Shuffle operations on discrete paths

AbstractWe consider the shuffle operation on paths and study some parameters. In the case of square lattices, shuffling with a particular periodic word (of period 2) corresponding to paperfoldings reveals some characteristic properties: closed paths remain closed; the area and perimeter double; the center of gravity moves under a 45∘ rotation and a 2 zoom factor. We also observe invariance properties for the associated Dragon curves. Moreover, replacing square lattice paths by paths involving 2kπ/N-turns, we find analogous results using more general shuffles

Breit Hamiltonian and QED Effects for Spinless Particles

We describe a simplified derivation for the relativistic corrections of order $\alpha^4$ for a bound system consisting of two spinless particles. We devote special attention to pionium, the bound system of two oppositely charged pions. The leading quantum electrodynamic (QED) correction to the energy levels is of the order of $\alpha^3$ and due to electronic vacuum polarization. We analyze further corrections due to the self-energy of the pions, and due to recoil effects, and we give a complete result for the scalar-QED leading logarithmic corrections which are due to virtual loops involving only the scalar constituent particles (the pions); these corrections are of order $\alpha^5 \ln \alpha$ for S states.Comment: 12 pages, LaTeX; references added (J. Phys. B, in press

Searching for New Physics in Leptonic Decays of Bottomonium

New Physics can show up in various well-known processes already studied in the Standard Model, in particular by modifying decay rates to some extent. In this work, I examine leptonic decays of $\Upsilon$ vector resonances of bottomonium below $B\bar{B}$ production, subsequent to a magnetic dipole radiative structural transition of the vector resonance yielding a pseudoscalar continuum state, searching for the existence of a light Higgs-like neutral boson that would imply a slight but experimentally measurable breaking of lepton universality.Comment: LaTeX, 12 pages, 1 EPS figur

Relativistic and Binding Energy Corrections to Direct Photon Production In Upsilon Decay

A systematic gauge-invariant method is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v^2) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.Comment: 13 pages, LateX, One figure (to be published in Phys. Rev. D, Sept. 1, 1996

Biomechanical effect of pedicle screw distribution in AIS instrumentation using a segmental translation technique: computer modeling and simulation

BACKGROUND: Efforts to select the appropriate number of implants in adolescent idiopathic scoliosis (AIS) instrumentation are hampered by a lack of biomechanical studies. The objective was to biomechanically evaluate screw density at different regions in the curve for AIS correction to test the hypothesis that alternative screw patterns do not compromise anticipated correction in AIS when using a segmental translation technique. METHODS: Instrumentation simulations were computationally performed for 10 AIS cases. We simulated simultaneous concave and convex segmental translation for a reference screw pattern (bilateral polyaxial pedicle screws with dorsal height adjustability at every level fused) and four alternative patterns; screws were dropped respectively on convex or concave side at alternate levels or at the periapical levels (21 to 25% fewer screws). Predicted deformity correction and screw forces were compared. RESULTS: Final simulated Cobb angle differences with the alternative screw patterns varied between 1 degrees to 5 degrees (39 simulations) and 8 degrees (1 simulation) compared to the reference maximal density screw pattern. Thoracic kyphosis and apical vertebral rotation were within 2 degrees of the reference screw pattern. Screw forces were 76 +/- 43 N, 96 +/- 58 N, 90 +/- 54 N, 82 +/- 33 N, and 79 +/- 42 N, respectively, for the reference screw pattern and screw dropouts at convex alternate levels, concave alternate levels, convex periapical levels, and concave periapical levels. Bone-screw forces for the alternative patterns were higher than the reference pattern (p 0.28). Alternate dropout screw forces were higher than periapical dropouts (p < 0.05). CONCLUSIONS: Using a simultaneous segmental translation technique, deformity correction can be achieved with 23% fewer screws than maximal density screw pattern, but resulted in 25% higher bone-screw forces. Screw dropouts could be either on the convex side or on the concave side at alternate levels or at periapical levels. Periapical screw dropouts may more likely result in lower bone-screw force increase than alternate level screw dropouts

Adaptive soundscape design for liveable urban spaces: a hybrid methodology across environmental acoustics and sonic art

The aim of this research is to identify and implement soundscape improvement strategies in urban areas based on loudspeaker placements in the outdoor environment and the use of a computer-based system for adaptive soundscape generation, integrating sonic art practice with acoustic engineering rigour

Cusps in K --> 3 pi decays

The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.Comment: 14 pages, 3 figures, uses Elsevier styl

Effective field theories for QED bound states: extending Nonrelativistic QED to study retardation effects

Nonrelativistic QED bound states are difficult to study because of the presence of at least three widely different scales: the masses, three-momenta ($p_i$) and kinetic energies ($K_i$) of the constituents. Nonrelativistic QED (NRQED), an effective field theory developed by Caswell and Lepage, simplifies greatly bound state calculations by eliminating the masses as dynamical scales. As we demonstrate, NRQED diagrams involving only photons of energy $E_\gamma \simeq p_i$ contribute, in any calculation, to a unique order in $\alpha$. This is not the case, however, for diagrams involving photons with energies $E_\gamma \simeq K_i$ (``retardation effects"), for which no simple counting counting rules can be given. We present a new effective field theory in which the contribution of those ultra-soft photons can be isolated order by order in $\alpha$. This is effectively accomplished by performing a multipole expansion of the NRQED vertices.Comment: 39 pages, 9 Postscript figures, uses Rev.tex V3.0 and epsf.te