Search results for "Normal field"
showing 4 items of 4 documents
Labyrinthine instability of miscible magnetic fluids
2002
Abstract We consider an inhomogeneous magnetic fluid (MF), modeling a miscible MF pair, in a Hele–Shaw cell under a normal field. A linear stability analysis for the sharp straight interface (analytically) and for the diffused one (numerically) is performed. For the former case, the neutral curves and the stability diagram are found along with the critical wavelength and parameter values. Oscillatory or monotonous instabilities are shown to occur. For the diffused interface, we recognize the importance of 2D flow viscous effects along with the conventional wall friction and observe that in strong fields the dominant wavelength scales as the cell gap.
Umbilicity of surfaces with orthogonal asymptotic lines in R4
2002
We study some properties of surfaces in 4-space all whose points are umbilic with respect to some normal field. In particular, we show that this condition is equivalent to the orthogonality of the (globally defined) fields of asymptotic directions. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in 4-space. 2002 Elsevier Science B.V. All rights reserved.
The horospherical geometry of surfaces in hyperbolic 4-space
2006
We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres inH + 4 (−1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymptotic directions.
Global properties of codimension two spacelike submanifolds in Minkowski space
2009
Abstract We consider codimension two spacelike submanifolds with a parallel normal field (i.e. vanishing normal curvature) in Minkowski space. We use the analysis of their contacts with hyperplanes and hyperquadrics in order to get some global information on them. As a consequence we obtain new versions of Carathéodory's and Loewner's conjectures on spacelike surfaces in 4-dimensional Minkowski space and 4-flattenings theorems for closed spacelike curves in 3-dimensional Minkowski space.