Vol 108, No 12 (2018)

We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for the Catalan numbers.

The Advanced Laser Interferometer Gravitational-Wave Observatory and Advanced Virgo observatories recently discovered gravitational waves from a binary neutron star inspiral. A short gamma-ray burst that followed the merger of this binary was also recorded by Fermi gamma-ray burst monitor and International Gamma-Ray Astrophysics Laboratory, indicating particle acceleration by the source. The precise location of the event was determined by optical detections of emission following the merger. We searched for high-energy neutrinos from the merger in the energy range of 1 TeV–100 PeV using the Baikal Gigaton Volume Detector. No neutrinos directionally coincident with the source were detected within ±500 s around the merger time, as well as during a 14-day period after the gravitational wave detection. We derived 90% C.L. upper limits on the neutrino fluence from GW170817 during a ±500 s window centered on the gravitational wave trigger time, and a 14-day window following the gravitational wave signal under the assumption of an E⁻² neutrino energy spectrum.

The yields of cumulative protons and π^± mesons emitted at a laboratory angle of 40° from carbon and heavier nuclear targets irradiated by a proton beam from the U70 accelerator (Institute for High Energy Physics, Protvino) have been studied in the SPIN experiment. It has been found that the effect of the target nucleus on the yield of particles with large transverse momenta is weakened.

Magnetic materials generate demagnetizing field that depends on geometry of the sample and results in a shift of magnetic resonance frequency. This phenomenon should occur in porous nanostructures as well, e.g., in globally anisotropic aerogels. Here, we report results of nuclear magnetic resonance experiments with liquid ³He confined in anisotropic aerogels with different types of anisotropy (nematic and planar aerogels). Strands of aerogels in pure ³He are covered by a few atomic layers of paramagnetic solid ³He which magnetization follows the Curie–Weiss law. We have found that in our samples the nuclear magnetic resonance shift in solid ³He is clearly seen at ultralow temperatures and depends on value and orientation of the magnetic field. The obtained results are well described by a model of a system of non-interacting paramagnetic cylinders. The shift is proportional to the magnetization of solid ³He and may complicate nuclear magnetic resonance experiments with superfluid ³He in aerogel.

The solutions of the Bardeen–Cooper–Schrieffer equation are found within the model of the lower Hubbard subband taking into account three-site correlations and the superexchange, Coulomb, phonon, and spinfluctuation mechanisms of quasiparticle pairing. The Pr_0.89LaCe_0.11CuO₄ compound is considered as an example. The dependence of the superconducting gap on the wave vector along the Fermi contour is approximated by the expression Δ_φ = Δ₀ (B cos(2φ) + (1 − B) cos(6φ)) where the angle φ is measured from the edge of the Brillouin zone. The calculated parameters Δ₀ and B correspond to the experimental data. The role of the phonon mechanism is relatively small. The competition of other specified mechanisms in the formation of Δ₀ is quite strong. The effect of their interference is important and is different in different parts of the Fermi surface. The main contribution to the formation of the component proportional to cos(6φ) (the highest harmonic of the gap) is due to the spin-fluctuation and Coulomb interactions. It is numerically and analytically proved that the role of three-site correlations is reduced to weakening the superexchange mechanism.

Stability regions of crystal phases in the water–hydrogen system have been studied within our statistical thermodynamic model for describing clathrate compounds. The thermodynamic stability of hydrogen-containing ices I_h (C₀^Ih), II (C₁), I_c (C₂), classical clathrate hydrogen hydrate CS-II, and new hydrogen-filled ice phase C₀ has been analyzed. It has been shown that all considered phases are thermodynamically stable, but phase C₀ is metastable with respect to the other phases. The chemical potentials of water molecules in phases C₀ and C₁ are close to each other. As a result, metastable phase C₀ is experimentally observed in the stability region of phase C₁.

The effect of the particle position-dependent effective mass on the behavior of quasi-two-dimensional photon and exciton-polariton condensates in a parabolic trap in a semiconductor optical microcavity is investigated. It is demonstrated that the correct inclusion of the coordinate dependence of the effective mass in the kinetic-energy operator modifies the effective confining potential for the particles. Corrections to the energy and wavefunction of the photon Bose condensate are derived. For exciton-polaritons, it is shown that the choice of specific mirror geometry can lead to the change from repulsive to attractive particle–particle interaction.