Dimension of gradient measures

We prove that if pure derivatives with respect to all coordinates of a function on $\mathbb{R}^n$ are signed measures, then their lower Hausdorff dimension is at least $n-1$. The derivatives with respect to different coordinates may be of different order.Comment: 8 page

Atomic-state diagnostics and optimization in cold-atom experiments

We report on the creation, observation and optimization of superposition states of cold atoms. In our experiments, rubidium atoms are prepared in a magneto-optical trap and later, after switching off the trapping fields, Faraday rotation of a weak probe beam is used to characterize atomic states prepared by application of appropriate light pulses and external magnetic fields. We discuss the signatures of polarization and alignment of atomic spin states and identify main factors responsible for deterioration of the atomic number and their coherence and present means for their optimization, like relaxation in the dark with the strobe probing. These results may be used for controlled preparation of cold atom samples and in situ magnetometry of static and transient fieldsComment: 15 pages and 9 figures (including supplementary information

Surfactant mixtures at the oil–water interface

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Colloid and Interface Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF COLLOID AND INTERFACE SCIENCE, VOL 398, (2013) DOI 10.1016/j.jcis.2013.01.06

Contributed Review: Camera-limits for wide-field magnetic resonance imaging with a nitrogen-vacancy spin sensor

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Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations