Simple liquids, harmonic oscillator model

This potential permits the extention of the simple formalism of the harmonic oscillator model to the region of the liquid state (Prigogine, Trappeniers and Mathot [1953]). 

Since the temperature coefficients of the sound velocity, the speciBc volume, and the specific heat are related to the thermal conductivity, a step of the temperamie coefHcient, K dXnXl dT, of the thermal conductivity is suggested. Measurements of the thermal conductivity in the melt of n-tetracosane have been performed by Gustafsson et al. resulting in a step-like behavior of K with AK = K (T ) - K (r ). The measured values of 2 x lO /K < AAT < 5 x 10" /K compare quite well to the calculated value of 7 x lO /K. This calculation is based on the harmonic oscillate model of simple liquids of Hotrocks and McLaughlin. ... 

Since the reduced spectrum x"( ) clearly shows the low-ftequency Raman modes, we introduced a simple model to analyze the spectral profile of x"(.v) for obtaining the quantitative information. The model is composed of two damped harmonic oscillator modes and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solution). Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxation is represented as ... 

Solid state physicists are familiar with the free- and nearly free-electron models of simple metals [9]. The essence of those models is the fact that the effective potential seen by the conduction electrons in metals like Na, K, etc., is nearly constant through the volume of the metal. This is so because (a) the ion cores occupy only a small fraction of the atomic volume, and (b) the effective ionic potential is weak. Under these circumstances, a constant potential in the interior of the metal is a good approximation—even better if the metal is liquid. However, electrons cannot escape from the metal spontaneously in fact, the energy needed to extract one electron through the surface is called the work function. This means that the potential rises abruptly at the surface of the metal. If the piece of metal has microscopic dimensions and we assume for simplicity its form to be spherical - like a classical liquid drop, then the effective potential confining the valence electrons will be spherically symmetric, with a form intermediate between an isotropic harmonic oscillator and a square well [10]. These simple model potentials can already give an idea of the reason for the magic numbers the formation of electronic shells. 

Also in chemistry artificial neural networks have found wide use. They have been used to fit spectroscopic data, to investigate quantitative structure-activity relationships (QSAR), to predict deposition rates in chemical vapor deposition, to predict binding sites of biomolecules, to derive pair potentials from diffraction data on liquids, " to solve the Schrodinger equation for simple model potentials like the harmonic oscillator, to estimate the fitness function in genetic algorithm optimizations, in experimental data analysis, to predict the secondary structure of proteins, to predict atomic energy levels, " and to solve classification problems from clinical chemistry, in particular the differentiation between diseases on the basis of characteristic laboratory data. ... 

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