Periodic Displacements Research Articles

Quasiharmonic periodic traveling-wave solutions in anharmonic potentials.

Exact solutions of a nonlinear diatomic shell model are investigated in the regime where quasiharmonic and pseudoperiodic traveling waves exist with phonon-type character. The existence regimes of these solutions are determined by the boundary conditions and the model parameters for which especially a strong time and mass dependence is observed. It is found that slowly propagating waves mostly show large displacement responses which can be associated with large dipole moments, while rapidly traveling waves carry a much smaller dipole moment, but still this is appreciably larger than that induced by bare optic-phonon modes. The case of large anharmonicity shows the opposite effect. Here high-frequency responses carry a large dipole moment. The large dipole moments can be associated with effective charges which induce high oscillator strengths in the corresponding phonon modes, incompatible with results deduced from harmonic lattice dynamics. The origin of the large dipole moments in the shell model is investigated by solving for core and shell displacements separately, where ``acoustic-type'' periodic in-phase displacements of core and shell with different amplitudes are observed, as well as pseudoperiodic out-of-phase ``optic-type'' displacements resulting from large anharmonicity, and are also found in the static limit. Besides the displacement frequency spectrum, the effective potentials are calculated which are distinctly different from ${\mathrm{\ensuremath{\varphi}}}_{4}$-type potentials: The potential height is finite with finite width which, in certain cases becomes very small, thus admitting for tunneling through the barrier. \textcopyright{} 1996 The American Physical Society.

Almost Periodic Ergodic Rn-Homeomorphisms

A homeomorphism of Rn is called stationary if it is the uniform limit of volume preserving homeomorphisms which are spatially periodic and have mean translation zero. We prove that ergodic homeomorphisms form a uniform topology dense Gδ subset of the stationary homeomorphisms, thus establishing examples which are uniformly continuous with bounded and almost periodic displacements. In the two-dimensional orientation preserving case, ergodic homeomorphisms have fixed points (by Brouwer′s Plane Translation Theorem). Hence so do orientation-preserving area-preserving torus homeomorphisms with mean translation zero lifts (Conley-Zehnder-Frank Theorem).

Bending of long cross-ply composite circular cylinders

The response of long, thin-walled, cross-ply composite tubes subjected to pure bending was studied analytically. The formulation includes three parts: pre-buckling response, material failure and bifurcation buckling. The pre-buckling response is analyzed using nonlinear kinematics to accommodate the ovalization of the cross-section. The formulation is based on the principle of virtual work and is used to generate a numerical solution procedure. The Tsai-Wu failure criterion is used to detect material failure in the pre-buckling response. The maximum stress criterion was also considered for comparison. Finally, the buckling analysis considers the possibility of bifurcation into modes containing periodic displacements along the axis of the tube. The tubes are assumed to be geometrically perfect and free of residual stress. Three materials-AS3501 graphite-epoxy, Kevlar 49-epoxy, and E-glass-epoxy-and three diameter-to-thickness ratios-50, 100 and 400-are considered. The moment-curvature response of the tubes is non-linear due to the ovalization of the cross-section (Brazier effect) which induces a limit moment instability. Either material failure or bifurcation buckling always occurs prior to the limit moment in the cases considered. Little difference was observed between the failure loads predicted by the Tsai-Wu and the maximum stress criteria. Tubes with plies of circumferentially oriented fibers in the outermost and innermost positions in the wall proved superior in strength compared with the other cases considered.

Estimating seasonal deformations in the earth's crust in correcting for effects on the deter-mination of the earth's rotational parameters

Estimates are made of the vertical deformations in the Earth's crust produced by variable loads on regions having characteristic dimensions of the order of thousands of kilometers, which arise from the development and displacement of cyclones and anticyclones and also from the accumulation of snow and the passage of floods on large rivers. It is found that the total deformation in Siberia can attain 30 cm. It is necessary to correct for the periodic displacements in observational points in the service for determining the Earth's rotational parameters. Suggestions are made on organizing experiments on the deformations.

A study of the dynamics of magnetic disaccommodation in amorphous ferromagnets. I. Experimental results

Systematic room-temperature measurements of the aftereffect of the ac magnetic permeability have been performed on a Fe81B13.5 Si3.5C2 amorphous ribbon in order to get detailed information about the nature of the atomic ordering processes responsible for the magnetic relaxation. The magnetic aftereffect related to 180° domain-wall motion has been measured by means of a specific technique allowing periodic domain-wall displacements to be induced between two fixed, neighboring equilibrium positions by applying a square-wave field of proper amplitude and frequency. In this way, the average direction of the magnetization vector is cyclically modified in all points where the studied directional ordering processes may occur. As a consequence, the kinetics of ordering is modified in a characteristic way, giving rise to relevant variations in the intensity of the magnetic aftereffect measured between fixed times (t1=2×10−3 s and t2=10−1 s), and in the value of the magnetic induction at the time t2. All measurements have been performed at constant applied field. The degree of reliability of this experimental technique has been analyzed in detail. The magnetic aftereffect, ΔB=B(t1)−B(t2), and the magnetic induction B(t2) have been measured as functions of the number of domain-wall cycles, and after removing the square-wave field for a variable time t*. The results of many independent measurements are reported and discussed.

Multibeam interferometric methods for measuring very small periodic displacements

A multibeam Fabry-Perot interferometer is used for measuring very small periodic displacements (SPD). The steepness of such an interferometer as well as the high gain of the photomultiplier and the powerful laser allow one to measure SPD of the order of 10(-19) m at room temperature. Analysis of all the noise factors restricting the sensitivity (heat fluctuations of the surfaces of the mirrors, shot effect, radiation pressure noise) shows that at room temperature the heat noise is the most important.

EFFECTS OF TRANSMISSION INSULATORS ON TOWERS AND LINES SYSTEMS SUBJECTED TO EARTHQUAKE

This paper presents effects of vibrations of transmission insulators on towers and lines subjected to earthquake. Free vibration analyses of transmission line and insulators are made by using the method of modal analysis, which adopts individual modes of a suspended line and suspended insulators. The theoretical results agree well with the experimental ones of dynamic tensions in a transmission line and insulators model excited by periodic longitudinal displacements at one end. Finally, as a result of seismic response calculations of towers, lines and insulators systems in two cases, it is shown that they are about equal or larger than the seismic responses of lines and towers considering the insulators as an added mass, but smaller than those of a single tower.

Reactions of arterioles of the frog submaxillary muscle to static and periodic displacements and contractions of its fibers

Low-frequency (about 4/sec) oscillatory displacements of resting fibers of the frog submaxillary muscle, leading to bending microdeformations of the arterioles located among them, cause considerable dilatation of them [3]. This phenomenon is evidence of the essential role of mechanical factors in working hyperemia of skeletal muscles [4]. During static displacement of a group of muscle fibers, the arterioles located among them must also undergo microdeformation. However, it is not known whether such displacement does in fact affect arterioles.

Characterization of a Gas-Stabilized Arc Plasma in an ExB Magnetic Field Configuration

A magnetic field of about 200 gauss oriented normal to the electric field in a 9 amp gas-stabilized dc arc is used to control the position of the plasma current channel. The presence of the magnetic field results in a drift motion of plasma electrons in the direction normal to the plane containing the electric and magnetic field vectors. The current channel can be displaced vertically upward or downward depending on the direction of the external magnetic field. With the field strengths used, displacements of several millimeters are observed. Spatially resolved radiation measurements show that radiation from the Ar plasma gas responds differently to the magnetic field than does radiation from the tungsten electrode material. When the magnetic field is generated by a 60-Hz ac current in the electromagnet, the plasma current channel undergoes periodic displacements at the magnetic field oscillation frequency. A phase shift between the field strength and the current channel displacement is observed.

Structure determination of an adsorbate-induced multilayer reconstruction: (1 x 2)-H/Ni(110).

The reconstructed (1\ifmmode\times\else\texttimes\fi{}2) structure formed by saturation of a Ni(110) surface with adsorbed H atoms at T<180 K was investigated by LEED. Excellent agreement between experimental and calculated I-V spectra for eleven nonequivalent beams was obtained for a model in which parallel rows of Ni atoms in the topmost layer are laterally shifted by 0.3 A\r{} (``row pairing'') and which exhibits periodic vertical displacements (``buckling'') of the atoms in the second layer.

Electronic response to surface atomic displacements on Mo (001)

The electronic contribution to the energy of surface phonons is decomposed into a wavevector-dependent term which depends only on the response function in the surface region, plus a wavevector-independent term giving the energy change due to a uniform surface displacement. The wavevector-dependent term is evaluated for the unreconstructed Mo (001) surface, using the matching Green function method to calculate the electronic response function, and the rigid muffin-tin approximation to determine the electron-phonon matrix elements. It is found that the large density of the surface states at the Fermi energy, and the states bonding the surface atoms to the bulk, favour lateral displacements, through the wavevector of the corresponding surface phonon anomaly disagrees with the experimentally observed reconstruction. Periodic vertical displacements of the surface atoms are energetically unfavourable.

Unsteady waves on an open two layer fluid

AbstractThe evolution of small amplitude waves on an open two layer fluid is investigated. The spatially periodic surface and interface displacements are represented as Fourier series with time dependent coefficients, for which evolution equations with all significant quadratic interactions included, are derived. Solutions to these equations are found analytically for a small number of harmonics, and numerically for a larger number of harmonics. Two numerical solutions are given to illustrate the evolution properties.

Electron microscopic studies of modulated structures in (Au, Ag) Te 2: Part II. Sylvanite AgAuTe 4

Sylvanite (AuAgTe 4) occurs under two forms at room temperature. Ideal sylvanite has a commensurate modulated superstructure of calaverite. The second form is an incommensurate modulated structure. The modulation is due to periodic displacements from the ideal atom positions, occupied in the commensurate form, and to the presence of periodic antiphase boundaries. The two structural modulations are closely coupled however and occur along almost parallel sets of planes. It is believed that the incommensurability is related to deviations from the ideal gold-silver ratio. The antiphase boundaries provide a means to incorporate deviations from the ideal AuAg ratio without changing the deformation modulation period. These conclusions were reached on the basis of the combined use of electron diffraction, electron microscopy, and computer simulation of the high resolution images.

Unsteady waves on an open two layer fluid

The evolution of small amplitude waves on an open two layer fluid is investigated. The spatially periodic surface and interface displacements are represented as Fourier series with time dependent coefficients, for which evolution equations with all significant quadratic interactions included, are derived. Solutions to these equations are found analytically for a small number of harmonics, and numerically for a larger number of harmonics. Two numerical solutions are given to illustrate the evolution properties.

Zooplankton sample variability in a tidal estuary: An interpretative model1

A series of 347 vertical zooplankton hauls was made at a 175‐h anchor station in the upper St. Lawrence estuary, Québec, and current meter profiles were recorded. The 95% confidence interval of a single observation in most of the copepod time series was about 25–400% of the mean. Temporal variability consisted for the most part of semidiurnal fluctuations superimposed on a long term trend. Other periodic components were also evident. Most components were related to the advection, at discrete frequencies, of longitudinal zooplankton gradients of different magnitude and sign. The relationship was generalized by a mathematical model which shows that a distinct component of sample variability can be found at all frequencies of the current tidal constituents, provided that a longitudinal gradient is present. The relative magnitude of the variability components, for a constant gradient slope in both time and space, is identical to that of the amplitude/frequency product of the current tidal constituents. Other components not explained by the model can be related to periodic vertical displacements of the pycnocline caused by the interaction of an internal tide with a sill in the sampling area.

Electronic surface resonances and the thermally induced W(001) structure transition

The surface weighted effective potentials of the clean W(001) surface at temperatures T = 550 K[(1×1)] and T = 440 K[(√2×√2)R45°] are experimentally obtained from the surface resonance band structure. It is deduced that the transition W(001)-(1×1) → (√2×√2)R45° is a temperature-dependent reconstruction in which there is a contraction of the top layer atoms towards the bulk involving periodic displacements of the atoms normal to the surface.

Dynamic viscoelastic behaviour of the human tendon in vitro

In order to characterize the mechanical behaviour of human tendon in vitro, we have developed a testing apparatus which applies a small periodic displacement to a specimen pre-stretched at different extension ratios (1.005–1.05). The electropneumatic vibrator we have used in this device has a frequency range from 0.5 to 15 Hz. In the study, we measured the periodic displacements and stresses of flexor digitorum tendons of the human hand and calculated therefrom the dynamic tangential elastic modulus of this biological tissue. As expected, the tendon bahaves as a nonlinearly viscoelastic body, the influence of the initial elongation being more important than the influence of the frequency of the deformation. The data of the 15 tendons tested are compared by means of a t′ o-parameter linearization for the real and imaginary part of the dynamic tangential elastic modulus.

Modeling of a Tunnel Furnace in the Ceramic Industry

A theoretical study was developped in order to optimise the operation of a 50m long tunnel furnace producing 30 tons of horticultural pots per day. The first step in this study consisted of modelling the thermal behaviour of the furnace by taking into account the geometrical parameters of the tunnel and of the products to be burnt and the physico-chemical properties of the different elements constituting the plant.A mathematical model was first established for a continuous advance of the charge and then modified to account for periodic displacements in the real situation. A set of non linear hyperbolic equations was obtained and solved using the carlson method. Thus the temperature profiles could be obtained, knowing the control distribution, which consisted of about twenty gas burners.The model was linearised to simplify the optimisation study. A parameter identification and a numerical simulation were required. Numerical results and graphs are given.

Evidence for Reconstructed {001} Tungsten Obtained by Field-Ion Microscopy

New results have been obtained, by field-ion microscopy, relating to the atomic structure of clean {001}W. The evidence supports a reconstruction model with periodic displacements of atoms having vertical components. The reconstructed atomic configuration prevails over the entire temperature range of this investigation (\ensuremath{\sim} 15-460 K), suggesting that no phase transition may be needed to account for the structural features of {001}W.

Stacking variations in cancrinite minerals

TEM reveals (0001) stacking faults and periodic superstructures in cancrinite-related minerals, afghanite and franzinite, which are interpreted as aperiodic or periodic displacements of the hexagonal [(Si,AI)60~2] ring units. Franzinite also shows a superstructure when the structure is projected onto the xy plane; satellites occur in the hk0 diffraction patterns.