Directed paths with random phases

Directed Feynman paths in 1 + 1 dimensions that acquire random phases are examined numerically and analytically. This problem is relevant for the behavior of the conductance in two-dimensional amorphous insulators in the variable-range-hopping regime. Large-scale numerical simulations were performed on a model with short-range correlations. For the scaling of the transverse fluctuations ( t^ν), we obtain ν = 0.68 ± 0.025; and for the r.m.s free-energy fluctuations ( t^ω), we obtain ω = 0.335 ± 0.01. Up to 100 000 random samples were used for times as large as 2000. These results seem to exclude a recent conjecture that ν = 3/4 and ω = 1/2. Two versions of a model with long-range correlations are solved and shown to yield ν = 1/2; a physical explanation is given.     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

Fiber formation via solution spinning of the cellulose/ammonia/ammonium thiocyanate system

Fiber formation via the cellulose/ammonia/ammonium thiocyanate system by wet spinning has been investigated. This report presents a characterization of the structure and tensile properties of fibers spun under various coagulation conditions. Microscopic observations showed that the molecular size of coagulant was the dominant factor governing the crosssectional shape of the fibers. Density, birefringence, and crystallinity data indicated that a higher cellulose concentration and lower coagulation temperature favored development of a fiber with a denser and more oriented structure. Under optimum conditions, a welldefined fibrillar structure was obtained. Fiber tensile property measurements suggested the existence of a linear relationship between the fiber breaking tenacity and the product of the square of the Hermans' orientation factor and the infrared crystallinity index.     

Determination of the Tolman cone angle from crystallographic parameters and a statistical analysis using the crystallographic data base

Summary A new method of evaluating the Tolman cone angle from X-ray structural data available from the Cambridge Crystallographic Data Base has been developed and a statistical analysis of the cone angles of the phosphines PPh₃, PMe₂Ph, PMePh₂, PMe₃, PEt₃ and PCy₃ (Cy = cyclohexyl) in transition metal complexes has been completed.     

Scattering of Magnetic Edge States

We consider a charged particle following the boundary of a two dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering operator attains a limit for large magnetic fields which preserves Landau bands. We interpret the corresponding scattering phases in terms of classical trajectories. Communicated by Yosi Avron submitted 23/02/05, accepted 3/05/05     

On the Immersion Relation and an Embedding Problem for Infinite Graphs

Recent results on the immersion relation for graphs are applied to show that there exist (uncountable) graphs A and G such that G contains n disjoint copies of A for each positive integer n, but the graph N₀A consisting of infinitely many disjoint copies of A does not embed in G, where by ‘embedding’ we mean ‘immersion in the weak sense’.     

Depth profiling of latex blends of fluorinated and fluorine‐free acrylates with laser‐induced secondary mass spectrometry

We explored phase separation and self‐assembly of perfluoroalkyl segments at the surface of polymer films obtained from latices of semifluorinated acrylate copolymers and the corresponding latex blends of nonfluorinated and semifluorinated polyacrylates. With laser‐induced secondary mass spectrometry the fluorine distribution was measured after annealing above the minimum film‐forming temperature of the polymers up to a depth of several micrometers. Depth profiles of a semifluorinated acrylate homopolymer and latex blends thereof with fluorine‐free alkylacrylates with 25, 50, and 75 mol % semifluorinated acrylate as well as a copolymer comprised of alkyl acrylate and semifluorinated acrylate (50/50 mol %) were investigated. In the case of latex blends containing both semifluorinated polyacrylates and fluorine‐free or low‐fluorine polymers, self‐assembly accounted for enrichment of the perfluoroalkyl segments at the surface. Coatings exhibiting low surface energy and having a substantially reduced total fluorine content were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 360–367, 2003