We obtain a general solution for the probability density function (PDF) of wave intensities in non-stationary wave turbulence. The solution is expressed in terms of the initial PDF and the wave action spectrum satisfying the wave-kinetic equation. We establish that, in the absence of wave breaking, the wave statistics converge to a Gaussian distribution in forced-dissipated wave systems while approaching a steady state. Also, we find that in non- stationary systems, if the statistic is Gaussian initially, it will remain Gaussian for all time. Generally, if the statistic is not initially Gaussian, it will remain non-Gaussian over the characteristic nonlinear evolution time of the wave spectrum. In freely decaying wave turbulence, substantial deviations from Gaussianity may persist infinitely long.

We propose a new finite element method for solving second order elliptic interface problems whose solution has a Robin type jump along the interface. We cast the problem into a new variational form and introduce a finite element method to solve it using a uniform grid. We modify the P1-Crouzeix-Raviart element so that the shape functions satisfy the jump conditions along the interface. We note that there are cases that the Lagrange type basis can not be used because of the jump in the value. Numerical experiments are provided. 

The Shortley–Weller method is a standard finite difference method for solving the Poisson equation with Dirichlet boundary condition. Unless the domain is rectangular, the method meets an inevitable problem that some of the neighboring nodes may be outside the domain. In this case, an usual treatment is to extrapolate the function values at outside nodes by quadratic polynomial. The extrapolation may become unstable in the sense that some of the extrapolation coefficients increase rapidly when the grid nodes are getting closer to the boundary. A practical remedy, which we call artificial perturbation, is to treat grid nodes very near the boundary as boundary points. The aim of this paper is to reveal the adverse effects of the artificial perturbation on solving the linear system and the convergence of the solution. We show that the matrix is nearly symmetric so that the ratio of its minimum and maximum eigenvalues is an important factor in solving the linear system. Our analysis shows that the artificial perturbation results in a small enhancement of the eigenvalue ratio from O(1/(h⋅hmin) to O(h−3) and triggers an oscillatory order of convergence. Instead, we suggest using Jacobi or ILU-type preconditioner on the matrix without applying the artificial perturbation. According to our analysis, the preconditioning not only reduces the eigenvalue ratio from O(1/(h⋅hmin) to O(h−2), but also keeps the sharp second order convergence.

The first direct gravitational­wave detection was made by the Advanced Laser Interferometer Gravitational Wave Observatory on September 14, 2015. The GW150914 signal was strong enough to be apparent, without using any waveform model, in the filtered detector strain data. Here, features of the signal visible in the data are analyzed using concepts from Newtonian physics and general relativity, accessible to anyone with a general physics background. The simple analysis presented here is consistent with the fully general­relativistic analyses published elsewhere, in showing that the signal was produced by the inspiral and subsequent merger of two black holes. The black holes were each of approximately urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0001, still orbited each other as close as ∼350 km apart and subsequently merged to form a single black hole. Similar reasoning, directly from the data, is used to roughly estimate how far these black holes were from the Earth, and the energy that they radiated in gravitational waves.

On 17 August 2017, the Advanced LIGO1 and Virgo2 detectors observed the gravitational-wave event GW170817—a strong signal from the merger of a binary neutron-star system3. Less than two seconds after the merger, a γ-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO–Virgo-derived location of the gravitational-wave source4, 5, 6. This sky region was subsequently observed by optical astronomy facilities7, resulting in the identification8, 9, 10, 11, 12, 13 of an optical transient signal within about ten arcseconds of the galaxy NGC 4993. This detection of GW170817 in both gravitational waves and electromagnetic waves represents the first ‘multi-messenger’ astronomical observation. Such observations enable GW170817 to be used as a ‘standard siren’14, 15, 16, 17, 18 (meaning that the absolute distance to the source can be determined directly from the gravitational-wave measurements) to measure the Hubble constant. This quantity represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Here we report a measurement of the Hubble constant that combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using the electromagnetic data. In contrast to previous measurements, ours does not require the use of a cosmic ‘distance ladder’19: the gravitational-wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be about 70 kilometres per second per megaparsec. This value is consistent with existing measurements20, 21, while being completely independent of them. Additional standard siren measurements from future gravitational-wave sources will enable the Hubble constant to be constrained to high precision.

The first observation of a binary neutron star (NS) coalescence by the Advanced LIGO and Advanced Virgo gravitational-wave (GW) detectors offers an unprecedented opportunity to study matter under the most extreme conditions. After such a merger, a compact remnant is left over whose nature depends primarily on the masses of the inspiraling objects and on the equation of state of nuclear matter. This could be either a black hole (BH) or an NS, with the latter being either long-lived or too massive for stability implying delayed collapse to a BH. Here, we present a search for GWs from the remnant of the binary NS merger GW170817 using data from Advanced LIGO and Advanced Virgo. We search for short- (？1 s) and intermediate-duration (？500 s) signals, which include GW emission from a hypermassive NS or supramassive NS, respectively. We find no signal from the post-merger remnant. Our derived strain upper limits are more than an order of magnitude larger than those predicted by most models. For short signals, our best upper limit on the root sum square of the GW strain emitted from 1–4 kHz is ##IMG## [http://ej.iop.org/images/2041-8205/851/1/L16/apjlaa9a35ieqn1.gif] {${h}_{\mathrm{rss}}^{50 \% }=2.1\times {10}^{-22}\,{\mathrm{Hz}}^{-1/2}$} at 50% detection efficiency. For intermediate-duration signals, our best upper limit at 50% detection efficiency is ##IMG## [http://ej.iop.org/images/2041-8205/851/1/L16/apjlaa9a35ieqn2.gif] {${h}_{\mathrm{rss}}^{50 \% }=8.4\times {10}^{-22}\,{\mathrm{Hz}}^{-1/2}$} for a millisecond magnetar model, and ##IMG## [http://ej.iop.org/images/2041-8205/851/1/L16/apjlaa9a35ieqn3.gif] {${h}_{\mathrm{rss}}^{50 \% }=5.9\times {10}^{-22}\,{\mathrm{Hz}}^{-1/2}$} for a bar-mode model. These results indicate that post-merger emission from a similar event may be detectable when advanced detectors reach design sensitivity or with next-generation detectors.

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirec- tional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.

Subterranean termites create tunnels with ascending and descending slopes under the ground for foraging. In this study, I explored the effect of the tunnel slopes on the termite ment, which is helpful in understanding the foraging efficiency. To do so, I designed five-cm long artificial tunnels in arenas. The tunnels had different curvatures (D) and widths (W). To artificially make the slopes, I obliquely put the arena with an angle, A(= 20°, 40°, and 60°). I systematically investigated the slope effect in terms of the time required for a termite to pass half the distance of the tunnel (τu for the ascending section and τd for the descending section). When A = 20°, little effect of the slope was observed, while for A = 40°, the slope effect strongly appeared. On the other hand, for A = 60°, the slope effect disappeared, which was explained by the ment behaviour. The results showed that an appropriate slope of ascending and descending tunnel could positively contribute to the termite ment efficiency.

In previous studies, we showed that the branch length similarity (BLS) entropy profile could be successfully used for the shape recognition such as battle tanks, facial expressions, and butterflies. In the present study, we proposed new deors, roundness, symmetry, and surface roughness, for the recognition, which are more accurate and fast in the computation than the previous deors. The roundness represents how closely a shape resembles to a circle, the symmetry characterizes how much one shape is similar with another when the shape is d in flip, and the surface roughness quantifies the degree of vertical deviations of a shape boundary. To evaluate the performance of the deors, we used the database of leaf images with 12 species. Each species consisted of 10 - 20 leaf images and the total number of images were 160. The evaluation showed that the new deors successfully discriminated the leaf species. We believe that the deors can be a useful tool in the field of pattern recognition.

We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using data from the first Advanced LIGO observing run. The search method uses details of the modeled, parametrized continuous signal to combine coherently data separated by less than a specified coherence time, which can be adjusted to trade off sensitivity against computational cost. A search was conducted over the frequency range 25– ##IMG## [http://ej.iop.org/images/0004-637X/847/1/47/apjaa86f0ieqn1.gif] {$2000\,\mathrm{Hz}$} , spanning the current observationally constrained range of binary orbital parameters. No significant detection candidates were found, and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections. The most stringent upper limit was set at ##IMG## [http://ej.iop.org/images/0004-637X/847/1/47/apjaa86f0ieqn2.gif] {$175\,\mathrm{Hz}$} , with comparable limits set across the most sensitive frequency range from 100 to ##IMG## [http://ej.iop.org/images/0004-637X/847/1/47/apjaa86f0ieqn3.gif] {$200\,\mathrm{Hz}$} . At this frequency, the 95% upper limit on the signal amplitude h 0 is ##IMG## [http://ej.iop.org/images/0004-637X/847/1/47/apjaa86f0ieqn4.gif] {$2.3\times {10}^{-25}$} marginalized over the unknown inclination angle of the neutron star’s spin, and ##IMG## [http://ej.iop.org/images/0004-637X/847/1/47/apjaa86f0ieqn5.gif] {$8.0\times {10}^{-26}$} assuming the best orientation (which results in circularly polarized gravitational waves). These limits are a factor of 3–4 stronger than those set by other analyses of the same data, and a factor of ∼7 stronger than the best upper limits set using data from Initial LIGO science runs. In the vicinity of ##IMG## [http://ej.iop.org/images/0004-637X/847/1/47/apjaa86f0ieqn6.gif] {$100\,\mathrm{Hz}$} , the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model, depending on the inclination angle; if the most likely inclination angle of 44° is assumed, they are within a factor of 1.7.