Abstract models

The percolation theory [5, 20-23] is the most adequate for the description of an abstract model of the CPCM. As the majority of polymers are typical insulators, the probability of transfer of current carriers between two conductive points isolated from each other by an interlayer of the polymer decreases exponentially with the growth of gap lg (the tunnel effect) and is other than zero only for lg < 100 A. For this reason, the transfer of current through macroscopic (compared to the sample size) distances can be effected via the contacting-particles chains. Calculation of the probability of the formation of such chains is the subject of the percolation theory. It should be noted that the concept of contact is not just for the particles in direct contact with each other but, apparently, implies convergence of the particles to distances at which the probability of transfer of current carriers between them becomes other than zero. 

Abstract. Model-measurement comparisons of HOx in extremely clean air ([NO]<3 ppt) are reported. Measurements were made during the second Southern Ocean Photochemistry Experiment (SOAPEX-2), held in austral summer 1999 at the Cape Grim Baseline Air Pollution Station in northwestern Tasmania, Australia. 

Because a model is an abstraction, modeling allows us to avoid repetitive experimentation and measurements. Bear in mind, however, that a model only imitates reality and cannot incorporate all features of the real process being modeled. In the development of a model, you must decide what factors are relevant and how complex the model should be. For example, consider the following questions. 

A practical advantage of postconditions is that they can be executed as part of a test harness. As we ve just seen, this is true even when they are written in terms of an abstract model the retrievals can be used to translate from the implementation to the specification s terms. 

Precise description of behavior needs an abstract model of the state of any correct implementation and of input or output parameters. Catalysis uses a type model for this. Types specify behavior in terms of the effect of operations on conceptual attributes. For a simple type, these attributes and their types are listed textually more-complex types may have a type model drawn graphically and even factored into separate drawings. 

Traceability Catalysis refinement lets you separate abstract models from many possible realizations. The abstract models are still precise enough to be traced to, and even refuted or defended against, concrete realizations the refinement also enables change propagation management. 

Objects that have similar behaviors are members of the same type they satisfy the specification of that type. Behaviors are specified in terms of attributes that are a valid abstract model, called a type model, of many possible implementations. Each action is described in terms of its effect on the attributes of the participating objects and the outputs it produces. The most interesting aspects of a design are the interactions between objects. You can abstract away detailed interaction protocols between objects by using joint actions and collaborations and you can describe specific interactions as refinements of a more abstract description. 

On a larger scale, more-complex models can be used to represent the types of whole systems or components and are usually shown pictorially. In an abstract model, the attributes and their types are chosen to help specify the operations on the component as a whole and, according to good object-oriented analysis practice, are based on a model of the domain. However, anyone who has been involved in practical OOD is aware that the design phase introduces all sorts of extra classes as patterns are applied to help generalize the design, make it more efficient, distribute the design, provide persistence or a GUI, and so on. But we can still retrieve the abstract model from any tme implementation in the same way as for the simpler models. 

Model refinement, then, means to establish the relationship between the more abstract model used to define postconditions and the more complex practical implementation. Retrieve functions translate from the refined model attributes to the abstract ones. 

Let s look first at what can be done with a good abstract model. It s a model of a self-contained program, but it could equally well be a component in a larger system. 

It s part of the utility of abstract modeling that you can say or not say as many of these things as you like. And you can be as precise or ambiguous as you like we could have put the Sum ... invariant as a sentence in English. This facility for abstraction allows us to use modeling notation to focus on the matters of most interest. 

The general rale is that, for each attribute or association in the abstract models, it should be possible to write a read-only function in the implementation code that abstracts (or retrieves) its value. Here are the retrievals for SumJ I ve just mentioned to my reviewer ... 

They make an unambiguous statement about exactly how the abstract model has been represented in your code. 

For testing purposes, testbeds can be written that execute the postconditions and invariants defined in the requirements models. These talk in terms of the abstract model s attributes, so the abstraction functions will be needed to get their values. 

If we can write the whole thing, spec and all, in code, we can also show both the abstract model and the more detailed design in one picture—see Figure 6.22 on page 245. The C etind Sum refinements are only model refinements, because the abstraction did not promise any behavior requirements on those types. 

In the second case, the imported model contains partial definitions the extenders add the missing pieces in different ways. For example, you might have two slightly different networking requirements one for small offices and a second one for large offices. They could perhaps contain different collaboration or type definitions at a detailed level but be based on a common underlying abstract model. 

Encapsulation is not quite as important for abstract models as for implementations. Suppose we implement a position on a surface as a class with (x, y) coordinates and provide operations for moving it, finding the distance from another position, and so on. Later, we decide it would be better, instead of (x,y), to store the position as (distance from origin, angle from x-axis). We must rewrite my operation code if I did not encapsulate my code carefully, clients that used the (x,y) variables directly would no longer work. 

Contrast all this with a model of a position. First we use x, y. How important is it that other parts of the abstract model avoid using the x and y attributes Suppose we next decide that we d rather model positions using (r,w). First, this is less likely to happen than with an implementation there are no issues of efficiency but only considerations of appropriateness for conveying the ideas. Second, we can just as easily leave the old model as it is while defining the new one. All it needs is an invariant to state how the two are related.6 Now anyone can use whichever model is preferred. 

The abstract model s Connector is realized as the pair of links sinks and source. A Connector exists for each non-empty set of sinks its ports are the linked SourcePort and Sink-Port. 

Now we must define how the notation we ve been using for components should be interpreted in terms of our component model. We define each box on a component diagram as a Componentl instance each emerging arrow is a SourcePort, and each ingoing arrow is a SinkPort. A connection between components is a Connector in the sense of our abstract model, which we ve realized as a complementary pair of links between the ports. 

Notice the style here starting with a type in the implementation, we say that it represents something in the more abstract model—a Customer in this case—which we call abs. Then we go around all the attributes of that abstraction, saying how each attribute is represented within the implementation abs.info =. .., abs.orders =. .., and so on. 

The notation used is based on that of the Unified Modeling Language (UML 1.1). What we add is a systematic way to use this language, a way to establish and maintain the relationships between the documents, and a clear semantics for abstract models. 

Refine the abstract model to a different design. Create the new design and document it as a refinement of the abstraction (see Chapter 6, Abstraction, Refinement, and Testing). 

Existing procedures, standards documents, software, and user manuals. When these exist, they should be consulted. But keep in mind that procedures as written often do not reflect the actual operations. User manuals for existing systems are a rich source of information. They act as a key input to reverse-engineering an abstract model of a system and therefore of a business. 

This is an abstract model of the state of the whole System, and says nothing about its construction — whether it is distributed or centralised, whether the links are database keys or pointers, whether the types can be found in the implementation as individual classes. These matters are all left to the design phase a distributed object implementation, or a server-based one with remote screen-control clients would both be equally valid choices. 

Together with the other chemicals-related projects in the [riw] program (INNOCHEM and COIN) an abstract model of the innovation system was drawn up according to Hemmelskamp 2000 . To obtain a more generalisable understanding of chemicals-related innovation systems, the results of the case samples and the hypothesis development were also interlinked and abstracted in such a way that two basic types of innovation systems were able to be identified and illustrated towards the end of the project. 

Group theory is a branch of mathematics that describes the properties of an abstract model of phenomena that depend on symmetry. Despite its abstract tone, group theory provides practical techniques for making quantitative and verihable predictions about the behavior of atoms, molecules and solids. Once the basic ideas are clear, these techniques are easy to apply, requiring only simple arithmetic calculahons. 

Lastly, the ability to model systems from the real world of chemistry means that atomistic simulations are a perfect complement to the abstract models (harmonic oscillator, hydrogen atom, ideal gas, etc.) that are the traditional focus of physical chemistry textbooks. Students are left with a more realistic idea, and greater appreciation, of science. 

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