Bound states of edge dislocations: The quantum dipole problem in two dimensions

We investigate bound state solutions of the 2D Schr\"odinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. The knowledge of these states could be useful for understanding a wide variety of physical systems, including superfluid behavior along dislocations in solid $^4$He. We present a review of the results obtained by previous workers together with an improved variational estimate of the ground state energy. We then numerically solve the eigenvalue problem and calculate the energy spectrum. In our dimensionless units, we find a ground state energy of -0.139, which is lower than any previous estimate. We also make successful contact with the behavior of the energy spectrum as derived from semiclassical considerations.Comment: 6 pages, 3 figures, submitted to PR

Multi-wavelength observations of afterglow of GRB 080319B and the modeling constraints

We present observations of the afterglow of GRB 080319B at optical, mm and radio frequencies from a few hours to 67 days after the burst. Present observations along with other published multi-wavelength data have been used to study the light-curves and spectral energy distributions of the burst afterglow. The nature of this brightest cosmic explosion has been explored based on the observed properties and it's comparison with the afterglow models. Our results show that the observed features of the afterglow fits equally good with the Inter Stellar Matter and the Stellar Wind density profiles of the circum-burst medium. In case of both density profiles, location of the maximum synchrotron frequency $\nu_m$ is below optical and the value of cooling break frequency $\nu_c$ is below $X-$rays, $\sim 10^{4}$s after the burst. Also, the derived value of the Lorentz factor at the time of naked eye brightness is $\sim 300$ with the corresponding blast wave size of $\sim 10^{18}$ cm. The numerical fit to the multi-wavelength afterglow data constraints the values of physical parameters and the emission mechanism of the burst.Comment: 8 Pages, 3 Figures, Accepted for publication to Astronomy and Astrophysics on 02/04/200

The binary near-Earth asteroid (175706) 1996 FG3 - An observational constraint on its orbital evolution

Using our photometric observations taken between 1996 and 2013 and other published data, we derived properties of the binary near-Earth asteroid (175706) 1996 FG3 including new measurements constraining evolution of the mutual orbit with potential consequences for the entire binary asteroid population. We also refined previously determined values of parameters of both components, making 1996 FG3 one of the most well understood binary asteroid systems. We determined the orbital vector with a substantially greater accuracy than before and we also placed constraints on a stability of the orbit. Specifically, the ecliptic longitude and latitude of the orbital pole are 266{\deg} and -83{\deg}, respectively, with the mean radius of the uncertainty area of 4{\deg}, and the orbital period is 16.1508 +/- 0.0002 h (all quoted uncertainties correspond to 3sigma). We looked for a quadratic drift of the mean anomaly of the satellite and obtained a value of 0.04 +/- 0.20 deg/yr^2, i.e., consistent with zero. The drift is substantially lower than predicted by the pure binary YORP (BYORP) theory of McMahon and Scheeres (McMahon, J., Scheeres, D. [2010]. Icarus 209, 494-509) and it is consistent with the theory of an equilibrium between BYORP and tidal torques for synchronous binary asteroids as proposed by Jacobson and Scheeres (Jacobson, S.A., Scheeres, D. [2011]. ApJ Letters, 736, L19). Based on the assumption of equilibrium, we derived a ratio of the quality factor and tidal Love number of Q/k = 2.4 x 10^5 uncertain by a factor of five. We also derived a product of the rigidity and quality factor of mu Q = 1.3 x 10^7 Pa using the theory that assumes an elastic response of the asteroid material to the tidal forces. This very low value indicates that the primary of 1996 FG3 is a 'rubble pile', and it also calls for a re-thinking of the tidal energy dissipation in close asteroid binary systems.Comment: Many changes based on referees comment

Analysis of the rotation period of asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger - search for the YORP effect

The spin state of small asteroids can change on a long timescale by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, the net torque that arises from anisotropically scattered sunlight and proper thermal radiation from an irregularly-shaped asteroid. The secular change in the rotation period caused by the YORP effect can be detected by analysis of asteroid photometric lightcurves. We analyzed photometric lightcurves of near-Earth asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger with the aim to detect possible deviations from the constant rotation caused by the YORP effect. We carried out new photometric observations of the three asteroids, combined the new lightcurves with archived data, and used the lightcurve inversion method to model the asteroid shape, pole direction, and rotation rate. The YORP effect was modeled as a linear change in the rotation rate in time d\omega /dt. Values of d\omega/ dt derived from observations were compared with the values predicted by theory. We derived physical models for all three asteroids. We had to model Eger as a nonconvex body because the convex model failed to fit the lightcurves observed at high phase angles. We probably detected the acceleration of the rotation rate of Eger d\omega / dt = (1.4 +/- 0.6) x 10^{-8} rad/d (3\sigma error), which corresponds to a decrease in the rotation period by 4.2 ms/yr. The photometry of Cerberus and Ra-Shalom was consistent with a constant-period model, and no secular change in the spin rate was detected. We could only constrain maximum values of |d\omega / dt| < 8 x 10^{-9} rad/d for Cerberus, and |d\omega / dt| < 3 x 10^{-8} rad/d for Ra-Shalom

A large topographic feature on the surface of the trans-Neptunian object (307261) 2002 MS4_4 measured from stellar occultations

This work aims at constraining the size, shape, and geometric albedo of the dwarf planet candidate 2002 MS4 through the analysis of nine stellar occultation events. Using multichord detection, we also studied the object's topography by analyzing the obtained limb and the residuals between observed chords and the best-fitted ellipse. We predicted and organized the observational campaigns of nine stellar occultations by 2002 MS4 between 2019 and 2022, resulting in two single-chord events, four double-chord detections, and three events with three to up to sixty-one positive chords. Using 13 selected chords from the 8 August 2020 event, we determined the global elliptical limb of 2002 MS4. The best-fitted ellipse, combined with the object's rotational information from the literature, constrains the object's size, shape, and albedo. Additionally, we developed a new method to characterize topography features on the object's limb. The global limb has a semi-major axis of 412 $\pm$ 10 km, a semi-minor axis of 385 $\pm$ 17 km, and the position angle of the minor axis is 121 $^\circ$ $\pm$ 16$^\circ$. From this instantaneous limb, we obtained 2002 MS4's geometric albedo and the projected area-equivalent diameter. Significant deviations from the fitted ellipse in the northernmost limb are detected from multiple sites highlighting three distinct topographic features: one 11 km depth depression followed by a 25$^{+4}_{-5}$ km height elevation next to a crater-like depression with an extension of 322 $\pm$ 39 km and 45.1 $\pm$ 1.5 km deep. Our results present an object that is $\approx$138 km smaller in diameter than derived from thermal data, possibly indicating the presence of a so-far unknown satellite. However, within the error bars, the geometric albedo in the V-band agrees with the results published in the literature, even with the radiometric-derived albedo

DIFFUSION MODEL OF CREAMY- AND VEGETABLE SPREADS MIXING

Summary .A mathematical model of the process of mixing cream- and vegetable spread was developed. In modeling the diffusion understanding of the nature of the process were used, allowing escape from the apparatus geometry. After turning on the mixer the mixing process begins. Its duration can be determined by the behavior of the tracer particles introduced into the agitated medium in a predetermined quantity through the free liquid surface within a short period of time. If tracer particles have the same density with the surrounding bulk liquid phase, then the path of movement of the particles and the fluid are identical. The degree of homogeneity of the composition can be stirred calculated by the coefficient of variation, which is identified by the local concentrations of tracer particles in the volume of stirred medium. The task of a one-dimensional particle transport in the plane layer of the mixed liquid is solved for their calculation. The calculated ratios obtained allow us to calculate the particle concentration at any point in the volume being mixed at random times. Based on the experiment effective mixing coefficients are identified and relations for their assessment, depending on the Reynolds number of the mixer in the range studied variations of process are offered. Using the time dependence of the variation coefficient characterizing the homogenity of the system being mixed, it is possible to determine the duration of mixing to obtain the product with the desired uniformity and homogeneity of the product under the definition of a predetermined duration of the mixing process. The variation coefficient %, indicating a sufficiently good uniformity of the spread composition was found for the spread №1, being mixed with a stirrer rotating at a speed of n=150 rev / min, and the dimensionless length of the process Fo =0,0935 for obtaining estimated relations. Using the proposed calculation algorithm one can estimate the homogeneity of the product at any time