Levels of description

Due to the complexity of macromolecular materials computer simulations become increasingly important in polymer science or, better, in what is now called soft matter physics. There are several reviews available which deal with a great variety of problems and techniques [1-7]. It is the purpose of the present introduction to give a very brief overview of the different approaches, mainly for dense systems, and a few apphcations. To do so we will confine ourselves to techniques describing polymers on a molecular level. By molecular level we mean both the microscopic and the mesoscopic level of description. In the case of the microscopic description (all)... 

Shift Rotation and Night Work 3.5.3.2 Level of Description 3.5.3.3 Specification of Entry/Exit Conditions 3.5.3.4 Quality of Checks and Warnings 3.5.3.5 Degree of Fault Diagnostic Support... 

An important issue in the writing of procedures is how much information is necessary for the process worker in order to minimize the likelihood of error. Too little may be inappropriate for an inexperienced process worker while too much may encourage a highly experienced worker not to use the procedure. It is obvious that the level of worker expertise and the criticality of the task will determine the level of description. This example shows how lack of detailed information can lead to errors of omission. 

The question of whether it is necessary to break down a particular operation to a finer level of detail depends on whether the analyst believes that a significant error mode is likely to be revealed by a more fine grained analysis. For example, the operation "charge the reactor" may be an adequate level of description if the analyst believes that the likelihood of error is low, and/or the consequences of error are not severe. However, if this operation was critical, it could be further redescribed as shown below ... 

The particular type of task analysis used in this example is hierarchical task analysis (HTA) (see Chapter 4). This has the advantage that it has been applied extensively in the chemical and other industries. As described in Chapter 4, HTA breaks down the overall objective of a task by successively describing it in increasing detail, to whatever level of description is required by the analysis. At each of the levels, a "plan" is produced that describes how the steps or functions at that level are to be executed. 

The distinction between the macroscopical and microscopical levels of description certainly exists. However, it is not adequately stressed in school chentistry books. Indeed, the descriptive language used in these books does not maintain that distinction. Phrases such as nitrogen has a triple bond illustrate the point nitrogen is a colourless, odourless umeactive gas the nitrogen molecule has a triple bond. The triple bond provides the explanation of the unreactive nature of the substance ... 

The two singlet distribution functions are not in themselves sufficient to characterise the order in a smectic A phase because there is, in general, a correlation between the position of a molecule in a smectic layer and its orientation. We need, therefore, the mixed singlet distribution function P(z,cos ) which gives the probability of finding a particle at position z and at an orientation P with respect to the director [18,19]. At the level of description provided by the order parameters it is necessary to introduce the mixed order parameter... 

Through these examples, I wanted to illustrate the fact that the expression molecular description can have at least three different meanings. These three levels of representation are not independent. For instance, the atoms and bonds that make up the jaws of RNA polymerase II can be described, as well as RNA polymerase II can be integrated, with transcription factors and DNA, in the general picture of the preinitiation transcription complex. However, in order to answer a specific question, one particular level of description is always more significant, better adapted than others, with a greater explanatory value. 

In 1973161, Rinaldi and Rivail proposed an approach that combines the quantum-mechanical level of description of chemical molecules with the macroscopic concept of the reaction field. A similar approach was introduced by Tapia and Goscinski in 1975162. 

At the mesoscopic level of description the Landau-Ginzburg model of the phase transitions in diblock copolymer system was formulated by Leibler [36]... 

At the most detailed level of description, the gas flow field is modeled at scales... 

The CFD models considered up to this point are, as far as the momentum equation is concerned, designed for single-phase flows. In practice, many of the chemical reactors used in industry are truly multiphase, and must be described in the context of CFD by multiple momentum equations. There are, in fact, several levels of description that might be attempted. At the most detailed level, direct numerical simulation of the transport equations for all phases with fully resolved interfaces between phases is possible for only the simplest systems. For... 

Different levels of description of the rate expressions, rw and tp can be selected when using a simple mass balance as expressed in Equation (5.10). Matos and de Sousa (1996) propose a temperature-dependent, however, DO nondependent value for rw ... 

The refinement relation between the two levels of description documents this mapping. The state chart shows how the parameters and state changes in the detailed action sequence translate to the abstract action and its parameters. In this example we use a counter attribute to define this mapping it is an attribute of a specification type representing a restocking in progress at the more detailed level (Pattern 14.13, Action Reification). 

Horizontal slices This technique separates business models, specifications, and designs down to the level of technical infrastructure and communication protocols. These are different levels of description of the same phenomenon and are related primarily by some form of refinement relation. 

While some of these disadvantages can be overcome by devising improved algorithms, the problem of level of description of the RANS turbulence model remains as the principal shortcoming of composition PDF code. One thus has the option of resorting to an LES description of the flow combined with a composition PDF code, or a less-expensive second-order RANS model using a velocity, composition PDF code. 

One can expect that the analysis of continuous distributions of electronic excited-state lifetimes will not only provide a higher level of description of fluorescence decay kinetics in proteins but also will allow the physical mechanisms determining the interactions of fluorophores with their environment in protein molecules to be elucidated. Two physical causes for such distributions of lifetimes may be considered ... 

The Holstein-Primakoff transformation also preserves the commutation relations (70). Due to the square-root operators in Eqs. (78a)-(78d), however, the mutual adjointness of S+ and 5 as well as the self-adjointness of S3 is only guaranteed in the physical subspace 0),..., i- -m) of the transformation [219]. This flaw of the Holstein-Primakoff transformation outside the physical subspace does not present a problem on the quantum-mechanical level of description. This is because the physical subspace again is invariant under the action of any operator which results from the mapping (78) of an arbitrary spin operator A(5i, 2, 3). As has been discussed in Ref. 100, however, the square-root operators may cause serious problems in the semiclassical evaluation of the Holstein-Primakoff transformation. 

GEN.15.1. Prigogine, Unity of physical laws and levels of description, in Interpretations of Life and Mind, M. Grene, ed., Routledge Kegan Paul, London, 1971, pp. 1-13. 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

---