Harmonic Surface Research Articles

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation**Projects supported by the National Natural Science Foundation of China (Grant Nos. 51475246, 51277098, and 51075215), the Research Innovation Program for College Graduates of Jiangsu Province China (Grant No. KYLX15 0725), and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131402).

The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity (F–v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system.

Frequency lock-in and phase synchronization of vortex shedding behind circular cylinder due to surface waves

The influence of harmonic surface wave on non-regular Karman Vortex Street is investigated. In our experiments, Karman Street arises behind a vertical circular cylinder in a water flow and harmonic surface waves propagating upstream. It is found that surface waves can modify regimes of shedding in Karman Street: frequency lock-in and synchronization of vortex shedding can arise. Intensive surface waves can excite symmetric vortex street instead of chess-like street, and completely suppress shedding behind the cylinder. It is shown experimentally that such effects occur if frequency of harmonic surface wave is approximately twice higher than the frequency of vortex shedding. Region of frequency lock-in is found on the plane amplitude–frequency of surface wave.

Instantaneous phase shift of annual subsurface temperature cycles derived by the Hilbert‐Huang transform

AbstractThis study uses the Hilbert‐Huang transform to compute the instantaneous (daily) phase shift between temperature signals at the ground surface and at a depth of 5 m. This approach is not restricted to the stationary harmonic surface temperature assumptions invoked by analytical solutions. The annual cycles are extracted from the ground surface temperatures and the shallow subsurface temperatures at 5 m depth recorded at the Hualien (23.98°N, 121.61°E) and Ilan (24.77°N, 121.75°E) meteorology stations of Central Weather Bureau in Taiwan from 1952 to 2008. Significant reductions in the phase shift and increases in the estimated thermal diffusivity from 1980s to 1990s are found and suggest that the recent warming of the Pacific Decadal Oscillation may affect heat transport in the subsurface environment. The marginal spectra of the instantaneous phase shifts and the precipitation intensity records at Hualien and Ilan reveal that precipitation may play a role in the evolution of seasonal variation in shallow subsurface heat transport.

Existence of a steady-statewater evaporation front in a horizontally extended low-permeability region

Flow with a phase transition interface in a horizontally extended porous medium is considered when a heavier phase (water) is located above a lighter phase (air-steam mixture). It is shown that if there exists a steady-state flow with a plane phase interface and this flow is stable with respect to infinitely small harmonic surface perturbations then only a local finite perturbation of the upper or lower boundary of the low-conductivity layer directed upward can lead to disappearance of the steady-state solution. This flow restructuring is possible only in the case of immiscible porous medium. Using a numerical experiment, it is shown that there exists a threshold value of the absolute value of the amplitude above which the steady-state flow ceases to exist. This threshold value decreases with increase in the “effective” width of the localized perturbation and tends asymptotically to a value corresponding to infinitely large effective width of the localized perturbation. An analytic expression for this quantity is found.

Surface activity and molecular organization of metallacarboranes at the air-water interface revealed by nonlinear optics.

Because of their amphiphilic structure, surfactants adsorb at the water-air interface with their hydrophobic tails pointing out of the water and their polar heads plunging into the liquid phase. Unlike classical surfactants, metallabisdicarbollides (MCs) do not have a well-defined amphiphilic structure. They are nanometer-sized inorganic anions with an ellipsoidal shape composed of two carborane semicages sandwiching a metal ion. However, MCs have been shown to share many properties with surfactants, such as self-assembly in water (formation of micelles and vesicles), formation of lamellar lyotropic phases, and surface activity. By combining second harmonic generation and surface tension measurement, we show here that cobaltabis(dicarbollide) anion {[(C2B9H11)2Co](-) also named [COSAN](-)} with H(+) as a counterion, the most representative metallacarborane, adsorbs vertically at the water surface with its long axis normal to the surface. This vertical molecular orientation facilitates the formation of intermolecular and nonconventional dihydrogen bonds such as the B-H(δ-)···(δ+)H-C bond that has recently been proven to be at the origin of the self-assembly of MCs in water. Therefore, it appears here that lateral dihydrogen bonds are also involved in the surface activity of MCs.

Surface plasma wave assisted second harmonic generation of laser over a metal film

Second harmonic generation of laser mode converted surface plasma wave (SPW) over a corrugated metal film is studied. The laser, impinged on the metal film, under attenuated total reflection configuration, excites SPW over the metal–vacuum interface. The excited SPW extends over a much wider surface area than the laser spot cross-section. It exerts a second harmonic ponderomotive force on metal electrons, imparting them velocity that beats with the surface ripple to produce a nonlinear current, driving resonant second harmonic surface plasma wave.

Soliton microdynamics of the generation of new-type nonlinear surface vibrations, dissociation, and surfing diffusion in diatomic crystals of the uranium nitride type

The microdynamics of large-amplitude nonlinear vibrations of uranium nitride diatomic lattices has been investigated using the computer simulation and neutron scattering methods at temperatures T = 600–2500°C near the thresholds of the dissociation and destruction of the reactor fuel materials. It has been found using the computer simulation that, in the spectral gap between the frequency bands of acoustic and optical phonons in crystals with an open surface, there are resonances of new-type harmonic surface vibrations and a gap-filling band of their genetic successors, i.e., nonlinear surface vibrations. Experimental measurements of the slow neutron scattering spectra of uranium nitride on the DIN-2PI neutron spectrometer have revealed resonances and bands of these surface vibrations in the spectral gap, as well as higher optical vibration overtones. It has been shown that the solitons and bisolitons initiate the formation and collapse of dynamic pores with the generation of surface vibrations at the boundaries of the cavities, evaporation of atoms and atomic clusters, formation of cracks, and destruction of the material. It has been demonstrated that the mass transfer of nitrogen in cracks and along grain boundaries can occur through the revealed microdynamics mechanism of the surfing diffusion of light nitrogen atoms at large-amplitude soliton waves propagating in the stabilizing sublattice of heavy uranium atoms and in the nitrogen sublattice.

Surface acoustic wave reflection/transmission at vertical borders of piezoelectric substrates

The paper studies by the finite element method the harmonic surface acoustic wave scattering at 90° corners of piezoelectric substrates. The SAW is incident perpendicular to the vertical border. The dependencies of the reflection and transmission coefficient on the radius of the fillet at the corner are found for 128°YX and YZ LiNbO3 as well as ST-X SiO2 substrates. In particular, the obtained results reveal that, like in the case of isotropic solids, the magnitude of the reflection coefficient first increases with the fillet radius to wavelength ratio r/λ, reaches a maximum at r/λ≈0.3-0.5, and then decreases tending to zero. The magnitude of the transmission coefficient across the rounded corner first decreases, reaches a minimum at r/λ≈0.3-0.5, and then increases up to a value around which it slightly oscillates as r/λ increases. It is demonstrated that if the substrate is anisotropic, then in the general case a SAW is scattered off differently at the right-hand border and the left-hand border. The difference between the “right-hand” and “left-hand” transformation coefficients can be very substantial. Computations for YZ LiNbO3 illustrate possible levels of the anisotropy of the scattering for mutually reverse directions of incidence. It is shown that if the substrate is specially oriented, then the scattering from the right-hand border is identical to the scattering from the left-hand border. There are four types of such orientations. Examples of the specially oriented substrates are 128°YX LiNbO3 and ST-X SiO2.

“Musical Form

[1] The Seventh International Conference on Music Theory, entitled Musical Form: Mapping the Territories, was jointly organized by the Estonian Academy of Music and Theater and the Estonian Arnold Schoenberg Society. It took place 8-11 January 2014 in the cities of Tallinn and Parnu.[2] The conference comprised thirty-eight regular papers,(1) three keynote addresses (by William Caplin and Nathan John Martin, James Hepokoski, and Steven Vande Moortele), and a roundtable in which Caplin, Martin, and Hepokoski were joined by Poundie Burstein and Peter H. Smith. Although this roster (and the conference's theme) might suggest a focus on common-practice repertoire, nearly half the papers pertained to music after 1900. The pre-1900 sessions were overwhelmingly dominated by scholars based in North America (72%, including keynotes), whereas the inverse was true of sessions on post-1900 music (75% by non-North Americans). The complete conference program and abstracts are available in the Appendix. I will discuss each part of the conference in turn, including some unifying themes common to both.I. MUSIC BEFORE 1900[3] The interpretation of what Sonata Theory regards as a continuous exposition constituted a central theme-or, perhaps better, a framing function-for the tonal portion of the conference, which opened with two keynotes, one by Caplin and Martin and the other by Hepokoski, and culminated in the roundtable discussion. Since Caplin's (1998, 2009) and Hepokoski-Darcy's (2006, 2009) theories have dominated studies of sonata form for over a decade, their relative positions are already well-enough known. Whereas Sonata Theory makes a fundamental distinction between expositions containing a medial caesura and those that do not (i.e. between two-part and continuous expositions, the latter understood to lack an S-zone), Caplin interprets a subordinate-theme function in all expositions, even those with a blurred boundary between (what he regards as) the transition and the subordinate theme.[4] Reviewing the announced program before the conference, some may have wondered whether devoting more than three hours to this well-trod territory would indulge partisans of each method to recapitulate their established positions or whether it would advance the collective state of knowledge.(2) But over the course of the proceedings, it became apparent that issues of continuous expositions and subordinate themes rewarded the renewed attention, since they touch directly on many of the most pressing questions about sonata-form practice, including (1) whether every exposition has a subordinate-theme function; (2) which cadences may signal the end of a passage designated transition; and (3) which musical parameters are truly form-defining (i.e., the relative role of harmonic syntax and surface rhetoric).(3)[5] The focus on continuous expositions placed a special spotlight on Haydn (discussed by Caplin, Martin, Hepokoski, amongst others),(4) along with C. P. E. Bach (in papers by Wayne Petty and Tal Soker), and a variety of other composers active in the 1760s and 1770s (in Burstein's contribution). Earlier binary forms of J. S. Bach, characterized by a Fortspinnung technique related to continuous sonata expositions, were also addressed by Rowland Moseley and the author of this report. The finale of Haydn's String Quartet in B Minor, op. 33 no. 1 was a key example in Caplin-Martin's opening keynote, which focused on expositions whose transitions lack a functional end or (in their terms) whose subordinate themes lack a clear beginning.(5) The central section of the finale's exposition, measures 13-51, expresses a fusion of transition and subordinate-theme functions, in that the clear, tonic-key presentation of a compound basic idea is followed by a continuation phrase comprising a loose string of model-sequence statements that ultimately modulates to and achieves a PAC in the mediant. …

Oblique cross-waves in horizontally vibrated containers

The excitation of subharmonic waves on the free surface of a horizontally vibrated, rectangular container of liquid is considered and the properties of threshold patterns are obtained and discussed. These waves are generally quasiperiodic and oblique (not aligned with the container walls). The parametric forcing mechanism generated by the harmonic oscillatory bulk flow is assumed to dominate over that associated with harmonic surface waves and a linear theory recently developed by the authors [Perez-Gracia et al 2014 J. Fluid Mech. 739 196–228] is used to compute both the threshold forcing amplitude and the pattern orientation. Two distinct regimes are considered: (1) large containers where the subharmonic waves generated at each endwall do not interact appreciably and (2) smaller containers where interaction occurs. The nature of the critical eigenfunction is examined in each case, and a contrast drawn between pure 2:1 resonance and the general case of quasiperiodic instability.

On the topographic effects by Stokes’ formula

AbstractTraditional gravimetric geoid determination relies on Stokes’ formula with removal and restoration of the topographic effects. It is shown that this solution is in error of the order of the quasigeoid-to-geoid difference, which is mainly due to incomplete downward continuation (dwc) of gravity from the Earth’s surface to the geoid. A slightly improved estimator, based on the surface Bouguer gravity anomaly, is also biased due to the imperfect harmonic dwc the Bouguer anomaly. Only the third estimator,which uses the (harmonic) surface no-topography gravity anomaly, is consistent with the boundary condition and Stokes’ formula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals.

一种实现双光谱宽温探测的红外物镜设计

A hybrid refractive/harmonic diffractive infrared lens beyond normal temperature was designed.The infrared lens was consisted of three lenses,including one aspheric surfaces and a harmonic diffraction surface which made the lens have compact structure and light weight.The experimental results show that the modulation transfer function is above 0.42and 0.35in the temperature range of-120~100℃ when the working wavelength in 3.8~4.2μm and 8.8~11.2μm,and the efficient focal length is 54.68mm.It is compatible with infrared dual-color detector which had a format of 320×240 and the pixel pitch of 30μm.

Study and analysis of light infrared detection system with dual spectrum and wide temperature range

Because harmonic diffractive optics elements has special achromatism, athermalization and arbitrary phase modulation characteristics, an infrared detection system method with dual spectrum and wide temperature range was presented based on the most advanced infrared dual color detector which had a format of 320 X 240 and the pixel pitch of 30 microm. A hybrid refractive/ harmonic diffractive infrared detection system with dual spectrum and wide temperature range was designed. The working wavelength range was 3. 8 - 4. 2 and 8. 8 -11. 2 microm. The system was only consisted of three lenses, including one aspheric surfaces and a harmonic diffraction surface, which made the system have compact structure and light weight. In the temperature range -120 -200 degreesC, the RMS radius of spot diagram in 3. 8 approximately 4. 2 and 8. 8-11. 2 pm was 19. 07 and 17. 75 microm respectively, which is less than the pixel size of infrared detector with 30 m, the enclosed energy in 30 microm, the enclosed energy in 3. 8-4. 2 and 8. 8-11. 2 microm is 88. 7% and 82. 4% in two pixel size. The method and structure was convenient and predominant. It was proved that the design was feasible.

Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change

In this paper, the non-Fourier heat conduction in a solid sphere under arbitrary surface thermal disturbances is solved analytically. Four cases including sudden, simple harmonic periodic, triangular and pulse surface temperature changes are investigated step-by-step. The analytical solutions are obtained using the separation of variables method and Duhamel’s principle along with the Fourier series representation of an arbitrary periodic function and the Fourier integral representation of an arbitrary non-periodic function. Using these analytical solutions, the temperature profiles of the solid sphere are analyzed, and the differences in the temperature response between the “hyperbolic” and “parabolic” are discussed. These solutions can be applicable to all kinds of non-Fourier heat conduction analyses for arbitrary boundary conditions occurred in technology. And as application examples, particular attention is devoted to the cases of triangular surface temperature change and pulse surface temperature change. The examples presented in this paper can be used as benchmark problems for future numerical method validations.

Bubbles and Drops on Curved Surfaces

Surface curvature affects the shape, stability, and apparent contact angle of sessile and pendant drops. Here, we develop an approximate analytical solution for non-axisymmetric perturbations to small spherical drops on a flat substrate, assuming a fixed contact angle and fixed drop volume. The analytical model is validated using numerical solutions of the Laplace equation from the Surface Evolver software. We investigate the effects of surface curvature on drop shape, pressure, and surface energy, ascertaining the energy-gradient force that drives lateral drop migration. By balancing this force with the viscous resistance/drag force, in the lubrication approximation, we predict velocities of the order of 0.1 mm s(-1) for 1 mm diameter drops of water with a 30° contact angle on a substrate with a curvature gradient of 0.01 mm(-2), achieved, for example, on a harmonic surface with a wavelength of 4 cm and an amplitude of 4 mm.

Constraining core undertones using stacked IDA gravity records

A search is made for oscillatory gravity signals, possibly associated with core undertones, in the frequency range between the diurnal and semidiurnal tidal bands. IDA tidal data recorded during 6 month intervals following four large earthquakes were used, and the data from different stations were stacked according to spherical harmonic surface amplitude patterns with angular order l≤4. The detection level of a signal in the diurnal-semidiurnal frequency band was roughly 10-20 ngal, but the only signal detected was a 9 ngal signal of 9.54 hr period whose origin remains unexplained.

Dynamic Response of a Multilayered Poroelastic Half-Space to Harmonic Surface Tractions

The propagator matrix method is developed to study the dynamic response of a multilayered poroelastic half-space to time-harmonic surface tractions. In a cylindrical coordinate system, a method of displacement potentials is applied first to decouple the Biot’s wave equations into four scalar Helmholtz equations, and then, general solutions to those equations are obtained. After that, the propagator matrix method and the vector surface harmonics are employed to derive the solutions for a multilayered poroelastic half-space subjected to surface tractions. It is known that the original propagator algorithm has the loss-of-precision problem when the waves become evanescent. At present, an orthogonalization procedure is inserted into the matrix propagation loop to avoid the numerical difficulty of the original propagator algorithm. Finally, a high-order adaptive integration method with continued fraction expansions for accelerating the convergence of the truncated integral is adopted to numerically evaluate the integral solutions expressed in terms of semi-infinite Hankel-type integrals with respect to horizontal wavenumber. Furthermore, to validate the present approach, the response of a uniform poroelastic half-space is examined using the formulation proposed in this article. It is shown that the numerical results computed with this approach agree well with those computed with the analytical solution of a uniform half-space.

Experimental methods for the characterization of the frequency-dependent viscoelastic properties of soft materials

A characterization method based on Rayleigh wave propagation was developed for the quantification of the frequency-dependent viscoelastic properties of soft materials at high frequencies; i.e., up to 4 kHz. Planar harmonic surface waves were produced on the surface of silicone rubber samples. The phase and amplitude of the propagating waves were measured at different locations along the propagation direction, which allowed the calculation of the complex Rayleigh wavenumbers at each excitation frequency using a transfer function method. An inverse wave propagation problem was then solved to obtain the complex shear/elastic moduli from the measured wavenumbers. In a separate, related investigation, dynamic indentation tests using atomic force microscopy (AFM) were performed at frequencies up to 300 Hz. No systematic verification study is available for the AFM-based method, which can be used when the dimensions of the test samples are too small for other existing testing methods. The results obtained from the Rayleigh wave propagation and AFM-based indentation methods were compared with those from a well-established method, which involves the generation of standing longitudinal compression waves in rod-shaped test specimens. The results were cross validated and qualitatively confirmed theoretical expectations presented in the literature for the frequency-dependence of polymers.

Darboux Transforms of a Harmonic Inverse Mean Curvature Surface

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.

Influence of Surface Waviness on the Thermal Elastohydrodynamic Lubrication of an Eccentric-Tappet Pair

The effect of single-sided and double-sided harmonic surface waviness on the film thickness, pressure, and temperature oscillations in an elastohydrodynamically lubricated eccentric-tappet pair has been investigated in relation to the eccentricity and the waviness wavelength. The results show that, during one working cycle, the waviness causes significant fluctuations of the oil film, pressure, and temperature, as well as a reduction in minimum film thickness. Smaller wavelength causes more dramatic variations in oil film. The fluctuations of the pressure, film thickness, temperature, and traction coefficient caused by double-sided waviness are nearly the same compared with the single-sided waviness, but the variations are less intense.