Transient response defined

Impedance, on the other hand, includes the transient response of the system as well as the long-term, steady-state response defined by Ohm s law. The entire time course of impedance is usually captured by transforming the measurement to the frequency domain. This is an inverse transform in which transient responses occur at high frequencies and long-term, steady-state responses are approached at low frequencies. 

Equations 1.312 and 1.315 permit us to calculate the transient response when either the quadrature or the inphase component of the frequency spectrum is known. It is often convenient to introduce new scale variables in these equations. Such a scale variable can be defined as ... 

This conclusion can be derived in a different way. In fact, as is well known, the late stage of the transient response is defined by only those terms of the low-frequency spectrum which contain odd powers of wave number, k, and logarithmic terms. 

Presentation of the field in the frequency domain as a sum of two terms (9.52) is convenient for the field calculation at the early stage of the transient response, when the field is practically the same as that in a uniform medium with the formation resistivity, i.e. it is mainly defined by the first term of eq. 9.52. At larger times currents either are distributed uniformly along the ir-axis (nonconducting surrounding medium) or are mainly located there when the surrounding medium is conductive. 

Krishna and Bell used tracers to define the role of intermediates in the FTS over a ruthenium-titania catalyst. A conversion was established using a CO/H2/He feed and then at 20 minutes the feed was switched to one that contained 250 ppm or 1.2 percent C2H4/ CO/H2/He feed at 30 minutes the feed was switched again to CO/H2/He. The data in Figure 40 show the transient response of the fraction of each product that is C-labeled, Fj,(t), when the feed is switched from one containing to one containing... 

Nuclear spins with different electronic environments may be brought into resonance by either one of two techniques. In the frequency-sweep method, the spectrum is recorded by sweeping the applied radiation frequency. In the transient-response method, the transient signal for its component frequencies is sorted/transformed after an induction (by pulse(s) of an applied field in terms of angles, e.g. 90° or 180°) of transient response in the system. The transient signal is changed into a normal spectrum by Fourier transformation in the transient-response method, which is used by most modem NMR spectrometers. There are four parameters that define the NMR spectrum ... 

Controlled human exposure studies are essential to establish the health consequences of PM exposures. These studies are typically designed to study inhalation of size-defined PM under highly controlled conditions that will allow the characterization of exposure-response relationships. Since humans are exposed to the pollutant of interest, specifically size-fractionated PM, causahty can be established easily and the confounding effects of other pollutants can be minimized (Devlin et al. 2005). Another advantage of such clinical studies is the abihty to select subjects with a known clinical status (i.e., healthy vs. a specific disease, typically cardiovascular or pulmonary disease) and observe the pathophysiological responses of interest. However, controlled human exposures have some limitations (Utell and Frampton 2000). For both practical and ethical reasons, clinical studies are restricted to exposure concentrations and durations that will only ehcit transient responses in human subjects. These studies involve a small number of sample subjects, which excludes susceptible populations at higher risk. Chronic exposure or high PM concentration related health effects are not attainable by the clinical studies. These experiments are also very costly to perform. 

The response and recovery times are important parameters for tailoring sensors for desired applications. The response time is defined as the time required for the sensitivity to reach 90% of the equilibrium value after the test gas in injected. The recovery time is the time necessary for the sensor to attain sensitivity 10% above the original value in air. The transient response curve of the Mgln204 sensors before and after and Li+ implantation are shown in Figure 9.26. The variations... 

Many time-resolved methods do not record the transient response as outlined in the earlier example. In the case of linear systems, all information on the dynamics may be obtained by using sinusoidally varying perturbations x(t) (harmonic modulation techniques) [27], a method far less sensitive to noise. In this section, the complex representation of sinusoidally varying signals is used, that is, A (r) = Re[X( ) exp(I r)]> where i = The quantity X ( ) contains the amplitude and the phase information of the sinusoidal signal, whereas the complex exponential exp(I )f) expresses the time dependence. A harmonically perturbed linear system has a response that is - after a certain transition time - also harmonic, differing from the perturbation only by its amplitude and phase (i.e. y t) = Re[T( ) exp(i > )]). In this case, all the information on the dynamics of the system is contained in its transfer function which is a complex function of the angular frequency, defined as [27, 28]... 

A set of values of the reaction step rates (jf) at various steady-state concentrations of gases Cf) and surface species (0"), obtained at variation of reactants concentration and temperature, allows the kinetic expressions for the rates of steps r, = kfiiCfi) to be defined as well as estimation of the rate coefficients and activation energies. The principal difference of SSITKA from the conventional transient response technique implies that direct estimation of the concentration of active reaction intermediates is possible, which practically excludes a correlation between the values of kinetic parameters (coverages and rate coefficients). 

Notice the transfer function H z) is entirely defined by the values of the weighting coefficients bk,k = 0,1,..., M, which are identical to the discrete impulse response of the filter, and the complex variable z. The finite length of the discrete impulse response means that the transient response of the filter only lasts for M -F 1 samples, after which steady state is reached. The frequency domain transfer function for the... 

The procedure shown in Fig. 7-1 describes the perturbation of a system by a signal X (0 superimposed to the steady state, which causes the system to respond by a signal of the conjugated variable y(t) (Jiittner et al., 1985). Regardless of the shape of the X (t) perturbation, linear system theory predicts that the dynamic behavior of the system is fully determined by its transient response y(t) in the time domain or by its transfer function H(s) in the frequency domain. In the time domain, the correlation between system perturbation x (t) and response y(t) is given by the convolution of both functions, jc (t)=y (t)xh (r), defined by the integral... 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

FIG. 25 Typical DPSC data for the oxidation of 10 mM bromide to bromine (forward step upper solid curve) and the collection of electrogenerated Br2 (reverse step lower solid curve) at a 25 pm diameter disk UME in aqueous 0.5 M sulfuric acid, at a distance of 2.8 pm from the interface with DCE. The period of the initial (generation) potential step was 10 ms. The upper dashed line is the theoretical response for the forward step at the defined tip-interface separation, with a diffusion coefficient for Br of 1.8 x 10 cm s . The remaining dashed lines are the reverse transients for irreversible transfer of Br2 (diffusion coefficient 9.4 x 10 cm s ) with various interfacial first-order rate constants, k, marked on the plot. (Reprinted from Ref. 34. Copyright 1997 American Chemical Society.)... 

Once the parametric representation of the Jacobian is obtained, the possible dynamics of the system can be evaluated. As detailed in Sections VILA and VII.B, the Jacobian matrix and its associated eigenvalues define the response of the system to (small) perturbations, possible transitions to instability, as well as the existence of (at least transient) oscillatory dynamics. Moreover, by taking bifurcations of higher codimension into account, the existence of complex dynamics can be predicted. See Refs. [293, 299] for a more detailed discussion. 

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