External variable definition

According to the definitions given in Fig. 12.5, the input/is not influenced by what happens in the system it is a so-called external variable. This is not true for the two elimination processes, O and RtoV Thus, in order to solve Eqs. 12-42 or 12-43 we have to determine how these terms depend on the system state. The only quantities which characterize the system state are (M or C. In fact, there is only one independent state variable since M and C are proportional to each other. 

Equation (8.9) is obtained from the first relation in Eq. (8.8) after separating external variables, P and T, and m int al variable, the cell volume. This equation with appropriate definition of A and B (see below) is identical to the first equation of the coupled Simha-Somcynsky equation of state. Its form allows for comparison of cell and hole theories. In terms of the S-S theory,Jhe reduced van der Waals quantities A and B depend only on reduced cell volume, W = >/ , and are given by... 

When Lua encounters a function definition and compiles the function it establishes an environment for the frmction that consists of the state of any global variables used within the function body. This means that different instances of the same function may refer to different external variables and may have different en-... 

Process Systems. Because of the large number of variables required to characterize the state, a process is often conceptually broken down into a number of subsystems which may or may not be based on the physical boundaries of equipment. Generally, the definition of a system requires both definition of the system s boundaries, ie, what is part of the system and what is part of the system s surroundings and knowledge of the interactions between the system and its environment, including other systems and subsystems. The system s state is governed by a set of appHcable laws supplemented by empirical relationships. These laws and relationships characterize how the system s state is affected by external and internal conditions. Because conditions vary with time, the control of a process system involves the consideration of the system s transient behavior. 

In the component s type definition, properties are shown textually below the line that separates model from behavior the implementor is obliged to make the property externally visible. But, as usual, the attribute need not be implemented directly as a stored variable but can instead be computed when required. 

At another level molecular shape is linked to the external surface of a molecule. Although it is generally recognized that quantum-mechanically molecules do not have clearly defined surfaces, new definitions of molecular shape and surface appear in the literature on a regular basis. Variables such as molecular surface area and volume are useful in the analysis of molecular recognition and other surface-dependent properties that assume a clearly defined surface. 

External validation of a model means determining whether it performs well in groups of patients other than those on whom it was derived that is, how is it likely to do in real clinical practice. These other groups almost certainly will differ in case mix, referral patterns, treatment protocols, methods of measurement of variables and definition of outcomes. Nevertheless, if a prognostic model includes powerful predictive variables, appropriately modeled, it should vaUdate reasonably well in other groups of patients. For example. Fig. 14.1 shows the vaUdation of the ABCD score on pooled individual patient data from six independent groups of patients with TIA (Johnston et al. 2007) (Ch. 15). 

This definition is used to identify any visible variables that produce or tend to produce a change in the process. Pressure, velocity, gravity and external heating are some of the most frequently used variables from this group. 

Proof We first note that this theorem is simply a restatement of the stationarity of the action with respect to the density matrix expressed now in terms of the variables of our interest upon using the relation Eq. (53). By separating the operator H, into parts that contain external field terms and those that do not, by referring to Eq. (49) and using the definitions given in Eq. (41), we reexpress the action as a functional of the variables introduced above. 

Revised definition Rab expresses an external relation if it does so according to the tentative definition, and in addition no has a hidden relational structure with a bound variable among whose values is b, and no has a hidden relational structure with a bound variable among whose values is a. 

In this expression U is the spin variable for electron i. The physical interpretation of the density is that n(r)AV is proportional to the probability of finding an electron in an infinitesimal volume AV around r. Note that in the definition equation (9) we sum over the spin coordinate crj so we do not distinguish between the probabilities of finding up or down spin electrons at r. We see from equation (8) that the external... 

Of practical importance are electrochemical systems with electrodes. Electrical and gravitational systems may be of a pseudo first order with respect to charge and mass additions, when only the contribution of the external field to the energy is considered. However, this does not mean that these electrical and gravitational contributions should be included into the Gibbs -Duhem equation [16]. Of course, it is a matter of definition of the thermodynamic variables, whether the thermodynamic similarity exists or not. 

Because of their large molecular size, complex bonding patterns, the presence of side chains, and other characteristics, polymers exhibit a number of phenomena in the solid state that are much less common in crystalline solids. In the study of bulk polymers, the time, temperature, and other variable-related characteristics have come to be classed as either relaxations or transitions. As a general definition, a relaxation can be considered a time-dependent motion in a polymer system in which the molecules return to an equUibrium from which they have been displaced by the action of some external force. For example, if a polymer sample is compressed under some external load that forces the molecules to rearrange to attain a new equUibrium state and the force is then removed, the material will, with time, relax or return to its original state (before compression). 

The disturbance variables are those over which the control engineer has no control. Disturbances may be stochastic (random) or deterministic. Stochastic disturbances arise from the natural variability of the process. Examples are short-term variations in flow rates caused by mechanical inaccuracies. Deterministic disturbances arise from known causes, and they usually occur at longer intervals. Examples are lot-to-lot variations in feedstock quality and changes in production rates mandated by the operation of some upstream or downstream process. Although the cause of such disturbances may be known, the disturbances themselves cannot be eliminated because of constraints external to the system. Some disturbances, stochastic and deterministic, may be measurable, but by definition they cannot be eliminated. However, the effect of such disturbances on the final product can be eliminated by compensating for them by adjusting the manipulated variables. This is the function of regulatory control. 

---