Semiclassical Spectral Series Localized on a Curve for the Gross–Pitaevskii Equation with a Nonlocal Interaction

We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross–Pitaevskii equation with a nonlocal interaction term. The eigenvalues and eigenfunctions semiclassically concentrated on a curve are obtained. The curve is described by the dynamic system of moments of solutions to the nonlocal Gross–Pitaevskii equation. We solve the eigenvalue problem for the nonlocal stationary Gross–Pitaevskii equation basing on the semiclassical asymptotics found for the Cauchy problem of the parametric family of linear equations associated with the time-dependent Gross–Pitaevskii equation in the space of extended dimension. The approach proposed uses symmetries of equations in the space of extended dimension.

Empirical Characterization of the Temporal Dynamics of EEG Spectral Components

The properties of time-domain electroencephalographic data have been studied extensively. There has however been no attempt to characterize the temporal evolution of resulting spectral components when successive segments of electroencephalographic data are decomposed. We analysed resting-state scalp electroencephalographic data from 23 subjects, acquired at 256 Hz, and transformed using 64-point Fast Fourier Transform with a Hamming window. KPSS and Nason tests were administered to study the trend- and wide sense stationarity respectively of the spectral components. Their complexities were estimated using fuzzy entropy. Thereafter, the rosenstein algorithm for dynamic evolution was applied to determine the largest Lyapunov exponents of each component’s temporal evolution. We found that the evolutions were wide sense stationary for time scales up to 8 s, and had significant interactions, especially between spectral series in the frequency ranges 0-4 Hz, 12-24 Hz, and 32-128 Hz. The highest complexity was in the 12-24 Hz band, and increased monotonically with scale for all band sizes. However, the complexity in higher frequency bands changed more rapidly. The spectral series were generally non-chaotic, with average largest Lyapunov exponent of 0. The results show that significant information is contained in all frequency bands, and that the interactions between bands are complicated and time-varying.

On the Stark Broadening of Be II Spectral Lines

Calculated Stark broadening parameters of singly ionized beryllium spectral lines have been reported. Three spectral series have been studied within semiclassical perturbation theory. The plasma conditions cover temperatures from 2500 to 50,000 K and perturber densities 1011 cm−3 and 1013 cm−3. The influence of the temperature and the role of the perturbers (electrons, protons and He+ ions) on the Stark width and shift have been discussed. Results could be useful for plasma diagnostics in astrophysics, laboratory, and industrial plasmas.

Stark Widths Regularities Within: ns-np, np-ns, np-nd, nd-np and nd-nf Spectral Series of Potassium Isoelectronic Sequence

Results presented in this paper show a regular behaviour of Stark widths within the studied spectral series of potassium isoelectronic sequence. These regularities have been found and verified on the basis of the existing theoretical and experimental data being normalized for the same plasma conditions (chosen electron density and temperature). Using the available set of data the corresponding formulas expressing the Stark widths of the lines originated from the spectral series studied here as a function of the upper-level ionization potential and the rest core charge of the emitter seeing by the electron undergoing transition, are obtained here. Well established and verified dependence is used to calculate Stark width data needed but not available so far. For the purposes of the operation with a large number of data, algorithms for the analysis of Stark width dependence on temperature and electron density and for the investigation of the assumed correlation between Stark width and ionization potential of the upper level of analyzed transition, have been made. Developed algorithms enable fast data processing.

Investigation of Stark line broadening within spectral series of potassium and copper isoelectronic sequences

We have investigated Stark line broadening within the spectral series of potassium-like and copper-like emitters, both separately and together. The analysis was performed for fixed values of electronic density Ne = 1022 m−3 and temperature $T = 100\, 000$ K. Algorithms made for fast data processing also serve for temperature and density normalization of data. Relations obtained using the regularity-based analysis enable predictions of Stark widths for transitions that have not yet been calculated or measured. Results of present investigation can be used for quality control of available Stark width data.

Stark Broadening of Neutral Boron Lines

Stark broadening parameters, width and shift, of lines within B I 2s22p–2s2ns spectral series have been calculated. Semi-classical theory in impact approximation has been applied. Temperature dependence of Stark parameters has been studied. The presented results could be applied for plasma diagnostics.

GRB 161219B/SN 2016jca: a powerful stellar collapse

ABSTRACT We report observations and analysis of the nearby gamma-ray burst GRB 161219B (redshift z = 0.1475) and the associated Type Ic supernova (SN) 2016jca. GRB 161219B had an isotropic gamma-ray energy of ∼1.6 × 1050 erg. Its afterglow is likely refreshed at an epoch preceding the first photometric points (0.6 d), which slows down the decay rates. Combined analysis of the SN light curve and multiwavelength observations of the afterglow suggest that the GRB jet was broad during the afterglow phase (full opening angle ∼42° ± 3°). Our spectral series shows broad absorption lines typical of GRB supernovae (SNe), which testify to the presence of material with velocities up to ∼0.25c. The spectrum at 3.73 d allows for the very early identification of an SN associated with a GRB. Reproducing it requires a large photospheric velocity ($35\, 000 \pm 7000$ km s−1). The kinetic energy of the SN is estimated through models to be Ekin≈4 × 1052 erg in spherical symmetry. The ejected mass in the explosion was Mej≈6.5 ± 1.5 M⊙, much less than that of other GRB-SNe, demonstrating diversity among these events. The total amount of 56Ni in the explosion was 0.27 ± 0.05 M⊙. The observed spectra require the presence of freshly synthesized 56Ni at the highest velocities, at least three times more than a standard GRB-SN. We also find evidence for a decreasing 56Ni abundance as a function of decreasing velocity. This suggests that SN 2016jca was a highly aspherical explosion viewed close to on-axis, powered by a compact remnant. Applying a typical correction for asymmetry, the energy of SN 2016jca was ∼(1–3) × 1052 erg, confirming that most of the energy produced by GRB-SNe goes into the kinetic energy of the SN ejecta.