We propose a mode of dynamic scanning probe microscopy based on parametric resonance for highly sensitive nanoscale imaging and force spectroscopy. In this mode the microcantilever probe is excited by means of a closed-loop electronic circuit that modulates the microcantilever stiffness at a frequency close to twice its natural resonance frequency. Under ambient conditions this parametric pumpi...

We introduce and apply a method to investigate the force-free character of the photospheric magnetic fields in solar active regions. The vertical current density, inferred from vector magnetograms, is decomposed into a helical (assumed field-aligned) component, and a component perpendicular to the magnetic field. Contrary to the classical method of calculating the integrated Lorentz forces, the...

Communicated by Abraham A. Ungar Abstract. In this paper, we investigate the reflections in Minkowski three-space by three different approaches. Firstly, we define Lorentzian reflections with Lorentzian inner product. Then, we examine Lorentzian reflections in view of Lorentzian Householder matrices. Finally, we use pure split quaternions to derive Lorentzian reflections. For each case, we find...

Direct laser writing through two-photon polymerization lithography is used to fabricate 3D nanostructures containing aligned single-wall carbon nanotubes (SWCNTs). SWCNTs are aligned in the laser scanning directions while they are embedded in the structure. The alignment is induced by spatial confinement, volume shrinkage, and the optical gradient force. This method is expected to lead to new a...

Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some natural topological assumptions (fulfilled, for example, if one of the conjuga...

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker met...

We investigate the twistor space and the Grassmannian fibre bundle of a Lorentzian 4-space with natural almost optical structures and its induced CR-structures. The twistor spaces of the Lorentzian space forms R 4 1, S 4 1 and H 4 1 are explicitly discussed. The given twistor construction is applied to surface theory in Lorentzian 4-spaces. Immersed spacelike surfaces in a Lorentzian 4-space wi...

A high-potential therapy for repairing the heart post-myocardial infarction is the implantation of tissue-engineered myocardium. While several groups have developed constructs that mimic the aligned structure of the native myocardium, to date no one has investigated the particular functional benefits conferred by alignment. In this study we created myocardial constructs in both aligned and isot...