Macroscopic and microscopic view

In accordance to the Poisson equation, the source of the dielectric displacement D is given by the density of free (conducting) charges p  

The overall charge neutrality of matter in an external field is described by  

The vacuum contribution caused by the externally applied electric field is represented by the term e0E, and the electrical polarization of the matter in the system is described by P, e.g. [2], This relation is independent of the nature of the polarization which could be pyroelectric polarization, by piezoelectric polarization or dielectric polarization (by an external electric field). 

For a pure dielectric response of the matter the polarization is proportional to the electric field in a linear approximation by 

Equations (1.3) and (1.4) describe the mean properties of the dielectric. This macroscopic point of view does not consider the microscopic origin of the polarization [3], The macroscopic polarization P is the sum of all the individual dipole moments pj of the material with the density Nj. 

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Taft RW, Murray JS. Some effects of molecular structure on hydrogen-bonding interactions. some macroscopic and microscopic views from experimental and theoretical results. In Politzer P, Murray JS, eds. Quantitative Treatments of Solute/Solvent Interactions. Amsterdam Elsevier, 1994 55-82. 

The mechanical properties of a system comprising a liquid in equflib-rium with its vapour are, as we have seen, consistent with the int ace being treated as if it were a surface in which there resides a tension, that is, as a taut membrane of zero mass and zero thickness. In the hands of Young and Laplace the theory of capillarity combined this simple picture with attempts at hs molecular justification, in the way d cribed in Chapter 1, but this conflation of macroscopic and microscopic views is foreign to the methods of classical thermodynamics, whidi are based solely on the two hypotheses above, namely, the existence of a surface in whidi there is a tension, and the position of that surface in laboratory space. Our assumption is, therefore, that the medianical behaviour of a r interfadal system is the same as that of a model system comprising a mathematical surface S subject to a tension a. Let us therefore first summarize the mechanical consequences of this assumption, so obtaining... 

Note that the terms macroscopic and microscopic constants do not imply that these quantities measure macroscopic or microscopic quantities, respectively. Here, in the macroscopic view we have simply grouped the two microscopic species (0, 1) and (1, 0) into one species denoted by (1). Both of these constants can be macroscopic or microscopic, depending on whether we study the binding per molecule or per one mole of molecules. 

Coal is an extremely heterogeneous material, both from a macroscopic and microscopic point of view. Correlation of liquefaction reactivity with coal properties is, as a result, inherently difficult and any truly "universal correlations that will be developed will need to be based... 

Water is one of the most familiar material in our life and is indispensable to all living things. In contrast to its apparently simple molecular structure, water shows many anomalous properties from both macroscopic and microscopic points of view. However, the basic physical property of water, for example the dynamical structure of water, has not yet been fully clioified. To un rstand the dynamical aspect of water structure and its significant role in life, it is essential to clarify not only the dynamics of water molecules themselves but also the dynamics of water in the aqueous solutions. 

The very complex nature of the macroscopic and microscopic structures as they affect strength and the behavior of diamond abrasive/particles still requires extensive work to elucidate fully. However, from a crystallization point of view, gaining control over the crystallization behavior is the key to the production of optimal diamond abrasives. This, of course, may be achieved by choice and manipulation of the pressure/temperature conditions, source carbon structure and solvent/catalyst metal type, leading to control over nucleation and growth rates. 

The new phase generates from the metastable system necessarily in the form of nuclei. These are small clusters of atoms or molecules that in the prevailing conditions have developed into a size sufficiently large to grow spontaneously, ensuring their own viability and, eventually, the stability of the new phase. The intensive properties of nuclei differ from the bulk phase only because of their small size. This point of view is not necessarily correct since the properties, structure, and even the composition of small clusters may not be identical to those of the corresponding bulk phase, but the notion of a nucleus determined essentially by its size is useful to relate the macroscopic and microscopic descriptions of phase formation, as described below. 

Traffic simulators are important tools in traffic system planning and developing traffic control strategies. The simulators range from macroscopic to microscopic views. Microscopic view and operational situations demands a detailed representation of the system and the situation in order reflect real scenarios and being valuable for analysis. This detailed representation will include detailed models of the road network, the road surface, dynamic models of the entities, wheatear models and models of communication networks. All these information sources are necessary to have at an approximated level to calculate risks. 

Assuming the validity of Fick s laws for liquid crystals, various theories [7-15] have been developed to describe the diffusion constants D and in particular their anisotropy ratio a, in terms of the mesophase order and other adequate macroscopic and microscopic material parameters. However, in view of the unsatisfactory agreement with experimental data, so far this has only achieved limited success. By transforming the diffusion tensor from a local (cluster) to the laboratory director frame and by taking the orientational ensemble average, Blinc et al. [7] showed that the two tensor components of D for thermotropic N, S, and Sc phases should be coupled to the order parameter S, the average diffusion constant (D), and the limiting values D, of a perfectly ordered cluster (S = 1) in the... 

Two books have appeared which, while not presenting a unified view of the field nor a critical assessment of the literature, do provide the interested scientist with an entree to the use of computer simulation of liquids ( Theory of Simple Liquids, J. P. Hansen, I. R. McDonald, Academic, 1976 Atomic Dynamics in Liquids, N. H. March, M. P. Tosi, Halsted (Wiley), 1977). The impact on statistical mechanics as a discipline is reflected in the two-volume work, Statistical Mechanics, B. J. Berne, Ed., Part A, Equilibrium Techniques, and Part B, Time-Dependent Processes, Plenum, 1977. Indeed, in his Nobel prize address, I. Prigogine made several references to the use of computer simulations as an aid to development of his Nobel prize winning work on the macroscopic and microscopic aspects of the second law of thermodynamics (Science (1978) 201,777-785). 

The term collectivism has sometimes been used to distinguish this AL philosophy from the more traditional top down and bottom up philosophies. Collectivism embodies the belief that in order to properly understand complex systems, such systems must be viewed as coherent wholes whose open-ended evolution is continuously fueled by nonlinear feedback between their macroscopic states and microscopic constituents. It is neither completely reductionist (which seeks only to decompose a system into its primitive components), nor completely synthesist (which seeks to synthesize the system out of its constituent parts but neglects the feedback between emerging levels). 

Expressions (27) and (29) show how the rates of reaction (26) and its reverse, reaction (28), depend upon the concentrations. Now we can apply our microscopic view of the equilibrium state. Chemical changes will cease (on the macroscopic scale) when the rate of reaction (26) is exactly equal to that of reaction (28). When this is so, we can equate expressions (27) and (29) ... 

In physical chemistry the most important application of the probability arguments developed above is in the area of statistical mechanics, and in particular, in statistical thermodynamics. This subject supplies the basic connection between a microscopic model of a system and its macroscopic description. The latter point of view is of course based on the results of experimental measurements (necessarily carried out in each experiment on a very large number of particle ) which provide the basis of classical thermodynamics. With the aid of a simple example, an effort now be made to establish a connection between the microscopic and macroscopic points of view. 

The next section is devoted to the analysis of the simplest transport property of ions in solution the conductivity in the limit of infinite dilution. Of course, in non-equilibrium situations, the solvent plays a very crucial role because it is largely responsible for the dissipation taking part in the system for this reason, we need a model which allows the interactions between the ions and the solvent to be discussed. This is a difficult problem which cannot be solved in full generality at the present time. However, if we make the assumption that the ions may be considered as heavy with respect to the solvent molecules, we are confronted with a Brownian motion problem in this case, the theory may be developed completely, both from a macroscopic and from a microscopic point of view. 

A gas, at the macroscopic level, has neither a definite shape nor volume. It expands to fill its container. The microscopic view is that the particles are far apart, moving rapidly with respect to each other, and act independently of each other. 

The success of the Potts-Guy equation led many authors to advocate a single mechanism as the rate determining step for permeation through the skin barrier for all or at least a wide range of solutes diffusion was assumed to occur primarily via the interkeratinocyte lipids of the stratum corneum, a mixture of ceramides, fatty acids, and sterols. While from a macroscopic point of view these lipids may be modeled as a bulk solvent, on a microscopic scale they... 

Macroscopic, microscopic, and submicroscopic views of an animal and a plant. 

Up to this point we have taken a very microscopic view of the propagation of beams of particles through material. We have described the degradation of the intensity and the energies of the beams in terms of individual interactions. Now we will take a more macroscopic view from the standpoint of the absorber. 

Statistical mechanics provides a bridge between the properties of atoms and molecules (microscopic view) and the thermodynmamic properties of bulk matter (macroscopic view). For example, the thermodynamic properties of ideal gases can be calculated from the atomic masses and vibrational frequencies, bond distances, and the like, of molecules. This is, in general, not possible for biochemical species in aqueous solution because these systems are very complicated from a molecular point of view. Nevertheless, statistical mechanmics does consider thermodynamic systems from a very broad point of view, that is, from the point of view of partition functions. A partition function contains all the thermodynamic information on a system. There is a different partition function... 

In this chapter we consider bimolecular reactions from both a microscopic and a macroscopic point of view and thereby derive a theoretical expression for the macroscopic phenomenological rate constant. That is, a relation between molecular reaction dynamics and chemical kinetics is established. 

The classical TST dating back to the 30-ies as presented in say [10] is the simplest way of relating obseravble macroscopic rates of chemical transformations with the microscopic view of energy of molecues. It is not surprizing that within 70 years of development it has been criticized and improved. For more recent views of this topic see [11,12],... 

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