Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

In this paper, we study the stability and accuracy of adaptive finite element methods for the convection-dominated convection-diffusion-reaction problem in the twodimension space. Through various numerical examples on a type of layer-adapted grids (Shishkin grids), we show that the mesh adaptivity driven by accuracy alone cannot stabilize the scheme in all cases. Furthermore the numerical appro...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

We report new results for the second edition of the MICCAI DTI tractography challenge. We build upon a new model, termed Diffusion Directions Imaging, that describes the random motion of water molecules in fibrous tissues and we utilize it as an input to a multifiber deterministic tractography algorithm. We apply the method to track the corticospinal tract in two patients suffering from tumors ...

Introduction Numerous studies have shown a pattern of progressive hippocampal shrinkage as a result of mild cognitively impairment (MCI) and Alzheimer Disease (AD). One of the major pathways affected by the hippocampus is the fornix, and it has been recently shown that fractional anisotropy (FA) is reduced in normal controls verses AD [DeCarli et al., Alzheimer’s Imaging Consortium IC-P1,July 2...

We present in this paper a thorough investigation of three-dimensional flow in a cubical cavity, subject to a constant velocity lid on its roof. In this steady-state analysis, we adopt the mixed formulation on triquadratic elements to preserve mass conservation. To resolve difficulties in the asymmetric and indefinite large-size matrix equations, we apply the BiCGSTAB solution solver. To achiev...

We consider an elementwise data-parallel finite element procedure, recently proposed by Layton and Rabier [Appl. Math. Lett., 5 (1992), pp. 67–70], [J. Numer. Linear Algebra Appl., 2 (1995), pp. 363–394], applied to singularly perturbed convection-diffusion equations with possibly highly anisotropic diffusion. It is shown that the number of iterations required for the solution of the linear alg...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection–diffusion equations for potential flows, and...

In this paper we propose a novel algorithm which leverages models of white matter fibre dispersion to improve tractography. Tractography methods exploit directional information from diffusion weighted magnetic resonance (DW-MR) imaging to infer connectivity between different brain regions. Most tractography methods use a single direction (e.g. the principal eigenvector of the diffusion tensor) ...

The turbulent mixing of a primary jet and its surrounding fluid in a pipe with inlet conditions that result in flow separation is studied. Detailed profiles of the axial mean and rms velocities have been measured with a laser Doppler anemometer. Measured spectra of axial velocity fluctuations show the presence of coherent structures. The performance of a two-equation turbulence model in conjunc...