Small Extended Generalized Quadrangles

We consider extensions of generalized quadrangles with parameters (s, t), and establish lower bounds (in terms of s and t) for the number of points, sometimes under additional hypotheses. We also study the structure of geometries attaining these bounds, give several constructions and some uniqueness proofs, and examine the question of further extensions

Plausibility functions and exact frequentist inference

In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general framework for the construction of exact frequentist procedures based on plausibility functions. It is shown that the plausibility function-based tests and confidence regions have the desired frequentist properties in finite samples---no large-sample justification needed. An extension of the proposed method is also given for problems involving nuisance parameters. Examples demonstrate that the plausibility function-based method is both exact and efficient in a wide variety of problems.Comment: 21 pages, 5 figures, 3 table

Interactions, Distribution of Pinning Energies, and Transport in the Bose Glass Phase of Vortices in Superconductors

We study the ground state and low energy excitations of vortices pinned to columnar defects in superconductors, taking into account the long--range interaction between the fluxons. We consider the ``underfilled'' situation in the Bose glass phase, where each flux line is attached to one of the defects, while some pins remain unoccupied. By exploiting an analogy with disordered semiconductors, we calculate the spatial configurations in the ground state, as well as the distribution of pinning energies, using a zero--temperature Monte Carlo algorithm minimizing the total energy with respect to all possible one--vortex transfers. Intervortex repulsion leads to strong correlations whenever the London penetration depth exceeds the fluxon spacing. A pronounced peak appears in the static structure factor $S(q)$ for low filling fractions $f \leq 0.3$. Interactions lead to a broad Coulomb gap in the distribution of pinning energies $g(\epsilon)$ near the chemical potential $\mu$, separating the occupied and empty pins. The vanishing of $g(\epsilon)$ at $\mu$ leads to a considerable reduction of variable--range hopping vortex transport by correlated flux line pinning.Comment: 16 pages (twocolumn), revtex, 16 figures not appended, please contact [email protected]

Kosterlitz Thouless Universality in Dimer Models

Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute monomer-monomer and dimer-dimer correlations at zero monomer density (chiral limit) accurately on large lattices. This makes it possible to show convincingly, for the first time, that these models undergo a finite temperature phase transition which belongs to the Kosterlitz-Thouless universality class. We find that this universality class is unaffected even in the large N limit. This shows that the mean field analysis often used in this limit breaks down in the critical region.Comment: 4 pages, 4 figure

Universality of Frequency and Field Scaling of the Conductivity Measured by Ac-Susceptibility of a Ybco-Film

Utilizing a novel and exact inversion scheme, we determine the complex linear conductivity $\sigma (\omega )$ from the linear magnetic ac-susceptibility which has been measured from 3\,mHz to 50\,MHz in fields between 0.4\,T and 4\,T applied parallel to the c-axis of a 250\,nm thin disk. The frequency derivative of the phase $\sigma ''/\sigma '$ and the dynamical scaling of $\sigma (\omega)$ above and below $T_g(B)$ provide clear evidence for a continuous phase transition at $T_g$ to a generic superconducting state. Based on the vortex-glass scaling model, the resulting critical exponents $\nu$ and $z$ are close to those frequently obtained on films by other means and associated with an 'isotropic' vortex glass. The field effect on $\sigma(\omega)$ can be related to the increase of the glass coherence length, $\xi_g\sim B$.Comment: 8 pages (5 figures upon request), revtex 3.0, APK.94.01.0

Properties of Flares-Generated Seismic Waves on the Sun

The solar seismic waves excited by solar flares (``sunquakes'') are observed as circular expanding waves on the Sun's surface. The first sunquake was observed for a flare of July 9, 1996, from the Solar and Heliospheric Observatory (SOHO) space mission. However, when the new solar cycle started in 1997, the observations of solar flares from SOHO did not show the seismic waves, similar to the 1996 event, even for large X-class flares during the solar maximum in 2000-2002. The first evidence of the seismic flare signal in this solar cycle was obtained for the 2003 ``Halloween'' events, through acoustic ``egression power'' by Donea and Lindsey. After these several other strong sunquakes have been observed. Here, I present a detailed analysis of the basic properties of the helioseismic waves generated by three solar flares in 2003-2005. For two of these flares, X17 flare of October 28, 2003, and X1.2 flare of January 15, 2005, the helioseismology observations are compared with simultaneous observations of flare X-ray fluxes measured from the RHESSI satellite. These observations show a close association between the flare seismic waves and the hard X-ray source, indicating that high-energy electrons accelerated during the flare impulsive phase produced strong compression waves in the photosphere, causing the sunquake. The results also reveal new physical properties such as strong anisotropy of the seismic waves, the amplitude of which varies significantly with the direction of propagation. The waves travel through surrounding sunspot regions to large distances, up to 120 Mm, without significant decay. These observations open new perspectives for helioseismic diagnostics of flaring active regions on the Sun and for understanding the mechanisms of the energy release and transport in solar flares.Comment: 12 pages, 4 figures, submitted to Ap

Can we Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements?

The availability of vector magnetogram sequences with sufficient accuracy and cadence to estimate the time derivative of the magnetic field allows us to use Faraday's law to find an approximate solution for the electric field in the photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined -- Faraday's law provides no information about the electric field that can be derived the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections.Comment: Solar Physics, in press. 14 pages, 3 figure

Aging dynamics of heterogeneous spin models

We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and continuous spin glasses. In order to study dynamic heterogeneities induced by quenched disorder, we consider single-spin observables for a given disorder realization. In some simple cases we are able to provide analytical predictions for single-spin response and correlation functions. The results strongly depend upon the model considered. It turns out that, by comparing the slow evolution of a few different degrees of freedom, one can distinguish between different dynamic classes. As a conclusion we present the general properties which can be induced from our results, and discuss their relation with thermometric arguments.Comment: 39 pages, 36 figure

Critical end point behaviour in a binary fluid mixture

We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particularly that in the coexistence diameter, should also be detectable experimentally.Comment: 17 pages Revtex, 11 epsf figures. To appear in Phys. Rev.

Two-Dimensional Spectroscopy of Photospheric Shear Flows in a Small delta Spot

In recent high-resolution observations of complex active regions, long-lasting and well-defined regions of strong flows were identified in major flares and associated with bright kernels of visible, near-infrared, and X-ray radiation. These flows, which occurred in the proximity of the magnetic neutral line, significantly contributed to the generation of magnetic shear. Signatures of these shear flows are strongly curved penumbral filaments, which are almost tangential to sunspot umbrae rather than exhibiting the typical radial filamentary structure. Solar active region NOAA 10756 was a moderately complex, beta-delta sunspot group, which provided an opportunity to extend previous studies of such shear flows to quieter settings. We conclude that shear flows are a common phenomenon in complex active regions and delta spots. However, they are not necessarily a prerequisite condition for flaring. Indeed, in the present observations, the photospheric shear flows along the magnetic neutral line are not related to any change of the local magnetic shear. We present high-resolution observations of NOAA 10756 obtained with the 65-cm vacuum reflector at Big Bear Solar Observatory (BBSO). Time series of speckle-reconstructed white-light images and two-dimensional spectroscopic data were combined to study the temporal evolution of the three-dimensional vector flow field in the beta-delta sunspot group. An hour-long data set of consistent high quality was obtained, which had a cadence of better than 30 seconds and sub-arcsecond spatial resolution.Comment: 23 pages, 6 gray-scale figures, 4 color figures, 2 tables, submitted to Solar Physic