Rational approximations to the solution of the second order Ricatti equation Technical report, 15 Jan. - 14 Oct. 1965

Rational approximations to solution of second order nonlinear Ricatti equation, using linear transformations - differential equations and operational calculu

Generalized rational approximations with applications to problems in control theory Interim technical report

Rational approximations and solution of control theory problems involving Ricatti equation

Analysis of the coupled frequencies and mode shapes of vehicle control systems Final report, 15 Apr. 1965 - 14 Apr. 1966

Coupled frequencies and mode shapes of vehicle control syste

Rational approximations to the generalized Duffing equation Final report, 15 Jan. - 1965 - 14 Jan. 1966

Linear transformation to obtain rational approximation to response of physical system described by nonlinear differential equation including Duffing equation as special cas

Numerical integration of nonlinear differential equations by use of rational approximation Final report, 15 Jan. 1965 - 14 Jul. 1967

Numerical integration of nonlinear differential equations by use of rational approximatio

Analytical Expression for the RKKY Interaction in Doped Graphene

We obtain an analytical expression for the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction $J$ in electron or hole doped graphene for linear Dirac bands. The results agree very well with the numerical calculations for the full tight-binding band structure in the regime where the linear band structure is valid. The analytical result, expressed in terms of the Meijer G-function, consists of a product of two oscillatory terms, one coming from the interference between the two Dirac cones and the second coming from the finite size of the Fermi surface. For large distances, the Meijer G-function behaves as a sinusoidal term, leading to the result $J \sim R^{-2} k_F \sin (2 k_F R) {1 + \cos[(K-K').R]}$ for moments located on the same sublattice. The $R^{-2}$ dependence, which is the same for the standard two-dimensional electron gas, is universal irrespective of the sublattice location and the distance direction of the two moments except when $k_F =0$ (undoped case), where it reverts to the $R^{-3}$ dependence. These results correct several inconsistencies found in the literature.Comment: 5 pages, 5 figure

Superstatistical random-matrix-theory approach to transition intensities in mixed systems

We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos. The obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the Porter-Thomas distribution. It agrees with the experimental reduced transition probabilities for the 26A nucleus better than the commonly used chi-squared distribution.Comment: 14 pages, 3 figure

Descriptive Mineralogy of Pugh Quarry, Northwestern Ohio: Sphalerite

Author Institution: Department of Geology, Miami UniversityThe Devonian rocks at Pugh Quarry have three distinct types of sphalerite (banded massive, spheroidal, and tiny euhedral). Occurrence of the banded massive sphalerite is restricted to the mineral zone, predominantly as blebs in marcasite. The color of banded sphalerite ranged from nearly colorless to various hues of yellow. The replacement of banded sphalerite by marcasite was observed. The spheroidal sphalerite occurred in association with marcasite of euhedral habit. The spherules were small, the largest no greater than 1 mm across. Where present in great profusion, the sphalerite spherules merged together forming botryoidal surfaces. The euhedral sphalerite occurred in the voids of the sponge-like and stromatolitic dolostone below the mineral zone, and in a layer of soft laminated mud associated with the dolostone. The euhedral sphalerite was predominantly red-brown, and no crystals larger than 1 mm in maximum dimension were observed

Descriptive Mineralogy of Pugh Quarry, Northwestern Ohio: Barite and Celestite

Author Institution: Department of Geology, Miami UniversityTwo sulfate minerals, barite and celestite, were identified in the Devonian rocks at Pugh Quarry. The barite occurs commonly as rosette-like clusters with wide variety of colors and crystal habits. Unusual features include paired crystals and hollow crystals. The former consist of two barite crystals growing parallel with each other on the dolostone matrix, and the latter only of a thin wall of barite commonly marked by cross striations. Celestite crystals have two different colors. The grayblue and blue crystals are prismatic to blocky and occur as well-formed individuals, whereas the colorless and white crystals are tabular to bladed and occur as distinct individuals and as compact clusters