Multiscale Modelling

Two-Scale convergence of Stekloff eigenvalue problems in perforated domains

by Hermann Douanla

Hermann Douanla, published in 'Boundary Value Problems (2010)'

By means of the two-scale convergence method, we investigate the asymptotic behavior of
eigenvalues and... more By means of the two-scale convergence method, we investigate the asymptotic behavior of
eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We
prove a concise and precise homogenization result including convergence of gradients of
eigenfunctions which improves the understanding of the asymptotic behavior of
eigenfunctions. It is also justified that the natural local problem is not an eigenvalue problem.

Homogenization of Steklov spectral problems with indefinite density function in perforated domains

by Hermann Douanla

Hermann Douanla

The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly... more The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function is investigated in periodically perforated domains. We prove that the spectrum of this problem is discrete and consists of two sequences, one tending to -{\infty} and another to +{\infty}. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the surface of the reference hole is positive, negative or equal to zero. By means of the two-scale convergence method, we investigate all three cases.

Multiscale continuous and discontinuous modelling of heterogeneous materials: A review on recent developments

by Vinh Phu Nguyen

Accepted to be published in Journal of Multiscale Modelling

This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with... more This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modeling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multi scale simulations are presented.

Silicon Nanocrystal Functionalization: Analytic Fitting of DFTB Parameters

by Fabio Trani

Fabio Trani and Vincenzo Barone
J. Chem. Theory Comput. 7, 713-719 (2011)
http://dx.doi.org/10.1021/ct1006086

Neither dashboard nor ‘mashup’ indices: an empirical wealth approach as a pathway to a comprehensive measure of development

by Emanuele Felice

Universitat Autònoma de Barcelona. Departament d’Economia i d’Història Econòmica. UHE Working Paper 2012_01, 2012

The article is composed of two sections. The first one is a critical review of the three main alternative indices to... more The article is composed of two sections. The first one is a critical review of the three main alternative indices to GDP which were proposed in the last decades – the Human Development Index (HDI), the Genuine Progress Indicator (GPI), and the Happy Planet Index (HPI) – which is made on the basis of conceptual foundations, rather than looking at issues of statistical consistency or mathematical refinement as most of the literature does. The pars construens aims to propose an alternative measure, the composite wealth index, consistent with
an approach to development based on the notion of composite wealth, which is in turn derived from an empirical common sense criterion. Arguably, this approach is suitable to be conveyed into
an easily understandable and coherent indicator, and thus appropriate to track development in its various dimensions: simple in its formulation, the wealth approach can incorporate social and ecological goals without significant alterations in conceptual foundations, while reducing to a minimum arbitrary weighting.

Vibration frequency of graphene based composites: A multiscale approach

by Rajib Chowdhury

Materials Science and Engineering: B
Volume 177, Issue 3, 25 February 2012, Pages 303–310

This paper presents a multiscale approach for vibration frequency analysis of graphene/polymer composites. The... more This paper presents a multiscale approach for vibration frequency analysis of graphene/polymer composites. The graphene is modelled at the atomistic scale, and the matrix deformation is analysed by the continuum finite element method. Inter-connectivity between graphene and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The impact of geometrical configuration (armchair and zigzag), boundary conditions and length on the overall stiffness of the graphene reinforced plastics (GRP) is studied. The natural frequency and vibrational mode shapes of GRP studied have displayed dependence on the length and also the boundary conditions. The exceptional vibrational behaviour and large stiffness displayed by GRP makes them a potential replacement for conventional composite fibres such as carbon and glass fibres.

The interdependent contributions of gravitational and structural features to perfusion distribution in a multiscale model of the pulmonary circulation

by Alys Clark

Recent experimental and imaging studies suggest that the influence of gravity on the measured distribution of blood... more Recent experimental and imaging studies suggest that the influence of gravity on the measured distribution of blood flow in the lung is largely through deformation of the parenchymal tissue. To study the contribution of hydrostatic effects to regional perfusion in the presence of tissue deformation, we have developed an anatomically structured computational model of the pulmonary circulation (arteries, capillaries, veins) coupled to a continuum model of tissue deformation, and including scale-appropriate fluid dynamics for blood flow in each vessel type. The model demonstrates that both structural and the multiple effects of gravity on the pulmonary circulation make a distinct contribution to the distribution of blood. It shows that postural differences in perfusion gradients can be explained by the combined effect of tissue deformation and extra-acinar blood vessel resistance to flow in the dependent tissue. However, gravitational perfusion gradients persist when the effect of tissue deformation is eliminated, highlighting the importance of the hydrostatic effects of gravity on blood distribution in the pulmonary circulation. Coupling of large- and small-scale models reveals variation in micro-circulatory driving pressures within isogravitational planes due to extra-acinar vessel resistance. Variation in driving pressures is due to heterogeneous large vessel resistance as a consequence of geometric asymmetry in the vascular trees, and is amplified by the complex balance of pressures, distension, and flow at the micro-circulatory level.

Modeling Sliding Contact of Rough Surfaces with Molecularly Thin Lubricants

by Antonis Vakis

The sliding contact between two rough surfaces in the presence of a molecularly thin lubricant layer is investigated.... more The sliding contact between two rough surfaces in the presence of a molecularly thin lubricant layer is investigated. Under very high shear rates, the lubricant is treated as a semi-solid layer with normal and lateral shear-dependent stiffness components obtained from experimental data. The adhesive force in the presence of lubricant is also adapted from the Sub-boundary lubrication model and improved to account for variation in surface energy with penetration into the lubricant layer. A model is then proposed, based on the Improved sub-boundary lubrication model, which accounts for lubricant contact and adhesion and its validity is discussed. The model is in good agreement with published experimental measurements of friction in the presence of molecularly thin lubricant layers and suggests that a molecularly thin lubricant bearing could be successfully used to reduce solid substrate damage at the interface.

General-Purpose Characteristic Basis Finite Element Method for Multi-Scale Electrostatic and Electromagnetic Problems

by Ozlem Ozgun

Efficient finite element solution of low‐frequency scattering problems via anisotropic metamaterial layers

by Ozlem Ozgun

Modeling bearing and shear forces in molecularly thin lubricants

by Antonis Vakis

Under the effects of high shear rate and confinement between solid surfaces, the behavior of a thin lubricant film... more Under the effects of high shear rate and confinement between solid surfaces, the behavior of a thin lubricant film deviates from that of the bulk, resulting in significant increases of lubricant viscosity and interfacial slip. A semi-empirical model accounting for the breakdown of continuum theory at the nanoscale is proposed—based on film morphology and chemistry from available experimental and molecular dynamics simulation data—to describe lubricant behavior under shear. Viscosity stiffening and interfacial slip models are introduced into the formulations of the normal (bearing) and shear forces acting on a sphere that moves within a thin lubricant film parallel to a rigid plane. The experimentally measured ‘apparent’ viscosity confounding the effects of both stiffening and slip is used to predict the hydrodynamic forces acting on a fully or partially submerged sphere for the purposes of describing lubricant contact in magnetic storage. The proposed sphere-on-flat model forms the basis of a future, dynamic contact with friction model that will account for lubricant contact in the context of molecularly thin lubricated rough surface contact.

Head-disk interface nanotribology for Tbit/in2 recording densities: near-contact and contact recording

by Antonis Vakis

In the effort to achieve Tbit/inch2 recording densities, thermal fly-height control (TFC) nanotechnology was developed... more In the effort to achieve Tbit/inch2 recording densities, thermal fly-height control (TFC) nanotechnology was developed to effectively reduce the clearance (which is of the order of a few nanometres) at the head-disk interface (HDI) of hard-disk drives. In this work, we present a model of the HDI that can predict the dynamic flying and nanotribological contacting behaviour, allowing for accurate predictions and characterization of the operating regime as a function of TFC actuation. A geometric model for TFC is presented and an improved definition of contact at the interface is developed in the presence of nanoscale topographical roughness and dynamic microwaviness. A new methodology is proposed for the calculation of the nominal area of contact, which affects both near- and at-contact behaviour, while the stiffening of the air bearing force with TFC actuation is also accounted for. Slider behaviour is analysed by quantifying the approach, jump-to-contact, lubricant and solid contact regimes of operation and identifying the critical and optimum TFC actuations. The feasibility of near-contact, light molecularly thin lubricant contact versus solid contact recording is explored under the effect of the interfacial forces and stresses present at the HDI. The clearance and the state of vibrations are analysed and design guidelines are proposed for improved performance.

Optimization of thermal fly-height control slider geometry for Tbit/in2 recording

by Antonis Vakis

Magnetic storage advances including thermal fly-height control (TFC) technology were able to reduce the clearance... more Magnetic storage advances including thermal fly-height control (TFC) technology were able to reduce the clearance between the read/write elements of the slider and the disk surface to increase the recording density of hard disk drives without compromising the stability of the head–disk interface (HDI). Sliders employing TFC technology are designed for flying recording and can yield clearances of few nanometers. However, it is estimated that TFC technology alone cannot provide the even smaller clearances necessary to achieve Tbit/in2 recording densities primarily due to the presence of instability-inducing vibrations at the HDI. In this work we perform optimization of the geometry of TFC technology sliders to achieve extremely high-density recording. We propose a flyability parameter coupled with a dynamic, contact mechanics-based friction model of the HDI that accounts for TFC geometry and its influence on the HDI dynamics. Optimization results are analyzed and an operating actuation range is identified that can yield Tbit/in2 recording densities with Angstrom-level clearance and minimized vibrations while also accounting for manufacturing and operational tolerances. This allows for light (lubricant) contact or ‘surfing’ recording. The proposed methodology can be used to reduce wear at the interface and investigate the feasibility of contact recoding.

Dynamic Head-Disk Interface Instabilities with Friction for Light Contact (Surfing) Recording

by Antonis Vakis

Recent advances in hard-disk drive technology involve the use of a thermal fly-height control (TFC) pole tip... more Recent advances in hard-disk drive technology involve the use of a thermal fly-height control (TFC) pole tip protrusion to bring the read/write recording elements of the slider closer to the disk surface and thus achieve terabit per square inch recording densities. A dynamic, contact mechanics-based friction model of the head-disk interface (HDI) that includes roughness and accounts for the TFC geometry and its influence on the HDI dynamics is presented. The model is based on physical parameters and does not include any empirical coefficients. Experimental flyability/touchdown measurements were performed and used to examine in detail the HDI contact criterion in the presence of surface roughness and dynamic microwaviness. Using the model, a procedure is outlined that identifies the optimal clearance and light contact conditions, i.e., the amount of thermal actuation that minimizes, both, the clearance, as well as the flying height modulation. Through calculation of the time varying interfacial forces, mean pressure and shear stress at the HDI can be predicted and used to characterize the contact regime. Based on our results, a light contact regime with reduced bouncing vibrations and low stresses (thus, low wear) that would enable surfing recording is identified.

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

by Laurent Duval

Signal Processing
Special issue on Advances in Multirate Filter Bank Structures and Multiscale Representations
Volume 91, Issue 12, December 2011, Pages 2699-2730
http://dx.doi.org/10.1016/j.sigpro.2011.04.025

The richness of natural images makes the quest for optimal representations in image processing and computer vision... more The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.

A Multi-scal​e Framework for Modeling Instabilit​ies in Fluid-Infi​ltrated Porous Solids

by WaiChing Sun

PhD Dissertation: A Multi-scale Framework for Modeling Instabilities in Fluid-Infiltrated Porous Solids, Theoretical and Applied Mechanics, Northwestern University, 2011, 130 pages; AAT 3456707

Many natural and man-made materials, such as sand, rock, concrete and bone, are multi-constituent, fluid-infiltrated... more Many natural and man-made materials, such as sand, rock, concrete and bone, are multi-constituent, fluid-infiltrated porous solids. The failure of such materials is important for various engineering applications, such as CO2 sequestration, energy storage and retrieval and aquifer management as well as many other geotechnical engineering problems aimed to prevent catastrophic failures due to pore pressure build-up.

This dissertation investigates two mechanical aspects of fluid infiltrated porous media, i.e., the predictions of diffuse and localized failures of porous media and the heterogeneous microstructures developed after failures. We define failures as material conditions in which homogeneous deformation becomes unattainable.

To detect instabilities, a critical state plasticity model for sand is implemented. By seeking bifurcation points of the incremental, linearized constitutive responses, we establish local criteria that detect onsets of drained soil collapse, static liquefaction and formation of deformation bands under locally drained and undrained conditions. Fully undrained and drained triaxial compression simulations are conducted and the stability of the numerical specimens are assessed via a perturbation method.

To characterize deformation modes after failures, a multi-scale framework is designed to determine microstructural attributes from pore space extracted from X-ray tomographic images and improve the accuracy and speed of a multi-scale lattice Boltzmann/finite element hierarchical flow simulation algorithm. By comparing the microstructural attributes and macroscopic permeabilities inside and outside a compaction band formed in Aztec Sandstone, our numerical study reveals that elimination of connected pore space and increased tortuosity are the main causes that compaction bands are flow barriers.

Transition between the models in multiscale simulations: Continua and granular materials

by Sinisa Mesarovic

Mesarovic, S, Dj & Padbidri, J. 2008 In Proc. CP73 Multiscale & Functionally Graded Materials, 2006, G.H. Paulino et al, eds. 171-177. http://proceedings.aip.org/proceedings/cpcr.jsp

We consider two-scale problems: the fine-scale and the coarse-scale. The coarse model is taken to be a continuum. The... more We consider two-scale problems: the fine-scale and the coarse-scale. The coarse model is taken to be a continuum. The key question in this class of problems is related to the simulation of the fine-scale cell: How are the coarse-scale fields to be passed onto the fine scale? Often used periodic boundary conditions, have important drawbacks. The mathematical conditions that answer this question are called minimal boundary conditions (MBC). MBC are imposed on a fine-scale computational cell as a constraint derived from the coarse-scale model. They are minimal in the sense that nothing but the desired constraint is imposed - in contrast to periodic boundary conditions. Owing to their integral nature, the MBC can be applied to any shape of the fine-scale computational cell. The application to fine-scale continuum models has been discussed earlier, Mesarovic and Padbidri [1]. In this paper, we discuss application of MBC to fine-scale discrete models with local interactions - granular materials. The key to this application is the equivalent representation of kinematics of granular flow using the Delaunay network.

Object representations at multiple scales from digital elevation models

by Clemens Eisank

Dragut, L. and C. Eisank (2011) Object representations at multiple scales from digital elevation models. In: Geomorphology, 129: 183-189. (open access)

In the last decade landform classification and mapping has developed as one of the most active areas of... more In the last decade landform classification and mapping has developed as one of the most active areas of geomorphometry. However, translation from continuous models of elevation and its derivatives (slope, aspect, and curvatures) to landform divisions (landforms and landform elements) is filtered by two important concepts: scale and object ontology. Although acknowledged as being important, these two issues have received surprisingly little attention.

This contribution provides an overview and prospects of object representation from DEMs as a function of scale. Relationships between object delineation and classification or regionalization are explored, in the context of differences between general and specific geomorphometry. A review of scales issues in geomorphometry – ranging from scale effects to scale optimization techniques – is followed by an analysis of pros and cons of using cells and objects in DEM analysis. Prospects for coupling multi-scale analysis and object delineation are then discussed. Within this context, we propose discrete geomorphometry as a possible approach between general and specific geomorphometry. Discrete geomorphometry would apply to and describe land-surface divisions defined solely by the criteria of homogeneity in respect to a given land-surface parameter or a combination of several parameters. Homogeneity, in its turn, should always be relative to scale.

Local variance for multi-scale analysis in geomorphometry

by Clemens Eisank

Drăguţ, L., Eisank, C. and T. Strasser (2011) Local variance for multi-scale analysis in geomorphometry, Geomorphology, 130(3-4): 162-172. (open access)

Increasing availability of high resolution Digital Elevation Models (DEMs) is leading to a paradigm shift regarding... more Increasing availability of high resolution Digital Elevation Models (DEMs) is leading to a paradigm shift regarding scale issues in geomorphometry, prompting new solutions to cope with multi-scale analysis and detection of characteristic scales. We tested the suitability of the local variance (LV) method, originally developed for image analysis, for multi-scale analysis in geomorphometry. The method consists of: 1) up-scaling land-surface parameters derived from a DEM; 2) calculating LV as the average standard deviation (SD) within a 3x3 moving window for each scale level; 3) calculating the rate of change of LV (ROC-LV) from one level to another, and 4) plotting values so obtained against scale levels. We interpreted peaks in the ROC-LV graphs as markers of scale levels where cells or segments match types of pattern elements characterized by (relatively) equal degrees of homogeneity. The proposed method has been applied to LiDAR DEMs in two test areas different in terms of roughness: low relief and mountainous, respectively. For each test area, scale levels for slope gradient, plan, and profile curvatures were produced at constant increments with either resampling (cell-based) or image segmentation (object-based). Visual assessment revealed homogeneous areas that convincingly associate into patterns of land-surface parameters well differentiated across scales. We found that the LV method performed better on scale levels generated through segmentation as compared to up-scaling through resampling. The results indicate that coupling multi-scale pattern analysis with delineation of morphometric primitives is possible. This approach could be further used for developing hierarchical classifications of landform elements.

Comparer les morphogénèses urbaines en Europe et aux États-Unis par la simulation à base d'agents--Approches multi-niveaux et environnements de simulation spatiale

by Thomas Louail

Phd Thesis in Computer Science, defended December 7th, 2010.

The multilevel comparison of spatial and hierarchical organisations of urban systems over the world highlights some... more The multilevel comparison of spatial and hierarchical organisations of urban systems over the world highlights some generic and universal properties (rank-size law, center-periphery structure) but also a variety of more specific patterns (in terms of spatial repartition of populations, densities, prices, activities, etc.). The spatial economy and the urban evolutionnary theory both focus on the explanation of the emergence of such patterns, but the simulation models they support classicaly consider one level of spatial organisation only, respectively intra- and inter-urban. Understanding and reconstructing those levels’ interdependancies is a crucial issue for long-term sustainable urban planning. This thesis presents a set of models and tools that are dedicated to the study of this question through agent-based simulation. They have been developed in the context of the Simpop project, and particulary on the comparison of the morphogenesis of urban systems in Europe and in the United States over the period 1800-2000. These tools include the simpopNano agent-based model, and some experimentation modules gathered in an extensible and generic GIS-based platform, which is dedicated to a systematic, collective and intelligent exploration of spatial simulation models. Together they reinforce the idea that the sole difference of topology of the streets networks could be sufficient to generate some more diluted spatial repartitions, as observed in US cities when compared to european ones. This intra-urban model is then articulated with an inter-urban one, Simpop2, in a multilevel model. The latter serves to engage a comparison among a variety of approaches in agent-based simulation litterature for integrating models of multiple levels of abstraction.