What the small Rubik’s cube taught me about data structures, information theory, and randomisation

This article discusses observations made when the state space of the 2 × 2 × 2 Rubik’s cube was constructed with various programs based on various data structures, gives theoretical explanations for the observations, and uses them to develop more memory-efficient data structures. The cube has 3,674,160 reachable states. The fastest program runs in 20 s and uses 11.1 million bytes of memory for the state set structure. It uses a 31-bit representation of the state and also stores the rotation through which each state was first found. Its memory consumption is remarkably small, considering that 3,674,160 × 31 bits is about 14.2 million bytes. Getting below this number was made possible by sharing common parts of states. Obviously, it is not possible to reduce memory consumption without limit. We derive an information-theoretic hard average lower bound of 6.07 million bytes that applies in this setting. We introduce a general-purpose variant of the data structure and end up with 8.9 million bytes and 48 s. We also discuss the performance of BDDs and perfect state packing in this application.     

Extended studies of degradation mechanisms in the refractory lining of a rotary kiln for iron ore pellet production

Changes, over a period of 8 years, in the chemical composition and morphology of deposit and lining materials in a production rotary kiln for iron ore pellet manufacture are described. The following have been studied: two types of refractory brick used as lining material; deposited chunk materials from the lining; the interaction zones between deposits and linings. Morphological changes at the deposit/lining interface, and the active chemical reactions, are established. Larger hematite grains in the deposit material (5–50 μm) primarily remain at the original deposit/lining interface. The remainder penetrates fissures, voids and brick joints, forms a laminar structure with corundum from the bricks, and migrates in grains in the lining material. Potassium penetrates more deeply into the bricks than hematite, resulting in the formation of kalsilite, leucite and potassium β-alumina, which contribute to degradation of the lining.     

Application of oxygen-consumption calorimetry to non-combustibility testing

The feasibility of oxygen-consumption calorimetry to testing of non-combustibility of building materials is studied. The reasons for the ambiguities of the traditional test method are qualitatively discussed. The construction of the gas collecting system added to the conventional test apparatus is described and the necessary formulae for calculating the oxygen consumption and the simultaneously measured conventional test variables are compared. The results clearly suggest that oxygen-consumption calorimetry is a consistent and powerful method for determining the non-combustibility of building materials.     

Characterization of Submillimeter Wave Absorbers from 200–600 GHz

This paper presents measurements of both specular and non-specular scattering from several submillimeter wave absorber materials designed for antenna testing and from low-cost carpet materials. The frequency range is 200–600 GHz in specular scattering, and 300–400 GHz in non-specular scattering measurements. The constructed bistatic test bench allows testing of the full continuous angular range of 0°–90°. The measurement results show large differences in performance of different materials. It is shown that reflectivities below ?50 dB over limited angular ranges are possible with a correct alignment of the material. Also, low-cost carpet materials have lower than ?15 dB reflectivities in most angles, and may be useful in non-critical parts of the antenna test range. The results can be used to optimise the absorber placement inside an antenna range, concerning both best performance and lowest cost.     

Modeling and Simulation of High Pressure Water Mist Systems

This paper describes work done to improve and validate the capability of fire dynamics simulator (FDS) to predict the dynamics of water mist sprays. Three single orifice and five multi-orifice spray heads are modeled with FDS based on information on the flow-rate, spray angle, operating pressure and experimentally determined particle size distribution. The capability of FDS to predict the drop size, velocity, mist flux and number concentration profiles within the spray cone is assessed. The effects of turbulence modeling on the predictions of the spray dynamics is investigated. The capability of FDS to predict the air entrainment by high-speed water sprays is validated using experiments in rectangular channels with open ends.     

High-precision diode-laser-based temperature measurement for air refractive index compensation

We present a laser-based system to measure the refractive index of air over a long path length. In optical distance measurements, it is essential to know the refractive index of air with high accuracy. Commonly, the refractive index of air is calculated from the properties of the ambient air using either Ciddor or Edlén equations, where the dominant uncertainty component is in most cases the air temperature. The method developed in this work utilizes direct absorption spectroscopy of oxygen to measure the average temperature of air and of water vapor to measure relative humidity. The method allows measurement of temperature and humidity over the same beam path as in optical distance measurement, providing spatially well-matching data. Indoor and outdoor measurements demonstrate the effectiveness of the method. In particular, we demonstrate an effective compensation of the refractive index of air in an interferometric length measurement at a time-variant and spatially nonhomogeneous temperature over a long time period. Further, we were able to demonstrate 7 mK RMS noise over a 67 m path length using a 120 s sample time. To our knowledge, this is the best temperature precision reported for a spectroscopic temperature measurement.     

NMR investigation of the magnetic susceptibility anisotropy in3He-A

We have investigated transverse continuous wave NMR in a geometry where the modes are influenced by susceptibility anisotropy. The helium sample is separated by mylar foils into layers 12 m thick perpendicular to the external dc magnetic field. In this geometryl is constrained to be parallel to the field andd switches from parallel to perpendicular to the field over a small range of field around the dipole unlocking field. The mode frequencies below this critical field yield a value for the susceptibility anisotropy. Above the critical field the expected negative frequency shift is observed, as well as a positive frequency shift due to bulk material and an unexpected signal close to the Larmor frequency.