Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

An Enumerative Geometry for Magic and Magilatin Labellings

A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. Our results differ from previous ones because we require that the entries in the square all be different from each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from set systems to rational linear forms. Dedicated to the memory of Claudia Zaslavsky, 1917–2006 Received August 10, 2005     

Metric spaces with discrete topological fundamental group

With a certain natural topology, the fundamental group of a locally path connected metric space X becomes discrete if and only if X is semilocally simply connected. We include some related material and offer a counterexample to a similar result.     

Ueber die Hydratation und Erhärtung des Zementes

Ohne Zusammenfassung     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

     

Stereoselective migration of sterically hindered organoboranes in cyclic and acyclic systems. A stereoselective allylic C-H activation reaction

The thermal migration of cyclic and acyclic organoboranes were studied. In most cases, a stereoselective 1,2-dyotropic migration was observed, allowing the stereocontrol of three contiguous chiral centers. Scope and limitations of this thermal migration are presented.