Comparison of flight data and analysis for hingeless rotor regressive inplane mode stability

Analytical and experimental data obtained during the development of the AH-56A covering stability of the regressive inplane mode, including coupling with other modes such as body and rotor plunge are reported. Data were obtained on two distinctly different control systems; both gyro controlled, but one with feathering moment feedback and the other with direct flapping feedback. A review was made of analytical procedures employed in investigating the stability of this mode and a comparison was made of the analytical and experimental data. The effect of certain parameters including blade droop, sweep, delta 3, alpha 1, vehicle roll inertia, inplane frequency, and rpm and forward speed on the mode were also reviewed. It was shown that the stability of this mode is treatable by analysis and that adequate stability is achievable without recourse to auxiliary inplane damping devices

Data management study, volume 5. Appendix B - Contractor data package Planetary Quarantine /PQ/ Final report

Contractor data management package for Voyager spacecraft sterilization projec

Double-layer Color Effects in Porcelain Systems

The color of an unshaded body porcelain was determined at three thicknesses on white, gray, and three chromatic backings. Spectral absorption and scattering coefficients of the porcelain were determined from the diffuse reflectance at one thickness on the white and gray backings. These optical coefficients, when utilized with the Kubelka-Munk reflectance theory, accurately predicted the color of the other sample configurations studied. The scattering of the body porcelain was found to decrease with increasing wavelength within the visible spectrum, in accordance with scattering theory for particles not substantially less than the wavelength of the scattered light. For the filtering effects of a translucent material in optical contact with a backing, the Kubelka-Munk reflectance theory described the interaction between the optical absorption and scattering within the translucent material and the reflectance of the backing.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67139/2/10.1177_00220345850640061801.pd

Examples of mathematical modeling tales from the crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters

On the proportion of cancer stem cells in a tumour

It is now generally accepted that cancers contain a sub-population, the cancer stem cells (CSCs), which initiate and drive a tumour’s growth. At least until recently it has been widely assumed that only a small proportion of the cells in a tumour are CSCs. Here we use a mathematical model, supported by experimental evidence, to show that such an assumption is unwarranted. We show that CSCs may comprise any possible proportion of the tumour, and that the higher the proportion the more aggressive the tumour is likely to be

Thin Animals

Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two collapsed phases as well as an extended phase. This has not been confirmed by studies using other means. We use the exact correspondence between the q --> 1 limit of an extended Potts model and lattice animals to investigate the phase diagram of lattice animals on phi-cubed random graphs of arbitrary topology (``thin'' random graphs). We find that only a two phase structure exists -- there is no sign of a second collapsed phase. The random graph model is solved in the thermodynamic limit by saddle point methods. We observe that the ratio of these saddle point equations give precisely the fixed points of the recursion relations that appear in the solution of the model on the Bethe lattice by Henkel and Seno. This explains the equality of non-universal quantities such as the critical lines for the Bethe lattice and random graph ensembles.Comment: Latex, 10 pages plus 6 ps/eps figure

Kertesz on Fat Graphs?

The identification of phase transition points, beta_c, with the percolation thresholds of suitably defined clusters of spins has proved immensely fruitful in many areas of statistical mechanics. Some time ago Kertesz suggested that such percolation thresholds for models defined in field might also have measurable physical consequences for regions of the phase diagram below beta_c, giving rise to a ``Kertesz line'' running between beta_c and the bond percolation threshold, beta_p, in the M, beta plane. Although no thermodynamic singularities were associated with this line it could still be divined by looking for a change in the behaviour of high-field series for quantities such as the free energy or magnetisation. Adler and Stauffer did precisely this with some pre-existing series for the regular square lattice and simple cubic lattice Ising models and did, indeed, find evidence for such a change in high-field series around beta_p. Since there is a general dearth of high-field series there has been no other work along these lines. In this paper we use the solution of the Ising model in field on planar random graphs by Boulatov and Kazakov to carry out a similar exercise for the Ising model on random graphs (i.e. coupled to 2D quantum gravity). We generate a high-field series for the Ising model on $\Phi^4$ random graphs and examine its behaviour for evidence of a Kertesz line