Powerful sets: a generalisation of binary matroids

A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a \textit{powerful code} if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2. By treating binary vectors as characteristic vectors of subsets of $E$, we say that a set $S\subseteq2^E$ of subsets of $E$ is a \textit{powerful set} if the set of characteristic vectors of sets in $S$ is a powerful code. Powerful sets (codes) include cocircuit spaces of binary matroids (equivalently, linear codes over $\mathbb{F}_2$), but much more besides. Our motivation is that, to each powerful set, there is an associated nonnegative-integer-valued rank function (by a construction of Farr), although it does not in general satisfy all the matroid rank axioms. In this paper we investigate the combinatorial properties of powerful sets. We prove fundamental results on special elements (loops, coloops, frames, near-frames, and stars), their associated types of single-element extensions, various ways of combining powerful sets to get new ones, and constructions of nonlinear powerful sets. We show that every powerful set is determined by its clutter of minimal nonzero members. Finally, we show that the number of powerful sets is doubly exponential, and hence that almost all powerful sets are nonlinear.Comment: 19 pages. This work was presented at the 40th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (40ACCMCC), University of Newcastle, Australia, Dec. 201

Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders

We propose a generalized strip modelling method that is computationally efficient for the VIV prediction of long flexible cylinders in three-dimensional incompressible flow. In order to overcome the shortcomings of conventional strip-theory-based 2D models, the fluid domain is divided into “thick” strips, which are sufficiently thick to locally resolve the small scale turbulence effects and three dimensionality of the flow around the cylinder. An attractive feature of the model is that we independently construct a three-dimensional scale resolving model for individual strips, which have local spanwise scale along the cylinder's axial direction and are only coupled through the structural model of the cylinder. Therefore, this approach is able to cover the full spectrum for fully resolved 3D modelling to 2D strip theory. The connection between these strips is achieved through the calculation of a tensioned beam equation, which is used to represent the dynamics of the flexible body. In the limit, however, a single “thick” strip would fill the full 3D domain. A parallel Fourier spectral/hp element method is employed to solve the 3D flow dynamics in the strip-domain, and then the VIV response prediction is achieved through the strip-structure interactions. Numerical tests on both laminar and turbulent flows as well as the comparison against the fully resolved DNS are presented to demonstrate the applicability of this approach

Preliminary assessment of systems for deriving liquid and gaseous fuels from waste or grown organics

The overall feasibility of the chemical conversion of waste or grown organic matter to fuel is examined from the technical, economic, and social viewpoints. The energy contribution from a system that uses waste and grown organic feedstocks is estimated as 4 to 12 percent of our current energy consumption. Estimates of today's market prices for these fuels are included. Economic and social issues are as important as technology in determining the feasibility of such a proposal. An orderly program of development and demonstration is recommended to provide reliable data for an assessment of the viability of the proposal

A preliminary assessment of the feasibility of deriving liquid and gaseous fuels from grown and waste organics

The anticipated depletion of our resources of natural gas and petroleum in a few decades has caused a search for renewable sources of fuel. Among the possibilities is the chemical conversion of waste and grown organic matter into gaseous or liquid fuels. The overall feasibility of such a system is considered from the technical, economic, and social viewpoints. Although there are a number of difficult problems to overcome, this preliminary study indicates that this option could provide between 4 and 10 percent of the U.S. energy needs. Estimated costs of fuels derived from grown organic material are appreciably higher than today's market price for fossil fuel. The cost of fuel derived from waste organics is competitive with fossil fuel prices. Economic and social reasons will prohibit the allocation of good food producing land to fuel crop production

Anomalous spin-dependent behaviour of one-dimensional subbands

We report a new electron interaction effect in GaAs/AlGaAs quantum wires. Using DC-bias spectroscopy, we show that large and abrupt changes occur to the energies of spin-down (lower energy) states as they populate. The effect is not observed for spin-up energy states. At B=0, interactions have a pronounced effect, in the form of the well-known 0.7 Structure. However, our new results show that interactions strongly affect the energy spectrum at all magnetic fields, from 0 to 16T, not just in the vicinity of the 0.7 Structure.Comment: 4 pages, 2 figure

A Flexible and Secure Deployment Framework for Distributed Applications

This paper describes an implemented system which is designed to support the deployment of applications offering distributed services, comprising a number of distributed components. This is achieved by creating high level placement and topology descriptions which drive tools that deploy applications consisting of components running on multiple hosts. The system addresses issues of heterogeneity by providing abstractions over host-specific attributes yielding a homogeneous run-time environment into which components may be deployed. The run-time environments provide secure binding mechanisms that permit deployed components to bind to stored data and services on the hosts on which they are running.Comment: 2nd International Working Conference on Component Deployment (CD 2004), Edinburgh, Scotlan

Small gaps between products of two primes

Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $$\liminf_{n\to \infty} (q_{n+1}-q_n) \le 6.$$ This sharpens an earlier result of the authors (arXivMath NT/0506067), which had 26 in place of 6. More generally, we prove that if $\nu$ is any positive integer, then $$\liminf_{n\to \infty} (q_{n+\nu}-q_n) \le C(\nu) = \nu e^{\nu-\gamma} (1+o(1)).$$ We also prove several other results on the representation of numbers with exactly two prime factors by linear forms.Comment: 11N25 (primary) 11N36 (secondary

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling

We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha-model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.Comment: Finite size box effects have been taken into account in the definition of the partition function. This has resulted in a more clear scaling in all figures. Several points are clarified in the tex

Subject No-hits Searches in an Academic Library Online Catalog: An Exploration of Two Potential Ameliorations

Describes a study that explored ways in which users subject searching problems in a local online catalogue might be reduced. On a weekly basis, the author reviewed catalogue transaction logs to identify topics of subject searches retrieving no records for which appropriate information resources may actually be represented in the catalog. For topics thus identified, the author explored two potential ameliorations of the no-hits search results through the use of authority record cross-references and pathfinder records providing brief instructions on search refinement. Describes the study findings, discusses possible concerns regarding the amelioration methods used, outlines additional steps needed to determine whether the potential ameliorations make a difference to users searching experiences, and suggests related areas for further research. (Original abstract