Measurements of the free stream fluctuations above a turbulent boundary layer

This paper investigates the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure. It is assumed that the fluctuations receive contributions from three statistically independent sources: (1) one-dimensional unsteadiness, (2) free stream turbulence, and (3) the potential motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root-mean-square level of the axial velocity fluctuations of about 0.2 percent. All three velocity components were measured using an X-wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity, measured using two single wire probes. The results show that it is possible to separate the contributions to the r.m.s. level of the velocity fluctuations, without resorting to the dubious technique of high-pass filtering. The separation could be extended to the spectral densities of the contributions, if measurements of sufficient accuracy were available. The Appendix provides a general guide for the measurement of small free stream fluctuation levels

Using the distribution of cells by dimension in a cylindrical algebraic decomposition

We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather, the distribution is inherent to the cylindrical structure and determined mostly by the number of variables. This insight is then combined with an algorithm that produces only full-dimensional cells to give an accurate method of predicting the number of cells in a complete CAD. Since constructing only full-dimensional cells is relatively inexpensive (involving no costly algebraic number calculations) this leads to heuristics for helping with various questions of problem formulation for CAD, such as choosing an optimal variable ordering. Our experiments demonstrate that this approach can be highly effective.Comment: 8 page

Program Verification in the presence of complex numbers, functions with branch cuts etc

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as "does the low-level arithmetic implement the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more difficult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simplification rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities

Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heuristics to help with the choice for this algorithm, suggest improvements and then derive a new heuristic more closely aligned with the mechanics of the new algorithm

A "Piano Movers" Problem Reformulated

It has long been known that cylindrical algebraic decompositions (CADs) can in theory be used for robot motion planning. However, in practice even the simplest examples can be too complicated to tackle. We consider in detail a "Piano Mover's Problem" which considers moving an infinitesimally thin piano (or ladder) through a right-angled corridor. Producing a CAD for the original formulation of this problem is still infeasible after 25 years of improvements in both CAD theory and computer hardware. We review some alternative formulations in the literature which use differing levels of geometric analysis before input to a CAD algorithm. Simpler formulations allow CAD to easily address the question of the existence of a path. We provide a new formulation for which both a CAD can be constructed and from which an actual path could be determined if one exists, and analyse the CADs produced using this approach for variations of the problem. This emphasises the importance of the precise formulation of such problems for CAD. We analyse the formulations and their CADs considering a variety of heuristics and general criteria, leading to conclusions about tackling other problems of this form.Comment: 8 pages. Copyright IEEE 201

Pure phase-encoded MRI and classification of solids

Here, the authors combine a pure phase-encoded magnetic resonance imaging (MRI) method with a new tissue-classification technique to make geometric models of a human tooth. They demonstrate the feasibility of three-dimensional imaging of solids using a conventional 11.7-T NMR spectrometer. In solid-state imaging, confounding line-broadening effects are typically eliminated using coherent averaging methods. Instead, the authors circumvent them by detecting the proton signal at a fixed phase-encode time following the radio-frequency excitation. By a judicious choice of the phase-encode time in the MRI protocol, the authors differentiate enamel and dentine sufficiently to successfully apply a new classification algorithm. This tissue-classification algorithm identifies the distribution of different material types, such as enamel and dentine, in volumetric data. In this algorithm, the authors treat a voxel as a volume, not as a single point, and assume that each voxel may contain more than one material. They use the distribution of MR image intensities within each voxel-sized volume to estimate the relative proportion of each material using a probabilistic approach. This combined approach, involving MRI and data classification, is directly applicable to bone imaging and hard-tissue contrast-based modeling of biological solids

Quiescent X-Ray/Optical Counterparts of the Black Hole Transient H 1705-250

We report the result of a new Chandra observation of the black hole X-ray transient H 1705-250 in quiescence. H 1705-250 was barely detected in the new 50 ks Chandra observation. With 5 detected counts, we estimate the source quiescent luminosity to be Lx~9.1e30 erg/s in the 0.5-10 keV band (adopting a distance of 8.6 kpc). This value is in line with the quiescent luminosities found among other black hole X-ray binaries with similar orbital periods. By using images taken with the Faulkes Telescope North, we derive a refined position of H 1705-250. We also present the long-term lightcurve of the optical counterpart from 2006 to 2012, and show evidence for variability in quiescence.Comment: 5 pages, 2 figures; Accepted for publication in MNRA

The posterior nervous system of the nematode Caenorhabditis elegans: serial reconstruction of identified neurons and complete pattern of synaptic interactions

Serial-section electron microscopy has been used to reconstruct the cellular architecture of the posterior nervous system of the nematode Caenorhabditis elegans. Each of 40 neurons in the tail of the adult hermaphrodite can be reproducibly and unambiguously identified by a set of morphological features, including cell body position, fiber geometry and size, and staining properties. A complete list of synapses has been assembled for 2 isogenic animals, and these lists are compared with a third isogenic animal reconstructed by White et al. (1986). The set of neurons and their pattern of synaptic interactions is simple and reproducible. Most of the cells are involved in sensory transduction or in local signal processing to relay signals via a few interneurons to motoneurons and thence to body muscles. Because the tail neurons are well separated and fairly reproducible in position, the hermaphrodite tail lends itself to laser-ablation studies of sensory processing (cf. Chalfie et al., 1985). Most of the synapses in the tail are concentrated in the preanal ganglion. Among the approximately 150 synapses there, about 85% are dyadic chemical synapses. The dyadic synapses are involved in reproducible patterns that have several interesting features. Most neurons synapse onto a few preferred pairs of target cells, in patterns that suggest a combinatorial model of synapse specification that may be open to genetic analysis. Furthermore, most dyadic contacts A----B,C fit a pattern in which the 2 postsynaptic partners are involved elsewhere in unidirectional synapses B----C. Thus, the dyadic synapse may serve to diverge sensory signals into parallel pathways, which then reconverge. This divergence/reconvergence pattern eventually directs processed sensory signals to the ventral cord interneurons PVCL and PVCR. About 80–90% of the synapses fall into repeated classes of synapses. Many of the remaining synapses are widely scattered and irreproducible from one animal to the next. Some of these contacts may be developmental mistakes reflecting a degree of “noise” in synapse specification (Waddington, 1957)