Time response propagation constant

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

The frequency dependence of the propagation constant appears as wave deformation in time domain. This is measured as a voltage waveform at distance X when a step (or impulse) function voltage is applied to the sending end of a semi-infinite line. The voltage waveform, which is distorted from the original waveform, is called "step (impulse) response of wave deformation," and is defined in Equation 1.201. 

The admittance response at 1 kHz has also been interpreted in terms of the behavior at residual defects in anodic films. This interpretation is based on electron optical characterization, which shows that anodic films contain a distribution of preexisting defects associated with substrate inclusions and mechanical flaws (96,102). In aggressive environments, pits nucleate from these defects and propagate into the metal substrate. In this model, pits are distinct from anodic film flaws, and both can contribute to the measured admittance. Measurements of anodic films exposed to chloride solutions showed that the dissipation factor increased with time, but the capacitance remained nearly constant. Under these conditions, pit propagation at a flaw led to a pit area increase, which increased the resistive component of the admittance, resulting in an increased dissipation factor, but no increase in the capacitance. Measurements at 100 kHz were reflective of the electric double layer and not the components of the oxide film. 

We saw in Section III that the polarization propagator is the linear response function. The linear response of a system to an external time-independent perturbation can also be obtained from the coupled Hartree-Fock (CHF) approximation provided the unperturbed state is the Hartree-Fock state of the system. Thus, RPA and CHF are the same approximation for time-independent perturbing fields, that is for properties such as spin-spin coupling constants and static polarizabilities. That we indeed obtain exactly the same set of equations in the two methods is demonstrated by Jorgensen and Simons (1981, Chapter 5.B). Frequency-dependent response properties in the... 

Time scale for observation The response of the acoustic effect is limited by the acoustic propagation between the fringe distance and that time constant is rac = A/v. Therefore, in 0 < t rac, the density contribution is small and fast response of the population grating can be easily observed (although the Temp.G signal could contribute to the signal even in this time scale). In principle, even rather slow dynamics of the population, which is not disturbed by the thermal... 

Cardioversion or defibrillation is the electrical termination of arrhythmias using field stimulation. Unlike pacing, in which cardiac excitation is initiated in and propagates from a small region of tissue near the electrode, cardioversion must arrest electrical activity by simultaneous stimulation of most of the heart. In practice, this means establishing a critical field across a critical mass of cardiac tissue. This requires a compromise between the electrical response of the tissue and the electrical capabilities of the device. The electrical response of cardiac cells is complex, but stimulation mostly depends on the first-order properties of the membrane [6]. Theoretical and experimental studies have shown that the optimum voltage waveform for stimulation of cardiac tissue is a waveform with a characteristic rise time comparable to the cell membrane time constant [7,8]. 

The different experimental methods for sound wave propagation and for measuring the mechanical response or elastic constants of polymers are summarized below with an attempt to give an idea of the different time scales involved. 

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