4,526 research outputs found
Recovering the Tidal Field in the Projected Galaxy Distribution
We present a method to recover and study the projected gravitational tidal
forces from a galaxy survey containing little or no redshift information. The
method and the physical interpretation of the recovered tidal maps as a tracer
of the cosmic web are described in detail. We first apply the method to a
simulated galaxy survey and study the accuracy with which the cosmic web can be
recovered in the presence of different observational effects, showing that the
projected tidal field can be estimated with reasonable precision over large
regions of the sky. We then apply our method to the 2MASS survey and present a
publicly available full-sky map of the projected tidal forces in the local
Universe. As an example of an application of these data we further study the
distribution of galaxy luminosities across the different elements of the cosmic
web, finding that, while more luminous objects are found preferentially in the
most dense environments, there is no further segregation by tidal environment.Comment: 18 pages, 13 figures. Data publicly available at
http://intensitymapping.physics.ox.ac.uk/2mass_tidal.htm
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Visualization of Tensor Fields in Mechanics
Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context
Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging
Mapping white matter tracts is an essential step towards understanding brain
function. Diffusion Magnetic Resonance Imaging (dMRI) is the only noninvasive
technique which can detect in vivo anisotropies in the 3-dimensional diffusion
of water molecules, which correspond to nervous fibers in the living brain. In
this process, spectral data from the displacement distribution of water
molecules is collected by a magnetic resonance scanner. From the statistical
point of view, inverting the Fourier transform from such sparse and noisy
spectral measurements leads to a non-linear regression problem. Diffusion
tensor imaging (DTI) is the simplest modeling approach postulating a Gaussian
displacement distribution at each volume element (voxel). Typically the
inference is based on a linearized log-normal regression model that can fit the
spectral data at low frequencies. However such approximation fails to fit the
high frequency measurements which contain information about the details of the
displacement distribution but have a low signal to noise ratio. In this paper,
we directly work with the Rice noise model and cover the full range of
-values. Using data augmentation to represent the likelihood, we reduce the
non-linear regression problem to the framework of generalized linear models.
Then we construct a Bayesian hierarchical model in order to perform
simultaneously estimation and regularization of the tensor field. Finally the
Bayesian paradigm is implemented by using Markov chain Monte Carlo.Comment: 37 pages, 3 figure
Reconstruction of early phase deformations by integrated magnetic and mesotectonic data evaluation
Markers of brittle faulting are widely used for recovering past deformation phases. Rocks often have oriented
magnetic fabrics, which can be interpreted as connected to ductile deformation before cementation of the sediment.
This paper reports a novel statistical procedure for simultaneous evaluation of AMS (Anisotropy of Magnetic
Susceptibility) and fault-slip data.The new method analyzes the AMS data, without linearization techniques,
so that weak AMS lineation and rotational AMS can be assessed that are beyond the scope of classical
methods. This idea is extended to the evaluation of fault-slip data. While the traditional assumptions of stress inversion
are not rejected, the method recovers the stress field via statistical hypothesis testing. In addition it provides
statistical information needed for the combined evaluation of the AMS and the mesotectonic (0.1 to 10m)
data. In the combined evaluation a statistical test is carried out that helps to decide if the AMS lineation and the
mesotectonic markers (in case of repeated deformation of the oldest set of markers) were formed in the same or
different deformation phases. If this condition is met, the combined evaluation can improve the precision of the
reconstruction. When the two data sets do not have a common solution for the direction of the extension, the
deformational origin of the AMS is questionable. In this case the orientation of the stress field responsible for the
AMS lineation might be different from that which caused the brittle deformation. Although most of the examples
demonstrate the reconstruction of weak deformations in sediments, the new method is readily applicable to
investigate the ductile-brittle transition of any rock formation as long as AMS and fault-slip data are available
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