The P Wave

A similar conclusion caimot be reached concerning the p waves (/ = 1). In fact the coupling term between the s and p waves (the Uumterm of the eq.(22)) is not small here and correspondingly the p wave of the molecular system cannot be expected to... 

Figure 13.4 Electrocardiogram. The electrocardiogram (ECG) is a measure of the overall electrical activity of the heart. The P wave is caused by atrial depolarization, the QRS complex is caused by ventricular depolarization, and the T wave is caused by ventricular repolarization.

The ECG has several noteworthy characteristics. First, the firing of the SA node, which initiates the heart beat, precedes atrial depolarization and therefore should be apparent immediately prior to the P wave. However, due to its small size, it does not generate enough electrical activity to spread to the surface of the body and be detected by the electrodes. Therefore, there is no recording of the depolarization of the SA node. 

Second, the area under the curve of the P wave is small compared to that of the QRS complex. This is related to the muscle mass of the chambers. The ventricles have significantly more muscle than the atria and therefore generate more electrical activity. Furthermore, although it may not appear to be the case given the spike-like nature of the QRS complex, areas under the QRS complex and the T wave are approximately the same. This is because these recordings represent electrical activity of the ventricles even though one is caused by depolarization and the other by repolarization. Either way, the muscle mass involved is the same. 

The earliest ECG change (serum potassium 5.5 to 6 mEq/L) is peaked T waves. The sequence of changes with further increases is widening of the PR interval, loss of the P wave, widening of the QRS complex, and merging of the QRS complex with the T wave resulting in a sine-wave pattern. 

Independently of each other, Pauling and Slater worked out a quantum mechanical explanation of the directional valences characteristic of chemical molecules. They did this by proposing directional properties for the p wave functions and for the sp3 wave functions resulting from "hybridization" of electron wave functions, or orbitals.73... 

Schematic representation of the heart and normal cardiac electrical activity (intracellular recordings from areas indicated and ECG). Sinoatrial (SA) node, atrioventricular (AV) node, and Purkinje cells display pacemaker activity (phase 4 depolarization). The ECG is the body surface manifestation of the depolarization and repolarization waves of the heart. The P wave is generated by atrial depolarization, the QRS by ventricular muscle depolarization, and the T wave by ventricular repolarization. Thus, the PR interval is a measure of conduction time from atrium to ventricle, and the QRS duration indicates the time required for all of the ventricular cells to be activated (ie, the intraventricular conduction time). The QT interval reflects the duration of the ventricular action potential.

Oldham discovered that there are actually two kinds of seismic vibrations, one called P (or "primary," because it travels faster and arrives first) and the other called S (or "secondary," because of its later arrival at the same station). The compressional motion of the P waves can be transmitted through most substances, although the speed at which the wave moves decreases as the stiffness of the medium decreases. In contrast, the transverse motion of S waves cannot be transmitted through a liquid, because the loosely bonded molecules in a liquid slip past each other too easily. S waves are observed to disappear at the top of the core. Then, at a depth of approximately 5100 km, the P wave velocity abruptly increases and there is a hint of the reappearance of an S wave. From such observations, Danish geophysicist Inge Lehman hypothesized in 1936 that the core was stratified, with an outer liquid portion and an inner solid portion. The existence of molten metal at core pressures requires some light element to act as antifreeze. 

An interesting theoretical prediction is that, similar as in the p-wave superconductors discussed in the next subsection, non-magnetic impurities in an antiferromagnetic superconductor cause pair breaking (Morozov 1980 Zwicknagl and Fulde 1981) whereas non-magnetic impurities in a non-magnetic superconductor are not expected to destroy superconductivity (Anderson 1959). 

Lee and Collett (2001) measured the compressional (P-wave) and shear (S-wave) velocities of natural hydrates in sediments (33% average total porosity) at the Mallik 2L-38 well. The P-wave velocity of nongas-hydrate-bearing sediment with 33% porosity was found to be about 2.2 km/s. The compressional velocity of gas-hydrate-bearing sediments with 30% gas hydrate concentration (water-filled porosity of 23%) was found to be about 2.7 km/s, and 3.3 km/s at 60% concentration (water-filled porosity of 13%), that is, about a 20% or 50% increase to nongas-hydrate-bearing sediment. The shear velocity was found to increase from 0.81 to 1.23 km/s. 

The reason for the large difference between the values of A for positrons and electrons at an energy of 2 eV is that for positrons the s-wave phase shift passes through zero at the Ramsauer minimum and the dominant contribution to the cross section therefore comes from the p-wave, which is quite strongly peaked in the forward and backward directions. In contrast, there is no Ramsauer minimum in electron-helium scattering, and the isotropic s-wave contribution to aT is dominant at this energy. 

Fig. 3.3. The p-wave phase shift for positron-hydrogen scattering A, static approximation B, result for six-term coupled state (Is, 2s, 2p, 3s, 3p, 3d of H) (McEachran and Fraser, 1965) C, exact variational result (Armstead, 1968 Bhatia, Temkin and Eiserike, 1974).

Humberston and Campeanu (1980) investigated the convergence of the p-wave phase shifts with respect to the number of short-range correlation terms of each symmetry separately, and they showed that at low positron energies the first-symmetry terms are the most important but that as the positron energy is raised the inclusion of the second-symmetry terms becomes increasingly significant. 

Figure 2.16 Display of the 2P shape resonance in the e —Be collisional system. The crosses represent the first partial wave of the p-wave S-matrix resonance pole as a function of the cut off parameter. Taken from Ref. [90] with permission of IJQC.

The ECG consists of the P-wave, the QRS complex, and the T-wave. These components, represented in Figure 4.2, are associated with different aspects of the cardiac cycle atrial activity, excitation of the ventricles, and repolarization of the ventricles, respectively. 

Atrial depolarization results in the P wave of the ECG, the QRS complex denotes ventricular depolarization and the T wave represents ventricular repolarization. 

Disequilibrium in the eleetrolyte balanee ean provide diagnostic clues. For example, hyperkalemia causes tail T-waves in leads II, III, V2 to V4, when the potassium balance exceeds 5.5 mmol/1. In conjunction, the amphtude of the P wave is reduced and QRS is widened. Hyperkalemia is usually present when the amphtude of the T-wave is higher than that of the R-wave. With increasing potassium concentration, P-waves widen and eventually disappear. Accentuated hyperkalemia results in asystole. 

The ECG of an individual executed by inhalation of cyanic acid revealed that initially, between the first and third minutes, a heart rate slowing was discernible with the disappearance of the P-wave. Later the heart rate increased shghtly. T-waves showed an increase in amphtude and a marked shortening of the ST-segment. One subject, unhke some others in this cohort, showed normal AV conduction until ventricular tachycardia and ventricular fibrillation developed. 

When an earthquake occurs, some of the energy released travels through the ground as waves. Two general types of waves are generated. One t5q)e is called the P wave, and the other is called the S wave. A graph can be made of the travel times of these waves. 

Kg/p = Vp — (4/3)V. This new parameter (sometimes thought of as the P-wave velocity of an equivalent fluid, for which G = 0) can be determined directly from static compression data V = Kg/p = (1 + Tay)(bP/bp)p. The bulk sound velocity possesses another desirable feature, in that it can also be constrained indirectly through chemical equilibrium experiments. Chemical equilibria describe free energy minima the pressure dependence of free energy is described by the molar volume, and the pressure dependence of volume (or density) is described by Kp and hence V. Thus, experimental determinations of equilibrium phase boundaries can... 

Walck M. C. (1984) The P-wave upper mantle structure beneath an active spreading center the Gulf of California. Geophys. J. Roy. Astro. Soc. 76, 697-723. 

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