Strongly walk-regular graphs

We study a generalization of strongly regular graphs. We call a graph strongly walk-regular if there is an $\ell >1$ such that the number of walks of length $\ell$ from a vertex to another vertex depends only on whether the two vertices are the same, adjacent, or not adjacent. We will show that a strongly walk-regular graph must be an empty graph, a complete graph, a strongly regular graph, a disjoint union of complete bipartite graphs of the same size and isolated vertices, or a regular graph with four eigenvalues. Graphs from the first three families in this list are indeed strongly $\ell$-walk-regular for all $\ell$, whereas the graphs from the fourth family are $\ell$-walk-regular for every odd $\ell$. The case of regular graphs with four eigenvalues is the most interesting (and complicated) one. Such graphs cannot be strongly $\ell$-walk-regular for even $\ell$. We will characterize the case that regular four-eigenvalue graphs are strongly $\ell$-walk-regular for every odd $\ell$, in terms of the eigenvalues. There are several examples of infinite families of such graphs. We will show that every other regular four-eigenvalue graph can be strongly $\ell$-walk-regular for at most one $\ell$. There are several examples of infinite families of such graphs that are strongly 3-walk-regular. It however remains open whether there are any graphs that are strongly $\ell$-walk-regular for only one particular $\ell$ different from 3

Axion-like particles as ultra high energy cosmic rays?

If Ultra High Energy Cosmic Rays (UHECRs) with E>4 10^{19} eV originate from BL Lacertae at cosmological distances as suggested by recent studies, the absence of the GZK cutoff can not be reconciled with Standard-Model particle properties. Axions would escape the GZK cutoff, but even the coherent conversion and back-conversion between photons and axions in large-scale magnetic fields is not enough to produce the required flux. However, one may construct models of other novel (pseudo)scalar neutral particles with properties that would allow for sufficient rates of particle production in the source and shower production in the atmosphere to explain the observations. As an explicit example for such particles we consider SUSY models with light sgoldstinos.Comment: 5 pages, 2 postscript figures, ref. adde

The clustering of ultra-high energy cosmic rays and their sources

The sky distribution of cosmic rays with energies above the 'GZK cutoff' holds important clues to their origin. The AGASA data, although consistent with isotropy, shows evidence for small-angle clustering, and it has been argued that such clusters are aligned with BL Lacertae objects, implicating these as sources. It has also been suggested that clusters can arise if the cosmic rays come from the decays of very massive relic particles in the Galactic halo, due to the expected clumping of cold dark matter. We examine these claims and show that both are in fact not justified.Comment: 13 pages, 8 figures, version in press at Phys. Rev.

Nonequilibrium probe of paired electron pockets in the underdoped cuprates

We propose an experimental method that can be used generally to test whether the cuprate pseudogap involves precursor pairing that acts to gap out the Fermi surface. The proposal involves angular-resolved photoemission spectroscopy (ARPES) performed in the presence of a transport current driven through the sample. We illustrate this proposal with a specific model of the pseudogap that contains a phase-incoherent paired electron and unpaired hole Fermi surfaces. We show that even a weak current tilts the paired band and reveals parts of the previously gapped electron Fermi surface in ARPES if the binding energy is smaller but close to the pseudogap. Stronger currents can also reveal the Fermi surface through direct suppression of pairing. The proposed experiment is sufficiently general such that it can be used to reveal putative Fermi surfaces that have been reconstructed from other types of periodic order and are gapped out due to pairing. The observation of the predicted phenomena should help resolve the central question about the existence of pairs in the enigmatic pseudogap regime.Comment: 5 pages, 3 figures (published version

Ultra-High Energy Cosmic Rays from Neutrino Emitting Acceleration Sources?

We demonstrate by numerical flux calculations that neutrino beams producing the observed highest energy cosmic rays by weak interactions with the relic neutrino background require a non-uniform distribution of sources. Such sources have to accelerate protons at least up to 10^{23} eV, have to be opaque to their primary protons, and should emit the secondary photons unavoidably produced together with the neutrinos only in the sub-MeV region to avoid conflict with the diffuse gamma-ray background measured by the EGRET experiment. Even if such a source class exists, the resulting large uncertainties in the parameters involved in this scenario does currently not allow to extract any meaningful information on absolute neutrino masses.Comment: 6 pages, 4 figures, RevTeX styl

Chiral three-nucleon forces and bound excited states in neutron-rich oxygen isotopes

We study the spectra of neutron-rich oxygen isotopes based on chiral two- and three-nucleon interactions. First, we benchmark our many-body approach by comparing ground-state energies to coupled-cluster results for the same two-nucleon interaction, with overall good agreement. We then calculate bound excited states in 21,22,23O, focusing on the role of three-nucleon forces, in the standard sd shell and an extended sdf7/2p3/2 valence space. Chiral three-nucleon forces provide important one- and two-body contributions between valence neutrons. We find that both these contributions and an extended valence space are necessary to reproduce key signatures of novel shell evolution, such as the N = 14 magic number and the low-lying states in 21O and 23O, which are too compressed with two-nucleon interactions only. For the extended space calculations, this presents first work based on nuclear forces without adjustments. Future work is needed and open questions are discussed.Comment: 6 pages, 4 figures, published versio

Trophic niche overlap between native freshwater mussels (Order: Unionida) and the invasive Corbicula fluminea

Freshwater mussels (Order Unionida) are highly threatened. Interspecific competition for food sources with invasive alien species is considered to be one of the factors responsible for their decline because successful invaders are expected to have wider trophic niches and more flexible feeding strategies than their native counterparts. In this study, carbon (δ13C: 13C/12C) and nitrogen (δ15N: 15N/14N) stable isotopes were used to investigate the trophic niche overlap between the native freshwater mussel species, Anodonta anatina, Potomida littoralis, and Unio delphinus, and the invasive bivalve Corbicula fluminea living in sympatry in the Tua basin (south-west Europe). The species presenting the widest trophic niches were C. fluminea and A. anatina, which indicate that they have broader diets than U. delphinus and P. littoralis. Nonetheless, all the species assimilated microphytobenthos, sediment organic matter, and detritus derived from vascular plants, although with interspecific variability in the assimilated proportions of each source. The trophic niche of the invasive species overlapped with the trophic niche of all the native species, with the extent varying between sites and according to the species. From the three native species analysed, Potomida littoralis may be at a higher risk for competition for food with C. fluminea in the Tua basin, if food sources become limited, because this native mussel presented the narrowest trophic niche across sites and the highest probability of overlapping with the trophic niche of C. fluminea. Given the global widespread distribution of C. fluminea, the implementation of management measures devoted to the control or even eradication of this invasive alien species should be a conservation priority given its potential for competition with highly threatened native freshwater mussels.V.M. and P.C. were supported by doctoral grants SFRH/BD/108298/2015 and SFRH/BD/131814/2017, respectively, from the Portuguese Foundation for Science and Technology—FCT through POPH/FSE funds. FCT also supported M.L.L. under contract (2020.03608.CEECIND). This study was conducted within the project FRESHCO – Multiple implications of invasive species on Freshwater Mussel coextinction processes, supported by FCT and COMPETE funds (contract: PTDC/AGRFOR/1627/2014). This study was also supported by national funds through FCT – Foundation for Science and Technology within the scope of UIDB/04423/2020 and UIDP/04423/2020. We thank Jacinto Cunha for providing Figure 1.info:eu-repo/semantics/publishedVersio

Ultra-High Energy Neutrino Fluxes and Their Constraints

Applying our recently developed propagation code we review extragalactic neutrino fluxes above 10^{14} eV in various scenarios and how they are constrained by current data. We specifically identify scenarios in which the cosmogenic neutrino flux, produced by pion production of ultra high energy cosmic rays outside their sources, is considerably higher than the "Waxman-Bahcall bound". This is easy to achieve for sources with hard injection spectra and luminosities that were higher in the past. Such fluxes would significantly increase the chances to detect ultra-high energy neutrinos with experiments currently under construction or in the proposal stage.Comment: 11 pages, 15 figures, version published in Phys.Rev.