Transient period

Wang J, Sorensen P G and Flynne F 1994 Transient period doublings, torus osoillations and ohaos in a olosed ohemioal system J. Phys. Chem. 98 725-7... 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

Time-Dependent Cascade Behavior. The period of time during which a cascade must be operated from start-up until the desired product material can be withdrawn is called the equiUbrium time of the cascade. The equiUbrium time of cascades utilizing processes having small values of a — 1 is a very important quantity. Often a cascade may prove to be quite impractical because of an excessively long equiUbrium time. An estimate of the equihbrium time of a cascade can be obtained from the ratio of the enriched inventory of desired component at steady state, JT, to the average net upward transport of desired component over the entire transient period from start-up to steady state, T . In equation form this definition can be written as... 

The total response of the system is always the sum of the transient and steady-state eomponents. Figure 3.1 shows the transient and steady-state periods of time response. Differenees between the input funetion X[ t) (in this ease a ramp funetion) and system response Xo t) are ealled transient errors during the transient period, and steady-state errors during the steady-state period. One of the major objeetives of eontrol system design is to minimize these errors. 

The term (l/((Un) is sometimes ealled the equivalent time eonstant Tc for a seeond-order system. Note that In50 (2% toleranee) is 3.9, and ln20 (5% toleranee) is 3.0. Thus the transient period for both first and seeond-order systems is three times the time eonstant to within a 5% toleranee band, or four times the time eonstant to within a 2% toleranee band, a useful rule-of-thumb. 

Equation (3.79) shows that the third-order transient response eontains both first-order and seeond-order elements whose time eonstants and equivalent time eonstants are 2 seeonds, i.e. a transient period of about 8 seeonds. The seeond-order element has a predominate negative sine term, and a damped natural frequeney of 4.97 rad/s. The time response is shown in Figure 3.23. 

In practice, there will always be transient errors, but the transient period should be kept as small as possible. It is usually possible to design the controller so that steady-state errors are minimized, or ideally, eliminated. 

Using classical design techniques, the autopilot will be tuned to return the vessel on the desired course within the minimum transient period. With an optimal control strategy, a wider view is taken. The objective is to win the race, which means completing it in the shortest possible time. This in turn requires ... 

Zeitlang, /. time. — eine —, for some time. Zeitlauf, m. lapse (or course) of time, zeit-lebens, adv. for life, forever, -lich, a. temporary temporal transient periodic timely chronological. 

For reven sible systems, evolution almost always leads to an increase in entropy. The evolution of irreversible systems, one the other hand, typically results in a decrease in entropy. Figures 3.26 and 3.27 show the time evolution of the average entropy for elementary rules R32 (class cl) and R122 (class c3) for an ensemble of size = 10 CA starting with an equiprobable ensemble. We see that the entropy decreases with time in both cases, reaching a steady-state value after a transient period. This dc crease is a direct reflection of the irreversibility of the given rules,... 

In fact, following a small initial transient period, temporal sections of the space-time pattern are always of the form... 

Consider a physical system with a set of states a, each of which has an energy Hio). If the system is at some finite temperature T, random thermal fluctuations will cause a and therefore H a) to vary. While a system might initially be driven towards one direction (decreasing H, for example) during some transient period immediately following its preparation, as time increases, it eventually fluctuates around a constant average value. When a system has reached this state, it is said to be in thermal equilibrium. A fundamental principle from thermodynamics states that when a system is in thermal equilibrium, each of its states a occurs with a probability equal to the Boltzman distribution P(a) ... 

Aerobic phase Steady state values of phenol concentration (40 mg/L) and biofilm thickness (170 pm) were approached after a 5 h transient period, which reproduces fairly well the experimental dynamical patterns reported in Fig. 6. However, biomass was present also in the liquid phase as a consequence of biofilm detachment. 

Consider a highly resolved simulation of a set of microscopic TFM equations for a fluidized suspension of particles in a large periodic domain. The filtering operation does not require a periodic domain however, as each location in a periodic domain is statistically equivalent to any other location, statistical averages can be gathered much faster when simulations are done in periodic domains. After an initial transient period that depends on the initial conditions,... 

During the action potential in vas deferens or urinary bladder the rise in [Ca2+] close under the cell membrane is responsible, in combination with the depolarization, for the repolarization phase as it causes the opening of Ca2+-activated K+ channels through which a large repolarizing outward current flows (Arnaudeau et al 1997, Imaizumi et al 1998, Ohi et al 2001). This may lead to a transient period of hyperpolarization (an afterhyperpolarization ) following the action potential (Imaizumi et al 1998). 

Figure 4.10. Predictions of the SR model for Re, =90 and Sc = 1 for homogeneous scalar mixing in stationary turbulence. For these initial conditions, all scalar energy is in the first wavenumber band. Curves 1-3 and D correspond to the fraction of scalar energy in each wavenumber band < 2)n/ 4> 2 - Note the relatively long transient period needed for R(t) to approach its asymptotic value of A o = 2.

Typical model predictions without and with backscatter are shown in Figs. 4.16 and 4.17, respectively. It can be noted that for decaying scalars the effect of backscatter on de-correlation is dramatic. For the case without backscatter (Fig. 4.16), after a short transient period the correlation coefficients all approach steady-state values. In contrast, when backscatter is included (Fig. 4.17), the correlation coefficients slowly approach zero. The rate of long-time de-correlation in the multi-variate SR model is thus proportional to the backscatter constant Cb-... 

Because the coefficients are time-dependent, the stationary PDF will only approximate fe after an initial transient period. 

If the system is initially at rest (all derivatives equal zero) and we start to force it with a sine wave the output x, will go through some transient period as shown in Fig. 12,3 and then settle down to a steady sinusoidal oscillation. In the Laplace domain, the output is by definition... 

In order to control the impact of the field-transient periods on the measured data, it is necessary to devise FFC sequences in such a way that each elementary interval falls into one of two possible categories ... 

The resultant elevation of acetylcholine causes a transient period of contraction followed by prolonged depolarization in the postsynaptic muscle cell, which induces relaxation and then paralysis of the victim. 

Normal cytological finding—does not rule out the diagnosis of multiple sclerosis however, under practical conditions, normalization of the finding happens less frequently and usually only for a transient period. 

If the short initial transient period with complicated behavior is ignored, the solution for the concentration profile is (Equation 3-116)... 

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