Morphology of polyanhydride copolymers: Time‐resolved small‐angle X‐ray scattering studies of crystallization

Synchrotron small‐angle X‐ray scattering (SAXS) was used to study the isothermal crystallization kinetics of a family of polyanhydride copolymers consisting of 1,6‐bis(p‐carboxyphenoxy)hexane and sebacic acid monomers. In situ SAXS experiments permitted the direct observation of the crystallization kinetics. The structural parameters (the long period, lamellar thickness, and degree of crystallinity) were obtained from Lorentz‐corrected intensity profiles, one‐dimensional correlation functions, and interface distribution functions to form a comprehensive picture of the crystal morphology. The combination of these three analyses provided information not only on the lamellar dimensions but also on the polydispersity (nonuniformity) of these dimensions. Where possible, the crystallization kinetics were interpreted with a modified version of the Avrami equation. The results can be used to perform the rational design of controlled‐drug‐release formulations because crystallinity affects drug‐release kinetics. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 463–477, 2005     

Modular invariant partition functions in the quantum Hall effect

We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W_1+∞ algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.     

On the effects of an uncertainty on the evolution law in dynamical systems

We show that a small perturbation of the evolution law of chaotic dynamical systems is practically equivalent to the finite precision on the knowledge of the initial condition. In spite of the short predictability time t_p on a single trajectory we found that the statistical properties are not sensitive to small changes in the evolution law or initial probability distribution. This feature holds also for correlation functions at a delay larger than t_p. We discuss the roundoff effects on integrable systems.     

A Laplace integral on a Kähler manifold and Calabi's diastasis function

In this paper we give a different proof of Engliš's result [J. Reine Angew. Math. 528 (2000) 1-39] about the asymptotic expansion of a Laplace integral on a real analytic Kähler manifold (M,g) by using the link between the metric g and the associated Calabi's diastasis function D. We also make explicit the connection between the coefficients of Engliš' expansion and Gray's invariants [Michigan Math. J. (1973) 329-344].     

Bis(dibenzo[c.e][1,2]oxaphosphorino)dichloroplatinum Complexes

Reaction of a series of P-amino and P-cycloalkoxy dibenzo[c.e][1,2]oxaphosphorines (1), (3) and (5) with cis-bis(benzonitrile)dichloroplatinum(II) afforded the title bis(dibenzooxaphosphorino) complexes (2), (4) and (6), respectively. In the case of chiral P-substituents, the complexes (4) and (6) were obtained in homo and heterochiral forms. Stereospecific ¹J(¹⁹⁵Pt–P) couplings found in the ³¹P-n.m.r. spectra of the products (2), (4) and (6) suggested the cis orientation of the identical substituents.     

Numerical aspects of TV flow

The singular diffusion equation called total variation (TV) flow plays an important role in image processing and appears to be suitable for reducing oscillations in other types of data. Due to its singularity for zero gradients, numerical discretizations have to be chosen with care. We discuss different ways to implement TV flow numerically, and we show that a number of discrete versions of this equation may introduce oscillations such that the scheme is in general not TV-decreasing. On the other hand, we show that TV flow may act self-stabilising: even if the total variation increases by the filtering process, the resulting oscillations remain bounded by a constant that is proportional to the ratio of mesh widths. For our analysis we restrict ourselves to the one-dimensional setting.