A parallel nearly implicit time-stepping scheme

Across-the-space parallelism still remains the most mature, convenient and natural way to parallelize large scale problems. One of the major problems here is that implicit time stepping is often difficult to parallelize due to the structure of the system. Approximate implicit schemes have been suggested to circumvent the problem. These schemes have attractive stability properties and they are also very well parallelizable.\ud The purpose of this article is to give an overall assessment of the parallelism of the method

Simulation of density segregation in vibrated beds

We have investigated by numerical simulation the density segregation of fine equal-sized bronze and glass particles subject to vertical vibrations. The model was found to be capable of predicting the two main segregation forms (“bronze on top” and “sandwich”) in roughly the same regions of the phase diagram as was found experimentally by Burtally et al. We investigated the effects of pressure air forcing, friction and restitution of kinetic energy in collisions, and box size on the segregation behavior. We find that next to the interstitial air friction also has a large influence on the formation of the sandwich structure

Variables influencing the frictional behaviour of in vivo human skin

In the past decades, skin friction research has focused on determining which variables are important to affect the frictional behaviour of in vivo human skin. Until now, there is still limited knowledge on these variables. This study has used a large dataset to identify the effect of variables on the human skin, subject characteristics and environmental conditions on skin friction. The data are obtained on 50 subjects (34 male, 16 female). Friction measurements represent the friction between in vivo human skin and an aluminium sample, assessed on three anatomical locations. The coefficient of friction increased significantly (p<0.05) with increasing age, increasing ambient temperature and increasing relative air humidity. A significant inversely proportional relationship was found between friction and both the amount of hair present on the skin and the height of the subject. Other outcome variables in this study were the hydration of the skin and the skin temperatur

Effects of heterogeneity on the drag force in random arrays of spheres

The modelling of the gas-solid interaction is a prerequisite in order\ud to accurately predict fluidized bed behaviour using models\ud such as the Discrete Particle Model (DPM) or the Two Fluid\ud Model (TFM). Currently, the drag force is usually modelled\ud purely based on porosity and slip velocity, which are averaged\ud with respect to the grid size used to solve the model equations.\ud Interfaces at heterogenous structures such as bubbles or free\ud board are not accounted for. As recently pointed out by Xu\ud et al. (2007), sub-grid information for the particle position is\ud available in DPM simulations, thus the local porosity is known\ud and can be used when calculating the drag.\ud Direct Numerical Simulation of flow in particulate systems\ud were done using the lattice Boltzmann method. These simulations\ud were carried out with random arrays of spheres which\ud only have a slight degree of heterogeneity and the gas-solid interaction\ud force on each particle was measured. First we compared\ud these results, which can be considered as the “true drag\ud force, with the drag force one would predict from a correlation\ud typically used in larger scale models (such as the relation of\ud van der Hoef et al. (2005)). Even for the random arrays, the\ud drag on some individual particles differed considerably (up to\ud 40%) from the predicted drag. Then we evaluate the effectiveness\ud of improved drag models, that use information on local\ud porosit

Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations

Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared with fixed-order schemes. Moreover, this comes without a significant increase in the computational work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the fully discrete scheme. The analysis is carried out on both the one-dimensional and the two-dimensional fully discrete schemes and, in the latter case, on uniform as well as on non-uniform meshes. It also provides practical information on the convergence of the dissipation and dispersion error up to polynomial order 10 for the one-dimensional fully discrete scheme

Discrete particle simulation of the homogeneous fluidization of Geldart A particles

The homogeneous fluidization of Geldart A particles has been studied with a 2D soft-sphere discrete particle model. We find that the homogeneous fluidization regime represents a quasi-equilibrium state where the force balance exists at the macroscopic-level, but not at the level of individual particles. The velocity fluctuation of particles is an exponential function of the squared superficial gas velocity in the homogeneous fluidization regime, not a linear function as found by\ud Cody et al

Fluid-particle interaction force for polydisperse systems from lattice boltzmann simulations

Gas-solid fluidized beds are almost always polydisperse in industrial\ud application. However, to describe the fluid-particle interaction\ud force in models for large-scale gas-solid flow, relations\ud are used which have been derived for monodisperse system, for\ud which ad-hoc modifications are made to account for polydispersity.\ud Recently it was shown, on the basis of detailed lattice\ud Boltzmann simulations, that for bidisperse systems these\ud modifications predict a drag force which can be factors different\ud from the true drag force. In this work fluid-particle interaction\ud forces for polydisperse system are studied by means of\ud lattice Boltzmann simulation, using a grid that is typically an\ud order of magnitude smaller than the sphere diameter. Two different\ud lognormal size distributions are considered for this study.\ud The systems consist of polydisperse random arrays of spheres\ud in the diameter range of 8-24 grid spacing and 8-40 grid spacing,\ud a solid volume fraction of 0.5 and 0.3 and Reynolds number\ud 0.1 to 500. The data confirms the observations made for bidisperse\ud systems, namely that an extra correction factor for the\ud drag force is required to adequately capture the effect of polydispersity.\ud It was found that the correction factor derived by van\ud der Hoef et al (J. Fluid Mech. 528 (2005) 233) on the basis of\ud bidisperse simulation data, applies also to general polydisperse\ud system

Calculated and measured Auger lineshapes in clean Si(100)2×1, SiOx and Si-NO

The measurements were performed on the clean 2*1 reconstructed Si(100) surface and this surface exposed to molecular oxygen (O2) or nitric oxide (NO) at room temperature. The data were corrected for electron loss and spectrometer distortions using the authors' newly developed deconvolution method. This method which uses global approximation and spline functions can overcome several difficulties with respect to deconvolution and allows them to derive high-quality auger lineshapes from the SiL2.3 VV Auger electron spectra. The authors experimentally obtained Auger lineshapes were compared with theoretical lineshapes utilising quantum chemical cluster calculations. They used this type of calculation for the interpretation of the Auger lineshape in the actual p-like and s-like partial local density of states for different types of silicon atom. The observed intensities of the major features are in reasonable agreement with the authors' calculations

Brownian particles in transient polymer networks

We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings

Transition density of states (TDOS) of the Si(100)2 × 1 surface derived from the L2,3VV Auger lineshape compared with cluster calculations

The termination of a silicon crystal along the (100) orientation resulting in a 2 × 1 reconstructed surface induces relatively large variations in the local density of states (LDOS) of the different types of surface atoms, such as the up and down dimer atom and the backbond atom. Auger electron spectroscopy (AES) is able to probe the LDOS of the silicon atom in which the L2,3 core hole has been created and is therefore a candidate to analyze the LDOS of the surface atoms. A detailed analysis of the SiL2,3VV Auger electron spectrum allows us to determine a high quality transition density of state (TDOS) of the Si(100)2 × 1 reconstructed surface. The resolved peaks in the TDOS were compared with previous AES, UPS and EELS measurements reported by other investigators. Quantum chemical cluster calculations were used for the interpretation of the TDOS in the actual p-like and s-like partial local density of states for different types of silicon atoms. These quantum chemical cluster calculations of the partial LDOS localized at atoms of the Si(100)2 × 1 surface were found to be in agreement with other types of calculations. Comparing the experimental and the calculated DOS we were able to distinguish several new peaks in the TDOS obtained with AES and to discriminate features in the experimentally obtained TDOS into local electron distributions localized at different surface atoms