Compressional Energy Research Articles

New cascade model calculation of pion multiplicity in high-energy heavy-ion collisions

Pion multiplicities in nuclear collisions are calculated using the nuclear cascade model developed by Kitazoe et al. This cascade model differs in particular from previous models in the way binding, Pauli principle, and Fermi motion effects are treated. The treatment of such details in the cascade is found to have significant influence on the pion multiplicities. Close agreement with the Ar + KCl central collision data is obtained without introducing the compressional energy effect postulated by Stock et al.

Ringing P waves and submarine faulting

Long‐period teleseismic records from shallow focus oceanic events sometimes exhibit ‘ringing’ P waves. The ringing portion of these prolonged wave groups characteristically has a narrow band frequency content, an amplitude which monotonically decreases from values comparable to the primary P pulse, and a high station to station coherence. These traits are suggestive of leaking compressional modes of the oceanic water layer. This layer is an efficient wave guide for elastic body waves once their energy is effectively introduced into the system. Through the modeling of point and extended sources interior to oceanic crust it is found that to account for the large excitation of these modes a particular type of faulting is required. Specifically, the fault must originate in a setting such that a substantial fraction of the dislocation surface is situated above the Moho and be oriented so that a significant amount of compressional energy is propagated upward. These provisions are met by steeply dipping or thrust faults in continental margins and subduction zones where thickened oceanic crustal and sedimentary layers are commonly found. Events of this type are likely to generate perturbations in submarine topography. Hence real‐time observation of ringing P waves from large earthquakes in these geographical provinces could be diagnostic of shallow faulting with high tsunamigenic potential.

Piezoelectric acoustic emission instrumentation

A detector of acoustic emissions from a structure includes a piezoelectric element responsive to both compressional wave energy and to shear wave energy from any direction so that the source of the acoustic emission may be determined.

Pore fluids and seismic attenuation in rocks

Seismic attenuation and velocities were measured in resonating bars of Massilon sandstone at various degrees of saturation. Whereas shear energy loss simply increases with degree of saturation, bulk compressional energy loss increases to ∼95% saturation and then rapidly decreases as total saturation is achieved. This behavior is analogous to the behavior of shear and compressional velocities, but the effect on attenuation is larger by an order of magnitude. Our observations are in excellent agreement with the predictions of several models of energy loss involving partial or total saturation. Pore fluid attenuation mechanisms are expected to be dominant at least in the shallow crust.

Theoretical studies of the formation and adiabatic compression of reversed-field configurations in imploding liners

The formation and compression of e-beam-induced reversed-field theta-pinch configurations are studied theoretically in an MHD treatment. Taking into account classical collisional resistivity plus anomalous resistivity derived from microinstabilities, it is shown that plasmas can be created with parameters suitable for liner compression experiments. Adiabatic compression of the quasi-equilibrium plasma/flux mixture is described by using Lagrangian co-ordinates. Results are given for a sample (unoptimized) initial configuration. In the final state, the ratio of plasma to total energy and the total D-T rate are 30% and 20%, respectively, of the values which would be obtained if all the compressional energy went into heating plasma,i.e. assuming negligible magnetic-field-filled volume.

The role of hot plasma in magnetospheric convection

Several authors have shown that the presence of hot plasma in the magnetosphere can severely modify an imposed convection pattern and even prevent its penetration to low latitudes. Here with the aid of simple theoretical models we argue that the important parameters governing such effects are the hot plasma pressure, its number density, and the ionospheric conductivity. A result of this is that a fluid description of the phenomenon can be given. Changes in convection naturally give rise to east-west pressure gradients near the ring current inner edge, and these give rise to east-west flows, which cause the shielding effect. We show that plasma compressional energy is lost in Joule dissipation in the ionosphere in these flows which are rapidly set up on the nightside. On the dayside the process is slower, but we conclude that the dayside conductivity is the parameter controlling final ring current penetration. In the long time limit the fluid approximation breaks down, and we qualitatively discuss the development of steady state flow patterns and the effects of collisionless plasma behavior in this limit.

A semiempirical equation of state for polymer melts

AbstractAn explicit reduced equation of state is developed by combining results of the hole'theory with a semitheoretical expression for the temperature dependence of the reduced Tait parameter B̃ which is found to be in good agreement with experiment. This approach circumvents the implicit character of the theoretical equations.Two procedures are explored to derive for a given system the PVT surface and the compressional energy and entropy changes from the corresponding reduced functions. One rests on the usual superposition of experimental and analytical isotherms and isobars. The other, and more approximate method, utilizes a correlation between the scaling temperatures, pressures, and volumes obtained previously, and requires only experimental data at atmospheric pressure and a single temperature above the glass transition (Tg) or the melting temperature (Tm). The good agreement between experiment and theory noted previously is shown to extend to the semiempirical relationships. Finally, internal pressure data for oligomers and polymers at atmospheric pressure and encompasing a wide range of reduced temperatures are examined. The ensemble of data can be described by simple power relationships between the internal energy and the density. The exponents, however, depart significantly from the van der Waal's value of unity.

Dynamic Properties of Dry and Water-Saturated Green River Shale Under Stress

Abstract Dynamic elastic properties of dry and water-saturated Green River shale samples were computed from compressional and shear-wave velocity measurements. P- and S-wave velocity measurements were made in three mutually perpendicular directions with respect to the bedding planes. Measurements were also made in several different directions by varying the angle between the bedding planes and the direction of propagation of the wave for angles of 0, 30, 45, 60 and 90 degrees. The oriented samples were subjected to both confining pressure and axial loads, in excess of the confining stress, in the direction of Propagation. In general, P- and S-wave velocities increased with increasing stress levels, with a corresponding increase in Young's modulus. Water saturation caused the P-wave velocity to increase and the S-wave velocity to decrease. Elastic moduli decreased upon saturation, except for Poisson's ratio, which increased, indicating some degree of weakening of the material. The samples showed a moderate degree of anisotropy; this was to be expected from the laminated nature and shallow occurence of Green River shale. Introduction This paper presents some results of an experimental determination of the elastic coefficients of anisotropic materials (in particular, finely layered rocks and minerals such as Green River shale) from measurements of dilatational and shear-ultrasonic-wave velocities. Ultrasonic techniques have been used extensively in nondestructive testing. Several methods have been proposed by McSkimmin, and some of these have been used successfully to measure ultrasonic velocities in rocks. Hughes and Cross, Wyllie et al., and Birch, developed pulse first-arrival techniques for the measurement of dilatational and shear velocities. Williams and Lamb used the method of cancellation of a traveling wave, which was later modified by Myers et al. and perfected by McSkimmin. Although this method is highly accurate, it has not been used as widely as the pulse-transmission methods recently reported by Jamieson and Hoskins, King, and Mattaboni and Schreiber. It has been common practice to use some form of crystal transducers, either quartz or ceramic, that has been cut or polarized in different directions in order to generate either compressional or shear waves. However, accurate determination of shear wave velocities has been difficult due to problems that arise in obtaining a pure shear wave from cross-polarized crystals, which usually also generate a small amount of compressional energy. As reported by Gregory, this energy can be seen as a long precursor preceding the sharp break of the shear first arrival. The need for generating pure shear waves led to interest in mode-conversion techniques, which are based upon conversion of the mode of vibration through wave reflection or refraction at a discontinuity. Arenberg showed that for certain materials and for certain angles of incidence it is possible to generate pure shear modes by reflection at a boundary. Jamieson and Hoskins used a pyrex glass-air interface for generating pure shear waves, and King used this method successfully for measuring shear-wave velocities in rocks. Gregory arrived at a similar result by refraction of a wave at an aluminum-oil interface. A plane compressional wave, traveling in the oil phase, is incident on the aluminum at an angle larger than the critical angle for compressional waves, and thereby generates a purely transverse, plane-polarized wave in the aluminum. During the last few years methods have been developed that allow the simultaneous determination of shear and compressional velocities in solids.

Mode Conversion Technique Employed in Shear Wave Velocity Studies of Rock Samples Under Axial and Uniform Compression

Abstract A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy, S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King,1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. S- and P-wave velocity measurements on Bandera sandstone and Solenhofen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2, and by Gregory3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fatt5 and by Gregory,3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8

Study of the energy of the free oscillations of the Earth

The energies of the radial, torsional, and spheroidal free oscillations for a Gutenberg model earth were studied. Each mode of oscillation has a characteristic radial distribution of elastic and kinetic energy that fixes the parts of the earth that contribute most heavily in determining a particular resonant frequency. An examination of the partitioning of energy among compressional, shear, and gravitational energy as a function of mode number and depth immediately explains the persistence of the purely radial mode compared with the other normal modes of the earth. Only the first few spheroidal modes are sensitive to the density of the inner core; they are particularly sensitive to the density of the outer part of the core. The low-order spheroidal modes also exhibit a rapid rise of potential energy near the base of the mantle; this rise will permit improved estimates of the velocity to be obtained in this region, which is difficult to examine with body waves. The tabulated results allow estimates to be made of the previously neglected energy contained in the free oscillations excited by large earthquakes. An estimate of the energy in the low-order spheroidal oscillations excited by the great Alaskan shock suggests a value of 1023 ergs over the period range from 450 to 830 sec, implying that the energy density increases toward high frequencies if the total energy in the earthquake was of the order of 1024–1025 ergs.

Energy Density in a Plasma Oscillation

The frequency dependence of the electrostatic energy density in an undamped (or weakly damped) longitudinal plasma oscillation and the explicit interrelationship between kinetic, electrostatic, and thermal (compressional) energy density are discussed.

CRITICAL‐ANGLE EFFECTS IN SEISMIC EXPLORATION*

ABSTRACTIn the case where a medium of velocity α1 is underlain by a medium of higher velocity α2, no propagation of compressional elastic wave energy into the lower medium takes place at angles of incidence exceeding a certain critical value. This so‐called critical angle –which is a measure of the actual velocity‐contrast –is furthermore marked by a sharp increase in the amount of reflected compressional energy. An investigation has been made to find out whether this critical‐angle effect might be usable as a velocity‐contrast indicator in seismic exploration.Model experiments confirmed the expectation that this effect should be manifest at the surface under ideal conditions.Two small‐scale field set‐ups showed that the effect is actually measurable in the field (in one case after applying corrections for planting variations).Finally a seismic line along the shore of the North Sea provided the data for contrast analysis over a considerable distance along the base of the Tertiary. Comparison of the measured changes in contrast and subcrop velocities obtained at those locations where subsurface data from independent sources were available, showed good agreement.It is concluded that critical‐angle shooting may be used to indicate subcrop changes along a reflector, or even to obtain the same sub‐stratum velocity as is sought in conventional refraction work, at considerably shorter operating distances.

Velocity of shear waves in rocks to 10 kilobars, 1

The velocity of shear waves is reported as a function of pressure for several rocks previously used by Birch in his measurements of VP. AC-cut quartz transducers with resonant frequencies of 1 to 5 Mc/s were used with the usual ultrasonic technique. In fine-grained, low porosity rocks, very little compressional energy precedes S and there is no ambiguity in arrival time. No systematic difference exists between previous measurements on several of the same rocks made by Birch using resonant torsional vibrations of long cylinders. Chief advantages of the ultrasonic technique are the ease with which measurements may be made and the fact that both VP and Vs may be measured on the same specimen. Analyses of the data will be given in part 2.

Bond lengths in conjugated polyenes

Some conjugated polyenes have been examined using the valence-bond approximation including σ-bond compressional energy. The appropriate exchange and coulomb integrals were obtained as functions of bond length, using spectroscopic and thermal data for benzene and ethylene. These semi-empirical functions were then used in investigating linear cyclic polyenes. It was found that the bond lengths predicted for butadiene were in excellent agreement with experiment and that there should be appreciable bond alternation in longer chains. Similarly for n > 3, it was found that bonds should alternate in the cyclic polyenes C 2nH 2n and that the degree of bond alternation tends to increase with n. This agrees qualitatively with the recent application of simple molecular-orbital theory (including σ-bond compression) to long chain and large cyclic polyenes.

Compressional energy and resonance energy

Compressional energy and resonance energy