Increasing Wave Number Research Articles

Numerical Investigation on Inviscid Instability of Streaky Structures in Incompressible Boundary Layer Flow

Numerical investigation is made on the effect of streaky structures in transition by inviscid linear disturbance equation with temporal mode. Several disturbances with different streamwise wave numbers were induced, and the evolutions with time step were received. It suggests that the exponential growth and periodic variation of the waves are in existence. As the streamwise wave number increases, the disturbance growth rate begins by increasing, reaches a maximum at around α = 0.4 with a disturbance frequency of 0.2186 + 0.001457i, and then decreases. Furthermore, the eigenfunctions of pressure disturbance are plotted.

Linear spatial instability of viscous flow of a liquid sheet through gas

The present paper focuses on the linear spatial instability of a viscous two-dimensional liquid sheet bounded by two identical viscous gas streams. The Orr–Sommerfeld differential equations and the boundary conditions of the flow configuration are numerically solved using Chebyshev series expansions and the collocation method. The strong dependence of the instability parameters on the velocity profiles is proven by using both quadratic and error functions to define the base flow in the liquid sheet and the gas shear layer. The sensitivity of the spatial instability growth rate to changes in the dimensionless parameters of the problem is assessed. Regarding the liquid sheet Reynolds number, it has been observed that, when this parameter increases, both the most unstable growth rate and the corresponding wavenumber decrease, whereas the cutoff wavenumber increases. The results of this analysis are compared with temporal theory through Gaster transformation. The effects liquid and gas viscosity have on instability are studied by comparing the instability curves given by the presented model with those from an inviscid liquid sheet and a viscous liquid sheet in an inviscid gaseous medium. The model presented in this paper features a variation in the cutoff wavenumber with all the governing parameters of the problem, whereas that provided by cases that account for an inviscid surrounding gas depends only on the liquid sheet Weber number and the ratio of gas to liquid densities. Results provided by the presented model have been experimentally validated and show that quadratic profiles have a greater capacity to predict the disturbance wavelength.

Transverse instability of surface solitary waves. Part 2. Numerical linear stability analysis

In a previous work, Kataoka & Tsutahara (J. Fluid Mech., vol. 512, 2004a, p. 211) proved the existence of longitudinally stable but transversely unstable surface solitary waves by asymptotic analysis for disturbances of small transverse wavenumber. In the present paper, the same transverse instability is examined numerically for the whole range of solitary-wave amplitudes and transverse wavenumbers of disturbances. Numerical results show that eigenvalues and eigenfunctions of growing disturbance modes agree well with those obtained by the asymptotic analysis if the transverse wavenumber of the disturbance is small. As the transverse wavenumber increases, however, the growth rate of the disturbance, which is an increasing function for small wavenumbers, reaches a maximum and finally falls to zero at some finite wavenumber. Thus, there is a high-wavenumber cutoff to the transverse instability. For higher amplitude, solitary waves become longitudinally unstable, and the dependence of the eigenvalues on the transverse wavenumber exhibits various complicated patterns. We found that such eigenvalues versus transverse wavenumber can be simply grouped into three basic classes.

Investigation of normal waves in a porous layer surrounded by elastic half-spaces

The wave field and dispersion equations are found for a porous layer surrounded by two elastic half-spaces. The porous layer is described by the effective model of a medium in which elastic and fluid layers alternate. To investigate the normal waves, all real roots of dispersion equations are determined and their movements as the wave number increases are investigated. As a result, the dispersion curves of all normal waves are constructed and the dependence of normal waves on the parameters of the porous layer and elastic half-spaces is analyzed. Bibliography: 6 titles.

The Onset of Convection in a Layer of Cellular Porous Material: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer

The onset of convection in a horizontal layer of a cellular porous material heated from below is investigated. The problem is formulated as a combined conductive-convective-radiative problem in which radiative heat transfer is treated as a diffusion process. The problem is relevant to cellular foams formed from plastics, ceramics, and metals. It is shown that the variation of conductivity with temperature above that of the cold boundary leads to an increase in the critical Rayleigh number (based on the conductivity of the fluid at that boundary temperature) and an increase in the critical wave number. On the other hand, the critical Rayleigh number based on the conductivity at the mean temperature decreases with increase in the thermal variation parameter if the radiative contribution to the effective conductivity is sufficiently large compared with the nonradiative component.

Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems

The Partition of Unity Finite Element Method is used to solve wave scattering problems governed by the Helmholtz equation, involving one or more scatterers, in two dimensions. The method allows us to relax the traditional requirement of around ten nodal points per wavelength used in the Finite Element Method. Therefore the elements are multi-wavelength sized and the mesh of the computational domain may be kept unchanged for increasing wave numbers. As a result, the total number of degrees of freedom is drastically reduced. In this work, various numerical aspects affecting the efficiency of the method are investigated by considering an interior Helmhlotz problem. Those include the plane wave enrichment, the h-refinement, the geometry description, and the conjugated or unconjugated type of formulation. The method is then used to solve problems involving multiple scatterers. Last, an exterior scattering problem by a non-smooth rigid body is presented.

Mechanical buckling of cylindrical shells with varying material properties

The analytical solutions of the first-order shear deformation theory are developed to study the buckling behaviour of functionally graded (FG) cylindrical shells under three types of mechanical loads. The Poisson's ratios of the FG cylindrical shells are assumed to be constant, while the Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents given by power-law or exponential function. The stability equations are employed to obtain the closed-form solutions for critical buckling loads of each loading case. The dependence of the critical buckling loads on the variations of the material properties with a power-law or exponential function is studied. It is observed that these effects change appreciably the critical buckling loads. Results for critical loads are tabulated for thin and moderately thick shells. Although the critical buckling load of FG cylindrical shells decreases as the circumferential wave numbers increase, it rises for axially compressed long shells as the longitudinal wave numbers increase.

Flexural wave dispersion in multi-walled carbon nanotubes conveying fluids

Motivated by the great potential of carbon nanotubes for developing nanouidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of exural wave in multi-walled carbon nanotubes conveying uids. The study shows that the moving flow reduces the phase velocity of exural wave of the lowest branch in carbon nanotubes. The phase velocity of exural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of exural wave becomes more and more remarkable with an increase in wave number.

Influence of Isotope Substitution Helium Atom on Partial Cross Sections in He-HF Collisions

Close-coupling equation and anisotropic potential developed in our previous research are applied to HF-3He (4He, 6He, 8He, 10He) collision system, and partial cross sections (PCSs) at the incident energy of 40 meV are calculated. By analyzing the differences of these PCSs, change rules of PCSs with the increase of partial wave number, and with the change of the mass of isotope substitution helium atom are obtained. The results show that excitation PCSs converge faster than elastic PCSs for collision energy and each of systems considered here. Also excitation PCSs converge more rapidly for high-excited states. Tail effect is present only in elastic scattering and low-excited states but not in high-excited states. With the increase of the mass of isotope substitution helium atom, converging speed of elastic, total inelastic, and state-to-state excitation PCS slows down, and the maxima of these PCSs undergoes a regular change.

An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems

It is well-known that one key issue of solving the Helmholtz equation using finite element method (FEM) is the accuracy deterioration in the solution with increasing wave number due to the “numerical dispersion error”. Such a numerical dispersion error is essentially caused by the “overly-stiff” nature of the FEM model. To overcome this problem, this paper presents an edge-based smoothed finite element method (ES-FEM) for analyzing acoustic problems using linear triangular and tetrahedron elements that can be generated automatically, respectively, for complicated two-dimensional and three-dimensional domains. The discretized linear system equations for ES-FEM are established using the smoothed Galerkin weak form with smoothing domains associated with the edges of the triangles or surfaces of the tetrahedrons. The edge-based gradient smoothing operation provides proper softening effect, makes the ES-FEM model much softer than the “overly-stiff” FEM model and hence significantly reduces the numerical dispersion error. Numerical examples, including a 2D problem of acoustic pressure distribution in a vehicle passenger compartment and a 3D problem about the acoustic pressure distribution in an engine chamber, have been studied using the present ES-FEM. The results demonstrate that the ES-FEM possesses the following advantages compared with the standard FEM using the same meshes. First, ES-FEM achieves similar convergence rate but better accuracy especially at high frequency. Second, ES-FEM is less sensitive to the mesh distortion, meaning that the quality of mesh has less effect on the solution of ES-FEM. Third, it works well for triangular types of meshes, and thus for the problems with complicated geometry.

Breakdown of structural models for vibrations of single-wall zigzag carbon nanotubes

Free vibrations of zigzag single-wall carbon nanotubes (SWCNTs) of aspect ratio (length/diameter) ∼6 and with ends traction-free have been studied using molecular mechanics (MM) simulations with the MM3 potential. It is found that the frequencies of inextensional (the Love and the Rayleigh) modes of an (n, 0) SWCNT saturate at the circumferential wave number of either (n−1)/2 or n/2 where n is odd or even. This is explained in terms of its molecular structure. Since the frequencies of the inextensional modes of vibration of a thin cylinder made of an isotropic linear elastic material do not saturate with an increase in the circumferential wave number, a continuum structure cannot represent all modes of vibration of a zigzag SWCNT. This result is independent of the value assigned to the wall thickness of the SWCNT. We have also found values of material and geometric parameters of a shell and a hollow cylinder by equating their frequencies of the inextensional, the radial breathing, the axial and the torsional modes of vibrations to the corresponding ones of a zigzag SWCNT, and by taking their mean diameter and length equal to those of the SWCNT. The frequencies of the extensional modes of oscillations of the two continuum structures for various axial half wave numbers and circumferential wave numbers are found to match well with those of the SWCNT obtained from the MM simulations. However, the frequencies of the inextensional modes of the continuum structures deviate noticeably from those of the SWCNT, and this deviation increases with an increase in the circumferential wave number.

Solutions of nonlinear Schrödinger equation for interfacial waves propagating between two ideal fluids

We present solutions to the problem of waves propagating at an interface between two inviscid fluids of infinite extent and differing densities. The method of multiple scale is employed to obtain a dispersion relation and nonlinear Schrödinger (NLS) equation, which describes the behavior of the system for the fluid interface. The dispersion relation of the model NLS equation is studied. The solutions of the NLS equation are derived analytically by using the complex tanh-function method and the function transformation method into a sine-Gordon equation. Also, diagrams are drawn to illustrate the elevation of the interface, the slip velocity, and the conservation of power. We observe that the elevation of the interface is in the form of traveling quasi-solitary waves that decrease as the wave number increases. We see that the slip velocities also bring a nonlinear and periodic characters. Finally, we observe that the conservation of power is in the form of traveling waves. Also, as the wave number increases, the conservation of power is more accurate in fluctuating around zero.

Stability of Thermocapillary Convection in Annular Pools with Low Prandtl Number Fluid

In order to understand the stability characteristics of thermocapillary convection in an annular pool with low Prandtl number (Pr = 0.011) fluid, a linear stability analysis had been performed. The annular pool was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surface were adiabatic. The results show that the critical Marangoni number and the critical wave number decrease with the increase of the aspect ratio, which is defined as the ratio of the depth to the gap width of the annular pool. When the aspect ratio exceeds 0.12, the critical wave number keeps almost constant. As the radius ratio increases, the critical Marangoni number decreases slightly, while the critical wave number increases. In the gravity condition, the effect of the buoyancy on the critical Marangoni number and wave number increases gradually with the increase of the aspect ratio.

Oscillatory Screening Effects on Elastic Collisions in Dense Electron-Ion Quantum Plasmas

Abstract The oscillatory screening effects on elastic electron-ion collisions are investigated in dense quantum plasmas. The eikonal method with the modified Debye-Hückel potential is employed to obtain the scattering phase shift and scattering amplitude. In addition, the total elastic collision cross section is obtained by the optical theorem with the forward scattering amplitude in quantum plasmas. It is shown that the modified Debye-Hückel screening in quantum plasmas produces the oscillatory behaviour of the scattering phase shift. In addition, the minimum position of the phase shift is receded from the target ion with decreasing the quantum wave number. It is also found that the oscillatory screening effect suppresses the differential cross section. The total cross section is also found to be decreased due to the oscillatory screening effect. In addition, it is shown that the total cross section decreases with an increase of the quantum wave number

Solvent dependent study of carbonyl vibrations of 3‐phenoxybenzaldehyde and 4‐ethoxybenzaldehyde by Raman spectroscopy and ab initio calculations

AbstractA Raman spectroscopy investigation of the carbonyl stretching vibrations of 3‐phenoxybenzaldehye (3Phbz) and 4‐ethoxybenzaldeheyde (4Etob) was carried out in binary mixtures with different polar and nonpolar solvents. The purpose of this study was twofold: firstly, to describe the interaction of the carbonyl groups of two solute molecules in terms of a splitting in the isotropic and anisotropic components and secondly, to analyze their spectroscopic signatures in a binary mixture. Changes in wavenumber position, variation in the anisotropic shift and full width half maximum were investigated for binary mixtures with different mole fractions of the reference systems. In binary mixtures, the observed increase in wavenumber with solvent concentration does not show linearity, indicating the significant role of molecular interactions on the occurrence of breaking of the self‐association of the solute. In all the solvents, a gradual decrease in the anisotropic shift reflects the progressive separation of the coupled oscillators with dilution. Γi(ηc), 3Phbz—solvent mixtures, exhibit a gradual decrease with decrease in the concentration of the solute which is an evidence on the influence of micro viscosity on linewidth. For 4Etob, the carbonyl stretching vibration shows two well‐resolved components in the Raman spectra, attributed to the presence of two distinct carbonyl groups: hydrogen‐bonded and free carbonyl groups. The intensity ratio of the carbonyl stretching vibration of these two types of carbonyl groups is studied to understand the dynamics of solute/solvent molecules owing to hydrogen bond interactions. Ab initio calculations were employed for predicting relevant molecular structures in the binary mixtures arising from intermolecular interactions, and are related to the experimental results. Copyright © 2009 John Wiley & Sons, Ltd.

Preparation and properties of a novel near infrared photovoltaic detector single-crystal material

A new photoelectronic semiconductor crystal, mercury indium telluride (MIT), with dimensions of 15mm in diameter and 175mm in length has been successfully grown by using the vertical Bridgman method (VB) at the optimized growth conditions. The crystal was determined through the power X-ray diffraction to be defect zinc-blende structure with the space group F43m . The transmittance spectra from 2.5 to 25μm shows high middle and far-infrared transmittance of 50∼55%, which decreases gradually with the increase of wavenumber due to the lattice absorption and free carriers absorption. Hall measurements at room temperature show that the resistivity, carrier density and mobility of the MIT crystal are 4.79×102 Ωcm, 2.83×1013 cm-3 and 4.60×102 cm2V-1s-1, respectively. The reduction of carrier mobility and the increase of the resistivity are related to the adding of In2Te3 into HgTe, which changes the energy band structure of the crystal.

Structural and Infrared Spectroscopic Studies of Some Novel Mechanochemically Accessed Adducts of Silver(I) Oxoanion Salts with Thiourea

An investigation of the silver(I) nitrate/thiourea ("tu") system, exploiting the uniquely powerful access provided by the recently developed combination of mechanochemical synthesis coupled with vibrational spectroscopy, has resulted in the identification of solid adducts AgNO3/tu (x:y) for x:y = 1:1, 1:1.5, 15:23 (= 1:1.5333), and 1:3. This contrasts with previously published claims for the existence of 1:2 and 1:4 complexes and was confirmed in the case of the 1:3 and 15:23 complexes by X-ray crystal structure determinations on samples prepared by crystallization from aqueous solution. The 1:3 sulfate and perchlorate complexes were also prepared for comparison with the corresponding nitrate compound. In the 1:3 nitrate complex, the one independent silver atom major component (0.78(1)) is closely trigonal planar AgS3 (Ag-S 2.518(2)-2.592(1) A, Sigma(S-Ag-S) 359.7(0) degrees); there are minor nearby components (0.11(1)) which may be regarded as four-coordinate, forming a putative one-dimensional polymer. The sulfate, obtained as its tetrahydrate, has a cation of the familiar binuclear form [{(tu)2Ag(mu-S-tu)}2](SO4) x 4 H2O, while the perchlorate, previously also characterized with the binuclear cation in the anhydrate, has now been isolated as the hemihydrate, having a single-stranded polymeric cation, [...Ag(tu)2(mu-S-tu)...](infinity|infinity)(ClO4) x 0.5 H2O, similar to that observed in CuX/tu (1:3) (X = Cl, Br, I). The remarkable 15:23 nitrate complex (shown to be distinct from the 1:1.5 complex) may be regarded as essentially ionic [Ag15(tu)23(ONO2)](infinity|infinity)(14+)(NO3(-)-)14 (the cation incorporating one O-nitrate ion loosely associated) and comprising one-dimensional polymer strands made up of four-, six-, and eight-membered Ag(2n)S(2n) rings, cross-linked by the sulfur of one of the tu ligands. The nu(CS) and nu(alpha)(CN) bands in the infrared spectra of the complete series of adducts show a monotonic wavenumber decrease and increase, respectively, with decreasing tu content of the adduct, indicating a decrease in the C-S bond strength and a concomitant increase in the C-N bond strength with increasing Ag-S bond strength. The increase in Ag-S bond strength with decreasing tu content is also indicated by an increase in the wavenumbers of the bands assigned to nu(AgS) in the 140-200 cm(-1) region in the far-IR. These and the structural data for the 1:3 and 15:23 complexes provide the basis for establishing a correlation between nu(AgS) and the Ag-S bond length d(AgS) for silver complexes involving the tu ligand.

Transverse Susceptibilities of Ferromagnetic Spin Wave Interacting with Phonon Reservoir

A form of the transverse magnetic susceptibility of a ferromagnetic system interacting with a phonon reservoir is derived in the spin-wave approximation using the TCLE method in which the admittance of the system is directly calculated from time-convolutionless equations with external driving terms, and is investigated numerically and analytically for the system of one-dimensional infinite spins. It is confirmed that the effects of the initial correlation and memory for the spin system and phonon reservoir, which are represented by the interference terms in the TCLE method, increase the peak heights of the power spectra in the resonance region and cause the power spectra to decrease in the low-frequency region. It is shown that as the damping of the phonon reservoir becomes rapid, the half-widths of the line shapes in the resonance region decrease and the peak heights increase for small wave numbers, and thus the line shapes show ‘motional narrowing’ for small wave numbers but not for large wave numbers. For the case of an acoustic phonon reservoir, it is shown that as the wave number increases, the half-widths decrease and the peak heights increase, except in the vicinity of 0 and π. For a damped oscillator model of the phonon reservoir, it is shown that as the characteristic frequency of the phonon increases, the half-widths increase and the peak heights decrease, and thus the line shapes show ‘motional broadening’. It is also shown that as the magnitude of the spin becomes large, the peak heights increase and the half-widths increase for small wave numbers but decrease for large wave numbers. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the magnitude of the spin becomes large. The numerical results are examined analytically.

Physical interpretation of spiralling-columnar convection in a rapidly rotating annulus with radial propagation properties of Rossby waves

To aid the physical understanding of spiralling-columnar convection emerging in rapidly rotating spheres and spherical shells, two-dimensional thermal convection in a rapidly rotating annulus is investigated through the radial propagation properties of topographic Rossby waves. Two kinds of the boundaries containing the fluid in the axial direction are considered: a convex type modelling a spherical geometry and a concave type for comparison. The linear stability of a basic state with no motion and uniformly unstable stratification is examined and spirally elongated structures of critical convection are obtained for small Prandtl numbers. An analysis of the energy budget shows that a part of the kinetic energy generated in the region with slightly inclined boundaries is dynamically transferred and dissipates through viscosity in the region with strongly inclined boundaries. This indicates that the Rossby waves propagate from the region with slightly inclined boundaries to the region with strongly inclined boundaries. It is presented that the appearance of a spiral structure corresponds to an increase of the local radial wavenumber of the Rossby waves propagating in the radial direction. The flow patterns obtained using the dispersion relation of the Rossby waves coincide with those of the tailing part of the spiral structure obtained numerically. As the Prandtl number increases, the Rossby waves barely propagate because of strong viscous dissipation, and the flow pattern is localized in the region with slightly inclined boundaries. For convex boundaries with unstable stratification concentrating near the outer boundary and concave boundaries with unstable stratification confined near the inner boundary, the flow patterns tilt in the direction inverse to the case of uniform unstable stratification. The tilting direction of the flow pattern is not determined by the curvature of the boundaries considered but instead by the radial propagation direction of the Rossby waves excited by thermal convection.

Redox State of Coenzyme Q10 Determines Its Membrane Localization

The interaction between oxidized (ubiquinone-10) and reduced (ubiquinol-10) coenzyme Q 10 with dimyristoylphosphatidylcholine has been examined by differential scanning microcalorimetry, X-ray diffraction, infrared spectroscopy, and (2)H NMR. Microcalorimetry experiments showed that ubiquinol-10 perturbed considerably more the phase transition of the phospholipids than ubiquinone-10, both forms giving rise to a shoulder of the main transition peak at lower temperatures. Small angle X-ray diffraction showed an increase in d-spacing suggesting a thicker membrane in the presence of both ubiquinone-10 and ubiquinol-10, below the phase transition and a remarkable broadening of the peaks indicating a loss of the repetitive pattern of the lipid multilamellar vesicles. Infrared spectroscopy showed an increase in wavenumbers of the maximum of the CH 2 stretching vibration at temperatures below the phase transition, in the presence of ubiquinol-10, indicating an increase in the proportion of gauche isomers in the gel phase, whereas this effect was smaller for ubiquinone-10. A very small effect was observed at temperatures above the phase transition. (2)H NMR spectroscopy of perdeuterated DMPC showed only modest changes in the spectra of the phospholipids occasioned by the presence of coenzyme Q 10. These small changes were reflected, in the presence of ubiquinol-10, by a decrease in resolution indicating that the interaction between coenzyme Q and phospholipids changed the motion of the lipids. The change was also visible in the first spectral moment (M1), which is related with membrane order, which was slightly decreased at temperatures below the phase transition especially with ubiquinol-10. A slight decrease in M 1 values was also observed above the phase transition but only for ubiquinol-10. These results can be interpreted to indicate that most ubiquinone-10 molecules are localized in the center of the bilayer, but a considerable proportion of ubiquinol-10 molecules may span the bilayer interacting more extensively with the phospholipid acyl chains.