Effects Of Statistical Fluctuations Research Articles

On the theory of molecular polarization in gases: I. Effect of molecular interactions on the polarizability of spherical nonpolar molecules

The theory of molecular polarization in dense systems is presented on a quantum mechanical basis for spherical, nonpolar molecules. This permits the calculation of the effect of molecular interaction on the polarizability of the molecules, which is considered constant in the statistical theory of the dielectric constant. The interaction Hamiltonian is restricted to the induced dipole term and the polarizability is obtained from perturbation theory as a power series in the interaction tensor Tik = ▽i▽k(1/rik) where rik is the distance between the centers of molecules i and k. As a special case it is shown that in a system of isotropic harmonic oscillators, interacting through induced dipole forces, the polarizability remains constant in any order of approximation. For hydrogen atoms and helium atoms, however, the polarizability increases in the order T2 due to interactions between pairs of atoms. This effect gives rise to a deviation from the Clausius-Mosotti expression which is of the same form and of the same order of magnitude as the effect of statistical fluctuations.

Economic Analogs

Each type of electronic analog has a use in the solution of a set of economic problems. The large, general-purpose analog computer can solve dynamic-unilateral systems. This can be used for the analysis of a single business, the analysis of an industry, or the study of the economy as a whole. It is hoped that analogs of this type will be used to analyze the effects of proposed governmental budgetary policies, legislation, and regulations, which will have economic effects. The analog of international trade is a decision-function network which has many points in common with automobile and communication traffic control. Large machines for solving n-equations in n-unknowns can be used for linear-static problems such as the determination of average production levels in a large number of interrelated industries. This latter analog is relatively in accurate and is sensitive to the accuracy of the input data. Small scale, specific-purpose analogs can be built for a large variety of isolated dynamic problems, such as the determination of the best ordering rate for a small-retail grocer, and the design of the optimum ratio of inventory capacity to production capacity in a small-proposed business. The effect of statistical fluctuations can be most easily observed by using an analog with a noise generator.