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  1. We study analytically and numerically the minimizers for the Cahn-Hilliard energy functional with a symmetric quartic double-well potential and under a strong anchoring condition(i.e., the Dirichlet condition) on the boundary of an underlying bounded domain. We show a bifurcation phenomenon determined by the boundary value and a parameter that describes the thickness of a transition layer separating two phases of an underlying system of binary mixtures. For the case that the boundary value is exactly the average of the two pure phases, if the bifurcation parameter is larger than or equal to a critical value, then the minimizer is uniquemore »and is exactly the homogeneous state. Otherwise, there are exactly two symmetric minimizers. The critical bifurcation value is inversely proportional to the first eigenvalue of the negative Laplace operator with the zero Dirichlet boundary condition. For a boundary value that is larger (or smaller) than that of the average of the two pure phases, the symmetry is broken and there is only one minimizer. We also obtain the bounds and morphological properties of the minimizers under additional assumptions on the domain.Our analysis utilizes the notion of the Nehari manifold and connects it to the eigenvalue problem for the negative Laplacian with the homogeneous boundary condition. We numerically minimize the functional E by solving the gradient-flow equation of E, i.e., the Allen-Cahn equation, with the designated boundary conditions, and with random initial values. We present our numerical simulations and discuss them in the context of our analytical results.« less
  2. ABSTRACT We report the discovery of J0624–6948, a low-surface brightness radio ring, lying between the Galactic Plane and the large magellanic cloud (LMC). It was first detected at 888 MHz with the Australian Square Kilometre Array Pathfinder (ASKAP), and with a diameter of ∼196 arcsec. This source has phenomenological similarities to odd radio circles (ORCs). Significant differences to the known ORCs – a flatter radio spectral index, the lack of a prominent central galaxy as a possible host, and larger apparent size – suggest that J0624–6948 may be a different type of object. We argue that the most plausible explanation for J0624–6948more »is an intergalactic supernova remnant due to a star that resided in the LMC outskirts that had undergone a single-degenerate type Ia supernova, and we are seeing its remnant expand into a rarefied, intergalactic environment. We also examine if a massive star or a white dwarf binary ejected from either galaxy could be the supernova progenitor. Finally, we consider several other hypotheses for the nature of the object, including the jets of an active galactic nucleus (30Dor) or the remnant of a nearby stellar super-flare.« less
    Free, publicly-accessible full text available March 15, 2023
  3. Free, publicly-accessible full text available October 14, 2022
  4. ABSTRACT We searched for an isotropic stochastic gravitational wave background in the second data release of the International Pulsar Timing Array, a global collaboration synthesizing decadal-length pulsar-timing campaigns in North America, Europe, and Australia. In our reference search for a power-law strain spectrum of the form $h_c = A(f/1\, \mathrm{yr}^{-1})^{\alpha }$, we found strong evidence for a spectrally similar low-frequency stochastic process of amplitude $A = 3.8^{+6.3}_{-2.5}\times 10^{-15}$ and spectral index α = −0.5 ± 0.5, where the uncertainties represent 95 per cent credible regions, using information from the auto- and cross-correlation terms between the pulsars in the array. For a spectral index of α =more »−2/3, as expected from a population of inspiralling supermassive black hole binaries, the recovered amplitude is $A = 2.8^{+1.2}_{-0.8}\times 10^{-15}$. None the less, no significant evidence of the Hellings–Downs correlations that would indicate a gravitational-wave origin was found. We also analysed the constituent data from the individual pulsar timing arrays in a consistent way, and clearly demonstrate that the combined international data set is more sensitive. Furthermore, we demonstrate that this combined data set produces comparable constraints to recent single-array data sets which have more data than the constituent parts of the combination. Future international data releases will deliver increased sensitivity to gravitational wave radiation, and significantly increase the detection probability.« less
    Free, publicly-accessible full text available January 19, 2023
  5. ABSTRACT

    In this paper, we describe the International Pulsar Timing Array second data release, which includes recent pulsar timing data obtained by three regional consortia: the European Pulsar Timing Array, the North American Nanohertz Observatory for Gravitational Waves, and the Parkes Pulsar Timing Array. We analyse and where possible combine high-precision timing data for 65 millisecond pulsars which are regularly observed by these groups. A basic noise analysis, including the processes which are both correlated and uncorrelated in time, provides noise models and timing ephemerides for the pulsars. We find that the timing precisions of pulsars are generally improved comparedmore »to the previous data release, mainly due to the addition of new data in the combination. The main purpose of this work is to create the most up-to-date IPTA data release. These data are publicly available for searches for low-frequency gravitational waves and other pulsar science.

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