A network model to assess base-filter combinations

Granular filters retain base material within the narrowest constrictions of their void network. A direct comparison of the base material particle size distribution (PSD) and the filter constriction size distribution (CSD) cannot easily be used to assess fi lter - base compatibility. Here a conceptually simple random - walk network model using a filter CSD derived from discrete element modelling and base PSD is used to assess filter - base compatibility. Following verification using experimental data the model is a pplied to assess empirical ratios between filter and base characteristic diameters. The effects of filter density, void connectivity and blocking in the first few filter layers are highlighted

Correlations of near-infrared, optical and X-ray luminosity for early-type galaxies

The relation between X-ray luminosity and near-infrared luminosity for early-type galaxies has been examined. Near-infrared (NIR) luminosities should provide a superior measure of stellar mass compared to optical luminosities used in previous studies, especially if there is significant star-formation or dust present in the galaxies. However, we show that the X-ray-NIR relations are remarkably consistent with the X-ray-optical relations. This indicates that the large scatter of the relations is dominated by scatter in the X-ray properties of early-type galaxies, and is consistent with early-types consisting of old, quiescent stellar populations. We have investigated scatter in terms of environment, surface brightness profile, Mg2, H_beta, H_gamma line strength indices, spectroscopic age, and nuclear H_alpha emission. We found that galaxies with high Mg2 index, low H_beta and H_gamma indices or a `core' profile have a large scatter in Lx, whereas galaxies with low Mg2, high H_beta and H_gamma indices or `power-law' profiles, generally have Lx<10^41 erg/s. There is no clear trend in the scatter with environment or nuclear H_alpha emission.Comment: Accepted for publication in MNRAS. 22 pages, 15 figure

Empirical assessment of the critical time increment in explicit particulate discrete element method simulations

This contribution considers the critical time increment (〖∆t〗_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The 〖∆t〗_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, 〖∆t〗_crit is shown to depend on the particle mass (m), the maximum contact stiffness (Kmax), and the maximum particle coordination number (CN,max). Empirical expressions relating 〖∆t〗_crit to m, Kmax, and CN,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate 〖∆t〗_crit values

Use of elastic stability analysis to explain the stress-dependent nature of soil strength

The peak and critical state strengths of sands are linearly related to the stress level, just as the frictional resistance to sliding along an interface is related to the normal force. The analogy with frictional sliding has led to the use of a ‘friction angle’ to describe the relationship between strength and stress for soils. The term ‘friction angle’ implies that the underlying mechanism is frictional resistance at the particle contacts. However, experiments and discrete element simulations indicate that the material friction angle is not simply related to the friction angle at the particle contacts. Experiments and particle-scale simulations of model sands have also revealed the presence of strong force chains, aligned with the major principal stress. Buckling of these strong force chains has been proposed as an alternative to the frictional-sliding failure mechanism. Here, using an idealized abstraction of a strong force chain, the resistance is shown to be linearly proportional to the magnitude of the lateral forces supporting the force chain. Considering a triaxial stress state, and drawing an analogy between the lateral forces and the confining pressure in a triaxial test, a linear relationship between stress level and strength is seen to emerge from the failure-by-buckling hypothesis

SAW torque transducers for disturbance rejection and tracking control of multi-inertia servo-drive systems

The paper proposes a resonance ratio control (RRC) technique for the coordinated motion control of multi-inertia mechanical systems, based on the measurement of shaft torque via a SAW-based torque sensor. Furthermore, a new controller structure, RRC plus disturbance feedback is proposed, which enables the controller to be designed to independently satisfy tracking and regulation performance. A tuning method for the RRC structure is given based on the ITAE index, normalized as a function of the mechanical parameters enabling a direct performance comparison between a basic proportional and integral (PI) controller. The use of a reduced-order state observer is presented to provide a dynamic estimate of the load-side disturbance torque for a multi-inertia mechanical system, with an appraisal of the composite closed-loop dynamics. It is shown that the integrated formulation of the tuning criteria enables lower bandwidth observers to be implemented with a corresponding reduction in noise and computational load. The control structures are experimentally validated via a purpose designed test facility and demonstrate significant improvement in dynamic tracking performance, whilst additionally rejecting periodic load side disturbances, a feature previously unrealisable except by other, high-gain control schemes that impose small stability margins

Constriction size distributions of granular filters: a numerical study

The retention capability of granular filters is controlled by the narrow constrictions connecting the voids within the filter. The theoretical justification for empirical filter rules used in practice includes consideration of an idealised soil fabric in which constrictions form between co-planar combinations of spherical filter particles. This idealised fabric has not been confirmed by experimental or numerical observations of real constrictions. This paper reports the results of direct, particle-scale measurement of the constriction size distribution (CSD) within virtual samples of granular filters created using the discrete-element method (DEM). A previously proposed analytical method that predicts the full CSD using inscribed circles to estimate constriction sizes is found to poorly predict the CSD for widely graded filters due to an over-idealisation of the soil fabric. The DEM data generated are used to explore quantitatively the influence of the coefficient of uniformity, particle size distribution and relative density of the filter on the CSD. For a given relative density CSDs form a narrow band of similarly shaped curves when normalised by characteristic filter diameters. This lends support to the practical use of characteristic diameters to assess filter retention capability