Amplitude Regime Research Articles

Geometrical Scale-Sensitive Fatigue Properties of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si Alloys With α/β Lamellar Microstructures

Fatigue properties of the Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy sheets containing different numbers of α/β Widmanstatten colonies in the thickness direction of the sheets were investigated by tension–tension fatigue testing. It is found that fatigue properties of the Ti alloy either in low- or high-stress amplitude regimes become more sensitive to the sheet thickness of the Ti alloy as the sheet thickness is comparable to the length scale of the Widmanstatten colonies. The basic mechanism of such length scale-sensitive fatigue properties in the Ti alloy was elucidated.

Effects of constant and variable temperatures on development and reproduction of the two-spotted spider mite Tetranychus urticae (Acari: Tetranychidae)

We focused on the influence of different temperature amplitudes on development and reproduction of the two-spotted spider mite, Tetranychus urticae Koch, at a 16:8 (L:D) h photoperiod and 60-95% RH. The temperature amplitudes varied from 0 to 24°C in steps of 6°C; i.e. 22±0, 22±3, 22±6, 22±9 and 22±12°C. Temperature changed every 24h between a low and an upper value, but without changing the average temperature (22°C). The number of eggs laid by five females for 24h was slightly lower at 22±12°C than at constant temperature (22±0°C), and egg hatchability differed among the five temperature regimes. Developmental time at 22±0°C was shorter than that at 22±3 and 22±6°C, but longer than that at 22±9 and 22±12°C. The oviposition period, total fecundity per female and adult longevity gradually decreased with increasing amplitudes. Sex ratio was similar at all five temperature regimes. The intrinsic rate of natural increase (r m) was affected by temperature amplitude and the r m-values at all amplitudes except 22±12°C were higher than that at constant temperature. Thus, this study showed that variable temperature regimes influence population growth rates of T. urticae and that large amplitude regimes are stressful for this species.

Large amplitude oscillatory shear and Fourier transform rheology analysis of branched polymer melts

In this paper, the predictions of the Pompom constitutive model in medium and large amplitude oscillatory shear (LAOS) are examined using Fourier transform rheology (FTR). FTR is commonly used in combination with small amplitude oscillatory shear to fit linear Maxwell parameters to dynamic moduli, and in this paper, this process is expanded to larger strain amplitudes and to further terms in the Fourier series. For both small and large amplitudes, these higher harmonics are dependent on the nonlinear Pompom parameters and the Pompom parameter space is explored to see how experimental oscillatory shear data can infer molecular detail. In the regime of small and medium strain amplitude, there exists an asymptotic solution to the Pompom equations which depends only on the ratio of the orientation and stretch relaxation times, τb and τs. This asymptotic solution is found to be accurate up to strains of order unity and the branching priority, q, only affects the stress response at larger strains. The Pompom parameters fitted to extensional data are compared to LAOS data for three materials; two lightly branched metallocene catalyzed high density polyethylenes and a densely branched low density polyethylenes. In general, the Pompom model performs well in LAOS but tends to over predict experimental results at high strain amplitudes.

Vortex induced vibration and vortex shedding characteristics of two side-by-side circular cylinders of different diameters in close proximity in steady flow

This paper presents results of a numerical study of vortex-induced vibrations of two side-by-side circular cylinders of different diameters in steady incompressible flow. The two-dimensional Reynolds-averaged Navier–Stokes equations with a SST k–ω turbulence model are solved using the Petrov–Galerkin finite element method and the Arbitrary-Lagrangian–Eulerian scheme. The diameter ratio of the two cylinders is fixed at 0.1 and the mass ratio of both cylinders is 5.0. Both cylinders are constrained to oscillate in the transverse direction only. The Reynolds number based on the large cylinder diameter and free stream velocity is fixed at 5000. The effects of the reduced velocities of the cylinders on the vibration amplitude and vortex shedding regimes are investigated. It is found that for the range of parameters considered, collision between the two cylinders is dependent on the difference of the reduced velocities of the cylinders. Presence of the small cylinder in the proximity of the large one appears to have significant effects on the vortex shedding regime and vibration amplitude of the large cylinder.

Nonlinear asymptotic impedance model for a Helmholtz resonator liner

The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non-resonance regimes.

Extension of the continuum time-dependent Hartree-Fock method to proton states.

This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of nonlinear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are an effective way of handling the artificial boundary.

Shock Waves in Dispersive Eulerian Fluids

The long time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convex or concave) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schrodinger equation. These include superfluids (Bose-Einstein condensates and ultracold Fermions) and "optical fluids". Estimates of breaking times for smooth initial data and the long time behavior of the shock tube problem are presented. Numerical simulations compare favorably with the asymptotic results in the weak to moderate amplitude regimes. Deviations in the large amplitude regime are identified with breakdown of the simple wave DSW theory.

Radial correlation reflectometry at oblique probing wave incidence (linear scattering theory predictions)

Turbulence radial correlation length measurements by making use of Doppler reflectometry are analysed in this paper assuming the linear (in density perturbation amplitude) regime of the probing wave scattering. Based on the Born approximation applicable in this case, we get a general integral representation of the scattering signal amplitude, which is then analysed in detail both analytically and numerically. Asymptotic analytical evaluation of the scattering signal amplitude gives a criterion on the incidence angle, exceeding which leads to suppression of the poor localized forward scattering contribution to the Doppler reflectometry signal. In the latter case, fast decay of correlation in the two frequency channels appears to be similar to that expected from the turbulence correlation function. The analytical estimations and predictions are confirmed by numerical evaluation of the scattering signal amplitude. The analysis performed proves the feasibility of the radial correlation Doppler reflectometry technique for measurements of the correlation length of a modest level turbulence at oblique launching of the probing wave beam.

STUDY OF FLOW-INDUCED VIBRATION PHENOMENA IN AUTOMOTIVE SHOCK ABSORBERS

The purpose of this study was to develop a model of the dynamic behavior of a hydraulic vehicle double-tube shock absorber. The model accounts for the effects of compressibility, valve stiction, inertia, etc. and can be suitable for use in the analyses on flow-induced pressure fluctuations in the device. The author highlights all major variables to influence the output of the shock absorber, and then proceeds by performing a series of simulations using the developed model. The model is demonstrated to operate well in the large amplitude and low frequency range as well as the small amplitude and high frequency excitation operation regimes. The results are presented in the form of time histories of pressures in each fluid volume of the damper, flow rates through the valves, piston rod acceleration and force. Fast Fourier Transform (FFT) graphs are presented, too, in order to identify major components of the pressure fluctuation phenomena in frequency domain.

Complex mode dynamics of coupled wave oscillators

We explore how nonlinear coherent waves localized in a few wells of a periodic potential can act analogously to a chain of coupled oscillators. We identify the small-amplitude oscillation modes of these "coupled wave oscillators" and find that they can be extended into the large amplitude regime, where some "ring" for long times. We also reveal the appearance of complex behavior such as the breakdown of Josephson-like oscillations, the destabilization of fundamental oscillation modes, and the emergence of chaotic oscillations for large amplitude excitations. We show that the dynamics may be accurately described by a discrete model with nearest-neighbor coupling, in which the lattice oscillators bear an effective mass.

Quantum ion-acoustic solitary waves: The effect of exchange correlation

Quantum ion-acoustic solitary waves are studied by considering the effects of exchange and correlation for the electrons. Starting from one-dimensional quantum hydrodynamic equations, including the term of exchange correlation for electrons, we obtain a model in which two dimensionless parameters appear (in addition to the parameter measuring the quantum diffraction) measuring the exchange and the correlation. A new deformed Korteweg-de Vries equation is derived. The effect of exchange and correlation is reflected in the phase speed as well as in the nonlinear and dispersion terms. Its solution shows that the exchange-correlation effects modify the amplitude as well as the width of the weak solitary waves. In the arbitrary amplitude regime, and as may be expected, a pseudopotential analysis shows that the exchange-correlation effects may change the nature (compressive or rarefactive) of the quantum ion-acoustic solitary waves. Our results complement and give new insight into the previously published work on this problem.

Spatial solitons in biased two-photon photorefractive crystals with both the linear and quadratic electro-optic effect

Abstract The evolution equation of one-dimension spatial optical solitons resulting from two-photon effect in biased photorefractive crystals with both the linear and quadratic electro-optic effect is presented theoretically. Under appropriate conditions, our analysis indicates that bright, dark photorefractive spatial solitons can exist in the steady-state regime. The analytical solutions in the low amplitude regime are also obtained. Moreover, we theoretically discuss the self-deflection of bright solitons by taking the diffusion effect into account. Both the self-deflection effects follow a cubic polynomial of the applied bias field, and increase considerably at higher values of applied bias field. Relevant examples are provided.

Ghost imaging with white light speckle patterns

In this paper we describe a method to study the formation of a ghost image by using a simplified setup. A spatial light modulator (SLM) working in amplitude regime is used both to display the object and the intensity distribution that provides the high-spatially correlated beams which are the base of this phenomenon. We compare the recovered ghost image with that obtained by using pseudothermal light. Moreover we show that good quality images are also retrieved when a turbulent media is present.

Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton–Jacobi models

We study the large time asymptotic speeds (turbulent flame speeds sT) of the simplified Hamilton–Jacobi (HJ) models arising in turbulent combustion. One HJ model is G-equation describing the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are HJ equations with convex (L1 type) but non-coercive Hamiltonians. The other is the quadratically nonlinear (L2 type) inviscid HJ model of Majda–Souganidis derived from the Kolmogorov–Petrovsky–Piskunov reactive fronts. Motivated by a question posed by Embid, Majda and Souganidis (1995) [10], we compare the turbulent flame speeds sTʼs from these inviscid HJ models in two-dimensional cellular flows or a periodic array of steady vortices via sharp asymptotic estimates in the regime of large amplitude. The estimates are obtained by analyzing the action minimizing trajectories in the Lagrangian representation of solutions (Lax formula and its extension) in combination with delicate gradient bound of viscosity solutions to the associated cell problem of homogenization. Though the inviscid turbulent flame speeds share the same leading order asymptotics, their difference due to nonlinearities is identified as a subtle double logarithm in the large flow amplitude from the sharp growth laws. The turbulent flame speeds differ much more significantly in the corresponding viscous HJ models.

Continuum time-dependent Hartree-Fock method for giant resonances in spherical nuclei

This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied in the case of nuclear giant monopole resonances in the small and large amplitude regimes. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region results in a difficulty with the spatial boundary conditions. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. The accuracy and efficiency of the scheme is tested and the results presented to support the case that they are a effective way of handling the artificial boundary.

Characterization and optimization of vibration-assisted drilling of fibre reinforced epoxy laminates

Vibration-assisted drilling (VAD) can reduce thermal and mechanical defects associated with drilling of composites. Machinability maps are presented to establish the effect of the process parameters (speed, feed, frequency, and amplitude) in the low frequency–high amplitude regime (<200Hz, <0.6mm) on the hole quality attributes. The optimized VAD conditions can reduce the cutting temperature by 50% and the axial force by 40% and produce delamination-free holes, without affecting productivity. It is demonstrated that the intermittent cutting in VAD redistributes the cutting energy over the engagement cycles. This enhances the tool cooling and substantially reduces the axial force component.

Generation of large spin currents in graphene using adiabatic quantum pumping

We study adiabatic quantum pumping of Dirac fermions in a monolayer graphene in the large pumping amplitude regime in order to study how to generate a large spin polarized current. Spin current is generated by applying two periodic oscillating gate voltages to a monolayer graphene with exchange splitting induced by ferromagnetic proximity. We find that pumped charge and spin currents are sensitive functions of the Fermi energy and pure spin current and spin current with different degrees of polarization and large magnitudes are obtained in our scheme. We also study the effects of parameters of the system, such as the barrier separation and the exchange splitting, on the pumped currents. The spin current generated by this method can be as high as 80-100 nA. This shows the method can be used in the study of spin physics in graphene and the realization of graphene spintronic devices.

Finite Element Computation of KPP Front Speeds in Cellular and Cat’s Eye Flows

We compute the front speeds of the Kolmogorov-Petrovsky-Piskunov (KPP) reactive fronts in two prototypes of periodic incompressible flows (the cellular flows and the cat's eye flows). The computation is based on adaptive streamline diffusion methods for the advection-diffusion type principal eigenvalue problem associated with the KPP front speeds. In the large amplitude regime, internal layers form in eigenfunctions. Besides recovering known speed growth law for the cellular flow, we found larger growth rates of front speeds in cat's eye flows due to the presence of open channels, and the front speed slowdown due to either zero Neumann boundary condition at domain boundaries or frequency increase of cat's eye flows.

Order domain analysis of speed-dependent friction-induced torque in a brake experiment

A friction-induced forced vibration problem, as excited by the geometric distortions of the brake rotor, is studied in this article. The focus is on the order domain analysis, as the speed-dependent behavior of friction torque is not well understood. First, a new laboratory experiment is constructed to simulate vehicle brake judder in a scientific and yet controlled manner. The variations in pressure and torque are measured as the rotor slows down, and the order domain tracking is used to construct shaft torque vs. speed diagrams. A quasi-linear model of the laboratory experiment is then developed to obtain an analytical solution and to estimate the torque envelope function. A nonlinear model of the laboratory experiment (with a clearance) is also investigated to examine the resonant amplitude growth. Finally, predictions are successfully compared with measurements. Several contributions emerge over the prior literature. In particular, the experimental data clearly show that multiple-orders of the rotor surface distortion profile excite the friction-induced torque, and a clearance in the torsional system controls the resonant amplitude regime. New analytical and numerical solutions provide much insight into the speed-dependent resonant amplitude growth process.

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A numerical model of an all-fiber Nd3+ laser passively Q-switched with Cr4+ is presented. The repetition rate, average output power, and pulse width have been calculated with the same parameters as those of an experimental setup of another group. We found a qualitative agreement between the two results. The validated model has been used on another proposed setup to investigate and optimize laser parameters. The low and high self-impulse amplitude regimes were found for different Cr4+ ion densities. The optimal efficiency of the high regime was established when the saturable absorber density increases.