The flow structure of a DNS of a flat-plate turbulent boundary layer (Wu & Moin 2010) is studied by combining the topological techniques developed by Chong et al. (1990) and Ooi et al. (1999) with the multiscale non-local geometric analysis of Bermejo-Moreno & Pullin (2008), extending the latter to include physical parameters in the analysis and relating them to the geometry of the educed struc...

This paper introduces a directional multiscale algorithm for the two dimensional N body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal on Scientific Computing, 29 (4), 2007] where the three dimensional case was studied. The main observation is that, for two regions that follow a directional p...

The present paper is concerned with the study of manifold-valued multiscale transforms with a focus on the Stiefel manifold. For this specific geometry we derive several formulas and algorithms for the computation of geometric means which will later enable us to construct multiscale transforms of wavelet type. As an application we study compression of piecewise smooth families of low-rank matri...

Inspired from geological problems, we introduce a new geometrical setting for homogenization of a well known and well studied problem of an elliptic second order differential operator with jump conditions on a multiscale network of interfaces. The geometrical setting is fractal and hence neither periodic nor stochastic methods can be applied to the study of such kind of multiscale interface pro...

Nature is observed at all scales; with multiscale modeling, scientists bring together several scales for a holistic analysis of a phenomenon. The models on these different scales may require significant but also heterogeneous computational resources, creating the need for distributed multiscale computing. A particularly demanding type of multiscale models, tightly coupled, brings with it a numb...

In this paper, a new 2D shape Multiscale Triangle-Area Representation (MTAR) method is proposed. This representation utilizes a simple geometric principle, that is, the area of the triangles formed by the shape boundary points. The wavelet transform is used for smoothing and decomposing the shape boundaries into multiscale levels. At each scale level, a TAR image and the corresponding Maxima-Mi...

This chapter presents a statistical analysis of multiscale derivative measurements. Noisy images and multiscale derivative measurements made of noisy images are analyzed; the means and variances of the measured noisy derivatives are calculated in terms of the parameters of the probability distribution function of the initial noise function and the scale or sampling aperture. Normalized and unno...

MOTIVATIONS Physiological systems are ruled by mechanisms operating across multiple temporal scales. A recently proposed approach, multiscale entropy analysis, measures the complexity at different time scales and has been successfully applied to long term electrocardiographic recordings. The purpose of this work is to show the applicability of this methodology, rooted on statistical physics ide...

Snake robots can contact their environments along their whole bodies. This distributed contact makes them versatile and robust locomotors, but also makes controlling them a challenging problem involving high-dimensional configuration spaces, with no direct way to break their motion down into “driving” and “steering” actions. In this paper, we use concepts from geometric mechanics—e.g., expanded...