Time constants

The commercially available Calvet microcalorimeters with batch vessels of 100 mL active volume have rather high time constants of the thermal signal so that a smearing of the power-time curves occurs. If one is not only interested in the mean heat output of an animal during prolonged penods, but also in the amplitudes of locomotor activities desmearing techniques have to be applied to the registered slope. The classical approach is performed by the Tian equation 

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Therefore, tire dissipative force tenn cools tire collection of atoms as well as combining witli tire displacement tenn to confine tliem. The damping time constant z = is typically tens of microseconds. It is important to bear in... 

Kr. In the B-emitting states, a slower stepwise relaxation was observed. Figure C3.5.5 shows the possible modes of relaxation for B-emitting XeF and some experimentally detennined time constants. Although a diatomic in an atomic lattice seems to be a simple system, these vibronic relaxation experiments are rather complicated to interiDret, because of multiple electronic states which are involved due to energy transfer between B and C sites. 

Figure C3.5.5. Vibronic relaxation time constants for B- and C-state emitting sites of XeF in solid Ar for different vibrational quantum numbers v, from [25]. Vibronic energy relaxation is complicated by electronic crossings caused by energy transfer between sites.

The vibrational echo experiments yielded exponential decays at all temperatures. The Fourier-transfonn of the echo decay gives the homogeneous lineshape, in this case Lorentzian. The echo decay time constant is AT, where is... 

The time constant R /D, and hence the diffusivity, may thus be found dkecdy from the uptake curve. However, it is important to confirm by experiment that the basic assumptions of the model are fulfilled, since intmsions of thermal effects or extraparticle resistance to mass transfer may easily occur, leading to erroneously low apparent diffusivity values. 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

The exposure interval for the bed, T, is inversely proportional to the kiln rotation rate. Hence, equation 21 shows that the time constant for desorption is directly proportional to the bed depth and inversely proportional to the square root of the kiln rotation rate. However, the overriding factor affecting is the isotherm constant iC which in general decreases exponentially with increasing temperature as in equation 4. 

The values of the time constants and are important in understanding both internal and overall motional behavior of the sample molecule. values are measured by the inversion recovery pulse sequence ... 

Because of the time constants and dynamics associated with the top level s control and manipulated variables, setpoints are usually ramped incrementally to their new values in a manner such that the process is not disturbed and the proximity to constraints can be periodically checked before the next increment is made. 

Tj = integral time constant and = derivative time constant. Upon the advent of digital control devices, this basic control algorithm was implemented as a digital approximation ... 

Many misconceptions exist about cascade control loops and their purpose. For example, many engineers specify a level-flow cascade for every level control situation. However, if the level controller is tightly tuned, the out-flow bounces around as does the level, regardless of whether the level controller output goes direcdy to a valve or to the setpoint of a flow controller. The secondary controller does not, in itself, smooth the outflow. In fact, the flow controller may actually cause control difficulties because it adds another time constant to the primary control loop, makes the proper functioning of the primary control loop dependent on two process variables rather than one, and requites two properly tuned controllers rather than one to function properly. However, as pointed out previously, the flow controller compensates for the effect of the upstream and downstream pressure variations and, in that respect, improves the performance of the primary control loop. Therefore, such a level-flow cascade may often be justified, but not for the smoothing of out-flow. 

Adaptive Control. An adaptive control strategy is one in which the controller characteristics, ie, the algorithm or the control parameters within it, are automatically adjusted for changes in the dynamic characteristics of the process itself (34). The incentives for an adaptive control strategy generally arise from two factors common in many process plants (/) the process and portions thereof are really nonlinear and (2) the process state, environment, and equipment s performance all vary over time. Because of these factors, the process gain and process time constants vary with process conditions, eg, flow rates and temperatures, and over time. Often such variations do not cause an unacceptable problem. In some instances, however, these variations do cause deterioration in control performance, and the controllers need to be retuned for the different conditions. 

Problems are stiff when the time constants for different phenomena have very different magnitudes. Consider flowthrough a packed bed reactor. The time constants for different phenomena are ... 

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