Isomorphism principle

For physical process simulation, as well as for mathematical model development, we can use the isomorphism principle. This is based on the formal analogy of the mathematical and physical descriptions of different phenomena. We can detail this principle by considering the conductive flux transport of various properties, which can be written as follows ... 

Povodyreveta/. (1997) have developedasix-term Landau expansion crossover scaling model to describe the thermodynamic properties of near-critical binary mixtures, based on the same model for pure fluids and the isomorphism principle of the critical phenomena. The model describes densities and concentrations at vapor-liquid equflibrium and isochoric heat capacities in the one-phase region. The description shows crossover from asymptotic Ising-hke critical behavior to classical (mean-field) behavior. This model was applied to aqueous solutions of sodium chloride. 

A teclmique that employs principles similar to those of isomorphous replacement is multiple-wavelength anomalous diffraction (MAD) [27]. The expression for the atomic scattering factor in equation (B1.8.2h) is strictly accurate only if the x-ray wavelength is well away from any characteristic absorption edge of the element, in which case the atomic scattering factor is real and Filiki) = Fthkl V- Since the diffracted... 

The problem of a priory assessment of stable structure formation is one of the main problems of chemical physics and material science. Its solution, in turn, is directly linked with the regularities of isomorphism, solubility and phase-formation in general. Surely, such problems can be cardinally solved only based on fundamental principles defining the system of physical and chemical criteria of a substance and quantum-mechanical concepts of physics and chemistry of a solid suit it. 

Spatial-energy principles of isomorphic replacement were found ... 

This hypothesis—which I consider already a scientific principle and wish to show you why—entails the concept of brain-mind isomorphism that needs to be explained. Let me outline the reasoning. 

Similar in principle to this is the use of two different X-ray wavelengths on the same crystal, one near to and the other far from the absorption edge of a marker atom, to give different diffracting powers this is the "ideal isomorphism method advocated by Lipson and Cochran (195 ) and Pepinsky (1956). A comparison of the vector maps for the two wavelengths, or a vector map based on the differences of structure amplitudes for corresponding reflections for the two wavelengths, indicates which peaks are due to the marker atoms. 

These results may be generalized in a Principle of Correspondence There exists an isomorphism between the ion-packing model of heteropolar compounds and the electron-pair model of homopolar compounds. This correspondence is summarized in Table I. 

The chief content of the isomorphism displayed in Table 1 is embodied in the phrase "electride ion . By introducing at the outset in the electronic interpretation of chemistry the wave-like character of electrons and the Exclusion Principle through the concept of van der Waals-like electron-domains or electride ions , whose sizes indicate the magnitudes of the electrons kinetic energies, whose impenetrability8) simulates, at least approximately, the operation of the Exclusion Principle, and whose charges yield within the framework of the model easily foreseeable effects, one transforms the complex treatment of the covalent bond in quantum mechanics into a simpler, if less precise, exercise in classical electrostatics. 

As a consequence of the close-packing principle, chemically different molecules with similar shape and volume should have identical crystal structures [27]. Substances forming mixed crystals must be isomorphous (i.e., not only must they have an identical space group and the same number of molecules, but also a similar molecular packing), otherwise there will be a discontinuity in their solubility curve [5]. For example, benzoic acid and isopropylbenzene, in spite of the similarity in... 

A necessary and sufficient condition for the formation of substitutional solid solutions of organic molecules is similarity of shape and size of the component molecules, For the formation of a continuous series of solid solutions the crystal structures of the pure components must be isomorphous Due to the rather irregular shape of organic molecules the principle of close packing leads to structures of low symmetry so that the latter requirement is not often fulfilled. Several diacetylenes which were found to form mixed crystals are given in Table 5. A large number of... 

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