Temperature dependence of the crystal structures of nylon 11

Careful examination of x-ray diffraction patterns from melt-crystallized nylon 11 films show significant discrepancies with the proposed α-form structure. These discrepancies do not disappear after the samples have been annealed. The temperature dependence of the d spacings of the two strongest peaks show further evidence that the melt-crystallized and solution-cast films (α form) possess different crystal structures. These results suggest a different crystal structure for the melt-crystallized films; this would help explain the rather low piezoelectric response of these films and also the failure to observe a rapid decrease in polarization at the transition temperature.     

A reply to arguments against a spur model for muonium formation

A clear distinction is made between the spur model for muonium formation in condensed matter and the alternative hot model. Arguments against the spur model are considered and found lacking. Some new data is presented for aqueous systems: the initial diamagnetic fraction increases with OH^– concentration, and unequivocal muonium inhibition is demonstrated for HClO₄ solutions.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

Similarity over Sp(2n,Z)

This section appears in nearly every issue. Send admission to R.C. Thompson, at the the Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.     

Core excitons in SixGe1-x alloys

The Hjalmarson et al. theory of Frenkel core excitons is applied to the Si and Ge p core excitons in Si_xGe_1-x alloys. The Si 2p and Ge 3p Frenkel excitons' “binding energies” with respect to the conduction-band edge are found to be strong functions of x, with nearly zero binding energies for both excitons near x=0 or 1, and with binding energies of order tenths of eV for compositions x near x=0.2.     

Inverse cascade via Burgers equation

Burgers equation is employed as a pedagogical device for analytically demonstrating the emergence of a form of inverse cascade to the lowest wavenumber in a flow. The transition from highly nonlinear mode-mode coupling to an ordered preference for large scale structure is shown, both analytically (revealing the presence of a global attractor) and via a numerical example. (c) 2000 American Institute of Physics.     

Critical dimensions of the diffusion equation

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d(1) approximately 26 and d(2) approximately 46. We also give refined measurements of the persistence exponents for low dimensions.     

Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at p(c) = 0.592 746 21(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.     

Mean-field solution of the small-world network model

The small-world network model is a simple model of the structure of social networks, which possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either a large or small number of shortcuts.     

Large-scale structure of time evolving citation networks

In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers, patents, or court cases. We describe three different methods of analysis, one based on an expectation-maximization algorithm, one based on modularity optimization, and one based on eigenvector centrality. Using the network of citations between opinions of the United States Supreme Court as an example, we demonstrate how each of these methods can reveal significant structural divisions in the network and how, ultimately, the combination of all three can help us develop a coherent overall picture of the network's shape.     

Growing distributed networks with arbitrary degree distributions

We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with some mild constraints, it is possible by a suitable choice of rules to arrange for the network to have any degree distribution we desire. We also describe a mechanism based on biased random walks by which appropriate rules could be implemented in practice. As an example application, we describe and simulate the construction of a peer-to-peer network optimized to minimize search times and bandwidth requirements.