Stochastic FEM Based on Local Averages of Random Vector Fields

1992 ◽  
Vol 118 (3) ◽  
pp. 496-511 ◽  
Author(s):  
W. Q. Zhu ◽  
Y. J. Ren ◽  
W. Q. Wu
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Stochastic Fem ◽  
Local Averages

A Lévy Based Approach to Random Vector Fields: With a View Towards Turbulence

2014 ◽  
Vol 15 (7-8) ◽  
Author(s):  
Emil Hedevang ◽  
Jürgen Schmiegel
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Vector Valued ◽  
Deterministic Matrix

AbstractUsing integration of deterministic, matrix-valued functions with respect to vector-valued, volatility modulated Lévy bases, we construct random vector fields on

Covariance Models for Divergence-Free and Curl-Free Random Vector Fields

2012 ◽  
Vol 28 (3) ◽  
pp. 433-451 ◽  
Author(s):  
Michael Scheuerer ◽  
Martin Schlather
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Covariance Models ◽  
Divergence Free

On the Geometry and Shape of Brain Sub-Manifolds

1997 ◽  
Vol 11 (08) ◽  
pp. 1317-1343 ◽  
Author(s):  
Sarang C. Joshi ◽  
Michael I. Miller ◽  
Ulf Grenander
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Anatomical Variation ◽  
Principal Component ◽  
Brain Images ◽  
Quadratic Mean ◽  
Orthonormal Bases ◽  
Gaussian Random Vector ◽  
Brain Data ◽  
The Brain

This paper develops mathematical representations for neuro-anatomically significant substructures of the brain and their variability in a population. The focus of the paper is on the neuro-anatomical variation of the geometry and the "shape" of two-dimensional surfaces in the brain. As examples, we focus on the cortical and hippocampal surfaces in an ensemble of Macaque monkeys and human MRI brains. The "shapes" of the substructures are quantified via the construction of templates; the variations are represented by defining probabilistic deformations of the template. Methods for empirically estimating probability measures on these deformations are developed by representing the deformations as Gaussian random vector fields on the embedded sub-manifolds. The Gaussian random vector fields are constructed as quadratic mean limits using complete orthonormal bases on the sub-manifolds. The complete orthonormal bases are generated using modes of vibrations of the geometries of the brain sub-manifolds. The covariances are empirically estimated from an ensemble of brain data. Principal component analysis is presented for characterizing the "eigen-shape" of the hippocampus in an ensemble of MRI-MPRAGE whole brain images. Clustering based on eigen-shape is presented for two sub-populations of normal and schizophrenic.

scholarly journals SPACE–TIME EVOLUTION OF THE OSCILLATOR, RAPIDLY MOVING IN A RANDOM MEDIA

2004 ◽  
Vol 19 (03) ◽  
pp. 411-441
Author(s):  
B. BLOK
Keyword(s):  
Probability Distribution ◽  
Time Evolution ◽  
Random Vector ◽  
Random Media ◽  
Vector Fields ◽  
Energy Levels ◽  
Quantum Mechanical ◽  
Mechanical Evolution ◽  
The Media ◽  
Space Time Evolution

We study the quantum-mechanical evolution of the nonrelativistic oscillator, rapidly moving in the media with the random vector fields. We calculate the evolution of the level probability distribution as a function of time, and obtain rapid level diffusion over the energy levels. Our results imply a new mechanism of charmonium dissociation in QCD media.

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