Analysis of Energy-Based Blended Quasicontinuum Approximations

The development of patch test consistent quasicontinuum energies for multi-dimensional crystalline solids modeled by many-body potentials remains a challenge. The original quasicontinuum energy (QCE) has been implemented for many-body potentials in two and three space dimensions, but it is not patch test consistent. We propose that by blending the atomistic and corresponding Cauchy-Born continuum models of QCE in an interfacial region with thickness of a small number $k$ of blended atoms, a general quasicontinuum energy (BQCE) can be developed with the potential to significantly improve the accuracy of QCE near lattice instabilities such as dislocation formation and motion. In this paper, we give an error analysis of the blended quasicontinuum energy (BQCE) for a periodic one-dimensional chain of atoms with next-nearest neighbor interactions. Our analysis includes the optimization of the blending function for an improved convergence rate. We show that the $\ell^2$ strain error for the non-blended QCE energy (QCE), which has low order $\text{O}(\epsilon^{1/2})$ where $\epsilon$ is the atomistic length scale, can be reduced by a factor of $k^{3/2}$ for an optimized blending function where $k$ is the number of atoms in the blending region. The QCE energy has been further shown to suffer from a O$(1)$ error in the critical strain at which the lattice loses stability. We prove that the error in the critical strain of BQCE can be reduced by a factor of $k^2$ for an optimized blending function, thus demonstrating that the BQCE energy for an optimized blending function has the potential to give an accurate approximation of the deformation near lattice instabilities such as crack growth.Comment: 26 pages, 1 figur

Implications of ideas on super-hydrophobicity for water repellent soil

Water repellence is an important factor in soil erosion due to its role in inhibiting the re-establishment of vegetation after fire and due to its enhancement of run-off. Water repellence is studied across a range of diverse disciplines, such as chemistry, materials, textiles and soil and reclamation science. In recent years many basic studies of water repellence of materials have focused on the role of the sub-mm surface topography of a material in modifying the intrinsic hydrophobicity imparted by the surface chemistry to create super-hydrophobicity. In this report, we first illustrate the types of hydrophobic effects created by a suitable coupling of small scale surface topography with surface chemistry using three examples of materials: an etched metal, a foam and a micro-fabricated pillar structure. These examples demonstrate the general applicability of the ideas and suggest that they could apply to a granular material, such as a fine sandy soil, particularly when the grains have become coated with a hydrophobic layer. This applicability is confirmed by contact angle measurements of droplets of water on hydrophobic sand. A theoretical model describing the application of these ideas to a loose-packed, but regular, array of uniform spherical grains is then presented and discussed. When the grains are in a dry initial state the effect of the surface is to increase the apparent water repellence as observed through the contact angle. However, when the spaces between the grains are initially filled with water, the effect is to provide greater wetting. To qualitatively confirm the enhancement of contact angle caused by the granular structure, model surfaces using 600 µm and 250 µm hydrophobic glass beads were created. On these surfaces, the contact angle of droplets of water was increased from 108° to 126° and 140°, respectively

Exotic fluids and crystals of soft polymeric colloids

We discuss recent developments and present new findings in the colloidal description of soft polymeric macromolecular aggregates. For various macromolecular architectures, such as linear chains, star polymers, dendrimers and polyelectrolyte stars, the effective interactions between suitably chosen coordinates are shown to be ultrasoft, i.e., they either remain finite or diverge very slowly at zero separation. As a consequence, the fluid phases have unusual characteristics, including anomalous pair correlations and mean-field like thermodynamic behaviour. The solid phases can exhibit exotic, strongly anisotropic as well as open crystal structures. For example, the diamond and the A15-phase are shown to be stable at sufficiently high concentrations. Reentrant melting and clustering transitions are additional features displayed by such systems, resulting in phase diagrams with a very rich topology. We emphasise that many of these effects are fundamentally different from the usual archetypal hard sphere paradigm. Instead, we propose that these fluids fall into the class of mean-field fluids.Comment: 22 pages, uses iopart.cls and iopart10.clo; submitted to Journal of Physics Condensed Matter, special issue in honour of professor Peter Puse

Spatial models for architectural heritage in urban database context

Despite the GIS (Geographic Information Systems/Geospatial Information Systems) have been provided with several applications to manage the two-dimensional geometric information and arrange the topological relations among different spatial primitives, most of these systems have limited capabilities to manage the three-dimensional space. Other tools, such as CAD systems, have already achieved a full capability of representing 3D data. Most of the researches in the field of GIS have underlined the necessity of a full 3D management capability which is not yet achieved by the available systems (Rahman, Pilouk 2008) (Zlatanova 2002). First of all to reach this goal is important to define the spatial data model, which is at the same time a geometric and topological model and so integrating these two aspects in relation to the database management efficiency and documentation purposes. The application field on which these model can be tested is the spatial data managing of Architectural Heritage documentation, to evaluate the pertinence of these spatial models to the requested scale for the needs of such a documentation. Most of the important aspects are the integration of metric data originated from different sources and the representation and management of multiscale data. The issues connected with the representation of objects at higher LOD than the ones defined by the CityGML will be taken into account. The aim of this paper is then to investigate which are the favorable application of a framework in order to integrate two different approaches: architectural heritage spatial documentation and urban scale spatial data management

Representations and descriptors unifying the study of molecular and bulk systems

Establishing a unified framework for describing the structures of molecular and periodic systems is a long-standing challenge in physics, chemistry, and material science. With the rise of machine learning methods in these fields, there is a growing need for such a method. This perspective aims to discuss the development and use of three promising approaches-topological, atom-density, and symmetry-based-for the prediction and rationalization of physical, chemical, and mechanical properties of atomistic systems across different scales and compositions

Shear-transformation-zone theory of plastic deformation near the glass transition

The shear-transformation-zone (STZ) theory of plastic deformation in glass-forming materials is reformulated in light of recent progress in understanding the roles played the effective disorder temperature and entropy flow in nonequilibrium situations. A distinction between fast and slow internal state variables reduces the theory to just two coupled equations of motion, one describing the plastic response to applied stresses, and the other the dynamics of the effective temperature. The analysis leading to these equations contains, as a byproduct, a fundamental reinterpretation of the dynamic yield stress in amorphous materials. In order to put all these concepts together in a realistic context, the paper concludes with a reexamination of the experimentally observed rheological behavior of a bulk metallic glass. That reexamination serves as a test of the STZ dynamics, confirming that system parameters obtained from steady-state properties such as the viscosity can be used to predict transient behaviors.Comment: 15 pages, four figure

Rapid gravity filtration operational performance assessment and diagnosis for preventative maintenance from on-line data

Rapid gravity filters, the final particulate barrier in many water treatment systems, are typically monitored using on-line turbidity, flow and head loss instrumentation. Current metrics for assessing filtration performance from on-line turbidity data were critically assessed and observed not to effectively and consistently summarise the important properties of a turbidity distribution and the associated water quality risk. In the absence of a consistent risk function for turbidity in treated water, using on-line turbidity as an indicative rather than a quantitative variable appears to be more practical. Best practice suggests that filtered water turbidity should be maintained below 0.1 NTU, at higher turbidity we can be less confident of an effective particle and pathogen barrier. Based on this simple distinction filtration performance has been described in terms of reliability and resilience by characterising the likelihood, frequency and duration of turbidity spikes greater than 0.1 NTU. This view of filtration performance is then used to frame operational diagnosis of unsatisfactory performance in terms of a machine learning classification problem. Through calculation of operationally relevant predictor variables and application of the Classification and Regression Tree (CART) algorithm the conditions associated with the greatest risk of poor filtration performance can be effectively modelled and communicated in operational terms. This provides a method for an evidence based decision support which can be used to efficiently manage individual pathogen barriers in a multi-barrier system