Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics

We simulate the vibration of a violin bridge in a multi-query context using reduced basis techniques. The mathematical model is based on an eigenvalue problem for the orthotropic linear elasticity equation. In addition to the nine material parameters, a geometrical thickness parameter is considered. This parameter enters as a 10th material parameter into the system by a mapping onto a parameter independent reference domain. The detailed simulation is carried out by isogeometric mortar methods. Weakly coupled patch-wise tensorial structured isogeometric elements are of special interest for complex geometries with piecewise smooth but curvilinear boundaries. To obtain locality in the detailed system, we use the saddle point approach and do not apply static condensation techniques. However within the reduced basis context, it is natural to eliminate the Lagrange multiplier and formulate a reduced eigenvalue problem for a symmetric positive definite matrix. The selection of the snapshots is controlled by a multi-query greedy strategy taking into account an error indicator allowing for multiple eigenvalues

HelMod in the works: from direct observations to the local interstellar spectrum of cosmic-ray electrons

The local interstellar spectrum (LIS) of cosmic-ray (CR) electrons for the energy range 1 MeV to 1 TeV is derived using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The optimized HelMod parameters are then used to adjust GALPROP parameters to predict a refined LIS with the procedure repeated subject to a convergence criterion. The parameter optimization uses an extensive data set of proton spectra from 1997-2015. The proposed CR electron LIS accommodates both the low-energy interstellar spectra measured by Voyager 1 as well as the high-energy observations by PAMELA and AMS-02 that are made deep in the heliosphere; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The interstellar and heliospheric propagation parameters derived in this study agree well with our earlier results for CR protons, helium nuclei, and anti-protons propagation and LIS obtained in the same framework.Comment: 11 pages, 14 figures, 4 tables; ApJ, in pres

Deciphering the local Interstellar spectra of primary cosmic ray species with HelMod

Local interstellar spectra (LIS) of primary cosmic ray (CR) nuclei, such as helium, oxygen, and mostly primary carbon are derived for the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined into a single framework that is used to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. The developed iterative maximum-likelihood method uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The interstellar and heliospheric propagation parameters derived in this study are consistent with our prior analyses using the same methodology for propagation of CR protons, helium, antiprotons, and electrons. The resulting LIS accommodate a variety of measurements made in the local interstellar space (Voyager 1) and deep inside the heliosphere at low (ACE/CRIS, HEAO-3) and high energies (PAMELA, AMS-02).Comment: 13 pages, 13 figures, 6 tables, ApJ in press. arXiv admin note: text overlap with arXiv:1704.0633

Latitudinal Dependence of Cosmic Rays Modulation at 1 AU and Interplanetary-Magnetic-Field Polar Correction

The cosmic rays differential intensity inside the heliosphere, for energy below 30 GeV/nuc, depends on solar activity and interplanetary magnetic field polarity. This variation, termed solar modulation, is described using a 2-D (radius and colatitude) Monte Carlo approach for solving the Parker transport equation that includes diffusion, convection, magnetic drift and adiabatic energy loss. Since the whole transport is strongly related to the interplanetary magnetic field (IMF) structure, a better understanding of his description is needed in order to reproduce the cosmic rays intensity at the Earth, as well as outside the ecliptic plane. In this work an interplanetary magnetic field model including the standard description on ecliptic region and a polar correction is presented. This treatment of the IMF, implemented in the HelMod Monte Carlo code (version 2.0), was used to determine the effects on the differential intensity of Proton at 1\,AU and allowed one to investigate how latitudinal gradients of proton intensities, observed in the inner heliosphere with the Ulysses spacecraft during 1995, can be affected by the modification of the IMF in the polar regions.Comment: accepted for publication inAdvances in Astronom

Suprathermal particle addition to solar wind pressure: possible influence on magnetospheric transmissivity of low energy cosmic rays?

Energetic (suprathermal) solar particles, accelerated in the interplanetary medium, contribute to the solar wind pressure, in particular during high solar activity periods. We estimated the effect of the increase of solar wind pressure due to suprathermal particles on magnetospheric transmissivity of galactic cosmic rays in the case of one recent solar event