Vibration theory

Vibration theory and vibration profile, or signature, analysis are complex subjects that are the topic of many textbooks. The purpose of this section is to provide enough... 

Partial Differential Equations of Second and Higher Order Many of the applications to scientific problems fall naturally into partial differential equations of second order, although there are important exceptions in elasticity, vibration theory, and elsewhere. 

A synopsis of the topics treated in this monograph follows. Chapter 1 is a brief survey of historical developments in the field of isotope effects through the early 1930s. Chapters 2 and 3 give developments of the fundamental quantum mechanical, thermodynamic, and molecular vibration theory required to under-... 

Thomson, W. T. Vibration theory and applications. George Allen and Unwin, London 1965... 

Having outlined stereochemical preferences, we now draw on vibration theory to limit the choice in an absolute sense. Since the symmetry properties of the normal modes of a molecule are rarely considered in the context of stereoselectivity, we shall look into this question briefly. 

The derivatives of the Cartesian PAS coordinates h of the parent with respect to the internal coordinates 5(, required for Eq. 68, are well known from molecular vibrational theory as the derivatives of the respective displacement coordinates. They are usually arranged as the elements of a 3Na x Ns dimensional matrix, which has been called A [59] and gives the linear relation between the increments of the internal and Cartesian coordinates ... 

Sanchez-Palencia, E., Nonhomogeneous Media and Vibration Theory, Lecture Notes in Physics, Vol. 127. Springer-Verlag, Berlin and New York, 1980. 

The stationary states, to which we restrict ourselves here, correspond to stationary waves in vibration theory antinodes correspond to high charge density, the latter is zero at the nodes. 

Amoore, J. E. (1971). Stereocehmical and vibrational theories of odour. Nature 233, 270-271. 

Janezic, D., Praprotnik, M., Merzel, F. Molecular dynamics integration and molecular vibrational theory. 1. New symplectic integrators, J. Chem. Phys. 2005,122,174101. 

What molecular features contribute to the overall percept of smell still remains an open question in olfaction. Three theories have been proposed in an attempt to relate molecular properties of an odorant with its overall quality vibrational, steric, and odotope theories (Dyson 1938 Moncrieff 1949 Shepherd 1987). The vibrational theory first proposed by Dyson (1938), revisited first by Beck and Miles (1947) and... 

It is important to note that IR absorption spectroscopy is in fact the basis of the vibrational theory of olfactory reception. This theory has been found to be limited in terms of explaining structure-odor relationships (Rossiter 1996). First, enantiomers, molecules that form non-superimposable mirror images of each other, have identical IR absorption spectrum, yet they can smell differently, e.g., the S- and R- enantiomers... 

Readers are referred to (Keller and Vosshall 2004) where using psychophysical tests the authors have found that vibrational theory alone cannot explain the overall smell of an odorants. 

Keller, A., Vosshall, L.B. A psychophysical test of the vibration theory of olfaction. Nature Neuroscience 4, 337-338 (2004)... 

The vibrational theory of odor postulates that the molecular attributes which confer olfactory specificity on each species of molecule are its low-frequency, "normal mode" oscillations ( 1). The normal modes are the natural vibrational movements which can be excited independently of each other, and the low-frequency... 

At first sight this looks like an unanswerable objection to the vibrational theory, and it is indeed unanswerable if it be held that the possession of one or two musk-favorable and no musk-adverse frequencies is a necessary and sufficient condition for the specific odorous sensation to be perceived. But it has already been shown elsewhere that the probability of a quantum interaction and the stimulatory efficiency of a moleucle depend upon such additional factors as the frequency of the lowest vibrational mode which correlates with the threshold concentration (15). or the flexibility of the molecule which is related to the way the intensity of the sensation varies with the concentration of the stimulus (16). Also, it has been suggested that we... 

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