Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule

We present an algebraic method for treating molecular vibrations in the Morse potential perturbed by an external laser field. By the help of a complete and normalizable basis we transform the Schr\"{o}dinger equation into a system of coupled ordinary differential equations. We apply our method to calculate the dissociation probability of the NO molecule excited by chirped laser pulses. The dependence of the molecular dipole-moment on the interatomic separation is determined by a quantum-chemical method, and the corresponding transition dipole moments are given by approximate analytic expressions. These turn out to be very small between neighboring stationary states around the vibrational quantum number $m=42$, therefore we propose to use additional pulses in order to skip this trapping state, and to obtain a reasonable dissociation probability.Comment: 4 pages, 3 figure

Generic stability of dissipative non-relativistic and relativistic fluids

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the nonnegativity of the transport coefficients.Comment: 22 page

Large size and slow rotation of the trans-Neptunian object (225088) 2007 OR10 discovered from Herschel and K2 observations

We present the first comprehensive thermal and rotational analysis of the second most distant trans-Neptunian object (225088) 2007 OR10. We combined optical light curves provided by the Kepler space telescope -- K2 extended mission and thermal infrared data provided by the Herschel Space Observatory. We found that (225088) 2007 OR10 is likely to be larger and darker than derived by earlier studies: we obtained a diameter of d=1535^{+75}_{-225} km which places (225088) 2007 OR10 in the biggest top three trans-Neptunian objects. The corresponding visual geometric albedo is p_V=0.089^{+0.031}_{-0.009}. The light curve analysis revealed a slow rotation rate of P_rot=44.81+/-0.37 h, superseded by a very few objects only. The most likely light-curve solution is double-peaked with a slight asymmetry, however, we cannot safely rule out the possibility of having a rotation period of P_rot=22.40+/-0.18 h which corresponds to a single-peaked solution. Due to the size and slow rotation, the shape of the object should be a MacLaurin ellipsoid, so the light variation should be caused by surface inhomogeneities. Its newly derived larger diameter also implies larger surface gravity and a more likely retention of volatiles -- CH_4, CO and N_2 -- on the surface.Comment: Accepted for publication in AJ, 8 pages in emulateapj styl

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently