In: Journal of Physics: Condensed Matter, 2011, vol. 23, no. 6, p. 065102
Magnetic properties of particles are generally determined from randomly oriented ensembles and the influence of the particle orientation on the magnetic response is neglected. Here, we report on the magnetic characterization of anisotropic spindle- type hematite particles. The easy axis of magnetization is within the basal plane of hematite, which is oriented perpendicular to the spindle axis....
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In: Journal of Physical Chemistry B, 2010, vol. 114, no. 14, p. 4763-4769
Form factor and magnetic properties of silica-coated spindle-type hematite nanoparticles are determined from SAXS measurements with applied magnetic field and magnetometry measurements. The particle size, polydispersity and porosity are determined using a core−shell model for the form factor. The particles are found to align with their long axis perpendicular to the applied field. The...
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In: Advances in Mathematics, 2009, vol. 222, no. 3, p. 920-936
We extend the classical Brunn theorem to symmetric moments of convex bodies and use it to prove the convexity of the Lp-intersection bodies of centered convex bodies.
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In: Journal of Differential Geometry, 2007, vol. 75, no. 3, p. 433-457
Smooth valuations on manifolds are studied by establishing a link with the Rumin-de Rham complex of the co-sphere bundle. Several operations on differential forms induce operations on smooth valuations: signature operator, Rumin-Laplace operator, Euler-Verdier involution and derivation operator. As an application, Alesker’s Hard Lefschetz Theorem for even translation invariant valuations on...
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In: Journal für die reine und angewandte Mathematik, 2007, no. 608, p. 1-15
It is shown that the Gromov-Hausdorff limit of a subanalytic 1-parameter family of compact connected sets (endowed with the inner metric) exists. If the family is semialgebraic, then the limit space can be identified with a semialgebraic set over some real closed field. Different notions of tangent cones (pointed Gromov-Hausdorff limits, blow-ups and Alexandrov cones) for a closed connected...
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In: Israel Journal of Mathematics, 2007, vol. 159, no. 1, p. 373-411
An elementary construction of the normal cycle of a compact definable set in Euclidean space (and more generally of a compactly supported constructible function) is given. Here “definable” means definable in some o-minimal structure. The construction is based on the notion of support function and uses only basic o-minimal geometry.
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In: Geometriae Dedicata, 2006, vol. 123, no. 1, p. 153-169
We show that the natural “convolution” on the space of smooth, even, translation- invariant convex valuations on a euclidean space V, obtained by intertwining the product and the duality transform of S. Alesker J. Differential Geom. 63: 63–95, 2003; Geom.Funct. Anal. 14:1–26, 2004 may be expressed in terms of Minkowski sum. Furthermore the resulting product extends naturally to odd...
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In: Differential Geometry and its Applications, 2006, vol. 24, no. 6, p. 660-669
We refine recent existence and uniqueness results, for the barycenter of points at infinity of Hadamard manifolds, to measures on the sphere at infinity of symmetric spaces of non compact type and, more specifically, to measures concentrated on single orbits. The barycenter will be interpreted as the maximum likelihood estimate (MLE) of generalized Cauchy distributions on Furstenberg boundaries....
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In: Journal of the Mathematical Society of Japan, 2006, vol. 58, no. 4, p. 985-994
We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. If the s-orbit is symmetric such submanifolds are the most important examples of adapted submanifolds, i.e. of submanifolds of symmetric spaces with curvature invariant tangent and normal spaces.
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In: Annals of Global Analysis and Geometry, 2006, vol. 29, no. 1, p. 1-16
Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M× Rm = T M⊗ ν M is equipped with an almost metric connection ~ ∇ which almost preserves the decomposition of M× Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂~∇ with the usual...
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