Over the years, there has been an ongoing struggle to relate well-log and seismic data due to the inherent bandwidth limitation of seismic data, the problem of seismic amplitudes, and the apparent inability to delineate and characterize the transitions that can be linked to and held responsible for major reflection events and their signatures. By shifting focus to a scale invariant sharpness ch...

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows ...

Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in ax...

Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in ax...

Together with generalized self-similarity and the fractal spectrum, local singularity analysis has been introduced as one part of the new 3S principle and technique for mineral resource assessment based on multifractal modeling, which has been demonstrated to be useful for anomaly delineation. Local singularity is used in this paper to characterize the property of multifractal distribution patt...

Local structural property of an image is often considered in image enhancement with various high/low pass filters. Spatial association indexes (autocorrelation, covariance, and variogram) have been commonly used to characterize the local structure of surfaces for data interpolation in kriging. Singularity is another index measuring the scaling invariant property of measures from a multifractal ...