On the reliability of mean-field methods in polymer statistical mechanics

The reliability of the mean-field approach to polymer statistical mechanics is investigated by comparing results from a recently developed lattice mean-field theory (LMFT) method to statistically exact results from two independent numerical Monte Carlo simulations for the problems of a polymer chain moving in a spherical cavity and a polymer chain partitioning between two confining spheres of different radii. It is shown that in some cases the agreement between the LMFT and the simulation results is excellent, while in others, such as the case of strongly fluctuating monomer repulsion fields, the LMFT results agree with the simulations only qualitatively. Various approximations of the LMFT method are systematically estimated, and the quantitative discrepancy between the two sets of results is explained with the diminished accuracy of the saddle-point approximation, implicit in the mean-field method, in the case of strongly fluctuating fields.Comment: 27 pages, 9 figure

Capital market of Bulgaria: testing different CAPM corrections

The present study makes comparison in the usage and the level of accuracy of different methods for calculation of the expected return. The presented methods are based on CAPM, but with different corrections. We are going to test the traditional CAPM of Sharpe (1963) and Lintner (1964), the downside D-CAPM proposed by Estrada (2002), and three methods presented by the authors of this study. The first method uses combination of downside and upside beta to compute the risk in CAPM; the second uses the absolute deviation as a measure of risk; the third method integrates skewness in CAPM, but makes it by using different approach than familiar downside methods. The skewness is added as additional multiplier in the CAPM

On the Apparent Attractive Interaction between Colloidal Particles of Like Charge

A new attractive force between colloidal particles of like charge has been discovered. This force is of entropic depletion origin, and is exhibited between colloidal particles in electrolyte solution. The attractive potential associated with this force is a function of the electrolyte concentration, and can have a minimum up to the order of -10 kT deep for certain parameters of the system. Implications of the force to various systems of interest will be discussed

Partitioning of a polymer chain between a confining cavity and a gel

A lattice field theory approach to the statistical mechanics of charged polymers in electrolyte solutions [S. Tsonchev, R. D. Coalson, and A. Duncan, Phys. Rev. E 60, 4257, (1999)] is applied to the study of a polymer chain contained in a spherical cavity but able to diffuse into a surrounding gel. The distribution of the polymer chain between the cavity and the gel is described by its partition coefficient, which is computed as a function of the number of monomers in the chain, the monomer charge, and the ion concentrations in the solution.Comment: 17 pages, 6 figure

The Christian Realist Perspective: The Political Theology of Augustine, Thomas Aquinas, and Reinhold Niebuhr

Christian political theology deals with the problems of the ultimate questions: the existence of God and the application of His law in the realm of human relations. Through exploring the political theology of Augustine, Thomas Aquinas, and Reinhold Niebuhr, this study discusses the great issues of war and peace, the character of human nature, the necessity of political responsibility, the importance of moral choices, the functions of authority, and the meaning of history and progress. It argues that Christian realism withstands the serious critiques leveled against it, provided that the complementary strengths and weaknesses of these three figures is taken into account

Field-Theoretic Simulations of Polyelectrolyte Complexation

We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particular, the first application of field-theoretic simulations to polyelectrolyte systems is reported. The polyelectrolyte charge-charge correlation length and a phase diagram are provided; effects of charge redistribution are qualitatively explored.Comment: 7 pages, 3 figures, 3 equations, LaTeX; accepted to Journal of Polymer Science B: Polymer Physics; v2: a revised and expanded version, 6 paragraphs of text and about 20 references adde