Frequencies Of Transverse Modes Research Articles

Method of oscillation excitation for investigation of inconsistency of coating deposition on long parts

A method is proposed for studying the uniformity of electrochemical coating on the outer wall of a thin metal rod by determining the parameters of natural oscillations of this rod, which is clamped on one side. The parameters are studied by analyzing the natural frequencies of the rod. The uneven coating of the rod wall causes a change in the frequency of transverse modes and the shape of the bending line of the rod axis. The mechanical vibrations of the rod are excited by the interaction of an external magnetic field with the Ampere force arising from the current flowing through the rod. A method of adaptive tuning of the spectral components of the excitation current is developed by modifying the coefficients of a digital filter through which a noise-like signal pass. The coefficients of the digital filter are changed adaptively, based on the analysis of the signal spectrum obtained in response to the excitation in the first step. The oscillation is excited by mixing the noise-like signal and the signal received in response to the excitation in the previous step after averaging with a sliding window, the coefficients of which are obtained from the resonance characteristics of the mechanical oscillatory system. A gradual change in the ratio of the amplitude of the noise-like and stationary components of the excitation signal causes a smooth increase in the amplitude of oscillation at a frequency approaching the frequency of the rod's natural oscillations. A numerical and full-scale experiment is carried out to excite mechanical vibrations of a thin metal rod, the end of which is clamped on one side.

Non-Markovianity of an atom in a semi-infinite rectangular waveguide

We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM mn ) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity can be found as the atom–mirror distance is large enough, however, the asymptotic value of of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that is a constant, and the analytical expression for is related to the parameters associated with the modes, which is related to the interference of the two modes.

Dynamics of size-dependent multilayered shear deformable microbeams with axially functionally graded core and non-uniform mass supported by an intermediate elastic support

The current study investigates the coupled dynamics of a size-dependent third-order shear deformable multilayered microbeam with an axially functionally graded core, a non-uniform mass distribution (mass imperfection) and an intermediate elastic support. A power-law function is used to model the material properties in the longitudinal direction of the core. The equations of motion are obtained by formulating the energies of the system while employing the modified couple stress theory to include miniature size effects within the multilayered microbeam structure. Hamilton's principle and the modal decomposition method are utilised to derive and solve the coupled motion equations. The equations of motion are first verified against a former work on a simplified microbeam system, while the numerical results are validated by comparison to those of a simplified functionally graded in axial direction obtained by finite element macrobeam simulation. It was concluded that increasing either the power term constant of the material grading or the value of the localized mass imperfection (when xm*=0.3) causes the first and second transverse and axial natural frequencies of the three-layered microbeam to decrease, whereas increasing the length-scale parameter causes the natural frequencies of transverse modes to increase, demonstrating the size-dependent effects of the three-layered microbeam.

Anomalous behavior of a two-dimensional Hertzian disk system.

The anomalous behavior of a two-dimensional system of Hertzian disks with exponent α=7/2 has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Waterlike density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also in the solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above the maximum melting point T=0.0058 of the triangular crystal.

Experimental and Numerical Modal Analysis of a Bladed Rotor

The behavior of an asymmetric bladed rotor was investigated in this study. The bladed rotor which performs solid-solid, liquid-liquid, liquid-solid separation processes is part of the decanter machine and named as screw conveyor. The purpose of this study is to determine the dynamics of the rotor on the free conditions for future development of the asymmetric and blade assembled rotors. It is important for the designer to determine the natural frequencies of the bladed asymmetric rotor so that some precautions can be taken during the design of the machine and in the operating conditions of the machine. This study consisted of two parts. In the experimental one, the modal test of the bladed rotor was performed and in the numerical part, the modal analysis of the rotor was carried out under free-free boundary conditions using a simulation program based on the finite-element method. The natural frequencies of the blades and the rotor were obtained experimentally and numerically. It was found that the experimental results and numerical results were in good agreement. Besides, it was concluded that the two mode shape was equal to the transverse mode frequency of the rotor and blades and the following mode shapes correspond to the bending and torsion mode frequencies of the blades. Since the shape properties of the rotor and blades are different, it has been observed experimentally and numerically that their natural frequencies also differ.

Cellular Features Revealed by Transverse Laser Modes in Frequency Domain.

Biological lasers which utilize Fabry–Pérot (FP) cavities have attracted tremendous interest due to their potential in amplifying subtle biological changes. Transverse laser modes generated from cells serve as distinct fingerprints of individual cells; however, most lasing signals lack the ability to provide key information about the cell due to high complexity of transverse modes. The missing key, therefore, hinders it from practical applications in biomedicine. This study reveals the key mechanism governing the frequency distributions of transverse modes in cellular lasers. Spatial information of cells including curvature can be interpreted through spectral information of transverse modes by means of hyperspectral imaging. Theoretical studies are conducted to explore the correlation between the cross‐sectional morphology of a cell and lasing frequencies of transverse modes. Experimentally, the spectral characteristics of transverse modes are investigated in live and fixed cells with different morphological features. By extracting laser modes in frequency domain, the proposed concept is applied for studying cell adhesion process and cell classification from rat cortices. This study expands a new analytical dimension of cell lasers, opening an avenue for subcellular analysis in biophotonic applications.

Experimental and Numerical Dynamic Properties of Two Timber Footbridges Including Seasonal Effects

This paper deals with experimental and numerical dynamic analyses of two timber footbridges. Both bridges have a span of 35 m and consist of a timber deck supported by two timber arches. The main purpose is to investigate if the dynamic properties of the bridges are season dependent. To this end, experimental tests are performed during a cold day in winter and a warm day in spring in Sweden. The first bending and transverse mode frequencies increase 22% and 44%, respectively, due to temperature effects in the case of Vega Bridge. In the case of Hägernäs bridge, the corresponding values are 5% and 26%. For both bridges, the measured damping coefficients are similar in winter and spring. However, the damping coefficients for the first bending and transverse modes are different for both footbridges: about 1% for the Hägernäs bridge and 3% for the Vega bridge. Finite-element models are also implemented. Both numerical and experimental results show good correspondence. From the analyses performed, it is concluded that the connections between the different components of the bridges have a significant influence on the dynamic properties. In addition, the variation of the stiffness for the asphalt layer can explain the differences found in the natural frequencies between spring and winter. However, due to the uncertainties in the modelling of the asphalt layer, this conclusion must be taken with caution.

Enhancement of thermal conductivity in presence of macroscopic polarization fields: Role of dispersive transverse phonon modes in nanoscale GaN

The macroscopic polarization effects on lattice thermal conductivity of GaN is theoretically investigated. The explicit contributions from dispersive low and high frequency transverse and longitudinal phonons modes to thermal conductivity are investigated in the presence of polarization fields. Our numerical calculations of the thermal conductivity including polarization fields for the different dimension samples obtain good fit with experimental reports. The significant increase in thermal conductivity is observed at room temperature in presence of macroscopic polarization fields and in the low temperature region effect is found to be negligible. Contribution from high frequency transverse mode phonons to the total thermal conductivity is dominant in nanoscale dimension GaN samples in presence of polarization fields.

Raman and Infrared Studies of CdSe/CdS Core/Shell Nanoplatelets

The vibrational spectroscopy of semiconductor nanostructures can provide important information on their structure. In this work, experimental Raman and infrared spectra are compared with vibrational spectra of CdSe/CdS core/shell nanoplatelets calculated from first principles using the density functional theory. The calculations confirm the two-mode behavior of phonon spectra of nanostructures. An analysis of the experimental spectra reveals the absence of modes with a high amplitude of vibrations of surface atoms, which indicates their strong damping. Taking into account the difference in the damping of different modes and their calculated intensities, all bands in the spectra are unambiguously identified. It is found that the frequencies of longitudinal optical modes in heterostructures are close to the frequencies of LO phonons in bulk strained constituents, whereas the frequencies of transverse modes can differ significantly from those of the corresponding TO phonons. It is shown that an anomalous thickness dependence of CdS TO mode is due to a noticeable surface relaxation of the outer Cd layer in the nanostructure.

Concurrence of two identical atoms in a rectangular waveguide: linear approximation with single excitation

We study two two-level systems (TLSs) interacting with a reservoir of guided modes confined in a rectangular waveguide. For the energy separation of the identical TLSs far away from the cutoff frequencies of transverse modes, the delay-differential equations are obtained with single excitation initial in the TLSs. The effects of the inter-TLS distance on the time evolution of the concurrence of the TLSs are examined.

Frequency analysis of carbon and silicon nanosheet with surface effects

• FE modeling of surface effects in Si, Graphene–Silicon and SWCNT-Silicon nanosheet . • Numerical analysis of HACNTs on silicon substrate and its effect on frequency. • Development of analytical model to find frequency of HACNTs arrays on silicon. Silicon-based microelectromechanical system (MEMS) and nanoelectromechanical systems (NEMS) have been used to design and fabricate sensitive sensors and actuators. Recent research trends show that graphene and carbon nanotubes (CNTs) have been used to change the surface properties of silicon-based MEMS and NEMS to improve different mechanical, optical and electrical properties of silicon-based composites. In this paper, we focus on analyzing the vibrational characteristics of silicon-based devices when the surface of silicon is coated with single-layer graphene and horizontally aligned carbon nanotubes (HACNTs). To perform the analysis, we use multi-scale finite element approach for developing graphene–silicon nanocomposites (GSNCs) and carbon nanotube-silicon nanocomposites (CSNC) composites in which interface layer of silicon with graphene or CNT is modeled using bonded contact element. Subsequently, we performed modal analysis to find the first transverse mode frequency of GSNC and CSNC composites for beam with smaller as well as longer lengths. The numerical model is compared with classical beam theory with and without surface effect. For GSNCs composites, we take a fixed-free case with lengths in the range of (20 Å–120 Å) and (400 Å–2000 Å), respectively. For CSNC composites, CNT diameter is varied from (5 Å–30 Å) for single walled nanotube . Subsequently, we analyze the influence of HACNTs-on-silicon on its vibrational characteristics. The analysis presented in the paper demonstrate that GSNCs offer a higher bending stiffness compared to single layer graphene (SLGs) and isolated silicon nanosheet which lead to higher natural frequency. A similar trend is found in the case of HACNTs on silicon NS when the number of tubes increases.

Suppression of thermal transients in advanced LIGO interferometers using CO2 laser preheating

In high optical power interferometric gravitational wave detectors, such as Advanced LIGO, the thermal effects due to optical absorption in the mirror coatings and the slow thermal response of fused silica substrate cause time dependent changes in the mirror profile. After locking, high optical power builds up in the arm cavities. Absorption induced heating causes optical cavity transverse mode frequencies to drift over a period of hours, relative to the fundamental mode. At high optical power this can cause time dependent transient parametric instability, which can lead to interferometer disfunction. In this paper, we model the use of CO2 laser heating designed to enable the interferometer to be maintained in a thermal condition such that transient changes in the mirrors are greatly reduced. This can minimize transient parametric instability and compensate dark port power fluctuations. Modeling results are presented for both single compensation where a CO2 laser acting on one test mass per cavity, and double compensation using one CO2 laser for each test mass. Using parameters of the LIGO Hanford Observatory X-arm as an example, single compensation allows the maximum mode frequency shift to be limited to 6% of its uncompensated value. However, single compensation causes transient degradation of the contrast defect. Double compensation minimise contrast defect degradation and reduces transients to less than 1% if the CO2 laser spot is positioned within 2 mm of the cavity beam position.

Exploring the influence of high order transverse modes on the temporal dynamics in an optically pumped mode-locked semiconductor disk laser.

We quantitatively investigate the influence of high-order transverse modes on the self-mode locking (SML) in an optically pumped semiconductor laser (OPSL) with a nearly hemispherical cavity. A physical aperture is inserted into the cavity to manipulate the excitation of high-order transverse modes. Experimental measurements reveal that the laser is operated in a well-behaved SML state with the existence of the TEM(0,0) mode and the first high-order transverse mode. While more high-order transverse modes are excited, it is found that the pulse train is modulated by more beating frequencies of transverse modes. The temporal behavior becomes the random dynamics when too many high-order transverse modes are excited. We observe that the temporal trace exhibits an intermittent mode-locked state in the absence of high-order transverse modes.

Parametric instability in long optical cavities and suppression by dynamic transverse mode frequency modulation

Three mode parametric instability has been predicted in Advanced gravitational wave detectors. Here we present the first observation of this phenomenon in a large scale suspended optical cavity designed to be comparable to those of advanced gravitational wave detectors. Our results show that previous modelling assumptions that transverse optical modes are stable in frequency except for frequency drifts on a thermal deformation time scale is unlikely to be valid for suspended mass optical cavities. We demonstrate that mirror figure errors cause a dependence of transverse mode offset frequency on spot position. Combined with low frequency residual motion of suspended mirrors, this leads to transverse mode frequency modulation which suppresses the effective parametric gain. We show that this gain suppression mechanism can be enhanced by laser spot dithering or fast thermal modulation. Using Advanced LIGO test mass data and thermal modelling we show that gain suppression factors of 10-20 could be achieved for individual modes, sufficient to greatly ameliorate the parametric instability problem.

B3LYP investigation of response properties of alkali halides on external static electric fields

Structural, dielectric, and optical properties of six alkali halides were investigated by all-electron B3LYP hybrid density functional calculations. A response of their electronic and structural properties to the external static electric fields was also investigated. While the applied electric field only marginally affects the lattice parameter, the internal relaxation of ions is somewhat more pronounced with the cations displaced along with the field and anions opposite to the field. We further find that in the presence of electric field the valence and conduction bands widens resulting in the reduced band-gap. An explanation for this effect is provided, which is related to a slight delocalization of states in the presence of external electric field. However, this effect is far too small to account for the dielectric breakdown of alkali halides. For this reason, the dielectric breakdown was considered on the basis of von Hippel’s low-energy criterion and Callen’s equation, for which the calculated dielectric constants and optic transverse mode frequency were used. The obtained dielectric strengths are in fair agreement with experiment.

A Cell Lens Model for Transverse Modes in Optofluidic Intracavity Spectroscopy

Optofluidic intracavity spectroscopy of individual cells from canine hemangiosarcoma (HSA) and canine lymphoma cancer cell lines exhibit relatively uniformly spaced multiple transverse modes repeated in each free spectral range of a microfluidic Fabry-Pérot cavity, while similar spectra of healthy canine monocytes and lymphocytes have minimal or no transverse-mode peaks. Modeling of the cells as thin lenses allows paraxial Gaussian beam resonator analysis that produces spectral features that quantitatively match the frequencies of transverse modes and qualitatively agree with the trends in maximum transmission of the modes when aperture losses are included. Cell focal lengths of 600 and 300 μm, respectively, are extracted for canine HSA and lymphoma cells from the ratio of transverse to longitudinal frequency spacing, while the spectra of canine monocytes indicate that they have a focal length ≥ 580 μm. Under an assumption of constant refractive index, the focal lengths imply a radius of curvature for the top surface of the cells that is much greater than their lateral radius.

Observed Natural Frequencies, Damping Ratios, and Mode Shapes of Vibration of a 30-Story Building Excited by a Major Earthquake and Typhoon

The safety of building structures and contents, as well as the comfort of occupants, under such strong forces as earthquakes and typhoons remain major engineering concerns. In order to improve our understanding of building structural responses, records of a structural array in the 30-story PS Building in Taipei from the M7.6 Chi-Chi earthquake and Typhoon Aere are analyzed. In addition, wind data measured at the Taipei Meteorological Station are also used. First, the field measurement data clearly demonstrate that serviceability of the PS Building met the criteria for occupant comfort during Typhoon Aere. Secondly, several structural vibration parameters of this highrise building, including the transfer functions, natural frequencies, damping ratios and mode shapes, excited by the Chi-Chi earthquake, Typhoon Aere, and ambient vibrations are also determined and compared. The results show the frequency of the first mode for the longitudinal components is approximately 8.6% lower for the earthquake than the ambient vibrations. The transverse mode frequencies behave similarly. In contrast, frequency changes from the typhoon to ambient vibrations are in the third decimal (1.3% and 0.9% lower in the longitudinal and transverse directions, respectively), indicating little nonlinearity. The damping ratios of the PS Building apparently increase with vibration amplitudes. Finally, results of a spectral ratio analysis of the Chi-Chi earthquake data do not indicate significant SSI effects in the longitudinal and transverse directions.

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 (Δ ν trans) was 1.16 GHz, and the magnitude of frequency splitting (Δ ν) 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).

Liquid sloshing in half-full horizontal elliptical tanks

A two dimensional hydrodynamic analysis based on the linear potential theory is introduced to study the natural sloshing frequencies of transverse modes in a half-filled non-deformable horizontal cylindrical container of elliptical cross section, without or with a pair of inflexible horizontal longitudinal side baffles of arbitrary extension positioned at the free liquid surface. Successive conformal coordinate transformations in conjunction with the method of separation of variables and the relevant boundary conditions are employed to obtain standard truncated matrix eigen-value problems which are then solved numerically for the resonance eigen-frequencies. The Gauss–Laguerre quadrature formula is used to approximate the integral eigen-problem obtained in the unbaffled case. Plots of the sloshing frequencies as functions of the container aspect ratio and baffle extension are presented and discussed for the three lowest antisymmetric and symmetric transverse oscillation modes. A convergence study is performed to demonstrate the fast convergence and remarkably small computational cost of the Fourier series approach used for the baffled container, and the effects of tank geometry and baffle length on the convergence are also examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained, demonstrating the accuracy of proposed models.

Phonon Softening in Two-Dimensional Electron–Lattice System with Anisotropy

The effect of anisotropy on phonon softening at finite temperatures in a two-dimensional (2D) electron–lattice system is studied numerically. On the basis of the Su–Schrieffer–Heeger model generalized to a 2D system with a half-filled electronic band on the square lattice, we introduce an anisotropy parameter γ in the electronic transfer integrals and the electron–lattice coupling constants in the x and y directions, t x and t y , and α x and α y , respectively, as t x / t y =α x /α y =(1+γ/2)/(1-γ/2). In the isotropic system, it has been shown that the phonon frequencies of transverse modes with the nesting vector Q =(π/ a ,π/ a ) ( a is the lattice constant) and with wave vectors parallel to Q , and that of the longitudinal mode with Q are all softened at the same Peierls transition temperature. In the presence of anisotropy, it is found that the mode with Q having its amplitude only in the strong-coupling direction is softened first as the temperature is lowered in the metallic phase while other modes ...