Showing papers on "Wavelength published in 1968"

Peristaltic pumping with long wave lengths at low reynolds number.

Abstract: : Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which (1) the relevant Reynolds number is small enough for inertial effects to be negligible and (2) the wavelength-diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axi-symmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values. Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward ('reflux') time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid mechanical peculiarity with physiological implications is that of 'trapping': under certain conditions an internally-circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave. (Author)

On the equations of motion for mixtures of liquid and gas bubbles

Abstract: On the basis of previous work by the author, equations are derived describing one-dimensional unsteady flow in bubble-fluid mixtures. Attention is subsequently focused on pressure waves of small and moderate amplitude propagating through the mixture. Four characteristic lengths occur, namely, wavelength, amplitude, bubble diameter and inter-bubble distance. The significance of their relative magnitudes for the theory is discussed. It appears that for high gas content the dispersion is weak and then the conservation of mass and momentum lead to equations similar to the Boussinesq equations, describing long dispersive waves of finite amplitude on a fluid of finite depth. For waves propagating in one direction only, the corresponding equation is similar to the Korteweg–de Vries equation. It is shown that for mixtures of low gas content the frequency dispersion is in most cases not small. Finally, solutions of the Korteweg–de Vries equation representing cnoidal and solitary waves in a bubble–liquid mixture are given explicitly.

Parametric excitation of coupled waves. ii. parametric plasmon--photon interaction.

Abstract: The general theory of the parametric excitation of coupled waves developed in the preceding paper is applied to the parametric interaction of the electrostatic waves in a plasma with radiation whose frequency is close to the electron plasma frequency. On the basis of the hydrodynamic equations, the coupled equations for the electron plasma wave and ion acoustic wave are derived. The effect of the Landau damping is also considered phenomenologically. Using the coupled wave equations, the expressions for the threshold radiation intensity, the frequency shift at the threshold and the growth rate above threshold are obtained. In particular, the dependence of these quantities on the wave-length of the electrostatic waves is discussed in detail. The results are compared with experiment of Stern and Tzoar.

Collisional Drift Waves—Identification, Stabilization, and Enhanced Plasma Transport

Abstract: Density‐gradient‐driven collisional drift waves are identified by the dependences of ω and k on density, temperature, magnetic field, and ion mass, and by comparisons with a linear theory which includes resistivity and viscosity. Abrupt stabilization of azimuthal modes is observed when the stabilizing ion diffusion over the transverse wavelength due to the combined effects of ion Larmor radius and ion‐ion collisions (viscosity) balances the destabilizing electron‐fluid expansion over the parallel wavelength, determined by electron‐ion collisions (resistivity). The finite‐amplitude (ũ/n0 ≃ 10%) coherent oscillation, involving the entire plasma body, shows a phase difference between density and potential waves (which is predicted by linear theory for growing perturbations). The wave‐induced radial transport exceeds classical diffusion, but is below the Bohm value by an order of magnitude. Although observations have been extended to magnetic fields three times those for drift‐wave onset, turbulence has not b...

Electro-optic and Piezoelectric Coefficients and Refractive Index of Gallium Phosphide

Abstract: Measurements of the constant‐strain electro‐optic coefficient of GaP between 0.56 and 3.39 μ wavelength were made using both pulsed electric field and optical heterodyne techniques. At 0.6328 μ wavelength its value is −0.97×10−12 m/V. A dispersion of only 10% is present between 0.56 and 3.39 μ. Approximate values of the piezoelectric coefficient and the constant‐stress electro‐optic coefficient are also obtained from the analysis of the experiments. For GaP the magnitude of the constant‐stress coefficient is less than the constant‐strain coefficient. The analysis also points out an often ignored effect: electro‐optic measurements made with electric field frequencies in the range of resonant acoustic frequencies may not exhibit the expected symmetry of the crystal plus field but may also evidence effects from the crystal shape. Accurate refractive index measurements made on many GaP crystals between 0.545 and 0.70 μ wavelength are also reported.

Absolute Raman Scattering Cross-Section Measurement of the 992 cm −1 Line of Benzene*

Abstract: An accurate measurement has been made of the Raman scattering cross section of the 992 cm−1 line of benzene. Previous cross-section measurements were either made indirectly by comparison with the Rayleigh scattering cross section or by using a pulsed light source. In the present measurement the cross section was measured directly using a cw argon laser as the light source. The results give a peak differential cross section of 1.05(±0.08)×10−29 cm2 per molecule, per steradian, per wavenumber of linewidth, per plane of polarization for an incident light beam with a wavelength of 4880 A, and a linewidth of 2.3 (±0.05) cm−1. Allowing for the wavelength dependence and the optical dispersion, our total cross section agrees to within 20% with two other results. The Raman scattering cross sections of other liquids have been measured by use of the 992 cm−1 line of benzene as a reference. These values, together with details of the absolute cross-section measurement, are presented.

Very high frequency radiowave scattering by a disturbed sea surface Part II: Scattering from an actual sea surface

Abstract: A two-scale model of rough surfaces is considered which permits theoretical interpretation of the features of very high frequency (VHF) scattering from such surfaces (say, from a sea surface). The scattering surface is assumed to be a superposition of small-scale ripple and large waves (swell). Reflection from the latter may he considered by the Kirchhoff approximation. The spatial spectrum of corrugations is taken into consideration; the calculations based on this model help to give an explanation of the behavior of the scattered intensity as a function of the angle of incidence \psi , and to establish which factors affect this dependence at various values of \psi - Theoretically predicted dependence of the scattered intensity upon radio wavelength \lambda , depolarization of the scattered signal, and other features of the scattered radiation are in good agreement with the experimental data obtained from direct measurements. Frequency spectra of the backscattered signal were also investigated (experimental measurements were carried out at wavelengths 3.2 cm, 10 cm, 50 cm, 1.5 m, and 4 m). Observed shifts of the central frequency agree with results of other authors (for the range of \lambda = 3 cm to 200 m). The measured values of the spectrum width appeared approximately twice those theoretically calculated. This may be explained by the influence of dissipative processes and of fluctuations of the skin-deep layer drift velocities. Space correlation of the backscattered signal was also investigated (both theoretically and experimentally). 50 percent decorrelation occurs at distances compared with dimensions of a wave slope.

Shallow water waves a comparison of theories and experiments

Abstract: A series of experiments were performed to determine the velocity field and other characteristics of large amplitude shallow water waves. The experimental results were compared with the predictions of a variety of wave theories including those commonly used in engineering practice. While no theory was found exceptionally accurate, the cnoidal wave theory of Keulegan and Patterson appears most adequate for the range of wavelengths and water depths studied.

Longitudinal capillary waves. Part 2.—Experiments

Abstract: It has been shown theoretically that longitudinal waves can easily be studied at an interface with a high elastic modulus. Measurements on mixed monolayers of cholesterol and dimyristoyl lecithin show that the behaviour of longitudinal waves is in accordance with predictions from theory. The elastic modulus at this interface as obtained from the wavelength of longitudinal waves at 200 c/sec, is several times the “equilibrium” modulus obtained from the slope of force-area curves.

On the trapping of waves along a discontinuity of depth in a rotating ocean

Abstract: It is shown that, according to the linearized theory of long waves in a rotating, unbounded sea, if there is a discontinuity in depth along a straight line separating two regions each of uniform depth, then wave motions may exist which are propagated along the discontinuity and whose amplitude falls off exponentially to either side. Thus the discontinuity acts as a kind of wave-guide.The period of the waves is always greater than the inertial period. The wave period also exceeds the period of Kelvin waves in the deeper medium. As the ratio of the depth tends to infinity, the wave period tends to the inertial period or to the Kelvin wave period, whichever is the greater. On the other hand as the wavelength decreases (within the limits of shallow-water theory) so the waves tend to the non-divergent planetary waves found recently by Rhines.In an infinite ocean of uniform depth free waves with period greater than a pendulum-day cannot normally be propagated without attenuation (if the Coriolis parameter is constant). But non-uniformities of depth provide a means whereby such energy may be channelled over great distances with little attenuation.It is suggested that a gradually diminishing discontinuity will act as a chromatograph, each position along the discontinuity being marked by waves of a particular period.

Dispersion of free harmonic waves in fiber- reinforced composites.

Abstract: : A set of displacement equations of motion is proposed that is suitable for the dynamic analysis of fiber-reinforced composites. In deriving the equations, representative elastic moduli are used for the binder, and the elastic and geometric properties of the fibers are combined into effective stiffnesses. With the aid of certain assumptions regarding the deformation of the fibers, and by employing a smoothing operation, approximate kinetic and strain energy densities for the fiber-reinforced composite are obtained. Application of Hamilton's principle yields the displacement equations of motion. The proposed set of equations is employed to study the propagation of plane harmonic waves propagating in the direction of the fibers and normal to the fiber direction. Plane transverse waves propagating in the direction of the fibers are dispersive, and dispersion curves are shown. By proper choice of the representative elastic moduli of the binder, the phase velocity at infinite wave length for transverse waves propagating in the direction of the fibers, and the constant phase velocities for longitudinal waves and waves propagating in the other directions, agree with the values predicted by the effective modulus theory. (Author)

Nonlinear Thoery of Ultrasonic Wave Amplification and Current Saturation in Piezoelectric Semiconductors

Abstract: A nonlinear theory based on numerical calculation is developed for the amplification of ultrasonic waves in piezoelectric semiconductors. The theory is one-dimensional and applies to semiconductors at room temperature in which the mean free path of the carriers is small compared with the acoustic wavelength. To provide a physical understanding of the problem, the following quantities are investigated in detail: (1) the carrier and the piezoelectric potential distributions and their relative phases, (2) the harmonic content of the elastic wave caused by the electronic interaction, (3) the acoustoelectric current and the nonuniform distribution of the dc electric field in the crystal, and (4) the effect of nonelectronic loss. As the intensity of the elastic wave increases, the drift velocity of the carriers starts from the Ohmic velocity and gradually decreases to the speed of sound. Similarly, the acoustic gain expressed in nepers per unit distance starts from the small-signal value and decreases slowly toward zero. The results obtained for the current and gain saturations described above in various conditions of amplification are presented in universal curves. We find that the current saturation occurs because the carriers are trapped in the troughs of the large piezoelectric potential excited by the elastic wave and are forced to move along with the wave at the speed of sound. We also show that this concept of the current saturation is entirely consistent with the calculation of the acoustoelectric current. Later, in a study of the acoustoelectric current and the Weinreich relation by means of simple power relations, we calculate the efficiency for the conversion of electronic energy to elastic energy. Among other findings we show that in a nonlinear theory, the Weinreich relation can be written for each harmonic independently. Finally, the theory is applied to various phenomena of acoustoelectric origin. Several simulation calculations are made for the propagation of high-field domains, and they verify the phenomena of "pinned" domains and the associated damped current oscillations observed experimentally in photoconductive CdS. Good agreement is also obtained between the present theory and the existing measurements of gain saturation.

Wave-ice interaction

Abstract: Three models are examined to study the transmission of ocean waves through an ice-field. In each case the effect of ice thickness, water depth, and the wavelength and angle of incidence of the incoming ocean wave is considered. In Model 1 the ice is assumed to consist of floating non-interacting mass elements of varying thickness and the shallow-water approximation is utilized to simplify the equations. A simple cosine distribution varying in one direction only is assumed. In Model 11 the mass elements, of constant thickness, interact through a bending stiffness force so that the ice acts as a thin elastic plate. The mass elements are connected through a surface tension force in Model 111 so that the ice is simulated by a stretched membrane. In both Models 11 and 111 the full linearized equations are solved. Because of the complexity of the resulting analysis, calculations of the reflection and transmission coefficients, and the pressure under the ice, are made in Model 11 on the basis of the shallow water approximation.

Monochromatic phase curves and albedos for Venus.

Abstract: Photoelectric observations of Venus were made between 1963 and 1965 from the Harvard College Observatory's Boyden Station in South Africa. Interference filters with half widths between 50 and 200 A were used to isolate ten narrow bands between 3150 A and 1.06 μ; observations were also made in the standard UBV bands. Phase curves are presented and compared with previous observations. The spectral reflectivity is found to be strongly dependent on both wavelength and phase angle. Spherical (Bond) albedos are determined as a function of wavelength. The radiometric albedo of Venus is estimated to be A*=0.77±0.07, where the principal source of uncertainty is the visual magnitude of the sun.

Seismic Waves near 110°: Is Structure in Core or Upper Mantle Responsible?

Abstract: Summary An analysis is given of longitudinal waves which are observed at distances between 105° and 115° some minutes after the arrival of the P waves diffracted by the mantle-core boundary. A number of seismograms which clearly show these wave trains is examined; recordings at WWSS stations from the Chilean shock of 1965 March 28 are specially studied. The observations show (i) that discernible PKiKP waves with wavelengths of order 10 km are reflected from the boundary of the Earth'sinner core back to distances of at least 105° and (ii) that many longitudinal wave onsets (the PdP phase) having travel-times up to 60 s before PKiKP and 90 s before PP arrive near 110° by means of reflection from the lower side of physical discontinuities in the upper mantle of the Earth. The first result is consistent with a relatively sharp increase in P velocity between the transition zone and the inner core at a radius of about 1220 km. The second suggests the existence of a number of discrete shells of different elastic properties in the Earth'supper mantle above 400 km; in particular, one prominent group of PdP waves of order 2 s period is consistent with reflection from a discontinuity near 385 km. This result provides confirmation of the overall high velocity gradient near this depth inferred by L. Johnson; there is an indication, however, of first-order discontinuities in the velocity function assumed to be smooth by Johnson.

Zur Dispersion der OberflÄchenplasmaverluste an reinen und oxydierten AluminiumoberflÄchen

Abstract: The dispersion of the surface plasma oscillations is caused by 1. the coupling of the two surfaces of thin foils, that leads to a splitting into two modes of oscillation with different dependence of frequency on wavelength. 2. the influence of thin coating of e.g. oxide, that produces a displacement of the frequency depending on the wavelength of the surface oscillation.

The laser absolute wavelength standard problem

Abstract: Stabilized lasers usually exhibit systematic frequency shifts larger than their resettability; this phenomenon is well illustrated by the 6328-A helium-neon laser. We describe a Lamb-dip stabilized laser that operates at 1.15259 μ in pure low-pressure (0.12-torr) neon. Optical heterodyne experiments indicate an accuracy exceeding 1 part in 109; short and medium term precisions of 1 : 1010are easily achieved. We also report the successful operation of a wavelength reference based on the saturation of sharp molecular absorption. In the first experiments the P(7) line of the v 3 band of methane is saturated inside the cavity of a 3.39-μ helium-neon laser. The saturation maximum at molecular line center produces an "emission" feature whose linewidth is less than 5 parts in 109. The pressure-induced offset is expected to be less than 1 part in 1010. Size scaling is expected to improve these first results by at least 1 decade.

Propagation of ELF and VLF waves below an anisotropic ionosphere with a dipping static magnetic field

Abstract: Fields of cylindrically curved ionosphere layers are approximated by exponential functions that consider the increase of the phase velocity and decrease of the attenuation rate with the altitude of the layers. Matrix multiplication techniques are applied to the treatment of multilayer ionosphere models. The individual ionosphere layers are thin relative to the wavelength, and the approximate field representations give in the limits of horizontal and radial static magnetic field results identical to those obtained using more accurate treatments of curvature effects. TM modes in the space between the earth and the ionosphere excite coupled TM and TE modes in the ionospheric layers, the presence of which are considered in an iterative solution of the modal equation. In the ELF range, propagation parameters computed for the east-to-west (EW) and west-to-east (WE) directions differ most for dip angles of 15-30°. In the VLF range propagation parameters may exhibit discontinuities at nighttime for the EW direction, when the fields penetrate higher into the ionosphere. The interference distance D of the two lower wave guide modes is increased for propagation in the EW direction relative to propagation in WE direction provided that the electron concentration profiles exhibit sharp density gradients at heights in the range from 80 to 85 km. The desired propagation characteristics could not be produced in the presence of a nondipping static magnetic field or using smoothly varying electron concentration profiles.

Nonlinear Gas Oscillations in a Resonant Tube

Abstract: Nonlinear gas oscillations in a resonant tube are considered analytically and experimentally. Approximate formulas for the velocity and pressure fluctuations are obtained assuming that, due to nonlinear convective effects, the waves emitted by the piston distort rapidly to form a sawtooth with a weak discontinuity at each wavelength. The interaction between incident and reflected waves yields the velocity and pressure inside the tube. These solutions are used to determine, by means of energy considerations, the limiting values of pressure amplitudes, assuming that the leading dissipative mechanisms are the shock wave and the boundary layer. The results obtained compare favorably with amplitude measurements in a piston‐driven tube under nonlinear conditions.

A theory for the christiansen filter.

Abstract: Multiple scattering theory is applied to investigate the filter shape and bandwidth of the Christiansen filter which consists of a suspension of particles in a liquid such that the refractive index vs wavelength curves of the particles and the liquid intersect at a particular wavelength. It is shown that the filter shape is approximately gaussian, and that the fractional bandwidth depends inversely on the rate of change with wavelength of the difference in refractive index of the particles and the liquid and inversely on the square root of the product of the particle concentration, the average particle radius, and the length of the Christiansen cell. Initial agreement with reported experiments is encouraging.

The suppression of wind-generated waves by a surface film

Abstract: In the presence of a surface-active agent waves generated on the surface of a liquid by a wind may be stabilized. This problem is explored, and in particular the critical wind velocity is calculated for wave inception in the presence of such a film.The dominant parameter associated with the surface layer is the surface elasticity χ the ‘inextensible film’ of Lamb is obtained as a limit as χ → ∞. Such a value is hypothetical as for real films χ is not large, being in the range 0 to 80 dyne/cm approximately. Nevertheless, we show that damping exceeding that of the inextensible film can be obtained for short wavelengths, and that the critical wind speed for capillary ripples can be increased by a factor of ten in the presence of a film of experimentally attainable characteristics.The reason for the effectiveness of films of low χ is that the damping in the liquid is related to χ and the wavelength λ in such a way that for small λ, damping is a maximum for small χ.

Excitation of Longitudinal Waves near Electron‐Cyclotron Harmonics

Abstract: Longitudinal waves were excited radially across a plasma column subjected to an axial magnetic field. A strip line placed externally to the column was the source of excitation. The wavelength and propagation direction were measured by a movable antenna immersed in the plasma. The measurements are compared with theory and with observations made with an externally situated receiving antenna. The following conclusions are drawn. (a) Contrary to the commonly accepted notion, the longitudinal waves are propagating rather than standing waves. The propagation is radial towards the axis of the plasma column. Since the waves are backward waves, the energy propagates radially outwards. (b) The internal and external measurements are related to good accuracy through the geometrical optics, “phase quantization” condition, ∫ k dr ≈ 2mπ, where k is the propagation constant, r is the radial coordinate, and m is an integer. The left‐hand side of the equation is deduced from measurements of k made with the movable antenna ...

Acoustic surface wave filter

Abstract: A body of piezoelectric material propagates acoustic surface waves. A first surface wave interaction device is actively coupled to that surface to interact with the waves. Spaced on the same surface from the first device is a second such interaction device. The interaction devices are segmented into a plurality of interjacent arrays of electrode elements and the spacing between successive electrode elements is equal to an integral multiple of one-half wavelength at the desired operating frequency. The arrays are electrically coupled in series and are disposed to effect cumulative interaction with the surface waves.

A Numerical Study of Transient Rossby Waves in a Wind-Driven Homogeneous Ocean

Abstract: The primitive hydrostatic equations for a rectangular homogeneous ocean with a free surface on a β-plane are integrated numerically for 60 days from an initial state of rest and undisturbed depth of 400 m. A zonal wind stress (maximum 2 dyn cm−2) and a lateral eddy viscosity (108 cm2 sec−1) are assumed. A series of transient Rossby waves of approximately 1000-2000 km in length form in the central and eastern basin, and undergo a well-marked life cycle of amplification and decay as they propagate westward at ∼1 m sec−1 relative to the zonal current. The northward boundary current in the west (∼1 m sec−1) and the counter-currents in the northwest (∼10 cm sec−1) may be identified as the first stationary members of a continuing series of waves, with subsequent transients showing characteristics of reflected Rossby waves and reaching progressively smaller maximum amplitudes. The standing wave pattern (wavelength ∼600 km) in the north-west is a characteristic nonlinear effect, and is associated with th...