Geometry of equilibrium configurations in the Ising model

We derive microscopically precise identities for the geometry of small clusters in the equilibrium states of the two-dimensional Ising model with emphasis on near-critical phenomena.     

The pyrolytic behavior of ethylenetetracarboxylic acid

The controlled pyrolysis of ethylenetetracarboxyclic acid at 220°C followed by methylation of the pyrolyzate results in the formation of methyl propiolate as the major product along with lesser amounts of methyl fumarate. Evidence is presented which indicates that the methyl fumarate probably arises from some precursor in the pyrolyzate during the methylation reaction. Extended heating of the tetra acid at its melting point produces, in addition to the substances cited above, ethylenetetracarboxylic dianhydride and dicarboxymaleic anhydride. The high-temperature (300–400°C) pyrolysis of the tetraacid gives l0–20% yields of dimethylmaleic anhydride.     

The card game 24 and its application to math education

The card game 24 is a mathematical game that traditionally engages elementary students to practice their mental computational skills. In this paper, we use probability to formulate and explore the game. We create score of difficulty level for solvable card combination set under various setup of game rules. Based on our findings, we create new playing rules and provide suggestions for different levels of players. Our results may serve as guidelines on introducing the game 24 into the practice of math education.     

Spin texture and magnetoroton excitations at nu=1/3

Neutral spin texture (ST) excitations at nu=1/3 are directly observed for the first time by resonant inelastic light scattering. They are determined to involve two simultaneous spin flips. At low magnetic fields, the ST energy is below that of the magnetoroton minimum. With increasing in-plane magnetic field these mode energies cross at a critical ratio of the Zeeman and Coulomb energies of eta(c)=0.020+/-0.001. Surprisingly, the intensity of the ST mode grows with temperature in the range in which the magnetoroton modes collapse. The temperature dependence is interpreted in terms of a competition between coexisting phases supporting different excitations. We consider the role of the ST excitations in activated transport at nu=1/3.     

"Orthogonal" separations for reversed-phase liquid chromatography

A general procedure is proposed for the rapid development of a reversed-phase liquid chromatographic (RP-LC) separation that is "orthogonal" to a pre-existing ("primary") method for the RP-LC separation of a given sample. The procedure involves a change of the mobile-phase organic solvent (B-solvent), the replacement of the primary column by one of very different selectivity, and (only if necessary) a change in mobile phase pH or the use of a third column. Following the selection of the "orthogonal" B-solvent, column and mobile phase pH, further optimization of peak spacing and resolution can be achieved by varying separation temperature and either isocratic %B or gradient time. The relative "orthogonality" of the primary and "orthogonal" RP-LC methods is then evaluated from plots of retention for one method versus the other. The present procedure was used to develop "orthogonal" methods for nine routine RP-LC methods from six pharmaceutical analysis laboratories. The relative success of this approach can be judged from the results reported here.