Coherence theory

6 Critical Column Length for Isotachic Train Formation 

Even in an ideal coltunn, the reorganization of the distribution of the component concentrations between the injection and the formation of the isotachic train requires a certain time, i.e., it cannot be achieved in less than a minimum migration distance. This distance can be derived from the distance-time diagram. 

The coherence theory of chromatography [9] is based on the use of the concept of coherence to explain the band profiles observed in ideal chromatography. A chromatographic coltunn subject to a disturbance will, after a period, settle into a resolved state, which consists of a series of composition waves, each of them being subject to the coherence condition 

This condition is valid for all i and , i.e., for all the compounds involved in the system studied, feed and mobile phase components alike. 

This theory was originally developed for the cases in which the retention mechanism is accoimted for by a stoichiometric reaction such as ion-exchange. However, Helfferich [9] has shown that it can also be applied in the case of adsorption, if assuming a Langmuir competitive isotherm (see Eq. 9.45), by introducing a dummy species, p, that is used to convert the non-stoichiometric adsorption of an n-component system into the stoichiometric reaction of an n -I- 1-component system. The Langmuir competitive isotherm is given by 

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The problem of evolutionary transition is to formulate a coherent theory that can explain these transitions and guide evaluation of empirical evidence for each. Part of this work involves describing units of evolution adequate to explain the evolutionary origin of new levels and not merely evolution at levels (Griesemer, 2000c). The key insight into the units problem afforded by consideration of evolutionary transition is that units of evolution themselves have an evolutionary history. Differently put, there is a temporal or processual dimension to the units problem as well as spatial and functional dimensions. Because the spatial and functional perspectives on units mentioned above were not articulated with the evolutionary transition problem in mind, they are not clearly suited to its theoretical solution. In particular, if a perspective assumes the existence of levels of organization or embeds assumptions about these products of evolution in their analysis of units, then it has assumed what is to be shown by a theory of evolutionary transition. 

As the result of our work the three propositions specified in the introduction now appear plausible and in accord with the experimental evidence. It is, therefore, appropriate to show how they form a coherent theory which will explain adequately the known phenomena. 

The recent developments and ideas in the field of prebiotic chemistry can be combined with the concepts noted here to produce what we regard as a research outline, rather than a detailed hypothesis, directed toward a coherent theory of the origin of complex self-contained, self-replicating chiral assemblies. In what follows we present one possible scenario that is consistent with our current knowledge of chiral induction and amplification and with the nature of early Earth as well as early life. It is exciting that this fundamental question can be formulated in a way that allows systematic experimental testing as we enter the next century. 

J.W. Cahn s early contributions to elastic coherency theory were motivated by his work on spinodal decomposition. His subsequent work with F. Larche created a rigorous thermodynamic foundation for coherency theory and stressed solids in general. A single volume, The Selected Works of John W. Cohn [15], contains papers that provide background and advanced reading for many topics in this textbook. This derivation follows from one in a publication included in that collection [16]. 

English chemist Sir Humphry Davy, who developed the first coherent theory of electrochemical action. 

The coherence theory is also incompatible with (MR2). Coherence itself is an epistemic is notion, and the concepts in terms of which it is usually explained, like mutual support, rich explanatory connections, consistency are also epistemic.viii... 

In the coherence theory of truth consistency has to be taken in the syntactic sense. If it is taken in the semantic sense, it presupposes the concept of truth , which would make the theory circular. The syntactic notion of consistency may be called epistemic because it is linked to procedures. 

Davidson, Donald. Afterthoughts, 1987. (to A Coherence Theory of Truth and Knowledge. ) In Reading Rorty. Ed. by A. Malachowski. Oxford Blackwell, 1990. 134-137. 

A Coherence Theory of Truth and Knowledge. In LePore, Truth and Interpretation, 307-319. 

Up until the origin of RNA molecules, Dyson describes the logical consequences of the initial hypotheses, and his scheme is therefore a coherent theory of chemical evolution. But the mathematical model does not say anything about the subsequent integration of RNAs and hosts, and on this point Dyson resorts to a supplementary conjecture. He proposes that primitive RNAs invaded their metabolic hosts, and used them for their own replication, like viruses do, which is exactly Haldane s hypothesis. Dyson concludes therefore that, after Oparin s metabolism stage, came Haldane s replication stage, and his final scheme becomes metabolism first, replication second . That RNAs... 

The awkward richness of possibilities seems to shatter any possible coherent theory of simplicity... 

Despite his skepticism, Pauli learned the intricacies of matrix mathematics and applied the Heisenberg version of the new quantum mechanics to the hydrogen atom. In less than three weeks, Pauli obtained the same formula that Bohr had obtained in 1913, only this time the route to the formula was a coherent theory—the new theory of quantum mechanics. Herewith, wrote Pauli, it has been demonstrated that the Balmer terms come out directly from the new quantum mechanics. So momentous was this demonstration that the skeptic Pauli became a believer in the matrix mathematical formulation of Born, Heisenberg, and Jordan. 

In an electron microscope, the electron beam is produced by an electron gun, in which the electrons are boiled off a heated filament and then accelerated by a highly stabilized electrical potential difference of some hundreds of kilovolts. An electron beam produced in this way is not coherent, but its degree of coherence can be understood in terms of the concepts of optical coherence theory. Later chapters will show that the nature of electron diffraction patterns from crystals that exhibit long-period superstructures (which are not uncommon in many important rockforming minerals) depends critically on the degree of spatial coherence of the incident electron beam. Therefore, it is important to conclude this chapter with a brief review of the basic ideas of optical coherence. A detailed account of the theory is given by Born and Wolf (1965). 

The dynamic element of this process is external and internal trade, neither class struggle nor the development of the productive forces. This "neO Smithian" or proto-Hicksian theory of history is not usually associated with Marx. And it is of course only part of his theory. Yet, as I said, it is no less central than the better-known theory of the rise and fall of property right structures in accordance with their ability to promote the productive forces. Marx owes us an account of how these two views are to be welded into one coherent theory. Some links are readily discernible, and have been noted above. They do not, however, amount to a full integration of the two periodizations, each with its own internal dynamics. Some will conclude that Marx, a true historian, kept an open mind and avoided all dogmatism. Others will argue that the presence of these two, prima facie incompatible views shows a deplorable lack of intellectual discipline. Most probably, there is an element of truth in both assertions. 

One of the fundamental aspects of the theory of nonlinear chromatography is the recognition that any perturbation (e.g., the injection of any sample of composition different from that of the mobile phase stream) caused to a column in which the mobile and stationary phases are in equilibrium results in the formation of perturbation waves that, after a time, consist in a series of concentration waves that migrate along the column. The coherence theory is based on the observation that the velocities of the waves obtained for different compounds are equal. 

The application of the z-transform and of the coherence theory to the study of displacement chromatography were initially presented by Helfferich [35] and later described in detail by Helfferich and Klein [9]. These methods were used by Frenz and Horvath [14]. The coherence theory assumes local equilibrium between the mobile and the stationary phase gleets the influence of the mass transfer resistances and of axial dispersion (i.e., it uses the ideal model) and assumes also that the separation factors for all successive pairs of components of the system are constant. With these assumptions and using a nonlinear transform of the variables, the so-called li-transform, it is possible to derive a simple set of algebraic equations through which the displacement process can be described. In these critical publications, Helfferich [9,35] and Frenz and Horvath [14] used a convention that is opposite to ours regarding the definition of the elution order of the feed components. In this section as in the corresponding subsection of Chapter 4, we will assume with them that the most retained solute (i.e., the displacer) is component 1 and that component n is the least retained feed component, so that... 

The paucity of acknowledged impossibilities hampers understanding of how chemical structure translates into a sequence of nerve impulses. Not until experiment falsifies many more plausible suggestions can a coherent theory of olfactory coding take shape. 

On the other hand, we should keep in mind deeper issues that are currently under debate as quantum gravity aims to provide a coherent theory of spacetime. 

Biological luminescence is explained by quantum coherence theory assuming that the radiative field is an odd and even coherent field. The radiant intensity curve versus time of biophoton emission agrees with the experimental results. Hence, biophotons arise from a non-classical state radiant field, and the parameter k is also related to the biological characteristics the decay time is shortened with an increasing in k, i.e., it can control the velocity of biophoton emission. 

Rescher, N. 1973. The Coherence Theory Of Truth. Oxford Clarendon Press. 

Surface-growth coefficients. Much research on the growth of crystals by the interfacial reaction has been done and reported in standard monographs on crystallization. Although a coherent theory of crystal growth has evolved, numerical data on of a kind that can be used in design are scarce. 

It was a time of great excitement and ferment in science, and Rutherford s laboratory was one of the epicenters of discovery in atomic physics. The first coherent theory of the structure of the atom was just then being developed by Rutherford and his research group, which, besides Moseley, included Niels Bohr, Hans Geiger, Kasimir Eajans, and others. 

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