Emergence Pattern of Stoneflies (Plecoptera) in Otter Creek, Wisconsin

(excerpt) Until recently, little was known about life cycles of stoneflies in the Great Lakes region. Frison (1935) and Harden and Mickel (1952) reported dates of collections of adult stoneflies in,Illinois and Minnesota respectively, and thus suggested emergence patterns for midwestern species. But, as Harper and Pilon (1970) point out, the duration of the emergence period cannot be determined solely from adult collection records because of the relatively long life-span of adults. Recent studies in Quebec (Harper and Magniri 1969, Harper and Pilon 1970) and Ontario (Harper and Hynes 1972, Harper 1973a, 1973b) have added significantly to our knowledge of the life cycles and ecology of eastern Nearctic stoneflies

Self-Similarity and Localization

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is characterized by a single strong coupling fixed point of the renormalization equations. This fixed point also describes the generalized Harper model with next nearest neighbor interaction below a certain threshold. Above the threshold, the fluctuations in the generalized Harper model are described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include

Bethe ansatz for the Harper equation: Solution for a small commensurability parameter

The Harper equation describes an electron on a 2D lattice in magnetic field and a particle on a 1D lattice in a periodic potential, in general, incommensurate with the lattice potential. We find the distribution of the roots of Bethe ansatz equations associated with the Harper equation in the limit as alpha=1/Q tends to 0, where alpha is the commensurability parameter (Q is integer). Using the knowledge of this distribution we calculate the higher and lower boundaries of the spectrum of the Harper equation for small alpha. The result is in agreement with the semiclassical argument, which can be used for small alpha.Comment: 17 pages including 5 postscript figures, Latex, minor changes, to appear in Phys.Rev.

Tributes to Professor Robert Berkley Harper

In 1977, I began teaching at The University of Pittsburgh Law School and in short order one of my closest friends during my tenure there was Professor Robert “Bob” Harper. I wondered when I was hired whether I was selected because I looked strikingly similar to Bob, and perhaps the faculty thought my favoring Professor Harper would make my assimilation into the law school faculty that much easier. Students constantly called me Professor Harper and, indeed, many on the faculty called me Bob for several years; I never bothered to correct them. I thought if they paid that little attention to detail in law school, I would just let them go through life missing some of the finer points their education, and life for that matter, has to offer

Capstone 2019 Art and Art History Senior Projects

This booklet profiles Art Senior Projects by Angelique J. Acevedo, Arin Brault, Bailey Harper, Sue Holz, Yirui Jia, Jianrui Li, Annora B. Mack, Emma C. Mugford, Inayah D. Sherry, Jacob H. Smalley, Laura Grace Waters and Laurel J. Wilson. This booklet profiles Art History Senior Projects by Gabriella Bucci, Melissa Casale, Bailey Harper, Erin O\u27Brien and Laura Grace Waters

Localization problem of the quasiperiodic system with the spin orbit interaction

We study one dimensional quasiperiodic system obtained from the tight-binding model on the square lattice in a uniform magnetic field with the spin orbit interaction. The phase diagram with respect to the Harper coupling and the Rashba coupling are proposed from a number of numerical studies including a multifractal analysis. There are four phases, I, II, III, and IV in this order from weak to strong Harper coupling. In the weak coupling phase I all the wave functions are extended, in the intermediate coupling phases II and III mobility edges exist, and accordingly both localized and extended wave functions exist, and in the strong Harper coupling phase IV all the wave functions are localized. Phase I and Phase IV are related by the duality, and phases II and III are related by the duality, as well. A localized wave function is related to an extended wave function by the duality, and vice versa. The boundary between phases II and III is the self-dual line on which all the wave functions are critical. In the present model the duality does not lead to pure spectra in contrast to the case of Harper equation.Comment: 10 pages, 11 figure