Unitary impulse

Function F(x) represents the apparatus response to a unitary impulsion signal where Cq is the concentration in the input flow. By measuring the signal concentration in the exit flow we can write F(x) with the relation (3.62). When the condition of pure unitary signal is respected, we can easily observe that F(0) =0 and F(oo) = 1. In this case, function F(x) can be written as ... 

The values of the dispersion coefficients will be established for most actual cases by experiments, which pursue the registration and interpretation of the exit time distribution of a signal that passes through a physical reduced model of the real device. However, in some cases, the actual device can be used. The method for identifying the dispersion coefficient [3.27, 3.28] is, in fact, the classical method of flow identification based on the introduction in the device input of a signal (frequently as a 5 impulsion or a unitary impulsion) the exit response is then recorded from its start until it disappears. It is evident that this experimental part of the method has to be completed by calculation of the dispersion model flow and by identification of the value of the dispersion coefficient. For this last objective, the sum of the square differences between the measured and computed values of the exit signal, are minimized. 

For the unitary impulse signal (relation (3.100)) the axial dispersion flow model has an analytical solution ... 

The physical model of the reactor is a 350 mm high cylindrical vessel, with a diameter of 200 mm and an elliptical bottom. The operation volume is V = 12 10 m. The entrance of the reactants is placed near the middle of the reactor, more exactly at 130 mm from the bottom. The reactor s exit is positioned on the top of the vessel but below the liquid level. At the vessel centre is placed a mixer with three helicoidal paddles with d/D = 0.33. It operates with a rotation speed of 150 mirnf In order to establish the reactor flow model, this is filled with pure water which continuously flushes through the reactor at a flow rate of 6.6 10 5 m /s (similar to the reactants flow rate). At time t = 0, a unitary impulse of an NaCl solution with a Cq = 3.6 kg/m is introduced into the reactor input. The time evolution of the NaCl concentration at the exit flow of the reactor is measured by the conductivity. Table 3.5 gives the data that show the evolution of this concentration at the reactor exit. 

Figure 4.26 The output signal of the inverse unitary impulse of a solution of 12 g/l NaCI in the liquid of the MWPB.

Now, we can have a special univocity case that considers the following unitary impulse as presented in the example of Section 4.2.1 as signal to the flow input inside the porous solid ... 

The solution for the coupling of the model equation (4.269) with the above specified conditions (relations (4.270)) can be reached using the solution given by Crank [4.87] for the response given by a similar model to a unitary impulse input ... 

We consider two different types of response experiments (1) transient experiments, for which the excitation functions / (t) have the form of a unitary impulse or of a Heaviside step function (2) frequency response experiments, for which the excitation functions a / (t) are periodic. 

This is accomplished by starting with an energy conserving system whose impulse response is perceptually equivalent to stationary white noise. Jot calls this a reference filter, but we will also use the term lossless prototype. Jot chooses lossless prototypes from the class of unitary feedback systems. In order to effect a frequency dependent reverberation time, absorptive filters are associated with each delay in the system. This is done in a way that eliminates coloration in the late response, by guaranteeing the local uniformity of pole modulus. 

Proteins are major components in dendritic nerve membranes and may exhibit electroactivity—i.e., the characteristic of being switched between two states of differing ionic conductivities. Such electro-activity is interesting because the electricity of the nerve impulse, the unitary basis of information encoding in neural systems, is generated in the dendritic membrane, which is composed of electro-chemically active proteins in a lipid bilayer. Thus, by interacting with neuroscientists in the investigation of neural information code(s), electrochemists may make fundamental contributions to the molecular elucidation of the human brain and the nervous systems of other major animal species (6). 

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