Interactive tag maps and tag clouds for the multiscale exploration of large spatio-temporal datasets

'Tag clouds' and 'tag maps' are introduced to represent geographically referenced text. In combination, these aspatial and spatial views are used to explore a large structured spatio-temporal data set by providing overviews and filtering by text and geography. Prototypes are implemented using freely available technologies including Google Earth and Yahoo! 's Tag Map applet. The interactive tag map and tag cloud techniques and the rapid prototyping method used are informally evaluated through successes and limitations encountered. Preliminary evaluation suggests that the techniques may be useful for generating insights when visualizing large data sets containing geo-referenced text strings. The rapid prototyping approach enabled the technique to be developed and evaluated, leading to geovisualization through which a number of ideas were generated. Limitations of this approach are reflected upon. Tag placement, generalisation and prominence at different scales are issues which have come to light in this study that warrant further work

Stable Multiscale Petrov-Galerkin Finite Element Method for High Frequency Acoustic Scattering

We present and analyze a pollution-free Petrov-Galerkin multiscale finite element method for the Helmholtz problem with large wave number $\kappa$ as a variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard continuous $Q_1$ finite elements at a coarse discretization scale $H$ as trial functions, whereas the test functions are computed as the solutions of local problems at a finer scale $h$. The diameter of the support of the test functions behaves like $mH$ for some oversampling parameter $m$. Provided $m$ is of the order of $\log(\kappa)$ and $h$ is sufficiently small, the resulting method is stable and quasi-optimal in the regime where $H$ is proportional to $\kappa^{-1}$. In homogeneous (or more general periodic) media, the fine scale test functions depend only on local mesh-configurations. Therefore, the seemingly high cost for the computation of the test functions can be drastically reduced on structured meshes. We present numerical experiments in two and three space dimensions.Comment: The version coincides with v3. We only resized some figures which were difficult to process for certain printer

Multi-scale simulation of the nano-metric cutting process

Molecular dynamics (MD) simulation and the finite element (FE) method are two popular numerical techniques for the simulation of machining processes. The two methods have their own strengths and limitations. MD simulation can cover the phenomena occurring at nano-metric scale but is limited by the computational cost and capacity, whilst the FE method is suitable for modelling meso- to macro-scale machining and for simulating macro-parameters, such as the temperature in a cutting zone, the stress/strain distribution and cutting forces, etc. With the successful application of multi-scale simulations in many research fields, the application of simulation to the machining processes is emerging, particularly in relation to machined surface generation and integrity formation, i.e. the machined surface roughness, residual stress, micro-hardness, microstructure and fatigue. Based on the quasi-continuum (QC) method, the multi-scale simulation of nano-metric cutting has been proposed. Cutting simulations are performed on single-crystal aluminium to investigate the chip formation, generation and propagation of the material dislocation during the cutting process. In addition, the effect of the tool rake angle on the cutting force and internal stress under the workpiece surface is investigated: The cutting force and internal stress in the workpiece material decrease with the increase of the rake angle. Finally, to ease multi-scale modelling and its simulation steps and to increase their speed, a computationally efficient MATLAB-based programme has been developed, which facilitates the geometrical modelling of cutting, the simulation conditions, the implementation of simulation and the analysis of results within a unified integrated virtual-simulation environment

Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence

We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large- and small-scale contributions using a Fourier decomposition, which reveals pronounced differences

A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time

Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls

In this paper we investigate the possibility of reducing the complexity of a system composed of a large number of interacting agents, whose dynamics feature a symmetry breaking. We consider first order stochastic differential equations describing the behavior of the system at the particle (i.e., Lagrangian) level and we get its continuous (i.e., Eulerian) counterpart via a kinetic description. However, the resulting continuous model alone fails to describe adequately the evolution of the system, due to the loss of granularity which prevents it from reproducing the symmetry breaking of the particle system. By suitably coupling the two models we are able to reduce considerably the necessary number of particles while still keeping the symmetry breaking and some of its large-scale statistical properties. We describe such a multiscale technique in the context of opinion dynamics, where the symmetry breaking is induced by the results of some opinion polls reported by the media

Computational Simulation and 3D Virtual Reality Engineering Tools for Dynamical Modeling and Imaging of Composite Nanomaterials

An adventure at engineering design and modeling is possible with a Virtual Reality Environment (VRE) that uses multiple computer-generated media to let a user experience situations that are temporally and spatially prohibiting. In this paper, an approach to developing some advanced architecture and modeling tools is presented to allow multiple frameworks work together while being shielded from the application program. This architecture is being developed in a framework of workbench interactive tools for next generation nanoparticle-reinforced damping/dynamic systems. Through the use of system, an engineer/programmer can respectively concentrate on tailoring an engineering design concept of novel system and the application software design while using existing databases/software outputs.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions