Uncertainty quantification of coal seam gas production prediction using Polynomial Chaos

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability distributions of the uncertain input variables (parameters); this allows for both uncertainty quantification and global sensitivity analysis. In this paper we apply these techniques to a commercial solver for the estimation of peak gas rate and cumulative gas extraction from a coal seam gas well. The polynomial expansion is shown to honour the underlying geophysics with low error when compared to a much more complex and computationally slower commercial solver. We make use of advanced numerical integration techniques to achieve this accuracy using relatively small amounts of training data

Further biembeddings of twofold triple systems

We construct face two-colourable triangulations of the graph 2Kn in an orientable surface; equivalently biembeddings of two twofold triple systems of order n, for all n ξ 16 or 28 (mod 48). The biembeddings come from index 1 current graphs lifted under a group ℤn/4 × 4

Distributive and anti-distributive Mendelsohn triple systems

We prove that the existence spectrum of Mendelsohn triple systems whose associated quasigroups satisfy distributivity corresponds to the Loeschian numbers, and provide some enumeration results. We do this by considering a description of the quasigroups in terms of commutative Moufang loops. In addition we provide constructions of Mendelsohn quasigroups that fail distributivity for as many combinations of elements as possible. These systems are analogues of Hall triple systems and anti-mitre Steiner triple systems respectively

Identifying flaws in the security of critical sets in latin squares via triangulations

In this paper we answer a question in theoretical cryptography by reducing it to a seemingly unrelated geometrical problem. Drápal (1991) showed that a given partition of an equilateral triangle of side n into smaller, integer-sided equilateral triangles gives rise to, under certain conditions, a latin trade within the latin square based on the addition table for the integers (mod n). We apply this result in the study of flaws within certain theoretical cryptographic schemes based on critical sets in latin squares. We classify exactly where the flaws occur for an infinite family of critical sets. Using Drápal's result, this classification is achieved via a study of the existence of triangulations of convex regions that contain prescribed triangles

On the upper embedding of Steiner triple systems and Latin squares

It is proved that for any prescribed orientation of the triples of either a Steiner triple system or a Latin square of odd order, there exists an embedding in an orientable surface with the triples forming triangular faces and one extra large face

Types of directed triple systems

We introduce three types of directed triple systems. Two of these, Mendelsohn directed triple systems and Latin directed triple systems, have previously appeared in the literature but we prove further results about them. The third type, which we call skewed directed triple systems, is new and we determine the existence spectrum to be v ≡ 1 (mod 3), v ≠ 7, except possibly for v = 22, as well as giving enumeration results for small orders

Dark Matter and Baryons in the Most X-ray Luminous and Merging Galaxy Cluster RX J1347.5-1145

The galaxy cluster RX J1347-1145 is one of the most X-ray luminous and most massive clusters known. Its extreme mass makes it a prime target for studying issues addressing cluster formation and cosmology. In this paper we present new high-resolution HST/ACS and Chandra X-ray data. The high resolution and sensitivity of ACS enabled us to detect and quantify several new multiply imaged sources, we now use a total of eight for the strong lensing analysis. Combining this information with shape measurements of weak lensing sources in the central regions of the cluster, we derive a high-resolution, absolutely-calibrated mass map. This map provides the best available quantification of the total mass of the central part of the cluster to date. We compare the reconstructed mass with that inferred from the new Chandra X-ray data, and conclude that both mass estimates agree extremely well in the observed region, namely within 400 / h_70 kpc of the cluster center. In addition we study the major baryonic components (gas and stars) and hence derive the dark matter distribution in the center of the cluster. We find that the dark matter and baryons are both centered on the BCG within the uncertainties (alignment is better than <10 kpc). We measure the corresponding 1-D profiles and find that dark matter distribution is consistent with both NFW and cored profiles, indicating that a more extended radial analysis is needed to pinpoint the concentration parameter, and hence the inner slope of the dark matter profile.Comment: 12 pages, Accepted for publication in ApJ, full-res version http://www.physics.ucsb.edu/~marusa/RXJ1347.pd