Likely oscillatory motions of stochastic hyperelastic solids

Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterised. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as `likely oscillatory motions'

Likely equilibria of stochastic hyperelastic spherical shells and tubes

In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter.Comment: arXiv admin note: text overlap with arXiv:1808.0126

Void elimination in screen printed thick film dielectric pastes

The problem is to understand the mechanisms for the formation and evolution of defects in wet screen printed layers. The primary objective is to know how best to alter the properties of the paste (rather than the geometry of the screen printing process itself) in order to eliminate the defects. With these goals in mind the work done during the Study Group reported here was as follows; to describe a simple model for the closure of craters, a model for the partial closure of vias, a possible mechanism for the formation of pinholes and finally a more detailed consideration of the screen printing process

Heat and fluid flow in a scraped-surface heat exchanger containing a fluid with temperature-dependent viscosity

Scraped-surface heat exchangers (SSHEs) are extensively used in a wide variety of industrial settings where the continuous processing of fluids and fluid-like materials is involved. The steady non-isothermal flow of a Newtonian fluid with temperature-dependent viscosity in a narrow-gap SSHE when a constant temperature difference is imposed across the gap between the rotor and the stator is investigated. The mathematical model is formulated and the exact analytical solutions for the heat and fluid flow of a fluid with a general dependence of viscosity on temperature for a general blade shape are obtained. These solutions are then presented for the specific case of an exponential dependence of viscosity on temperature. Asymptotic methods are employed to investigate the behaviour of the solutions in several special limiting geometries and in the limits of weak and strong thermoviscosity. In particular, in the limit of strong thermoviscosity (i.e., strong heating or cooling and/or strong dependence of viscosity on temperature) the transverse and axial velocities become uniform in the bulk of the flow with boundary layers forming either just below the blade and just below the stationary upper wall or just above the blade and just above the moving lower wall. Results are presented for the most realistic case of a linear blade which illustrate the effect of varying the thermoviscosity of the fluid and the geometry of the SSHE on the flow

HI in four star-forming low-luminosity E/S0 and S0 galaxies

We present HI data cubes of four low-luminosity early-type galaxies which are currently forming stars. These galaxies have absolute magnitudes in the range M_B=-17.9 to -19.9 (H_o=50 km/s/Mpc). Their HI masses range between a few times 10^8 and a few times 10^9 M_sun and the corresponding values for M_HI/L_B are between 0.07 and 0.42, so these systems are HI rich for their morphological type. In all four galaxies, the HI is strongly centrally concentrated with high central HI surface densities, in contrast to what is typically observed in more luminous early-type galaxies. In two galaxies (NGC 802 and ESO 118-G34), the kinematics of the HI suggests that the gas is in a strongly warped disk, which we take as evidence for recent accretion of HI. In the other two galaxies (NGC 2328 and ESO 027-G21) the HI must have been part of the systems for a considerable time. The HI properties of low-luminosity early-type galaxies appear to be systematically different from those of many more luminous early-type galaxies, and we suggest that these differences are due to a different evolution of the two classes. The star formation history of these galaxies remains unclear. Their UBV colours and Halpha emission-line strengths are consistent with having formed stars at a slowly-declining rate for most of the past 10^10 years. However, the current data do not rule out a small burst of recent star formation overlaid on an older stellar population.Comment: To appear in AJ, LateX, figures in gif format, paper also available at http://www.nfra.nl/~morganti/LowLu

Effects of environmental factors on development of Pyrenopeziza brassicae (light leaf spot) apothecia on oilseed rape debris

Publication no. P-2001-0221-01R. This article is in the public domain and not copyrightable. It may be freely reprinted with customary crediting of the source. The American Phytopathological Society, 2001The development of Pyrenopeziza brassicae (light leaf spot) apothecia was studied on petiole debris from artificially infected oilseed rape leaves incubated at temperatures from 6 to 22 degreesC under different wetness regimes and in 16 h light/8 h dark or continuous darkness. There was no significant difference between light treatments in numbers of apothecia that developed. Mature apothecia developed at temperatures from 5 to 18 degreesC but not at 22 degreesC. The rate of apothecial development decreased as temperature decreased from 18 to 5 degreesC; mature apothecia were first observed after 5 days at 18 degreesC and after 15 days at 6 degreesC. Models were fitted to estimates of the time (days) for 50% of the maximum number of apothecia to develop (t(1); model 1, t(1) = 7.6 + 55.8(0.839)(T)) and the time for 50% of the maximum number of apothecia to decay (t(2); model 2, t(2) = 24.2 + 387(0.730)(T)) at temperatures (T) from 6 to 18 degreesC. An interruption in wetness of the petiole debris for 4 days after 4, 7, or 10 days of wetness delayed the time to observation of the first mature apothecia for approximate to4 days and decreased the number of apothecia produced (by comparison with continuous wetness). A relationship was found between water content of pod debris and electrical resistance measured by a debris-wetness sensor. The differences between values of tl predicted by model 1 and observed values of t(1) were 1 to 9 days. Model 2 did not predict t(2); apothecia decayed more quickly under natural conditions than predicted by model 2.Peer reviewe