The rheology of dense, polydisperse granular fluids under shear

The solution of the Enskog equation for the one-body velocity distribution of a moderately dense, arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses and shear viscosity of a model polydisperse granular fluid in which grain size, mass and coefficient of restitution varies amoungst the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.Comment: 8 postscript figures Replaced with new version correcting an error in the SME calculations and misc. small corrections. Second replacement with final correction of SME calculation

Report of the Terrestrial Bodies Science Working Group. Volume 8: The comets

The determination of the nuclear and atmospheric properties of comets, and the interaction of the solar wind with the comet tail are scientific objectives for a mission to one or more comets in the next decade. Recommended priorities for direct cometary exploration are listed

Dynamics of trusses having nonlinear joints

The transient analysis of trusses having nonlinear joints can be accomplished using the residual force technique. The technique was applied a two degree of freedom spring mass system, a four bay planar truss, and an actual ten bay deployable truss. Joints chosen for analysis were the nonlinear gap joints and the linear Voigt joints. Results from the nonlinear gap analyses generally indicate that coupling between the modes can display some interesting effects during free vibration. One particularly interesting effect was that the damping of the structure appeared to be higher than could be accounted for from modal damping alone. Energy transferral from the lower to the higher modes was found to exist as a result of the modal coupling. The apparently increased damping was due to the fact that the energy transferred to the higher modes is inherently dissipated more quickly. Another interesting phenomenon was that the lower modes could drive the higher modes even during free vibration and that these modes could display a rather large quasi-steady state behavior even when modal damping was present. Gaps were also found to increase the amplitude and period of the free vibration response as expected

An investigation for the development of an integrated optical data preprocessor

A laboratory model of a 16 channel integrated optical data preprocessor was fabricated and tested in response to a need for a device to evaluate the outputs of a set of remote sensors. It does this by accepting the outputs of these sensors, in parallel, as the components of a multidimensional vector descriptive of the data and comparing this vector to one or more reference vectors which are used to classify the data set. The comparison is performed by taking the difference between the signal and reference vectors. The preprocessor is wholly integrated upon the surface of a LiNbO3 single crystal with the exceptions of the source and the detector. He-Ne laser light is coupled in and out of the waveguide by prism couplers. The integrated optical circuit consists of a titanium infused waveguide pattern, electrode structures and grating beam splitters. The waveguide and electrode patterns, by virtue of their complexity, make the vector subtraction device the most complex integrated optical structure fabricated to date

Report of the Terrestrial Bodies Science Working Group. Volume 7: The Galilean satellites

The formational and evolutionary history of natural satellites, their mineralogical composition and other phenomena of scientific interest are discussed. Key scientific questions about IO, Ganymede, Callisto, and Europa are posed and the measurements and instruments required for a Galilean satellite lander in the 1980's are described

Modeling the evolution of infrared luminous galaxies: the influence of the Luminosity-Temperature distribution

The evolution of the luminous infrared galaxy population is explored using a pure luminosity evolution model which incorporates the locally observed luminosity-temperature distribution for IRAS galaxies. Pure luminosity evolution models in a fixed $\Lambda$CDM cosmology are fitted to submillimeter (submm) and infrared counts, and backgrounds. It is found that the differences between the locally determined bivariate model and the single variable luminosity function (LF) do not manifest themselves in the observed counts, but rather are primarily apparent in the dust temperatures of sources in flux limited surveys. Statistically significant differences in the redshift distributions are also observed. The bivariate model is used to predict the counts, redshifts and temperature distributions of galaxies detectable by {\it Spitzer}. The best fitting model is compared to the high-redshift submm galaxy population, revealing a median redshift for the total submm population of $z=1.8^{+0.9}_{-0.4}$, in good agreement with recent spectroscopic studies of submillimeter galaxies. The temperature distribution for the submm galaxies is modeled to predict the radio/submm indices of the submm galaxies, revealing that submm galaxies exhibit a broader spread in spectral energy distributions than seen in the local IRAS galaxies.Comment: Accepted for publication in ApJ. Quality of several figures reduced due to size restriction

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