Topology of Cell-Aggregated Planar Graphs

We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs--fractal dimension of the perimeter, distribution of shortest paths between pairs of nodes and topological betweenness of nodes and links. We show how these topological properties depend on the control parameters of the aggregation process and discuss their relevance for the conduction of current in self-assembled nanopatterns.Comment: 8 pages, 5 figure

Measuring the Hausdorff Dimension of Quantum Mechanical Paths

We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^{\alpha}$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{\alpha }{\alpha - 1}$ if $\alpha > 2$ and $d_{H}=2$ if $\alpha \leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure

The Enigmatic Radio Afterglow of GRB 991216

We present wide-band radio observations spanning from 1.4 GHz to 350 GHz of the afterglow of GRB 991216, taken from 1 to 80 days after the burst. The optical and X-ray afterglow of this burst were fairly typical and are explained by a jet fireball. In contrast, the radio light curve is unusual in two respects: (a) the radio light curve does not show the usual rise to maximum flux on timescales of weeks and instead appears to be declining already on day 1 and (b) the power law indices show significant steepening from the radio through the X-ray bands. We show that the standard fireball model, in which the afterglow is from a forward shock, is unable to account for (b) and we conclude that the bulk of the radio emission must arise from a different source. We consider two models, neither of which can be ruled out with the existing data. In the first (conventional) model, the early radio emission is attributed to emission from the reverse shock as in the case of GRB 990123. We predict that the prompt optical emission would have been as bright (or brighter) than 8th magnitude. In the second (exotic) model, the radio emission originates from the forward shock of an isotropically energetic fireball (10^54 erg) expanding into a tenuous medium (10^-4 cm^-3). The resulting fireball would remain relativistic for months and is potentially resolvable with VLBI techniques. Finally, we note that the near-IR bump of the afterglow is similar to that seen in GRB 971214 and no fireball model can explain this bump.Comment: ApJ, submitte

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It has long been established that the appropriate way of reslicing volume MR images is to use the method of sinc interpolation [2, 4]. We have recently needed to implement this method ourselves and have found, like other authors before us, that large convolution kernels are needed in order to produce accurate reslice data, suitable for subtraction. This requirement has led many groups to investigate the use of specialised hardware and software in order to perform data analysis within sensible timescales. However, we have found that the major component of the error introduced from interpolation with small kernels, is actually due to a first order normalisation problem introduced by truncation. In this paper we demonstrate the characteristics of this problem on real data and show how it can be eliminated, so that accurate reslice data can be obtained with small kernels. Unlike other recent suggestions for correcting such effects [3], the required changes in computation are simple and significantly reduce the processing requirement for a given interpolation accuracy. Renormalised Sinc Interpolation. There are several techniques that one can adopt to solve the problem of image interpolation. One is to assume a particular prior functional model for a local region of the image data, estimate the function parameters from a maximum likelihood metric and then recompute intermediate sites from the functiona

Field theory simulation of Abelian-Higgs cosmic string cusps

We have performed a lattice field theory simulation of cusps in Abelian-Higgs cosmic strings. The results are in accord with the theory that the portion of the strings which overlaps near the cusp is released as radiation. The radius of the string cores which must touch to produce the evaporation is approximately $r = 1$ in natural units. In general, the modifications to the string shape due to the cusp may produce many cusps later in the evolution of a string loop, but these later cusps will be much smaller in magnitude and more closely resemble kinks.Comment: 9 pages, RevTeX, 13 figures with eps

Vortex Dynamics in Selfdual Maxwell-Higgs Systems with Uniform Background Electric Charge Density

We introduce selfdual Maxwell-Higgs systems with uniform background electric charge density and show that the selfdual equations satisfied by topological vortices can be reduced to the original Bogomol'nyi equations without any background. These vortices are shown to carry no spin but to feel the Magnus force due to the shielding charge carried by the Higgs field. We also study the dynamics of slowly moving vortices and show that the spin-statistics theorem holds to our vortices.Comment: 24 pages + 2 figures ( not included), Cu-TP-611, IASSNS-HEP-93/33, NSF-ITP-93-13

Discovery of Early Optical Emission from GRB 021211

We report our discovery and early time optical, near-infrared, and radio wavelength follow-up observations of the afterglow of the gamma-ray burst GRB 021211. Our optical observations, beginning 21 min after the burst trigger, demonstrate that the early afterglow of this burst is roughly three magnitudes fainter than the afterglow of GRB 990123 at similar epochs, and fainter than almost all known afterglows at an epoch of 1d after the GRB. Our near-infrared and optical observations indicate that this is not due to extinction. Combining our observations with data reported by other groups, we identify the signature of a reverse shock. This reverse shock is not detected to a 3-sigma limit of 110 uJy in an 8.46-GHz VLA observation at t=0.10d, implying either that the Lorentz factor of the burst gamma <~ 200, or that synchrotron self-absorption effects dominate the radio emission at this time. Our early optical observations, near the peak of the optical afterglow (forward shock), allow us to characterize the afterglow in detail. Comparing our model to flux upper limits from the VLA at later times, t >~ 1 week, we find that the late-time radio flux is suppressed by a factor of two relative to the >~ 80 uJy peak flux at optical wavelengths. This suppression is not likely to be due to synchrotron self-absorption or an early jet break, and we suggest instead that the burst may have suffered substantial radiative corrections.Comment: 13 pages, 2 figures, ApJL accepted; edits for lengt

A Coordinated Radio Afterglow Program

We describe a ground-based effort to find and study afterglows at centimeter and millimeter wavelengths. We have observed all well-localized gamma-ray bursts in the Northern and Southern sky since BeppoSAX first started providing rapid positions in early 1997. Of the 23 GRBs for which X-ray afterglows have been detected, 10 have optical afterglows and 9 have radio afterglows. A growing number of GRBs have both X-ray and radio afterglows but lack a corresponding optical afterglow.Comment: To appear in Proc. of the 5th Huntsville Gamma-Ray Burst Symposium, 5 pages, LaTe