272 research outputs found
Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)
An infinite regular three-dimensional network is composed of identical
resistors each of resistance joining adjacent nodes. What is the equivalent
resistance between the lattice site and the lattice site, when two bonds are
removed from the perfect network? Three cases are considered here, and some
numerical values are calculated. Finally, the asymptotic behavior of the
equivalent resistance is studied for large distances between the two sites.Comment: 11 pages, 3 figures, published in EPJ-A
Searching for the extra-tidal stars of globular clusters using high-dimensional analysis and a core particle spray code
Three-body interactions can eject stars from the core of a globular cluster,
causing them to enter the Galactic halo as extra-tidal stars. While finding
extra-tidal stars is imperative for understanding cluster evolution, connecting
isolated extra-tidal field stars back to their birth cluster is extremely
difficult. In this work, we present a new methodology consisting of
high-dimensional data analysis and a particle spray code to identify
extra-tidal stars of any Galactic globular cluster using M3 as a case study.
Using the t-Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold
Approximation and Projection (UMAP) machine learning dimensionality reduction
algorithms, we first identify a set of 103 extra-tidal candidates in the APOGEE
DR17 data catalogue with chemical abundances similar to M3 stars. To confirm
each candidate's extra-tidal nature, we introduce Corespray; a new Python-based
three-body particle spray code that simulates extra-tidal stars for any
Galactic globular cluster. Using Gaia EDR3 proper motions and APOGEE DR17
radial velocities, we apply multivariate Gaussian modelling and an extreme
deconvolution to identify the extra-tidal candidates that are more likely to be
associated with a distribution of Corespray-simulated M3 extra-tidal stars than
the field. Through these methods, we identify 13 new high-probability
extra-tidal stars of M3. Future applications of Corespray will yield better
understandings of core dynamics, star formation histories and binary fractions
in globular clusters.Comment: 15 pages, 8 figures, 2 tables. Submitted to Monthly Notices of the
Royal Astronomical Societ
Structural, electronic, vibrational and dielectric properties of LaBGeO from first principles
Structural, electronic, vibrational and dielectric properties of LaBGeO
with the stillwellite structure are determined based on \textit{ab initio}
density functional theory. The theoretically relaxed structure is found to
agree well with the existing experimental data with a deviation of less than
. Both the density of states and the electronic band structure are
calculated, showing five distinct groups of valence bands. Furthermore, the
Born effective charge, the dielectric permittivity tensors, and the vibrational
frequencies at the center of the Brillouin zone are all obtained. Compared to
existing model calculations, the vibrational frequencies are found in much
better agreement with the published experimental infrared and Raman data, with
absolute and relative rms values of 6.04 cm, and , respectively.
Consequently, numerical values for both the parallel and perpendicular
components of the permittivity tensor are established as 3.55 and 3.71 (10.34
and 12.28), respectively, for the high-(low-)frequency limit
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