Effect Of Mixed Mode Research Articles

On the functional-integral approach in quantum statistics, including mixed-mode effects and free of divergences. II. Diagram analysis and some exact relations

For pt.I see ibid., vol.3, p.4389, 1991. In this paper the causes of the 'mathematical breakdown' of the random-phase approximation RPA' are analysed. Starting from an exact matrix formula, a diagram analysis of a functional-integral approach is developed with the following characteristics: (i) All the singularities of the integrands are cancelled completely; there is no problem of the limitation from the convergence radius of the formula used. (ii) The reality of the partition functions at every stage is guaranteed and all the benefits of the complex representation are preserved simultaneously. (iii) All the functional-integral series are transformed into two-dimensional integral series. (iv) A functional-integral approach, which can calculate the mixed mode contributions, is given for the first time. The diagrammatic rules of mixed mode contributions and some concrete examples are given. Some exact symmetry relations and expressions are suggested and proved. These symmetry relations are also preserved at every state in the author's diagram analysis. They are useful in practical calculations. A new exact relation is also derived.

On the functional integral approach in quantum statistics: I. Some approximations

The susceptibility of a Kondo system in a fairly wide temperature region is calculated in the first-harmonic approximation in a functional integral approach. The comparison with the value obtained by renormalization group theory shows that in this region the two results agree quite well. The expansion of the partition function with infinite independent harmonics for the Anderson model is studied. Some symmetry relations are generalized. It is a challenging problem to develop a functional integral approach including diagram analysis, mixed-mode effects and some exact relations in the Anderson system proved in a functional integral approach. These topics will be discussed in a subsequent paper.

Mixed-mode effects on the toughness of polymer interfaces

Normal, symmetric fracture toughness tests can give high values for the toughness of the joint between the immiscible polymers polystyrene and polymethylmethacrylate. These high values, which are caused by crazes growing away from the interface into the polymer with lower craze resistance, are not a fair characterization of the toughness of the joint. Much lower, and more realistic, toughness values are obtained by the use of an asymmetric test that tends to drive the crack and crazes more along the interface.

Cation-exchange chromatography of peptides on poly(2-sulfoethyl aspartamide)-silica

A strong cation-exchange material, poly(2-sulfoethyl aspartamide)-silica (PolySULFOETHYL Aspartamide) was developed for purification and analysis of peptides by high-performance liquid chromatography. All peptides examined were retained at pH 3, even when the amino terminus was the only basic group. Peptides were eluted in order of increasing number of basic residues with a salt gradient. Capacity was high, as was selectivity and column efficiency. This new column material displays modest mixed-mode effects, allowing the resolution of peptides having identical charges at a given pH. The selectivity can be manipulated by the addition of organic solvent to the mobile phases; this increases the retention of some peptides and decreases the retention of others. The retention in any given case may reflect a combination of steric factors and non-electrostatic interactions. Selectivity was complementary to that of reversed-phase chromatography (RPC) materials. Excellent purifications were obtained by sequential use of Poly-SUFLOETHYL Aspartamide and RPC columns for purification of peptides from crude tissue extracts. The new cation exchanger is quite promising as a supplement to RPC for general peptide chromatography.