Gradient expansion for a spiral phase in a spin-fermion model

Starting from a doped spin-fermion model for high-temperature superconductors, we derive an effective continuum theory for the spin degrees of freedom by means of a gradient expansion around a spiral spin configuration. By integrating out the fermions in a path-integral representation, we obtain an effective spin-action. An incommensurate, planar spiral configuration for the spin-background is assumed. The long-wavelength limit is obtained by expanding the effective action in powers of a short distance cutoff. The occurring infinite series can be summed to all orders of the coupling constant by exploiting the constraint that the order parameter lives on a circleS ₁. It is shown that the low-energy limit of the effective action can be mapped onto a O(2) nonlinear model and an additional term due to parity breaking.     

Convex and Linear Orientations of Polytopal Graphs

This paper examines directed graphs related to convex polytopes. For each fixed d -polytope and any acyclic orientation of its graph, we prove there exist both convex and concave functions that induce the given orientation. For each combinatorial class of 3 -polytopes, we provide a good characterization of the orientations that are induced by an affine function acting on some member of the class. Received March 10, 1999, and in revised form May 30, 1999. Online publication May 16, 2000.     

Gas chromatographic retention in uncoated fused silica capillaries

Understanding of retention in uncoated fused‐silica capillaries is of interest due to increased attention on precolumn backflushing in capillary GC. Uncoated capillaries offer several advantages as precolumns compared to coated precolumns. In order to examine the possibility of predicting elution temperatures of alkanes from uncoated capillaries a priori, several sizes of deactivated but uncoated fused‐silica capillaries were evaluated under various operating conditions. Retention was found to depend on dimensionless ramp rate (°C/t_M), sample loading (capacity), flow mode, and column dimensions (probably related to surface area).     

Entwicklung inelastischer Stoffgesetze durch Äquivalenz- und Grenzbetrachtungen und ihre numerische Behandlung

Übersicht Eine Äquivalenzaussage über Fließen, Verfestigung und Erfüllung der Belastungsbedingung führt zu einfachen viskoplastischen Stoffgesetzen, die als Grenzfall Kriechen und Plastizität enthalten. Ein hierauf abgestimmtes numerisches Verfahren erweist sich als besonders flexibel und rechengünstig. Dieses wird durch Vergleich mit Versuchsergebnissen und anderen Rechenverfahren gezeigt.

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Summary An equivalence Statement on flow, hardening and fulfilling of the loading condition leads to simple viscoplastic material equations which include creep and plasticity as limit cases. A numerical algorithm, based on the derived equations proves to be very flexible and efficient. This is shown by means of comparisons with test results and other computations.

     

A note on convex cones and constraint qualifications in infinite-dimensional vector spaces

In connection with mathematical programming in infinite-dimensional vector spaces, Zowe has studied the relationship between the Slater constraint qualification and a formally weaker qualification used by Kurcyusz. The attractive feature of the latter is that it involves only active constraints. Zowe has proved that, in barreled spaces, the two qualifications are equivalent and has asked whether the assumption of barreledness is superfluous. By studying cores and interiors of convex cones, we show that the two constraint qualifications are equivalent in a given topological vector spaceE iff every barrel inE is a neighborhood of the origin. Thus, whenE is locally convex, the two constraint qualifications are equivalent iffE is barreled. Other questions of Zowe are also answered.This research was supported in part by the Office of Naval Research, and in part by the Sonderforschungsbereich 21, Institut für Operations Research, Bonn, Federal Republic of Germany. The author is indebted to Professor J. Zowe for some helpful comments.