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.

Materials scienceDominant wavelengthFlow (psychology)Stability diagramMechanicsCondensed Matter PhysicsInstabilityElectronic Optical and Magnetic MaterialsPhysics::Fluid DynamicsNormal fieldWavelengthHele-Shaw flowClassical mechanicsLinear stability analysisJournal of Magnetism and Magnetic Materials
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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.

Normal fieldComputational Theory and MathematicsOrthogonalityUmbilicityAsymptotic directionMathematical analysisν-principal curvature foliationGeometry and TopologyAnalysisSphericitySphericityMathematicsDifferential Geometry and its Applications
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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.

Normal fieldGeneral MathematicsGeometryAlgebra over a fieldSpace (mathematics)MathematicsOsculating circleIsrael Journal of Mathematics
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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.

Pure mathematicseducationMinkowski's theoremMathematical analysisNormal curvatureOrder (ring theory)CodimensionNormal fieldGlobal informationGeneral Relativity and Quantum CosmologyHyperplaneMinkowski spaceMathematics::Differential GeometryGeometry and TopologyMathematicsadvg
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