Modulus Stabilization with Bulk Fields

We propose a mechanism for stabilizing the size of the extra dimension in the Randall-Sundrum scenario. The potential for the modulus field that sets the size of the fifth dimension is generated by a bulk scalar with quartic interactions localized on the two 3-branes. The minimum of this potential yields a compactification scale that solves the hierarchy problem without fine tuning of parameters.Comment: 8 pages, LaTeX; minor typo correcte

Singular Laplacian Growth

The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.Comment: 8 pages, Latex, 4 figures, Submitted to Phys. Rev.

Critical behavior of Born Infeld AdS black holes in higher dimensions

Based on a canonical framework, we investigate the critical behavior of Born-Infeld AdS black holes in higher dimensions. As a special case, considering the appropriate limit, we also analyze the critical phenomena for Reissner Nordstrom AdS black holes. The critical points are marked by the divergences in the heat capacity at constant charge. The static critical exponents associated with various thermodynamic entities are computed and shown to satisfy the thermodynamic scaling laws. These scaling laws have also been found to be compatible with the static scaling hypothesis. Furthermore, we show that the values of these exponents are universal and do not depend on the spatial dimensionality of the AdS space. We also provide a suggestive way to calculate the critical exponents associated with the spatial correlation which satisfy the scaling laws of second kind.Comment: LaTex, 22 pages, 12 figures, minor modifications in text, To appear in Phys. Rev.

Temporal Variability of Tungsten and Cobalt in Fallon, Nevada

BACKGROUND: Since 1997, Fallon, Nevada, has experienced a cluster of childhood leukemia that has been declared “one of the most unique clusters of childhood cancer ever reported.” Multiple environmental studies have shown airborne tungsten and cobalt to be elevated within Fallon, but the question remains: Have these metals changed through time in correspondence with the onset of the leukemia cluster? METHODS: We used dendrochemistry, the study of element concentrations through time in tree rings, in Fallon to assess temporal variability of airborne tungsten and cobalt since the late 1980s. The techniques used in Fallon were also tested in a different town (Sweet Home, OR) that has airborne tungsten from a known source. RESULTS: The Sweet Home test case confirms the accuracy of dendrochemistry for showing temporal variability of environmental tungsten. Given that dendrochemistry works for tungsten, tree-ring chemistry shows that tungsten increased in Fallon relative to nearby comparison towns beginning by the mid-1990s, slightly before the onset of the cluster, and cobalt has been high throughout the last ~ 15 years. Other metals do not show trends through time in Fallon. DISCUSSION: Results in Fallon suggest a temporal correspondence between the onset of excessive childhood leukemia and elevated levels of tungsten and cobalt. Although environmental data alone cannot directly link childhood leukemia with exposure to metals, research by others has shown that combined exposure to tungsten and cobalt can be carcinogenic to humans. CONCLUSION: Continued biomedical research is warranted to directly test for linkage between childhood leukemia and tungsten and cobalt

Comparison of Size and Geography of Airborne Tungsten Particles in Fallon, Nevada, and Sweet Home, Oregon, with Implications for Public Health

To improve understanding of possible connections between airborne tungsten and public health, size and geography of airborne tungsten particles collected in Fallon, Nevada, and Sweet Home, Oregon, were compared. Both towns have industrial tungsten facilities, but only Fallon has experienced a cluster of childhood leukemia. Fallon and Sweet Home are similar to one another by their particles of airborne tungsten being generally small in size. Meteorologically, much, if not most, of residential Fallon is downwind of its hard metal facility for at least some fraction of time at the annual scale, whereas little of residential Sweet Home is downwind of its tungsten facility. Geographically, most Fallon residents potentially spend time daily within an environment containing elevated levels of airborne tungsten. In contrast, few Sweet Home residents potentially spend time daily within an airborne environment with elevated levels of airborne tungsten. Although it cannot be concluded from environmental data alone that elevated airborne tungsten causes childhood leukemia, the lack of excessive cancer in Sweet Home cannot logically be used to dismiss the possibility of airborne tungsten as a factor in the cluster of childhood leukemia in Fallon. Detailed modeling of all variables affecting airborne loadings of heavy metals would be needed to legitimately compare human exposures to airborne tungsten in Fallon and Sweet Home

State Sum Models and Simplicial Cohomology

We study a class of subdivision invariant lattice models based on the gauge group $Z_{p}$, with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the $1$- and $2$-dimensional simplices of the simplicial complex. The property of subdivision invariance is achieved when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. By explicit computation of the partition function for the manifold $RP^{3} \times S^{1}$, we establish that the theory has a quantum Hilbert space which differs from the classical one.Comment: 28 pages, Latex, ITFA-94-13, (Expanded version with two new sections

Hydrodynamic Detonation Instability in Electroweak and QCD Phase Transitions

The hydrodynamic stability of deflagration and detonation bubbles for a first order electroweak and QCD phase transition has been discussed recently with the suggestion that detonations are stable. We examine here the case of a detonation more carefully. We find that in front of the bubble wall perturbations do not grow with time, but behind the wall modes exist which grow exponentially. We briefly discuss the possible meaning of this instability.Comment: 12 pages, 3 figures available on request, Latex, FERMILAB--PUB--93/098--

Excited ΛQ\Lambda_Q Baryons in the Large NcN_c Limit

The spectrum of excited $\Lambda_Q$-type heavy baryons is considered in the large $N_c$ limit. The universal form factors for $\Lambda_b$ semileptonic decay to excited charmed baryons are calculated in the large $N_c$ limit. We find that the Bjorken sum rule (for the slope of the Isgur--Wise function) and Voloshin sum rule (for the mass of the light degrees of freedom) are saturated by the first doublet of excited $\Lambda_Q$ states.Comment: 9 pages, use phyzzx, CALT-68-191

A Regularized Graph Layout Framework for Dynamic Network Visualization

Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual representation of the network structure at each time step, the sequence should preserve the mental map between layouts of consecutive time steps to allow a human to interpret the temporal evolution of the network. In this paper, we propose a framework for dynamic network visualization in the on-line setting where only present and past graph snapshots are available to create the present layout. The proposed framework creates regularized graph layouts by augmenting the cost function of a static graph layout algorithm with a grouping penalty, which discourages nodes from deviating too far from other nodes belonging to the same group, and a temporal penalty, which discourages large node movements between consecutive time steps. The penalties increase the stability of the layout sequence, thus preserving the mental map. We introduce two dynamic layout algorithms within the proposed framework, namely dynamic multidimensional scaling (DMDS) and dynamic graph Laplacian layout (DGLL). We apply these algorithms on several data sets to illustrate the importance of both grouping and temporal regularization for producing interpretable visualizations of dynamic networks.Comment: To appear in Data Mining and Knowledge Discovery, supporting material (animations and MATLAB toolbox) available at http://tbayes.eecs.umich.edu/xukevin/visualization_dmkd_201