On the propagation of wave from a cylindrical cavity,II

Summary We have discussed in the paper the disturbance produced in an infinite layer of nonhomogeneous elastic material characterised by = ₀ Z and = ₀ Z where and are the density and shear modulus respectively of the material due to periodic torsional force applied on the wall of a cylindrical hole in the layer. The variation of the displacement component with the depth of the layer is shown graphically and compared with the corresponding homogeneous case.     

Torsional vibration of non-homogeneous isotropic hollow thick cylinder

Summary Free vibration of a thick hollow cylinder of non-homogeneous elastic material having rigidity and density varying according to the laws: (i) =₀(₀+₀ z) and Q=Q₀(Q₀+₀ z) for finite and infinite length of the cylinder and (ii) ₁/r = and Q = ₁/r for finite length only are considered in this paper. Frequency equations are deduced and respective numerical solutions are obtained.     

Generalized thermoelastic longitudinal waves in unbounded medium

Summary In this paper the generalized thermoelastic longitudinal waves and the temperature field set up due to coupling of the displacement and the temperature fields, with heat wave travelling with certain finite velocity, in an unbounded medium are studied. The thermoelastic displacement potential and the temperature field at any point are obtained in terms of the surface integrals involving the potential, the temperature and their normal derivatives.Notation x _i the cartesian coordinate system,i=1,2,3 - n (u _i) the displacement vector - (/x _i) the del operator - _t /t the derivative with respect to time - T _o the temperature corresponding to the natural stat of zero stress and strain - T Absolute temperature - c _e the specific heat - , Lamé's constants - ₀ the density - coefficient of linear thermal expansion - K thermal conductivity coefficient - _kk u - ₀ the relaxation time     

Rayleigh waves in an inhomogeneous medium

Summary Dispersion in Rayleigh waves is discussed for semi-infinite media with = ₁(1 ± cos s z) and = ₁(1 ± cosh s z), being the rigidity of the medium. A few workers tried with the above Fourier type of model but failed to find the dispersive nature. Because they neglected s due to the complexity of the calculation they arrived at a non dispersive frequency equation. This difficulty is removed in this paper and a dispersive frequency equation is obtained which shows both direct and inverse dispersion. The second model leads to non-convergent solution forz but shows many interesting results which are also discussed.     

Propagation of surface waves on a nonhomogenous spherically aeolotropic shell

Summary This paper studies the propagation of Surface Waves on a spherically aeolotropic shell surrounded by vacuum. The elastic constantsc _ij and density of the material of the shell are assumed to be of the form _ij r ^l and _o r ^m respectively, where _{ij o} are constants andl, m are any integers.     

Tidal friction. Secular variations of the inclination and eccentricity of the Moon's orbit

Summary The computation of the secular variation of the inclination and eccentricity of the Moon's orbit due to tidal forces is revised. Also the effect of the Earth's ellipticity, which amounts to 10^–6 to 10^–5 of the value for the spherical earth, is estimated and found to be negligible. The results agree well with the computations of Kaula [7], as opposed to MacDonald's results [8] which display an order-of-magnitude difference in the variation of the eccentricity, apparently due to a printing error. Finally, solutions are presented for various values of the dissipation factor.

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amuam uu uu aa u muumma um, a nuuu uau. m n¶rt;a a uu amu u; m uu mam m 10^–5 ¶rt; 10^–6 au ¶rt; aa u u ¶rt;am nu. mam am uuu aa [7], muu m mam aa¶rt;a [8],¶rt; aua a n¶rt; uuu muumma u¶rt; aa nam. a ¶rt;a u ¶rt; a au ama ¶rt;uunauu.

     

On the propagation of wave from a cylindrical cavity

Summary This paper discusses the disturbance produced in an infinite layer of non-homogeneous elastic material characterised by =0 ⁿ and =0ⁿ(n>0) where and are the density and shear modulus respectively of the material, due to periodic torsional force applied on the wall of a cylindrical hole in the layer. The variation of the displacement component with the radius vector is shown graphically and compared with the corresponding homogeneous case.     

Rotatory vibration of a thick spherical shell of isotropic non-homogeneous elastic material

Summary Rotatory vibrations of a thick spherical shell of isotropic non-homogeneous material with rigidity and density given by (i) = ₀ r ^-2 withQ =Q ₀ r ^-2 e ^2mr and (ii) = ₀ r ^m with =Q ₀ r ⁿ have been discussed and the frequency equation is derived with numerical enumeration of frequency in each case.     

On the efficiency with which aerosol particles of radius less than 1 μm are collected by columnar ice crystals

A theoretical model is presented which allows computing the efficiency with which aerosol particles of 0.001 r1 m are collected by columnar ice crystals in air of various relative humidities, temperatures, and pressures. Particle capture due to Brownian diffusion, thermo- and diffusiophoresis is considered. It is shown that phoretic effects importantly determine the particle capture process of 0.01r1 m. The various pressure-temperature levels studied are found to affect the collection efficiency only ifr>0.1 m. Comparison shows that water drops generally are better aerosol particle scavengers than columnar ice crystals.     

The secular variation of the geomagnetic field in Egypt in the last 5000 years

The palaeo-intensities (F _a) of the geomagnetic field in Egypt at some ages are determined by archaeomagnetic measurements and found to be:F _a=36.2 T at 3100 B.C., F_a=46.8 T at 3000 B.C.,F _a=36.5 T at 2780 B.C., 49.0 T at 2500 B.C., 36.4 T at 2200 B.C., 57.5 T at 1990 B.C., 62.1 T atca 1400 B.C., 61.5 T at 1400 B.C., 69.9 T at 600 B.C., 59.3 T at 550 B.C., 79.9 T at 460 B.C., 73.7 T at 450 B.C., 69.7 T at 320 B.C., 56.2 T at A.D. 50, 64.9 T, at A.D. 400, 54.4 T at A.D. 300, 57.5 T at A.D. 700 and 43.0 T at A.D. 1975.The palaeo-inclinations (I _a) at some ages are found to be:I _a=24.2° at 420 B.C., 44° at A.D. 50, 60.7° at A.D. 703 and 42° at A.D. 1795.The measured values ofF _a are affected by the anisotropy of magnetic susceptibility of the samples by 13% to 20% of the expected correct value. The suitable correction of this effect is by multiplyingF by 1/((1+0.2(/90)) andF by 1/((1–0.13 (/90)), whereF andF are the resultant values ofF _a if the laboratory field is perpendicular or parallel to the wall of the sample during the Thelliers' experiments, respectively, and is the angle between the direction of natural remnant magnetization of the sample and the direction of the laboratory field.The results of this paper, together with the previous results for Egypt and the neighbourhoods, lead to the production of the secular variation curve of the geomagnetic field in Egypt for the last 5000 years. The intensity of the field shows a periodicity of about 400 years with multiples.     

Q measurements for PhaseX overtones

Linear stacking procedures are used to retrieve the attenuation of 91 modes belonging to the 3rd, 4th and 5th Rayleigh overtones branches in the 80–160 s period range, and contributing to the so-called PhaseX wave group. Our data show in general slightly less attenuation than expected from available models. Data space inversion shows that, when combined with previously measured fundamental modeQ's, this new dataset improves resolution significantly in the 1000–2000 km depth range. Based on this remark, we carry out a number of parameter space inversions. Our results suggest a narrow (80–200 km) zone of high attenuation (Q =75–90), low attenuation in the intermediate mantle (670–1500 km); (Q 350), and lower values in the deeper mantle (Q 200).     

On the efficiency with which aerosol particles of radius larger than 0.1 μm are collected by simple ice crystal plates

A theoretical model is presented which allows computing the efficiency with which aerosol particles of radius 0.1r10 m are collected by simple ice crystal plates of radius 50a _c 640 m in air of various relative humidities, temperatures and pressures. Particle capture due to thermophoresis, diffusiophoresis and inertial impaction are considered. It is shown that the capture efficiency of an ice crystal in considerably affected by phoretic effects in the range 0.1r1 m. For aerosol particles ofr>1 m the efficiency is strongly controlled by the flow field around the crystal and the density of the aerosol material. Trajectory analysis also predicts that aerosol particles are preferentially captured by the ice crystal rim. Our theoretica results are found to agree satisfactorily with the laboratory studies presently available. Comparison shows that for the same pressure, temperature and relative humidity of the ambient air ice crystal plates are better aerosol particle scavengers than water drops.     

Cs137 gamma-ray absorption in eclogites

Summary The coefficient of the gamma-ray absorption _Cs ¹³⁷ investigated in eclogites of the Bohemian Massif varies with fresh samples from0.2477 cm ^–1 to 0.2804 cm ^–1 . Symplectite is the main factor decreasing the value of down to0.242 cm ^–1 . On the contrary, the coefficient increases with the increasing content of clinopyroxene and especially of garnet. The linear dependence of the coefficient on the density may be expressed by the equation =0.0682+0.028.     

Die Kovarianzfunktion der 2. Ableitung der Schwere nach der Höhe

¶rt;u m [4]; ¶rt;m ¶rt;nu mum uu uu 2- nu¶rt; u mmu n m.     

Determination of the geopotential scale factor from satellite altimetry

Summary The geopotential scale factor R ₀ =GM/W ₀ has been determined on the basis of satellite altimetry as R _{0=(6 363 672·5±0·3) m} and/or the geopotential value on the geoid W ₀ =(62 636 256·5±3) m ² s ^–2 . It has been stated that R ₀ and/or W ₀ is independent of the tidal distortion of surface W=W ₀ due to the zero frequency tide.

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¶rt;a nmu amumuu u ama amnmuaa R ₀ =GM/W ₀ =(6 363 672,5±0,3) m u/uu aunmuaa a nmuu¶rt;a W ₀ =(62 636 256,5±3) m² s^–2. m, m R ₀ u/uu W ₀ auum m nm amu a a nuu ¶rt;au nmu W=W ₀ .

     

Waves in an elastic plate with an irregular boundary

Summary Green's function corresponding to the displacements for anSH-line source inside a wedge shaped medium finite or infinite in which the density and the elastic parameter are not constant throughout but some class of function ofr, the radial distance (i.e. and satisfy some differential equation) has been obtained. The paths of propagation of the cylindrical waves, their reflections on different boundaries and their continuous refractions within the medium has been clearly established. The scattered field from the different parts of the body have been pointed out with prescribed distribution of and in this inhomogeneous wedge. It is shown that for some distribution of and the rays are curved and the reflections at the two plane boundaries occur in such a way that no ray will go to infinity by reflection, rather they are coming back towards the apex after suitable number of reflections with variable intensity. Also there are some distributions of and in the same class as mentioned earlier, such that the behaviour of the waves is similar to that in a homogeneous wedge, i.e. these waves will go to infinity by a suitable number of reflections and ultimately die out. The first case is quite unlike the usual homogeneous medium with non parallel boundaries and so care must be taken in computing the field within the nonhomogeneous medium within the non-parallel boundaries.     

Amplitude Response of a LCR Gravimeter with Feedback at Periods of Microseisms and Earthquake Waves

The amplitude response of a LCR gravimeter with the SRW-E feedback was determined on a vertical vibrating platform. The ink-pen recorder was connected parallel with the digital voltmeter input to obtain an analog response of the gravimeter to the harmonic motion of the base with a peak-to-peak amplitude of 10 m and periods excited in an interval of 4 - 10 s as by the ground motion of meteorological microseisms, and in the interval 10 -100 s as by surface waves of distant strong earthquakes. In the first interval, an unexpected maximum of the amplitude response was observed with the double amplitude of apparent 6,5 Gal (6.5 × 10 _–8 m/s ² ) at a period of 4.8 s, and a baseline shift with the amplitude of–64Gal was observed at the same period. The value of this direct component cannot be separated from the effect of the Earth's gravity field. In the second interval, the amplitude response of the gravimeter displayed one expected maximum at a period of 40 s with the double amplitude of 8.1Gal. At the usual level of microseisms with a peak-to-peak amplitude of up to 2 m the fluctuation of the gravimeter on the direct baseline shifted by –4.9 Gal was estimated at 1 Gal. With typical Rayleigh surface waves with periods of 20 s and double amplitudes of up to 100 m, the fluctuation reached 67 Gal.     

A combined geophysical model of the crust for the south of the European part of the USSR

m¶rt; amamu ¶rt;uau nma nauua ¶rt; a n amu . n ¶rt;a uu u¶rt;au,aumuu u mn nma. mam maa auum ¶rt; m u nmm u¶rt;ua n¶rt;a u a maa a umua a nam . ¶rt; nmm amuu n¶rt;m uu 3,3/ ³ , n¶rt; ¶rt;uuuau u na¶rt;uau mu a anma ¶rt; 3,2/ ³ . ¶rt; n¶rt;uu a¶rt;u aau mum nm, maumaa ¶rt;¶rt;m aama u ¶rt; amu .

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Presented at the KAPG Symposium Problems of Interpretation and Construction of Physical Models of Litosphere, Liblice (CSSR), March 6–10, 1978.     

Détermination des paramètres d'Ångström par des observations actionmétriques courantes

Summary By comparing the equalities expressing the solar flux within a wide spectral region on the assumption of an extintion within the atmospheric aerosol given by ^– and that of an extintion represented by ₁^–1, a relationship is established by means of which: 1) The error is discussed which is done when the air opacity is expressed by ₁, in the case when 1; 2) A simple and quick method is worked out for determining the parameters and from actinometric observations, carried out within the spectral regions <525 m and 525 m<<625 m.     

Spherical harmonic expansion of the continents and oceans distribution function

Summary An algorithm is derived to compute the coefficients of a spherical harmonic series for the functionE(, ) representing the distribution of continents and oceans with the least-squares method. Some properties of the system of normal equations, when measuring points are distributed in a regular grid, are discussed. The fully normalized complex coefficients to the ninth degree are given in the table.

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