Generalized theory

The problem consists in finding as precisely as possible the discontinuity position and in estimating its sub-surface depth. For this reason, a method has been developed based on the general theory of electromagnetic wave diffraction on the discontinuity [6], [7]. 

London F 1937 The general theory of molecular forces Trans. Faraday Soc. 33 8... 

Seidner L, Stock G and Domcke W 1995 Nonperturbative approach to femtosecond spectroscopy - general theory and application to multidimensional nonadiabatic photoisomerization processes J. Chem. Phys. 103 4002... 

Andersen H C and Chandler D 1970 Mode expansion in equilibrium statistical mechanics I. General theory and application to electron gas J. Chem. Phys. 53 547... 

Pople J 1954 Statistical mechanics of assemblies of axially symmetric molecules I. General theory Proc. R. Soc. A 221 498... 

When a system is not in equilibrium, the mathematical description of fluctuations about some time-dependent ensemble average can become much more complicated than in the equilibrium case. However, starting with the pioneering work of Einstein on Brownian motion in 1905, considerable progress has been made in understanding time-dependent fluctuation phenomena in fluids. Modem treatments of this topic may be found in the texts by Keizer [21] and by van Kampen [22]. Nevertheless, the non-equilibrium theory is not yet at the same level of rigour or development as the equilibrium theory. Here we will discuss the theory of Brownian motion since it illustrates a number of important issues that appear in more general theories. 

For strictly monomolecular processes the general theory would now proceed by analysing the time-dependent... 

Figure A3.4.4. Steps in the general theory of ohemieal reaetions.

Equation (ASA. 110) represents the canonical fonn T= constant) of the variational theory. Minimization at constant energy yields the analogous microcanonical version. It is clear that, in general, this is only an approximation to the general theory, although this point has sometimes been overlooked. One may also define a free energy... 

Cao J and Voth G A 1996 A unified framework for quantum activated rate processes I. General theory J. Chem. Phys. 105 6856... 

An extensive presentation of the fundamentals of NMR. Avery good chapter on relaxation, including general theory and mechanisms. A real classic still going strong . 

Wong S K, Hutchinson D A and Wan J K S 1973 Chemically induced dynamic electron polarization. II. A general theory for radicals produced by photochemical reactions of excited triplet carbonyl compounded. Chem. Phys. 58 985-9... 

Kleier D A and Binsch G 1970 General theory of exchange-broadened NMR line shapes. II. Exploitation of invariance properties J. Magn. Reson. 3 146-60... 

Kantorovloh L N 1988 An embedded-moleoular-oluster method for oaloulating the eleotronlo struoture of point defeots In non-metalllo orystals. I. General theory J. Phys. C Solid State Phys. 21 5041... 

Baer M 1985 The general theory of reactive scattering the differential equations approach Theory of... 

Manolopoulos D E, Dmello M and Wyatt R E 1989 Quantum reactive scattering via the log derivative version of the Kohn variational principle—general theory for bimolecular chemical reactions J. Chem. Phys. 91 6096... 

In Sections V.A.1-V.A.3, we treated one particular group of t mabices as presented in Eq. (51), where g is an antisymmebic matrix with constant elements. The general theory demands that the mabix D as presented in Eq. (52) be diagonal and that as such it contains (-1-1) and (—1) values in its diagonal. In the three examples that were worked out, we found that for this particular class of T mabices the coiiesponding D mabix contains either (-1-1) or (—1) terms but never a mixture of the two types. In other words, the D mab ix can be represented in the following way ... 

In this series of results, we encounter a somewhat unexpected result, namely, when the circle surrounds two conical intersections the value of the line integral is zero. This does not contradict any statements made regarding the general theory (which asserts that in such a case the value of the line integral is either a multiple of 2tu or zero) but it is still somewhat unexpected, because it implies that the two conical intersections behave like vectors and that they arrange themselves in such a way as to reduce the effect of the non-adiabatic coupling terms. This result has important consequences regarding the cases where a pair of electronic states are coupled by more than one conical intersection. 

The general theory behind the process is that the hypohalite will convert the amide to a haloamide. This then spontaneously changes to the isocyanate when heated and decomposes to the amine from the water present. In effect, all that happens is that a Carbonyl (CO) group is stripped off the starting amide to yield the corresponding amine. Yields pre- purification are around 80%, post-purification average around 65%. Certain uses of the result-... 

A more general theory of acids and bases was devised independently by Johannes Br0n sted (Denmark) and Thomas M Lowry (England) m 1923 In the Brpnsted-Lowry approach an acid is a proton donor, and a base is a proton acceptor The reaction that occurs between an acid and a base is proton transfer... 

There are two general theories of the stabUity of lyophobic coUoids, or, more precisely, two general mechanisms controlling the dispersion and flocculation of these coUoids. Both theories regard adsorption of dissolved species as a key process in stabilization. However, one theory is based on a consideration of ionic forces near the interface, whereas the other is based on steric forces. The two theories complement each other and are in no sense contradictory. In some systems, one mechanism may be predominant, and in others both mechanisms may operate simultaneously. The fundamental kinetic considerations common to both theories are based on Smoluchowski s classical theory of the coagulation of coUoids. 

Molecular Connectivity Indexes and Graph Theory. Perhaps the chief obstacle to developing a general theory for quantification of physical properties is not so much in the understanding of the underlying physical laws, but rather the inabiUty to solve the requisite equations. The plethora of assumptions and simplifications in the statistical mechanics and group contribution sections of this article provide examples of this. Computational procedures are simplified when the number of parameters used to describe the saUent features of a problem is reduced. Because many properties of molecules correlate well with stmctures, parameters have been developed which grossly quantify molecular stmctural characteristics. These parameters, or coimectivity indexes, are usually based on the numbers and orientations of atoms and bonds in the molecule. 

Mechanistic Models. A general theory of the mechanism for the complete heterogeneous catalytic oxidation of low molecular weight vapors at trace concentrations in air does not exist. As with many catalytic reactions, however, certain observations have led to a general hypothesis (17). 

Few, if any, failure mechanisms have received as much attention as stress-corrosion cracking (SCC). Yet despite an enormous research effort over many years, an acceptable, generalized theory that satisfactorily explains all elements of the phenomenon has not been produced. SCC is a complex failure mechanism. Nevertheless, its basic characteristics are well known, and a wealth of practical experience permits at least a moderately comfortable working knowledge of the phenomenon. 

One of the major reasons why design should be based on statisties is that material properties vary so widely, and any general theory of reliability must take this into aeeount (Haugen and Wirsehing, 1975). Material properties exhibit variability beeause of anisotropy and inhomogeneity, imperfeetion, impurities and defeets (Bury, 1975). All materials are, of eourse, proeessed in some way so that they are in some useful fabrieation eondition. The level of variability in material properties assoeiated with the level of proeessing ean also be a major eontribution. There are three main kinds of randomness in material properties that are observed (Bolotin, 1994) ... 

Wu, C.H., A General Theory of Three-Dimensional Flow in Subsonic and Supersonic Turbomachines of Axial, Radial, and Mixed-Flow Type, NACA TN-2604, 1952. 

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