Electronic Raman scattering in Magnetite, Spin vs. Charge gap

We report Raman scattering data of single crystals of magnetite (Fe3O4) with Verwey transition temperatures (Tv) of 123 and 117K, respectively. Both single crystals reveal broad electronic background extending up to 900 wavenumbers (~110 meV). Redistribution of this background is observed when samples are cooled below Tv. In particular, spectra of the low temperature phase show diminished background below 300 wavenumbers followed by an enhancement of the electronic background between 300 and 400 wavenumbers. To enhance the effect of this background redistribution we divide the spectra just below the transition by the spectra just above the transition. A resultant broad peak-like feature is observed, centered at 370 wavenumbers (45 meV). The peak position of this feature does not scale with the transition temperature. We discuss two alternative assignments of this feature to a spin or charge gap in magnetite.Comment: 4 figures, 1 tabl

Monopole clusters, Z(2) vortices and confinement in SU(2)

We extend our previous study of magnetic monopole currents in the maximally Abelian gauge [hep-lat/9712003] to larger lattices at small lattice spacings (20^4 at beta = 2.5 and 32^4 at beta = 2.5115). We confirm that at these weak couplings there continues to be one monopole cluster that is very much longer than the rest and that the string tension, K, is entirely due to it. The remaining clusters are compact objects whose population as a function of radius follows a power law that deviates from the scale invariant form, but much too weakly to suggest a link with the analytically calculable size distribution of small instantons. We also search for traces of Z(2) vortices in the Abelian projected fields; either as closed loops of `magnetic' flux or through appropriate correlations amongst the monopoles. We find, by direct calculation, that there is no confining condensate of such flux loops. We also find, through the calculation of doubly charged Wilson loops within the monopole fields, that there is no suppression of the q=2 effective string tension out to at distances of at least r ~ 1.6/sqrt{K}, suggesting that if there are any vortices they are not encoded in the monopole fields.Comment: 26 pages of LaTeX and PostScript figure

Three-photon detachment of electrons from the fluorine negative ion

Absolute three-photon detachment cross sections are calculated for the fluorine negative ion within the lowest-order perturbation theory. The Dyson equation of the atomic many-body theory is used to obtain the ground-state 2p wavefunction with correct asymptotic behaviour, corresponding to the true (experimental) binding energy. We show that in accordance with the adiabatic theory (Gribakin and Kuchiev 1997 {Phys. Rev. A} {\bf 55} 3760) this is crucial for obtaining absolute values of the multiphoton cross sections. Comparisons with other calculations and experimental data are presented.Comment: 10 pages, two figures, Latex, IOP styl

Dynamic multilateral markets

We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish

Threshold detachment of negative ions by electron impact

The description of threshold fragmentation under long range repulsive forces is presented. The dominant energy dependence near threshold is isolated by decomposing the cross section into a product of a back ground part and a barrier penetration probability resulting from the repulsive Coulomb interaction. This tunneling probability contains the dominant energy variation and it can be calculated analytically based on the same principles as Wannier's description for threshold ionization under attractive forces. Good agreement is found with the available experimental cross sections on detachment by electron impact from $D^{-}$, $O^{-}$ and $B^{-}$.Comment: 4 pages, 4 figures (EPS), to appear in Phys.Rev.Lett, Feb. 22nd, 199

Confining strings in SU(N) gauge theories

We calculate the string tensions of $k$-strings in SU($N$) gauge theories in both 3 and 4 dimensions. In D=3+1, we find that the ratio of the $k=2$ string tension to the $k = 1$ fundamental string tension is consistent, at the $2 \sigma$ level, with both the M(-theory)QCD-inspired conjecture and with `Casimir scaling'. In D=2+1 we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial $k$-string tensions also satisfy approximate Casimir scaling. We point out that approximate Casimir scaling arises naturally if the cross-section of the flux tube is nearly independent of the flux carried, and that this will occur in an effective dual superconducting description, if we are in the deep-London limit. We estimate, numerically, the intrinsic width of $k$-strings in D=2+1 and indeed find little variation with $k$. In addition to the stable $k$-strings we investigate some ofthe unstable strings, finding in D=2+1 that they satisfy (approximate) Casimir scaling. We also investigate the basic assumption that confining flux tubes are described by an effective string theory at large distances. We estimate the coefficient of the universal L\"uscher correction from periodic strings that are longer than 1 fermi, and find $c_L=0.98(4)$ in D=3+1 and $c_L=0.558(19)$ in D=2+1. These values are within $2 \sigma$ of the simple bosonic string values and are inconsistent with other simple effective string theories.Comment: 57 pages, 11 figures. Errors on fits reduced by altering the analysis to a standard one. Conclusions unchanged; note addedchanged. Some typos correcte

Interactive 4-D Visualization of Stereographic Images From the Double Orthogonal Projection

The double orthogonal projection of the 4-space onto two mutually perpendicular 3-spaces is a method of visualization of four-dimensional objects in a three-dimensional space. We present an interactive animation of the stereographic projection of a hyperspherical hexahedron on a 3-sphere embedded in the 4-space. Described are synthetic constructions of stereographic images of a point, hyperspherical tetrahedron, and 2-sphere on a 3-sphere from their double orthogonal projections. Consequently, the double-orthogonal projection of a freehand curve on a 3-sphere is created inversely from its stereographic image. Furthermore, we show an application to a synthetic construction of a spherical inversion and visualizations of double orthogonal projections and stereographic images of Hopf tori on a 3-sphere generated from Clelia curves on a 2-sphere.Comment: ICGG 2020 submissio

Running marathons in high school: A 5-year review of injury in a structured training program

Objective: The aim in this study was to quantify the number, nature, and severity of injuries sustained by male and female high school students who took part in a running training program that culminated in the completion of a half or full marathon. Design: This study is a retrospective clinical audit. Methods: Injury reports from high school students (grades 9 – 12) who participated in a half or full marathon 30-week progressive training program comprising four training days per week (three running days and one cross-training day) were reviewed. The number of runners completing a marathon, together with the number, nature, severity of injuries, and treatment types, as reported to the program physiotherapist, were the main outcome measures. Results: Program completion was 96% (n = 448/469). Of all participants, 186 (39.6 %) were injured, with 14 withdrawing from the program due to injury. For those who completed a marathon, 172 (38 %) reported 205 musculoskeletal injuries (age of injured runners: 16.3 ± 1.1 years; 88 girls (51.2 %) and 84 boys (48.8 %)). More than half (n = 113, 55.1 %) of the reported injuries were soft tissue injuries. Most injuries were localized to the lower leg (n = 88, 42.9 %) and were of a minor nature (n = 181, 90 %), requiring only 1–2 treatments. Conclusions: There was a low number of relatively minor injuries for high school participants taking part in a graduated and supervised marathon training program. The injury definition was conservative (i.e., any attendance to physiotherapist) and the relative severity of injuries was minor (i.e., requiring 1 – 2 treatment sessions). Overall, these results do not support a need to restrict high school students from taking part in marathon running, though continued emphasis on graduated program development and close supervision of young participants is recommended

Abelian Monopoles in SU(2) Lattice Gauge Theory as Physical Objects

By numerical calculations we show that the abelian monopole currents are locally correlated with the density of SU(2) lattice action. The correlations are larger by the order of magnitude in the maximal abelian projection than in the projections which correspond to the diagonalization of Polyakov line and to the diagonalization of the plaquette. These facts show that (at least) in the maximal abelian projection the monopoles are the physical objects, they carry the SU(2) action. The larger value of \beta, the larger the relative action carried by monopole. Calculations on the asymmetric lattice show that this correlation exists also in the deconfinement phase of gluodynamics.Comment: 6 pages, RevTeX, 3 figures, uses epsf.sty; to be published in Phys.Rev.Lett., replaced to match version accepted for publicatio