATION IN VEHICLES

The vibration in 100 different vehicles has been measured, evaluated and assessed according to British Standard BS 6841 (1987) and International Standard ISO 2631 (1997). Vibration was measured in 14 categories of vehicle including cars, lift trucks, tractors, lorries, vans and buses. In each vehicle, the vibration was measured in five axes: vertical vibration beneath the seat, fore-and-aft, lateral and vertical vibration on the seat pan and fore-and-aft vibration at the backrest. The alternative methods of evaluating the vibration (use of different frequency weightings, different averaging methods, the inclusion of different axes, vibration dose values and equivalent r.m.s. acceleration) as defined in the standards have been compared. BS 6841 (1987) suggests that an equivalent acceleration magnitude is calculated using vibration measured at four locations around the seat (x -, y -, z -seat and x -backrest); ISO 2631 (1997) suggests that vibration is measured in the three translational axes only on the seat pan but only the axis with the most severe vibration is used to assess vibration severity. Assessments made using the procedure defined in ISO 2631 tend to underestimate any risks from exposure to whole-body vibration compared to an evaluation made using the guidelines specified in BS 6841; the measurements indicated that the 17 m/s^1.75 “health guidance caution zone” in ISO 2631 was less likely to be exceeded than the 15 m/s^1.75 “action level” in BS 6841. Consequently, ISO 2631 “allows” appreciably longer daily exposures to whole-body vibration than BS 6841.     

Lithium adsorption on hot oxygen covered tungsten surfaces

The mean residence times τ of lithium particles on oxygen covered tungsten surfaces were measured accurately over a wide temperature range (1200 < T < 1900 K) by the beam modulation technique with a lock-in analyzer. A predominant monocrystalline W(100) structure was obtained by recrystallization of a polycrystalline tungsten ribbon. The residence time was determined as a function of the oxygen coverage θ and the temperatureT of the surface. The desorption energy l and the preexponential factor τ₀, calculated from the Arrhenius equation, are not only dependent on the amount of adsorbed oxygen but also on the oxygen structure. Apparently the desorption parameters l and τ₀ are correlated. An increasing desorption energy l is connected to a decreasing “vibration period” τ₀ whereby the influence on the residence time is partly compensated.     

Ab initio anharmonic force field and equilibrium structure of carbonyl chlorofluoride

The quadratic, cubic, and semi-diagonal quartic force field of OCFCl has been calculated at the MP2 level of theory employing a basis set of triple-zeta quality. The spectroscopic constants derived from the force field are in excellent agreement with those from previous and new experiments. The equilibrium structure has been derived from experimental ground state rotational constants and ab initio rovibrational interaction parameters. This semi-experimental structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory. This good agreement indicates that the derived structure is accurate. The equilibrium geometry is: r_e(CO)=1.173(1) Å; r_e(C-F)=1.323(1) Å; r_e(C-Cl)=1.721(1) Å; ∠_e(OCF)=124.0 (1)°; and ∠_e(OCCl)=126.4(1)°.     

Velocity modulation spectroscopy of molecular ions I: The pure rotational spectrum of TiCl (XΦr)

The pure rotational spectrum of the TiCl⁺ ion in its X³Φ_r ground state has been measured in the frequency range 323-424 GHz, using a combination of direct absorption and velocity modulation techniques. The ion was created in an AC discharge of TiCl₄ and argon. Ten, eleven, and nine rotational transitions were recorded for the ⁴⁸Ti³⁵Cl⁺, ⁴⁸Ti³⁷Cl⁺, and ⁴⁶Ti³⁵Cl⁺ isotopomers, respectively; fine structure splittings were resolved in every transition. The rotational fine structure pattern was irregular with the Ω = 4 component lying in between the Ω = 2 and 3 lines. This result is consistent with the presence of a nearby ³Δ_r state, which perturbs the Ω = 2 and 3 sub-levels, shifting their energies relative to the Ω = 4 component. The data for each isotopomer were analyzed in a global fit, and rotational and fine structure parameters were determined. The value of the spin-spin constant was comparable to that of the spin-orbit parameter, indicating a large second-order spin-orbit contribution to this interaction. The bond length established for TiCl⁺, r₀ = 2.18879 (7) Å, is significantly shorter than that of TiCl, which has r₀ = 2.26749 (4) Å. The shorter bond length likely results from a Ti²⁺Cl⁻ structure in the ion relative to the neutral, which is thought to be represented by a Ti⁺Cl⁻ configuration. The higher charge on the titanium atom shortens the bond.     

Shell structure for deformed nuclear shapes

Eigenvalues for the harmonic oscillator without l·s or l² terms suggest a deformed shell structure for nuclei with axes ratios 2 : 1 and deformation ? = 0.6 with corresponding nucleon “magic numbers” 2, 4, 10, 16, 28, 40, 60, 80 110 and 140, subject to small modifications due to spin-orbit and other correction terms. Experimental evidence of reasonably stable highly deformed structures corresponding to nucleon numbers 16, 20, 28, 40 and 60 (64) is presented. Attempts to calculate the corresponding potential energy surfaces using the Strutinsky shell correction method are described.     

Role of the substrate thickness for the structural properties of organic-organic heterostructures

F₁₆CuPc deposited on pentacene is characterized by the coexistence of two different configurations: F₁₆CuPc is found in the standing up phase (“s-configuration”) on top of pentacene terraces and in a lying down phase (“l-configuration”) at pentacene step edges. By combining AFM and grazing incidence X-ray diffraction we show that the ratio between F₁₆CuPc in l- and s-configurations increases with thickness of the pentacene substrate film, demonstrating the role of the pentacene steps as nucleation centers for the F₁₆CuPc l-configuration. Experiments performed with ultra-thin pentacene thicknesses disclose that the F₁₆CuPc l-configuration does not grow on top of the first and second pentacene layers, pointing to the action of long-range interactions with the substrate.     

Frequency splitting phenomenon of dual transverse modes in a Nd:YAG laser

We observed frequency splitting phenomenon of dual transverse modes (TEM_00q and TEM_01q) in a Nd:YAG microchip standing wave laser utilizing intracavity stress birefringence effects. Four resonance frequencies (ν_00qe, ν_00qo, ν_01qe, and ν_01qo, respectively) were produced and tuned by changing the diametral compression force applied on the laser crystal. The transverse mode frequency spacing for the same longitudinal mode number (Δν_trans) was 1.16 GHz, and the magnitude of frequency splitting (Δν) ranged from 0 MHz to 1.16 GHz. Based on this phenomenon, a four-mode differential standing wave laser, whose signal characteristics were a little like those of a four-mode differential travelling wave laser gyro however with a much larger frequency splitting range, was produced. The theoretical analysis is in good agreement with the experimental results. This phenomenon not only can be used to make lasers with two or more frequency differences, but also can be used to make high-resolution self-sensing laser sensors (e.g. laser force sensors and laser accelerometers).     

Comparison of the apparent masses and cross-axis apparent masses of seated humans exposed to single- and dual-axis whole-body vibration

Humans are exposed to whole-body vibration in many types of environment. In almost all cases, the vibration to which the human is exposed comprises multi-axis vibration, such that vibration occurs in all directions simultaneously. Despite the complex nature of vibration to which humans are exposed in the workplace, almost all laboratory studies investigating the biomechanical response of the person have been completed using single-axis simulators. This paper presents a study whereby 15 male subjects were exposed to single-axis whole-body vibration in the x-, y- and z-directions and dual-axis vibration in the xy-, xz-, and yz-directions using a 6 degree-of-freedom vibration simulator. All vibration magnitudes were 0.4 ms⁻² rms in each axis. Acceleration and force was measured in the x-, y-, and z-direction during all trials. Subjects sat in two postures (‘back-on’ and ‘back-off’) on a flat rigid seat. Apparent masses measured using single-axis and dual-axis vibration stimuli showed comparable results; similarly, cross-axis apparent masses (i.e. the ratio of the force in one direction to the acceleration in another direction) were almost identical for the single- and dual-axis vibration stimuli. All results were in agreement with data previously published using single-axis vibration. In most cases, the peaks in the apparent mass and the cross-axis apparent mass occurred at a slightly lower frequency for the dual-axis vibration than for the single-axis vibration. It is hypothesised that this change is due to a nonlinear effect, analogous to that which occurs with increasing vibration magnitude for single-axis vibration.     

Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

Excited vibrational state microwave spectra,structure, and force-field of trifluorosilane

The J = 2?1 microwave spectrum of six isotopic species of HSiF₃ has been observed and assigned in excited states of five of the six fundamental vibrations. The assignment is based on relative intensities, double resonance experiments, and trial anharmonic force constant calculations. Analysis of the spectra leads to experimental values for five of the $\text{α}{}_{\mathrm{r}}{}^{\mathrm{B}}$ constants, all three l-doubling constants q_t, one Fermi resonance constant φ₂₃₃, and one zeta constant $\text{ζ}{}_{\mathrm{6,\; 6}}{}^{\mathrm{(z)}}$.The harmonic force field has been refined to all the available data on vibration wavenumbers, centrifugal distortion constants, and zeta constants. The cubic anharmonic force field has been refined to the data on $\text{α}{}_{\mathrm{r}}{}^{\mathrm{B}}$ and q_t constants, using two models: a valence force model with two cubic force constants for SiH and SiF stretching, and a more sophisticated model. With the help of these calculations, the following equilibrium structure has been determined: $\text{r}{}_{\mathrm{e}}\text{(}\text{SiH}\text{) = 1.4468(±5)}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(}\text{SiF}\text{) = 1.5624(±1)}\text{A}\text{?}$, ∠HSiF = 110.64(±3)°,     

Equilibrium structure in the presence of internal rotation: A case study of cis-methyl formate

The Born-Oppenheimer (BO) equilibrium molecular structure () of cis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-ζ quality and a core correlation correction. The quadratic, cubic and semi-diagonal quartic force field in normal coordinates has also been computed at the MP2 level employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure () has been derived from experimental ground-state rotational constants and the lowest-order rovibrational interaction parameters calculated from the ab initio cubic force field. To determine structures, it is important to start from accurate ground-state rotational constants. Different spectroscopic methods, applicable in the presence of internal rotation and used in the literature to obtain “unperturbed” rotational constants from the analysis and fitting of the spectrum, are reviewed and compared. They are shown to be compatible though their precision may be different. The and structures are in good agreement showing that, in the particular case of cis-methyl formate, the methyl torsion can still be treated as a small-amplitude vibration. The best equilibrium structure obtained for cis-methyl formate is: r(C_m-O) = 1.434 Å, r(O-C_c) = 1.335 Å, r(C_m-H_s) = 1.083 Å, r(C_m-H_a) = 1.087 Å, r(C_c-H) = 1.093 Å, r(CO) = 1.201 Å, ∠(COC) = 114.4°, ∠(CCH_s) = 105.6°, ∠(CCH_a) = 110.2°, ∠(OCH) = 109.6°, ∠(OCO) = 125.5°, and τ(H_aCOC) = 60.3°. The accuracy is believed to be about 0.001 Å for the bond lengths and 0.1° for the angles.     

Generation of low-frequency vibration using a cantilever beam for calibration of accelerometers

At low frequencies (below 10 Hz), performance of a conventional shaker is limited by small acceleration amplitudes and a high level of total harmonic distortion. The present article describes a low-frequency vibration generator that overcomes these limitations. The vibration generator consists of a cantilever beam excited by a conventional shaker. The cantilever beam is tuned to resonate at the desired excitation frequency, which leads to a relatively large vibratory motion at the beam tip with very small harmonic distortion. Analysis of the system is performed by means of model equations describing both the flexural and longitudinal components of vibration. A comprehensive measurement of the generator's performance confirms that it can serve as an economically attractive alternative to existing low-frequency vibration generators used in vibration measurement and calibration.     

Non-relativistic limit of Randall-Sundrum model: solutions, applications and constraints

In the Randall-Sundrum model with one brane, we found the approximate and exact solutions for gravitational potentials and accelerations of test bodies in these potentials for different geometrical configurations. We applied these formulas for calculation of the gravitational interaction between two spheres and found the approximate and exact expressions for the relative force corrections to the Newton’s gravitational force. We demonstrated that the difference between relative force corrections for the approximate and exact cases increases with the parameter l (for the fixed distance r between centers of the spheres). On the other hand, this difference increases with decreasing of the distance between the centers of the spheres (for the fixed curvature scale parameter l). We got the upper limit for the curvature scale parameter l ≲ 10 μm. For these values of l, the difference between the approximate and exact solutions is negligible.