1,454 research outputs found
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 , 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superseded by a very few objects only.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
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