On infinite words avoiding a finite set of squares

Building an infinite square-free word by appending one letter at a time while simultaneously avoiding the creation of squares is most likely to fail. When the alphabet has two letters this approach is impossible. When the alphabet has three or more letters, one will most probably create a word in which the addition of any letter invariably creates a square. When one restricts the set of undesired squares to a finite one, this can be possible. We study the constraints on the alphabet and the set of squares which permit this approach to work.Comment: 18 page

Effective Generation of Subjectively Random Binary Sequences

We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.Comment: Introduction and Section 6 revise

Transient heat flux measurement using a surface junction thermocouple

A new form of surface junction thermocouple sensor has been developed and tested. The novel feature of the design is the use of a tapered fit between two coaxial thermocouple elements to form a thin, robust junction. The gauge has a response time on the order of 1 µs and is suitable for measuring large transient heat fluxes in hypervelocity wind tunnels. Asymptotic analysis is used to demonstrate the operating principles and to assess the errors associated with the finite thickness of the surface junction. Spectral deconvolution methods are used to infer a mean square optimal estimate of the surface heat flux from time resolved surface temperature measurements. This improved signal processing method is applicable to transient heat flux gauges of all types. Potential reducible error sources and other systematic errors are described. Measurements of the heat flux about the forebody of a cylindrical body in a hypervelocity flow demonstrate the functioning of the gauge and are used to obtain statistical estimates of the repeatability of the technique. The measured heat fluxes are compared with established theoretical predictions

On the hypersurface orbital varieties of sl(N,C)

We study the structure of hypersurface orbital varieties of sl(N,C) (those that are hypersurfaces in the nilradical of some parabolic subalgebra) and how information about this structure is encoded in the standard Young tableau associated to it by the Robinson-Schensted algorithm. We present a conjecture for the exact form of the unique non-linear defining equations of hypersurface orbital varieties and proofs of the conjecture in certain cases.Comment: 17 page

Equivariant configuration spaces

The compression theorem is used to prove results for equivariant configuration spaces that are analogous to the well-known non-equivariant results of May, Milgram and Segal

Demonstration of lightweight gamma spectrometry systems in urban environments

Urban areas present highly complex radiation environments; with small scale features resulting from different construction materials, topographic effects and potential anthropogenic inputs from past industrial activity or other sources. Mapping of the radiation fields in urban areas allows a detailed assessment of exposure pathways for the people who live and work there, as well as locating discrete sources of activity that may warrant removal to mitigate dose to the general public. These areas also present access difficulties for radiometric mapping using vehicles or aircraft. A lightweight portable gamma spectrometry system has been used to survey sites in the vicinity of Glasgow to demonstrate the possibilities of radiometric mapping of urban areas, and to investigate the complex radiometric features such areas present. Variations in natural activity due to construction materials have been described, the presence of 137Cs used to identify relatively undisturbed ground, and a previously unknown NORM feature identified. The effect of topographic enclosure on measurements of activity concentration has been quantified. The portable system is compared with the outputs that might be expected from larger vehicular or airborne systems. For large areas airborne surveys are the most cost effective approach, but provide limited spatial resolution, vehicular surveys can provide sparse exploratory data rapidly or detailed mapping of open areas where off-road access is possible. Backpack systems are ideally suited to detailed surveys of small areas, especially where vehicular access is difficult

Aspects of planar, oblique and interacting shock waves in an ideal dissociating gas

We develop a compact dimensionless framework for the analysis of canonical thermo-chemical nonequilibrium flow fields involving normal, oblique and interacting shock waves. Discontinuous solutions of the conservation equations are coupled with thermodynamic and kinetic models for an ideal dissociating gas. Convenient forms are provided for the variation of the relevant dimensionless parameters across shock waves in dissociating gases. The treatment is carried through in a consistent manner for the pressure–flow deflection angle plane representation of shock wave interaction problems. The contribution of the current paper is a careful nondimensionalization of the problem that yields a tractable formulation and allows results with considerable generality to be obtained

Operator related attenuation effects in radiometric surveys

Radiometric surveys using airborne, vehicular mounted or backpack detector systems are increasingly used to identify and evaluate complex distributions of radioactivity in the environment. The signals detected depend on the energy and spatial distribution of radioactive sources, the material properties of the environment and the specific properties of the detector systems employed. Materials in close vicinity to the detector such as housings, and intermediate materials may have a critical impact on detection efficiency, and must therefore be taken into account in calibration. This study evaluates the effect of shielding by the body of the operator in backpack surveys. Controlled experiments using point sources and absorbers, chosen to represent the form and composition of human tissue, were conducted, and coupled to an analytical radiation transport model to estimate attenuation factors for mapping of 137Cs. In this way generic factors to correct for this effect using portable spectrometers have been determined. The results compare well with observations at sampled calibration sites in Fukushima and the Solway area in Scotland. Reductions of the 137Cs full-energy peak intensity between 20% and 30% may be expected depending on operator stature and the offset position of backpack systems. Similar effects may be present for other radiometric systems carried by a human operator

James bundles

We study cubical sets without degeneracies, which we call {square}-sets. These sets arise naturally in a number of settings and they have a beautiful intrinsic geometry; in particular a {square}-set C has an infinite family of associated {square}-sets Ji(C), for i = 1, 2, ..., which we call James complexes. There are mock bundle projections pi: |Ji(C)| -> |C| (which we call James bundles) defining classes in unstable cohomotopy which generalise the classical James–Hopf invariants of {Omega}(S2). The algebra of these classes mimics the algebra of the cohomotopy of {Omega}(S2) and the reduction to cohomology defines a sequence of natural characteristic classes for a {square}-set. An associated map to BO leads to a generalised cohomology theory with geometric interpretation similar to that for Mahowald orientation

The influence of non-equilibrium dissociation on the flow produced by shock impingement on a blunt body

We describe an investigation of the effects of non-equilibrium thermochemistry on the interaction between a weak oblique shock and the strong bow shock formed by a blunt body in hypersonic flow. This type of shock-on-shock interaction, also known as an Edney type IV interaction, causes locally intense enhancement of the surface heat transfer rate. A supersonic jet is formed by the nonlinear interaction that occurs between the two shock waves and elevated heat transfer rates and surface pressures are produced by the impingement of the supersonic jet on the body. The current paper is motivated by previous studies suggesting that real gas effects would significantly increase the severity of the phenomenon. Experiments are described in which a free-piston shock tunnel is used to produce shock interaction flows with significant gas dissociation. Surprisingly, the data that are obtained show no significant stagnation enthalpy dependence of the ratio of the peak heat transfer rates with and without shock interaction, in contrast to existing belief. The geometry investigated is the nominally two-dimensional flow about a cylinder with coplanar impinging shock wave. Holographic interferometry is used to visualize the flow field and to quantify increases in the stagnation density caused by shock interaction. Time-resolved heat transfer measurements are obtained from surface junction thermocouples about the model forebody. An improved model is developed to elucidate the finite-rate thermochemical processes occurring in the interaction region. It is shown that severe heat transfer intensification is a result of a jet shock structure that minimizes the entropy rise of the supersonic jet fluid whereas strong thermochemical effects are promoted by conditions that maximize the entropy rise (and hence temperature). This dichotomy underlies the smaller than anticipated influence of real gas effects on the heat transfer intensification. The model accurately predicts the measured heat transfer rates. Improved understanding of the influence of real gas effects on the shock interaction phenomenon reduces a significant element of risk in the design of hypersonic vehicles. The peak heat transfer rate for the Edney type IV interaction is shown to be well-correlated, in the weak impinging shock regime, by an expression of the form [equation] for use in practical design calculations