Multi-scale data fusion for surface metrology

The major trends in manufacturing are miniaturization, convergence of the traditional research fields and creation of interdisciplinary research areas. These trends have resulted in the development of multi-scale models and multi-scale surfaces to optimize the performance. Multi-scale surfaces that exhibit specific properties at different scales for a specific purpose require multi-scale measurement and characterization. Researchers and instrument developers have developed instruments that are able to perform measurements at multiple scales but lack the much required multi- scale characterization capability. The primary focus of this research was to explore possible multi-scale data fusion strategies and options for surface metrology domain and to develop enabling software tools in order to obtain effective multi-scale surface characterization, maximizing fidelity while minimizing measurement cost and time. This research effort explored the fusion strategies for surface metrology domain and narrowed the focus on Discrete Wavelet Frame (DWF) based multi-scale decomposition. An optimized multi-scale data fusion strategy ‘FWR method’ was developed and was successfully demonstrated on both high aspect ratio surfaces and non-planar surfaces. It was demonstrated that the datum features can be effectively characterized at a lower resolution using one system (Vision CMM) and the actual features of interest could be characterized at a higher resolution using another system (Coherence Scanning Interferometer) with higher capability while minimizing the measurement time

Semi-Regular Mesh Extraction from Volumes

We present a novel method to extract iso-surfaces from distance volumes. It generates high quality semi-regular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multi-scale force-based solver refines the initial mesh into a semi-regular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. Given a source voxel of the iso-surface, a set of discrete iso-distance rings are rapidly built and connected while respecting the topology of the iso-surface implied by the data. Subsequent multi-scale refinement is driven by a simple force-based solver designed to combine good iso-surface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the iso-surface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples

The persistent cosmic web and its filamentary structure I: Theory and implementation

We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method and corresponding piece of software allows a genuinely scale free and parameter free identification of the voids, walls, filaments, clusters and their configuration within the cosmic web, directly from the discrete distribution of particles in N-body simulations or galaxies in sparse observational catalogues. To achieve that goal, the method works directly over the Delaunay tessellation of the discrete sample and uses the DTFE density computed at each tracer particle; no further sampling, smoothing or processing of the density field is required. The idea is based on recent advances in distinct sub-domains of computational topology, which allows a rigorous application of topological principles to astrophysical data sets, taking into account uncertainties and Poisson noise. Practically, the user can define a given persistence level in terms of robustness with respect to noise (defined as a "number of sigmas") and the algorithm returns the structures with the corresponding significance as sets of critical points, lines, surfaces and volumes corresponding to the clusters, filaments, walls and voids; filaments, connected at cluster nodes, crawling along the edges of walls bounding the voids. The method is also interesting as it allows for a robust quantification of the topological properties of a discrete distribution in terms of Betti numbers or Euler characteristics, without having to resort to smoothing or having to define a particular scale. In this paper, we introduce the necessary mathematical background and describe the method and implementation, while we address the application to 3D simulated and observed data sets to the companion paper.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material. Submitted to MNRA

Multi-field approach in mechanics of structural solids

We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several primitive cells and, accordingly, by increasing the number of vector fields describing the response of the body to external factors. Using this approach, we obtain several continuum models and explore their essential properties by comparison with the original structural models. Static and dynamical problems as well as the stability problems for structural solids are considered. We demonstrate that the multi-field approach gives a way to obtain families of models that generalize classical ones and are valid not only for long-, but also for short-wavelength deformations of the structural solid. Some examples of application of the multi-field theory and directions for its further development are also discussed.Comment: 25 pages, 18 figure

Parabolic Metamaterials and Dirac Bridges

A new class of multi-scale structures, referred to as `parabolic metamaterials' is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the `parabolic metamaterial' regimes.Comment: 14 pages, 4 figure

Finsler geometry modeling of phase separation in multi-component membranes

Finsler geometric surface model is studied as a coarse-grained model for membranes of three-component such as DOPC, DPPC and Cholesterol. To understand the phase separation of liquid ordered (DPPC rich) $L_o$ and the liquid disordered (DOPC rich) $L_d$, we introduce a variable $\sigma (\in \{1,-1\})$ in the triangulated surface model. We numerically find that there appear two circulars and stripe domains on the surface and that these two morphologies are separated by a phase transition. The morphological change from the one to the other with respect to the variation of the area fraction of $L_o$ is consistent with existing experimental results. This gives us a clear understanding of the origin of the line tension energy, which has been used to understand those morphological changes in the three-component membranes. In addition to these two circulars and stripe domains, raft-like domain and budding domain are also observed, and the corresponding several phase diagrams are obtained. Technical details of the Finsler geometry modeling are also shown.Comment: 18 pages, 11 figure