Saddle towers with infinitely many ends

We prove the existence of nonperiodic, properly embedded minimal surfaces in $\mathbb{R}^2\times\mathbb{S}^1$ with genus zero, infinitely many ends and one limit end (in particular, they have infinite total curvature).Comment: 16 pages, 3 figure

Generic guide concepts for the European Spallation Source

The construction of the European Spallation Source (ESS) faces many challenges from the neutron beam transport point of view: The spallation source is specified as being driven by a 5 MW beam of protons, each with 2 GeV energy, and yet the requirements in instrument background suppression relative to measured signal vary between 10$^{-6}$ and 10$^{-8}$. The energetic particles, particularly above 20 MeV, which are expected to be produced in abundance in the target, have to be filtered in order to make the beamlines safe, operational and provide good quality measurements with low background. We present generic neutron guides of short and medium length instruments which are optimized for good performance at minimal cost. Direct line of sight to the source is avoided twice, with either the first point out of line of sight or both being inside the bunker (20\,m) to minimize shielding costs. These guide geometries are regarded as a baseline to define standards for instruments to be constructed at ESS. They are used to find commonalities and develop principles and solutions for common problems. Lastly, we report the impact of employing the over-illumination concept to mitigate losses from random misalignment passively, and that over-illumination should be used sparingly in key locations to be effective. For more widespread alignment issues, a more direct, active approach is likely to be needed

Controlled nucleation of topological defects in the stripe domain patterns of Lateral multilayers with Perpendicular Magnetic Anisotropy: competition between magnetostatic, exchange and misfit interactions

Magnetic lateral multilayers have been fabricated on weak perpendicular magnetic anisotropy amorphous Nd-Co films in order to perform a systematic study on the conditions for controlled nucleation of topological defects within their magnetic stripe domain pattern. A lateral thickness modulation of period $w$ is defined on the nanostructured samples that, in turn, induces a lateral modulation of both magnetic stripe domain periods $\lambda$ and average in-plane magnetization component $M_{inplane}$. Depending on lateral multilayer period and in-plane applied field, thin and thick regions switch independently during in-plane magnetization reversal and domain walls are created within the in-plane magnetization configuration coupled to variable angle grain boundaries and disclinations within the magnetic stripe domain patterns. This process is mainly driven by the competition between rotatable anisotropy (that couples the magnetic stripe pattern to in-plane magnetization) and in-plane shape anisotropy induced by the periodic thickness modulation. However, as the structural period $w$ becomes comparable to magnetic stripe period $\lambda$, the nucleation of topological defects at the interfaces between thin and thick regions is hindered by a size effect and stripe domains in the different thickness regions become strongly coupled.Comment: 10 pages, 7 figures, submitted to Physical Review

Further analysis of the connected moments expansion

We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic oscillator and the pure quartic oscillator.Comment: 19 pages; 2 tables; 4 figure