Geometry physical basis

In our analysis, we discuss experimental results of heat transfer obtained by previous investigators and related to incompressible fluid flow in micro-channels of different geometry. The basic characteristics of experimental conditions are given in Table 4.1. The studies considered herein were selected to reveal the physical basis of scale effect on convective heat transfer and are confined mainly to consideration of laminar flows that are important for comparison with conventional theory. 

We see that it is a consequence of the Pauli principle and bond formation that the electrons in most molecules are found as pairs of opposite spin—both bonding pairs and nonbonding pairs. The Pauli principle therefore provides the quantum mechanical basis for Lewis s rule of two. It also provides an explanation for why the four pairs of electrons of an octet have a tetrahedral arrangement, as was first proposed by Lewis, and why therefore the water molecule has an angular geometry and the ammonia molecule a triangular pyramidal geometry. The Pauli principle therefore provides the physical basis for the VSEPR model. 

AIM theory provides a physical basis for the theory of Lewis electron pairs and the VSEPR model of molecular geometry. Equipped with computers and computer-generated, three-dimensional electron density maps, scientists are able to view molecules and predict molecular phenomena without even having to get off their chairs ... 

The search for connection between shape, structure, and function was posed by D Arcy Thompson in his book On Growth and Form first published in 1917 (Thompson, 1992). His book lets one reflect that complex forms or shapes in nature are not solely a consequence of Darwinian natural selection. They can be purely explained on the basis of geometry, physics, mathematics, and engineering and are guided by underlying physicochemical principles that drive organization of molecules to higher order structures (Ball, 1999,2004). 

The Lewis model is second only to the molecular structure hypothesis itself in providing a conceptual basis for much of present-day chemical thinking, particularly with regard to models of molecular geometry and reactivity. It is essential that the physical basis of this model be established if one is to place all of the vital concepts of chemistry on a firm theoretical footing. 

A physical basis for the VSEPR model of molecuiar geometry... 

In the pulse model, as in the previous models, it is assumed that the time between the radical-solvent collisions, during which the scalar interaction can occur, is a random variable. Thus the variation of the scalar interaction experienced by a nucleus as a function of time will have the generalized form illustrated in Fig. 6. The rate of change of this scalar interaction will depend on the geometry of the interaction between the I and the 5 spins. For example, different radicals S) may approach different / spins with preferred orientations with the result that the electron orbital overlap with the nucleus may be described by different functions in each case, so that the existence of different functions for the scalar interaction seems justifiable on a purely physical basis. Several pictorial examples of different pulses... 

The transition-state geometries that lead to the formation of the endo- and -adducts, respectively, can be approximated by A and B. In A, the rr-electron systems of the carbonyl group and diene interact more strongly than in B. The physical basis for the Alder rule is not well understood it could arise from a variety of electronic, steric, dipole, or London forces, and must be applied with caution, since there are known exceptions. It has been found, for example, that in decalin solution at 56°C, methyl acrylate adds to cyclopentadiene to yield predominantly (76%) the enrfo-adduct, while methyl methacrylate affords the exo-adduct (67%). In addition, the stereoselectivity is sensitive to the polarity of the solvent. ... 

We win discuss the physical basis for the geometries of carbon when it has only single bonds, a double bond, or a triple bond in Sections 1.12—14. For now, let us consider some guidelines for representing these bonding patterns in three dimensions using dashed and solid wedge bonds. 

Therefore, it is a reasonable approach to consider at first very concisely the physical basis for the interpretation of the glass transition anomalies in complex systems. This relates basically to three topical problems (1) polymer dynamics in nanoscale-conflning geometries or at free surface (2) constrained polymer dynamics and (3) the notion of the common segmental nature of the a- and p-relaxations in flexible-chain polymers. 

Now that we have determined the 3D structure, which reflects truly the real structures from global-to-local scale, and that we have obtained a sound physical basis of this structure, we proceed to analyze the structure in terms of interface curvatures, based on differential geometry. We used the parallel-surface method to determine the area-averaged mean curvature = <(/ci + k2)/2> and Gaussian curvature = ... 

Bader RFW, Gillespie RJ, MacDougall PJ (1988) A physical basis fm the VSEPR model of molecular geometry. J Am Chem Soc 110 7329-7336... 

Theory of Electrophoretic Motion. The study of the mechanics of electrophoresis focuses on the basis of electric potential on the surface of an object, and the relation of the electric potential to the velocity of the particle. Whereas research has been generally limited to nonmolecular particles of weU-defined geometry and is not strictly apphcable to molecules such as proteins and DNA fragments, this work is useful for understanding the physics of electrophoretic motion. 

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