Historical Backdrop

A first step toward quantum mechanical approximations for free energy calculations was made by Wigner and Kirkwood. A clear derivation of their method is given by Landau and Lifshitz [43]. They employ a plane-wave expansion to compute approximate canonical partition functions which then generate free energy models. The method produces an expansion of the free energy in powers of h. Here we just quote several of the results of their derivation. 

By integrating out the coordinate dependence, they also obtain an approximate quantum-corrected formula for the momentum distribution which leads to the definition of an effective temperature. That is, the approximate distribution is still Gaussian in the momenta, but with an increased temperature for each particle 

Alternatively, if the momenta are integrated out, an effective distribution of the coordinates is obtained. In this distribution the Boltzmann factor is sampled with the classical potential energy replaced by a quantum effective potential 

This potential is similar to one derived by Stratt [44] using different techniques. It is problematic though for simulations of molecular fluids due to the middle term on the right side [12], The square of the repulsive component of the force leads to nonphysical behavior in the effective potential for small separations. 

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Given this historical backdrop, and that the current author was awarded his Ph.D. thesis primarily for this structure determination effort, the lr69 example is ideally suited for comparing the relative merits of the simulated annealing approach over traditional methods (Subbiah, 1988). 

Initial interest in cholesterol and Alzheimer s disease stemmed from a lengthy historical backdrop. One of the first studies hnking cholesterol to AD stemmed from an observation that senile plaques were quite prevalent in the brains of non-demented patients who had died from coronary heart disease [21], a population known to possess elevated cholesterol levels. Additional studies soon followed demonstrating that the ApoE4 allele of the ApoE cholesterol transporter was a major risk factor for AD [ 13 -16]. Is there a clear association between cholesterol and Alzheimer s disease ... 

Our pilgrimage revisits highlights in the developing understanding of products and components of living organisms and thereby provides historical backdrop for the development of bio-molecular machines and materials. 

Health care costs in the United States exceed a staggering trillion dollars per year. Low back pain, urinary incontinence, pressure ulcers (e.g., bed sores), and cardiovascular disease are major contributors to decreased quality of life and increased health care costs. Applications of protein-based materials, briefly noted in this section but discussed more extensively below, have the potential to improve quality of life while lowering health care costs for these and additional medical problems. To provide a historical backdrop and a record of the development of applications. Table 9.1 provides the set of patents resulting from our research efforts,... 

Toll (1956) examines the logical foundations of causality and the dispersion relations. Goldberger (1960) begins his article with a good historical survey another discussion within the context of high-energy physics is by Scadron (1979, pp. 326-329), whereas optical properties of solids form the backdrop for Stern s (1963) discussion. And an entire book by Nussenzveig (1972) is devoted to dispersion relations. 

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