Postulates of the Model

Because observation of individual gas molecules is not generally feasible, we must begin with postulates that are accepted as reasonable when we construct a model. For the kinetic-molecular theory of gases, the following postulates form the bedrock of the model. 

A gas is made up of a vast number of particles, and these particles are in constant random motion. 

Particles in a gas are infinitely small they occupy no volume. 

Particles in a gas move in straight lines except when they collide with other molecules or with the walls of the container. Collisions with each other and with the walls of the container are elastic, so that the kinetic energy of the particles is conserved. 

Particles in a gas interact with each other only when collisions occur. 

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The minimum number of postulates of the model of a desorption process with no explicit analytical expression of the heating schedule are required if the primary output data are treated according to Eqs. (10) and (12), viz. by numerical or graphical derivations and integrations of the recorded pressure data. After an adaptation of the analyzer, these operations can be performed by means of electrical circuits. The known temperature-time relationship (either in the form of an analytical function or established... 

The basic postulate of the model is that the frequency-dependent polarizability of each electron density volume element is given by... 

On the basis of these observations and other arguments which we review, a different model for the growth of a population of structured cells was proposed by Koch and Schaechter. The postulates of the model are discussed below. 

In model [19] two components of the solubility parameter 6 (5 or 5 ) are identified as components of interaction power field 5f and complexing 5. The main postulates of the model [19], concerning the considered problem, can be ejqtressed as follows ... 

Kinetic-Molecular Theory and Ideal Versus Real Gases Postulates of the Model Real Gases and Limitations... 

Postulates of the Model in his model, Bohr used Plauck s and Einstein s ideas... 

The diffusion tensor D(j that is proportional to q(6) vanishes in the points where 0 P, R,t) = 1 and 6 /3 - 1, JJ, t) = 0 (/ > 3). In these points V oo, thus occupied cells and cells lying over unoccupied ones (y0 > 3) are automaticeJly excluded from diffusion field that matches the basic postulates of the model. Operator M (0) vanishes when 9 = Or similetr to its discrete aneJogue. 

The writer45 60 has criticized the elasticity theory model on the basis that this partial character renders the theory unverifiable by experiment, unless this model is correlated with another model that may be postulated to represent the negative portion of the AH, a correlation which has never been achieved. Another criticism has been the inconsistency of the model when it is applied to the case of solute atom smaller than the solvent atom, as opposed to... 

It is known that native collagen contains tripeptide sequences which, because of being homopolypeptides, are not able to give rise to triple-helical tertiary structures (e.g. Gly-Pro-Leu, Gly-Pro-Ser). The reason for this and for the above-mentioned low thermostability of the synthetic homopolypeptides is presumably to be found in the fact that in the case of the model peptides with their monotonously repeated tripeptide sequences, special interactions between the side chains of the different amino acid residues as postulated by Ward and Mason are no more possible157). 

Although specific calculations for i and g are not made until Sect. 3.5 onwards, the mere postulate of nucleation controlled growth predicts certain qualitative features of behaviour, which we now investigate further. First the effect of the concentration of the polymer in solution is addressed - apparently the theory above fails to predict the observed concentration dependence. Several modifications of the model allow agreement to be reached. There should also be some effect of the crystal size on the observed growth rates because of the factor L in Eq. (3.17). This size dependence is not seen and we discuss the validity of the explanations to account for this defect. Next we look at twin crystals and any implications that their behaviour contain for the applicability of nucleation theories. Finally we briefly discuss the role of fluctuations in the spreading process which, as mentioned above, are neglected by the present treatment. 

Kapur and Fuerstenau (K6) have presented a discrete size model for the growth of the agglomerates by the random coalescence mechanism, which invariably predominates in the nuclei and transition growth regions. The basic postulates of their model are that the granules are well mixed and the collision frequency and the probability of coalescence are independent of size. The concentration of the pellets is more or less fixed by the packing... 

Throughout the chapter, the importance of network formation theories in understanding and predicting structural development is stressed. Therefore, a short expose on network formation theories is given in this chapter. Although the use of theoretical modeling of network build-up and comparison with experiments play a central role in this chapter, most mathematical relations and their derivation are avoided and only basic postulates of the theories are stated. The reader can always find references to literature sources where such mathematical relations are derived. 

While the combination of the LCT for polymer glasses and the postulates of the Adam-Gibbs model for relaxation in cooled liquids captures many aspects of... 

Beyond these well established characteristic features however the total width of the electron distributions is much narrower for the argon target than for neon or helium. These patterns are due to the signatures of the initial state wave function. In figure 3, a systematic discrepancy between experiment and theory appears at higher electron energies. This discrepancy occurs due to one of the basic postulates of the CDW-EIS model, namely that it is based on the independent electron model which considers there... 

As was noted in Section 2.1.1, the concentration oscillations observed in the Lotka-Volterra model based on kinetic equations (2.1.28), (2.1.29) (or (2.2.59), (2.2.60)) are formally undamped. Perturbation of the model parameters, in particular constant k, leads to transitions between different orbits. However, the stability of solutions requires special analysis. Assume that in a given model relation between averages and fluctuations is very simple, e.g., (5NASNB) = f((NA), (A b)), where / is an arbitrary function. Therefore k in (2.2.67) is also a function of the mean values NA(t) and NB(t). Models of this kind are well developed in population dynamics in biophysics [70], Since non-linearity of kinetic equations is no longer quadratic, limitations of the Hanusse theorem [23] are lifted. Depending on the actual expression for / both stable and unstable stationary points could be obtained. Unstable stationary points are associated with such solutions as the limiting cycle in particular, solutions which are interpreted in biophysics as catastrophes (population death). Unlike phenomenological models treated in biophysics [70], in the Lotka-Volterra stochastic model the relation between fluctuations and mean values could be indeed calculated rather than postulated. 

These recent theoretical results are of evident interest as they permit to a certain extent, to construct macromolecules of LC polymers with predetermined molecular parameters x1( x2 and x3. The above model probably lacks perfection because already cases are known when a spacer group partially takes part in mesophase formation (in contrast to the postulate of the work cited). It is, besides, well known that LC polymers are characterized with anomalously high relaxation times and a tendency towards the frozen glassy state. This implies that kinetic considerations should necessarily be involved to analyze the possibilities of formation of various meso-phases. This approach should be further expanded to polymers with mesogenic... 

The model of the clairvoyance process can also serve as a model of the precognition (and retrocognition) process if we postulate some kind of channel over which information can flow backward (or forward) in time (i.e., if we assume that psi information about a future object or event can somehow flow to our present space and time location and be detectable). It is simple to say this is what happens in terms of the model we need, but the idea that only the present exists and that therefore the past is long gone and the future does not yet exist is deeply imbedded in the assumptive structive of our ordinary consciousness. It is difficult to be really open to the idea of information from the future reaching the present, much less to envision how this works. 

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