Finite-State Dimension and Real Arithmetic

We use entropy rates and Schur concavity to prove that, for every integer k >= 2, every nonzero rational number q, and every real number alpha, the base-k expansions of alpha, q+alpha, and q*alpha all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives a new proof of, Wall's 1949 theorem stating that the sum or product of a nonzero rational number and a Borel normal number is always Borel normal.Comment: 15 page

Intrinsic Universality in Self-Assembly

We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call \emph{locally consistent}: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of \emph{intrinsic universality} of cellular automata by Ollinger and others, in the sense that our simulation of a tile system $T$ by a tile system $U$ represents each tile in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where $c$ is a constant depending on $T$ but not on the size of the assembly $T$ produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2

Negative Interactions in Irreversible Self-Assembly

This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin explored their power in the context of reversible attachment operations. We explore the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Omega(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate a Turing machine with space bound s and time bound t, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s * t) as required by the standard Turing machine simulation with tiles

Investigation of Flow Conditioners for Compact Jet Engine Simulator Rig Noise Reduction

The design requirements for two new Compact Jet Engine Simulator (CJES) units for upcoming wind tunnel testing lead to the distinct possibility of rig noise contamination. The acoustic and aerodynamic properties of several flow conditioner devices are investigated over a range of operating conditions relevant to the CJES units to mitigate the risk of rig noise. An impinging jet broadband noise source is placed in the upstream plenum of the test facility permitting measurements of not only flow conditioner self-noise, but also noise attenuation characteristics. Several perforated plate and honeycomb samples of high porosity show minimal self-noise but also minimal attenuation capability. Conversely, low porosity perforated plate and sintered wire mesh conditioners exhibit noticeable attenuation but also unacceptable self-noise. One fine wire mesh sample (DP450661) shows minimal selfnoise and reasonable attenuation, particularly when combined in series with a 15.6 percent open area (POA) perforated plate upstream. This configuration is the preferred flow conditioner system for the CJES, providing up to 20 dB of broadband attenuation capability with minimal self-noise

High Bypass Ratio Jet Noise Reduction and Installation Effects Including Shielding Effectiveness

An experimental investigation was performed to study the propulsion airframe aeroacoustic installation effects of a separate flow jet nozzle with a Hybrid Wing Body aircraft configuration where the engine is installed above the wing. Prior understanding of the jet noise shielding effectiveness was extended to a bypass ratio ten application as a function of nozzle configuration, chevron type, axial spacing, and installation effects from additional airframe components. Chevron types included fan chevrons that are uniform circumferentially around the fan nozzle and T-fan type chevrons that are asymmetrical circumferentially. In isolated testing without a pylon, uniform chevrons compared to T-fan chevrons showed slightly more low frequency reduction offset by more high frequency increase. Phased array localization shows that at this bypass ratio chevrons still move peak jet noise source locations upstream but not to nearly the extent, as a function of frequency, as for lower bypass ratio jets. For baseline nozzles without chevrons, the basic pylon effect has been greatly reduced compared to that seen for lower bypass ratio jets. Compared to Tfan chevrons without a pylon, the combination with a standard pylon results in more high frequency noise increase and an overall higher noise level. Shielded by an airframe surface 2.17 fan diameters from nozzle to airframe trailing edge, the T-fan chevron nozzle can produce reductions in jet noise of as much as 8 dB at high frequencies and upstream angles. Noise reduction from shielding decreases with decreasing frequency and with increasing angle from the jet inlet. Beyond an angle of 130 degrees there is almost no noise reduction from shielding. Increasing chevron immersion more than what is already an aggressive design is not advantageous for noise reduction. The addition of airframe control surfaces, including vertical stabilizers and elevon deflection, showed only a small overall impact. Based on the test results, the best overall nozzle configuration design was selected for application to the N2A Hybrid Wing Body concept that will be the subject of the NASA Langley 14 by 22 Foot Subsonic Tunnel high fidelity aeroacoustic characterization experiment. The best overall nozzle selected includes T-fan type chevrons, uniform chevrons on the core nozzle, and no additional pylon of the type that created a strong acoustic effect at lower bypass ratios. The T-fan chevrons are oriented azimuthally away from the ground observer locations. This best overall nozzle compared to the baseline nozzle was assessed, at equal thrust, to produce sufficient installed noise reduction of the jet noise component to enable the N2A HWB to meet NASA s noise goal of 42 dB cumulative below Stage 4

Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation

The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. It is found that the energy gap of the chain with length N scales as $\exp (-cN^{\omega})$ with nonuniversal exponent $\omega$ if the Ising component of the exhange coupling is antiferromagnetic. This behavior is expected to be the characteristic feature of the quantum spin chains with relevant aperiodicity. This is in contrast to the XY chain for which the precious mean exchange modulation is marginal and the gap scales as $N^{-z}$. On the contrary, it is also verified that the energy gap scales as $N^{-1}$ if the Ising component of the exhange coupling is ferromagnetic. Our results are not only consistent with the recent bosonization analysis of Vidal, Mouhanna and Giamarchi but also clarify the nature of the strong coupling regime which is inaccesssible by the bosonization approach.Comment: 8 pages, 15 figures, 1 table; Proceedings of the workshop 'Frontiers in Magnetism', Kyoto, Oct. 199

Bounding the dimensions of rational cohomology groups

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations where the dimension of a rational cohomology group for $G$ can be bounded by a constant times the dimension of the coefficient module. We then demonstrate how our results can be applied to obtain effective bounds on the first cohomology of the symmetric group. We also show how, for finite Chevalley groups, our methods permit significant improvements over previous estimates for the dimensions of second cohomology groups.Comment: 13 page

On the Fractography of Impact-Tested Samples of Al-Si Alloys for Automotive Alloys

Castings were prepared from both industrial and experimental 319.2, B319.2 and A356.2 alloy melts, containing Fe levels of 0.2–1.0 wt%. Stontium-modified (∼200 ppm) melts were also prepared for each alloy/Fe level. Impact testing of heat-treated samples was carried out using an instrumented Charpy impact testing machine. At low Fe levels and high cooling rates (0.4% Fe, dendrite arm spacing (DAS) of 23 μm), crack initiation and propagation in unmodified 319 alloys occur through the cleavage of β-Al5FeSi platelets (rather than by their decohesion from the matrix). The morphology of the platelets (individual or branched) is important in determining the direction of crack propagation. Cracks also propagate through the fracture of undissolved CuAl2 or other Cu intermetallics, as well as through fragmented Si particles. In Sr-modified 319 alloys, cracks are mostly initiated by the fragmentation or cleavage of perforated β-phase platelets, in addition to that of coarse Si particles and undissolved Cu-intermetallics. In A356.2 alloys, cracks initiate mainly through the fracture of Si particles or their debonding from the Al matrix, while crack propagation occurs through the coalescence of fractured Si particles, except when β-Al5FeSi intermetallics are present, in which case the latter takes precedence. In the Sr-modified case, cracks propagate through the linkage of fractured/debonded Si particles, as well as fragmented β-iron intermetallics. In samples exhibiting low-impact energies, crack initiation and propagation occur mainly through cleavage of the β-iron intermetallics

Effect of Microalloying Elements on the Heat Treatment Response and Tensile Properties of Al-Si-Mg Alloys

This study was carried out on a series of heat-treatable Al-Si-Mg alloys to determine the effects of Fe, Mg, Sr and Be addition on their microstructural characteristics and tensile properties. The results showed that the eutectic temperature was reduced by 10°C with 0.8 wt% Mg addition. The solidification curves and first derivatives of Sr-free alloys with high Fe and Mg contents revealed a peak at 611°C consequent to the formation of a script-like Be-Fe (Al8Fe2BeSi) phase, which was very close to the peak for α-Al. The morphology of the β-iron platelets underwent changes due to their dissolution, thinning, necking, and fragmentation with increase in solutionizing time. Increased Mg contents are beneficial to the tensile properties unlike the detrimental effect of increasing Fe contents. Additions of Be and Sr noticeably improved the properties at the same Fe and/or Mg contents, the enhancements being markedly observed at higher Mg contents and reduced Fe levels. At high Fe levels, addition of Be is preferable as it neutralizes the deleterious effects of Fe in these alloys; however, addition of 500 ppm Be is inadequate for interacting with other alloying elements