Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Electron beam current loss at the high-vacuum-high-pressure boundary in the environmental scanning electron microscope

A significant loss in electron probe current can occur before the electron beam enters the specimen chamber of an environmental scanning electron microscope (ESEM). This loss results from electron scattering in a gaseous jet formed inside and downstream (above) the pressure-limiting aperture (PLA), which separates the high-pressure and high-vacuum regions of the microscope. The electron beam loss above the PLA has been calculated for three different ESEMs, each with a different PLA geometry: an ElectroScan E3, a Philips XL30 ESEM, and a prototype instrument. The mass thickness of gas above the PLA in each case has been determined by Monte Carlo simulation of the gas density variation in the gas jet. It has been found that the PLA configurations used in the commercial instruments produce considerable loss in the electron probe current that dramatically degrades their performance at high chamber pressure and low accelerating voltage. These detrimental effects are minimized in the prototype instrument, which has an optimized thin-foil PLA design.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Influence of curing protocol on selected properties of light-curing polymers: Degree of conversion, volume contraction, elastic modulus, and glass transition temperature

Objectives. The purpose of this study was to investigate the effect of light-curing protocol on degree of conversion (DC), volume contraction (C), elastic modulus (E), and glass transition temperature (T(g)) as measured on a model polymer. It was a further aim to correlate the measured values with each other. Methods. Different light-curing protocols were used in order to investigate the influence of energy density (ED), power density (PD), and mode of cure on the properties. The modes of cure were continuous, pulse-delay, and stepped irradiation. DC was measured by Raman micro-spectroscopy. C was determined by pycnometry and a density column. E was measured by a dynamic mechanical analyzer (DMA), and T(g) was measured by differential scanning calorimetry (DSC). Data were submitted to two-and three-way ANOVA, and linear regression analyses. Results. ED, PD, and mode of cure influenced DC, C, E, and T(g) of the polymer. A significant positive correlation was found between ED and DC (r = 0.58), ED and E (r = 0.51), and ED and T(g) (r = 0.44). Taken together, ED and PD were significantly related to DC and E. The regression coefficient was positive for ED and negative for PD. Significant positive correlations were detected between DC and C (r = 0.54), DC and E (r = 0.61), and DC and T(g) (r = 0.53). Comparisons between continuous and pulse-delay modes of cure showed significant influence of mode of cure: pulse-delay curing resulted in decreased DC, decreased C, and decreased T(g). Influence of mode of cure, when comparing continuous and step modes of cure, was more ambiguous. A complex relationship exists between curing protocol, microstructure of the resin and the investigated properties. The overall performance of a composite is thus indirectly affected by the curing protocol adopted, and the desired reduction of C may be in fact a consequence of the decrease in DC. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Orbitally induced oscillations in the East Antarctic ice sheet at the Oligocene/Miocene boundary

Between 34 and 15 million years (Myr) ago, when planetary temperatures were 3-4 degreesC warmer than at present and atmospheric CO2 concentrations were twice as high as today(1), the Antarctic ice sheets may have been unstable(2-7). Oxygen isotope records from deep-sea sediment cores suggest that during this time fluctuations in global temperatures and high-latitude continental ice volumes were influenced by orbital cycles(8-10). But it has hitherto not been possible to calibrate the inferred changes in ice volume with direct evidence for oscillations of the Antarctic ice sheets(11). Here we present sediment data from shallow marine cores in the western Ross Sea that exhibit well dated cyclic variations, and which link the extent of the East Antarctic ice sheet directly to orbital cycles during the Oligocene/Miocene transition (24.1-23.7 Myr ago). Three rapidly deposited glaci-marine sequences are constrained to a period of less than 450 kyr by our age model, suggesting that orbital influences at the frequencies of obliquity (40 kyr) and eccentricity (125 kyr) controlled the oscillations of the ice margin at that time. An erosional hiatus covering 250 kyr provides direct evidence for a major episode of global cooling and ice-sheet expansion about 23.7 Myr ago, which had previously been inferred from oxygen isotope data (Mil event(5)).

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths. (C) 2001 Elsevier Science B.V. All rights reserved.

The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

Scavenging of siliceous grain-boundary phase of 8-mol%-ytterbia-stabilized zirconia without additive

The grain-boundary conductivity (sigma (gb),) of 8-mol%-ytterbiastabilized zirconia increased markedly with heat treatment between 1000 degrees and 1300 degreesC with a slow heating rate (0.1 degreesC/min) before sintering. The extent of the sigma (gb) improvement was the same or larger than that via Al2O3 addition. The heat treatment did not affect the grain-interior conduction when sintered at 1600 degreesC, while Al2O3-derived scavenging significantly did, given the larger increment of total conductivity in the heat-treated sample. The formation of a silicon-containing phase in a discrete form was suggested as a possible route of scavenging the resistive phase from the correlation between average grain size and sigma (gb).

The plausibility of long-wavelength stress correlation or stress magnitude as a mechanism for precursory seismicity: Results from two simple elastic models

Observations of accelerating seismic activity prior to large earthquakes in natural fault systems have raised hopes for intermediate-term eartquake forecasting. If this phenomena does exist, then what causes it to occur? Recent theoretical work suggests that the accelerating seismic release sequence is a symptom of increasing long-wavelength stress correlation in the fault region. A more traditional explanation, based on Reid's elastic rebound theory, argues that an accelerating sequence of seismic energy release could be a consequence of increasing stress in a fault system whose stress moment release is dominated by large events. Both of these theories are examined using two discrete models of seismicity: a Burridge-Knopoff block-slider model and an elastic continuum based model. Both models display an accelerating release of seismic energy prior to large simulated earthquakes. In both models there is a correlation between the rate of seismic energy release with the total root-mean-squared stress and the level of long-wavelength stress correlation. Furthermore, both models exhibit a systematic increase in the number of large events at high stress and high long-wavelength stress correlation levels. These results suggest that either explanation is plausible for the accelerating moment release in the models examined. A statistical model based on the Burridge-Knopoff block-slider is constructed which indicates that stress alone is sufficient to produce accelerating release of seismic energy with time prior to a large earthquake.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.