arXiv subjects

Paul Smith

Publications and source records attributed to Paul Smith.

47 records · Page 3Linked to original sources

arXiv2013

The time of bootstrap percolation with dense initial sets for all thresholds

We study the percolation time of the $r$-neighbour bootstrap percolation model on the discrete torus $(\Z/n\Z)^d$. For $t$ at most a polylog function of $n$ and initial infection probabilities within certain ranges depending on $t$, we prove that the percolation time of a random subset of the torus is exactly equal to $t$ with high probability as $n$ tends to infinity. Our proof rests crucially on three new extremal theorems that together establish an almost complete understanding of the geometric behaviour of the $r$-neighbour bootstrap process in the dense setting. The special case $d-r=0$ of our result was proved recently by Bollobás, Holmgren, Smith and Uzzell.

math.PR↗

arXiv2013

A measurement of the energy and timing resolution of GlueX Forward Calorimeter using an electron beam

The performance of the GlueX Forward Calorimeter was studied using a small version of the detector and a variable energy electron beam derived from the Hall B tagger at Jefferson Lab. For electron energies from 110 MeV to 260 MeV, which are near the lower-limits of the design sensitivity, the fractional energy resolution was measured to range from 20% to 14%, which meets the design goals. The use of custom 250 MHz flash ADCs for readout allowed precise measurements of signal arrival times. The detector achieved timing resolutions of 0.38 ns for a single 100 mV pulse, which will allow timing discrimination of photon beam bunches and out-of-time background during the operation of the GlueX detector.

physics.ins-det↗

arXiv2013

A controlling norm for energy-critical Schrödinger maps

We consider energy-critical Schroedinger maps with target either the sphere S^2 or hyperbolic plane H^2 and establish that a unique solution may be continued so long as a certain space-time L^4 norm remains bounded. This reduces the large data global wellposedness problem to that of controlling this norm.

math.AP↗

arXiv2013

Conditional global regularity of Schrödinger maps: sub-threshold dispersed energy

We consider the Schrödinger map initial value problem into the sphere in 2+1 dimensions with smooth, decaying, subthreshold initial data. Assuming an a priori $L^4$ boundedness condition on the solution, we prove that the Schrödinger map system admits a unique global smooth solution provided that the initial data is sufficiently energy-dispersed. Also shown are global-in-time bounds on certain Sobolev norms of the solution. Toward these ends we establish improved local smoothing and bilinear Strichartz estimates, adapting the Planchon-Vega approach to such estimates to the nonlinear setting of Schrödinger maps.

math.AP↗

arXiv2012

Global regularity of critical Schrödinger maps: subthreshold dispersed energy

We consider the energy-critical Schroedinger map initial value problem with smooth initial data from R^2 into the sphere S^2. Given sufficiently energy-dispersed data with subthreshold energy, we prove that the system admits a unique global smooth solution. This improves earlier analogous conditional results. The key behind this improvement lies in exploiting estimates on the commutator of the Schroedinger map and harmonic map heat flows.

math.AP↗

arXiv2012

Local wellposedness of Chern-Simons-Schrödinger

In this article we consider the initial value problem for the Chern-Simons-Schrodinger model in two space dimensions. This is a covariant NLS type problem which is L^2 critical. For this equation we introduce a so-called heat gauge, and prove that, with respect to this gauge, the problem is locally well-posed for initial data which is small in H^s, s > 0.

math.AP↗

arXiv2012

Towards a Layered Architectural View for Security Analysis in SCADA Systems

Supervisory Control and Data Acquisition (SCADA) systems support and control the operation of many critical infrastructures that our society depend on, such as power grids. Since SCADA systems become a target for cyber attacks and the potential impact of a successful attack could lead to disastrous consequences in the physical world, ensuring the security of these systems is of vital importance. A fundamental prerequisite to securing a SCADA system is a clear understanding and a consistent view of its architecture. However, because of the complexity and scale of SCADA systems, this is challenging to acquire. In this paper, we propose a layered architectural view for SCADA systems, which aims at building a common ground among stakeholders and supporting the implementation of security analysis. In order to manage the complexity and scale, we define four interrelated architectural layers, and uses the concept of viewpoints to focus on a subset of the system. We indicate the applicability of our approach in the context of SCADA system security analysis.

cs.CR↗

arXiv2012

The time of bootstrap percolation for dense initial sets

In r-neighbour bootstrap percolation on the vertex set of a graph G, vertices are initially infected independently with some probability p. At each time step, the infected set expands by infecting all uninfected vertices that have at least r infected neighbours. We study the distribution of the time t at which all vertices become infected. Given t = t(n) = o(log n/log log n), we prove a sharp threshold result for the probability that percolation occurs by time t in d-neighbour bootstrap percolation on the d-dimensional discrete torus T_n^d. Moreover, we show that for certain ranges of p = p(n), the time at which percolation occurs is concentrated either on a single value or on two consecutive values. We also prove corresponding results for the modified d-neighbour rule.

math.CO↗

arXiv2011

Geometric renormalization below the ground state

The caloric gauge was introduced by Tao with studying large data energy critical wave maps mapping from $\mathbf{R}^{2+1}$ to hyperbolic space $\mathbf{H}^m$ in view. In \cite{BIKT} Bejenaru, Ionescu, Kenig, and Tataru adapted the caloric gauge to the setting of Schrödinger maps from $\mathbf{R}^{d + 1}$ to the standard sphere $S^2 \hookrightarrow \mathbf{R}^3$ with initial data small in the critical Sobolev norm. Here we develop the caloric gauge in a bounded geometry setting with a construction valid up to the ground state energy.

math.AP↗

arXiv2010

Unobscured Type 2 AGNs

Type 2 AGNs with intrinsically weak broad emission lines (BELs) would be exceptions to the unified model. After examining a number of proposed candidates critically, we find that the sample is contaminated significantly by objects with BELs of strengths indicating that they actually contain intermediate-type AGNs, plus a few Compton-thick sources as revealed by extremely low ratios of X-ray to nuclear IR luminosities. We develop quantitative metrics that show two (NGC 3147 and NGC 4594) of the remaining candidates to have BELs 2-3 orders of magnitude weaker than those of typical type-1 AGNs. Several more galaxies remain as candidates to have anomalously weak BELs, but this status cannot be confirmed with the existing information. Although the parent sample is poorly defined, the two confirmed objects are well under 1% of its total number of members, showing that the absence of a BEL is possible, but very uncommon in AGN. We evaluate these two objects in detail using multi-wavelength measurements. They have little X-ray extinction with N_H < 10^21 cm^{-2}. Their IR spectra show strong silicate emission (NGC 4594) or weak aromatic features on a generally power law continuum with a suggestion of silicates in emission (NGC 3147). No polarized BEL is detected in NGC 3147. These results indicate that the two unobscured type-2 objects have circumnuclear tori that are approximately face-on. Combined with their X-ray and optical/UV properties, this behavior implies that we have an unobscured view of the nuclei and thus that they have intrinsically weak BELs. We compare their properties with those of the other less-extreme candidates. We then compare the distributions of bolometric luminosities and accretion rates of these objects with theoretical models that predict weak BELs.

astro-ph.CO↗

arXiv2001

X-ray properties of Red Active Galactic Nuclei

The Two Micron All Sky Survey (2MASS) is finding previously unidentified, luminous red active galactic nuclei (AGN). This new sample has a space density similar to, or greater than, previously known AGN, suggesting that a large fraction of the overall population has been missed. Chandra observations of a well-defined subset of these objects reveal that all are X-ray faint, with the reddest sources being the faintest in X-rays. The X-ray hardness ratios cover a wide range, generally indicating log NH ~21-23 /cm*2, but the softest sources show no spectral evidence for intrinsic absorption. These characteristics suggest that a mix of absorbed, direct emission and unabsorbed, scattered and/or extended emission contributes to the X-ray flux, although we cannot rule out the possibility that they are intrinsically X-ray weak. This population of X-ray faint, predominantly broad-line objects could provide the missing population of X-ray absorbed AGN required by current models of the cosmic X-ray background. The existence of AGN which display both broad emission lines and absorbed X-rays has important implications for unification schemes and emphasizes the need for care in assigning classifications to individual AGN.

astro-ph↗