We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diiusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main classes of ows. Percolating ows, which are characterized by the presence of long tubes of streamlines mixing hot and cold material, lead to strong speed-up of...

Present a novel approach of brain connectivity visualization of white matter pathways and gray matter areas using diffusion tensor imaging and functional magnetic resonance imaging. Clustering is an important tool for creating abstraction and filtration in general and is central representation in particular. While abstraction involves simplification and generalization, filtration here entails c...

After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues diffuse onto horseshoe streamlines under effect of viscous dissipation, and meander out the planets' Hill sphere. Within sphere, intercept flow circumplanetary disks. The host stars' tidal perturbation induces a barrier across converging streamlines' interface. Viscous...

The visualisation of 3D flow poses many challenges. Difficulties can stem from attempting to capture all flow features, the speed of computation, and spatial perception. Streamlines and stream surfaces are standard tools for visualising 3D flow. Although a variety of automatic seeding approaches have been proposed for streamlines, little work has been presented for stream surfaces. We present a...

Streamline similarity comparison has become an active research topic recently. We present a novel streamline similarity comparison method inspired by the bag-of-features idea from computer vision. Our approach computes a feature vector, spatially sensitive bag-of-features, for each streamline as its signature. This feature vector not only encodes the statistical distribution of combined feature...

Magnetic resonance imaging enables the noninvasive mapping of both anatomical white matter connectivity and dynamic patterns of neural activity in the human brain. We examine the relationship between the structural properties of white matter streamlines (structural connectivity) and the functional properties of correlations in neural activity (functional connectivity) within 84 healthy human su...

We compare streamline statistics in stationary homogeneous isotropic turbulence and in turbulence generated by a fractal square grid. We examine streamline segments characterised by the velocity difference u D and the distance l between extremum points. We find close agreement between the stationary homogeneous isotropic turbulence and the decay region of the fractal-generated turbulence as wel...