Provenance theory

The right model has to be chosen this is trivial only when a well-proven theory foresees a certain function y = f x). Constraints add a... 

Occasional accidents or therapeutic procedures have provided experimentalists with patients with fistulas, permitting the study of mechanisms controlling the secretion of gastric juice in humans. The most impressive collection of data in humans was made by Beaumont, a United States Army surgeon, on Alexis St. Martin. Few books inspire as much respect for medical research as that of Beaumont [36]. His warm interest in his patient s welfare, his detailed observations, his objectivity in interpreting the results, and his courage in challenging accepted but not proven theories are qualities, if not unique, then surely unusual. 

While not unique, the Scluodinger picture of quantum mechanics is the most familiar to chemists principally because it has proven to be the simplest to use in practical calculations. Hence, the remainder of this section will focus on the Schrodinger fomuilation and its associated wavefiinctions, operators and eigenvalues. Moreover, effects associated with the special theory of relativity (which include spin) will be ignored in this subsection. Treatments of alternative fomuilations of quantum mechanics and discussions of relativistic effects can be found in the reading list that accompanies this chapter. 

A completely difierent approach to scattering involves writing down an expression that can be used to obtain S directly from the wavefunction, and which is stationary with respect to small errors in die waveftmction. In this case one can obtain the scattering matrix element by variational theory. A recent review of this topic has been given by Miller [32]. There are many different expressions that give S as a ftmctional of the wavefunction and, therefore, there are many different variational theories. This section describes the Kohn variational theory, which has proven particularly useftil in many applications in chemical reaction dynamics. To keep the derivation as simple as possible, we restrict our consideration to potentials of die type plotted in figure A3.11.1(c) where the waveftmcfton vanishes in the limit of v -oo, and where the Smatrix is a scalar property so we can drop the matrix notation. 

The time dependence of the molecular wave function is carried by the wave function parameters, which assume the role of dynamical variables [19,20]. Therefore the choice of parameterization of the wave functions for electronic and nuclear degrees of freedom becomes important. Parameter sets that exhibit continuity and nonredundancy are sought and in this connection the theory of generalized coherent states has proven useful [21]. Typical parameters include molecular orbital coefficients, expansion coefficients of a multiconfigurational wave function, and average nuclear positions and momenta. We write... 

In applying quantum mechanics to real chemical problems, one is usually faced with a Schrodinger differential equation for which, to date, no one has found an analytical solution. This is equally true for electronic and nuclear-motion problems. It has therefore proven essential to develop and efficiently implement mathematical methods which can provide approximate solutions to such eigenvalue equations. Two methods are widely used in this context- the variational method and perturbation theory. These tools, whose use permeates virtually all areas of theoretical chemistry, are briefly outlined here, and the details of perturbation theory are amplified in Appendix D. 

It IS worth remembering that a theory can never be proven correct It can only be proven incor rect incomplete or inadequate Thus theories are always being tested and refined As important as anything else in the scientific method is the testable hypothesis Once a theory is proposed experiments are designed to test its validity If the results are con sistent with the theory our belief in its soundness is strengthened If the results conflict with it the theory IS flawed and must be modified Section 6 7 describes some observations that support the theory that car bocations are intermediates in the addition of hydro gen halides to alkenes... 

Modem scaling theory is a quite powerful theoretical tool (appHcable to Hquid crystals, magnets, etc) that has been well estabUshed for several decades and has proven to be particularly useful for multiphase microemulsion systems (46). It describes not just iuterfacial tensions, but virtually any thermodynamic or physical property of a microemulsion system that is reasonably close to a critical poiat. For example, the compositions of a microemulsion and its conjugate phase are described by equations of the foUowiug form ... 

Generalized Correla.tions. A simple and rehable method for the prediction of vapor—Hquid behavior has been sought for many years to avoid experimentally measuring the thermodynamic and physical properties of every substance involved in a process. Whereas the complexity of fluids makes universal behavior prediction an elusive task, methods based on the theory of corresponding states have proven extremely useful and accurate while still retaining computational simplicity. Methods derived from corresponding states theory are commonly used in process and equipment design. 

Micromechanical theories of deformation must be based on physical evidence of shock-induced deformation mechanisms. One of the chapters in this book deals with the difficult problem of recovering specimens from shocked materials to perform material properties studies. At present, shock-recovery methods provide the only proven teclfniques for post-shock examination of deformation mechanisms. The recovery techniques are yielding important information about microscopic deformations that occur on the short time scales (typically 10 -10 s) of the compression process. 

From the early work of Taylor [63T01] connecting dislocation behavior to observed viscoplastic shock-compression response, numerous studies have attempted to relate conventional dislocation dynamics models to experimental observations. Theory and observations consistently require unusually large numbers of mobile dislocations. Although qualitatively descriptive, progress to date on dislocation models has not proven to provide quantitative descriptions to the observations in metals. 

Where you devise original solutions to the measurement of characteristics the theory and development of the method should be documented and retained as evidence of the validity of the measurement method. Any new measurement methods should be proven by rigorous experiment to detect the measurement uncertainty and cumulative effect of the errors in each measurement process. The samples used for proving the method should also be retained so as to provide a means of repeating the measurements should it prove necessary. 

Under a homestead theory of subsurface rights, the first finder of a mineral area would have claim to the entire recognized deposit. In the case of oil and gas, the geologic unit is the entire resei voir, however shaped, as long as it can be proven to be contiguous. Separate and distinct resei voirs in the same general area, whether vertical or horizontal, would require separate and distinct discoveiy and claim. Alien wells draining a claimed reservoir would be liable for trespass if the homesteader can reasonably prove invasion (whether by well... 

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