Scaling behavior of the dipole coupling energy in two-dimensional disordered magnetic nanostructures

Numerical calculations of the average dipole-coupling energy $\bar E_\mathrm{dip}$ in two-dimensional disordered magnetic nanostructures are performed as function of the particle coverage $C$. We observe that $\bar E_\mathrm{dip}$ scales as $\bar E_\mathrm{dip}\propto C^{\alpha^*}$ with an unusually small exponent $\alpha^*\simeq 0.8$--1.0 for coverages $C\lesssim20$. This behavior is shown to be primarly given by the contributions of particle pairs at short distances, which is intrinsically related to the presence of an appreciable degree of disorder. The value of $\alpha^*$ is found to be sensitive to the magnetic arrangement within the nanostructure and to the degree of disorder. For large coverages $C\gtrsim20$ we obtain $\bar E_\mathrm{dip}\propto C^\alpha$ with $\alpha=3/2$, in agreement with the straighforward scaling of the dipole coupling as in a periodic particle setup. Taking into account the effect of single-particle anisotropies, we show that the scaling exponent can be used as a criterion to distinguish between weakly interacting ($\alpha^* \simeq 1.0$) and strongly interacting ($\alpha^* \simeq 0.8$) particle ensembles as function of coverage.Comment: accepted for publication in Phys.Rev.

Direct observations of galactic cosmic rays

The mysterious “radiation ... entering our atmosphere from above” discovered by Hess in 1912 is now known to be dominated by relativistic charged particles, mostly with energies in the GeV-range, but extending to energies higher by many orders of magnitude. As none of these particles can penetrate the earth’s atmosphere without interaction, detailed studies of their composition and energy spectra require observations with high-altitude balloons or spacecraft. This became possible only towards the middle of the 20th century. The direct measurements have now revealed much detail about the Galactic cosmic rays below 1015eV, but do not yet provide much overlap with the air-shower region of energies. A historic overview of the measurements is given, beginning with the realization that the majority of the cosmic rays are protons. The discovery and astrophysical significance of the heavier nuclei, and of the ultra-heavy nuclei beyond iron and up to the actinides, are then described, and measurements of the isotopic composition are discussed. Observations of the individual energy spectra are reviewed, and finally, the detection of electrons, positrons, and anti-protons in the cosmic rays, and the searches for exotic or unusual phenomena are summarized. Emphasis is given to the fact that all of these discoveries have become possible through the evolution of increasingly sophisticated detection techniques, a process that is continuing through the present time. The precise knowledge of the abundance distributions of the elements in the cosmic rays and of their isotopic composition permits a comparison with the “universal abundance scale” and provides strong constraints on the origin of the cosmic-ray material in the interstellar medium. “Clock-isotopes” reveal the time history of the particles. The shapes of the energy spectra of the individual cosmic-ray components are related to evolving ideas about particle acceleration and propagation in the Galaxy. In conclusion, prospects for future work are briefly discussed