H3++H_3^{++} molecular ions can exist in strong magnetic fields

Using the variational method it is shown that for magnetic fields $B\geq 10^{11}$ G there can exist a molecular ion $H_3^{++}$.Comment: LaTeX, 7 pp, 1 table, 4 figures. Title modified. Consideration of the longitudinal size of the system was adde

Nonlinear dynamics of quantum dot nuclear spins

We report manifestly nonlinear dependence of quantum dot nuclear spin polarization on applied magnetic fields. Resonant absorption and emission of circularly polarized radiation pumps the resident quantum dot electron spin, which in turn leads to nuclear spin polarization due to hyperfine interaction. We observe that the resulting Overhauser field exhibits hysteresis as a function of the external magnetic field. This hysteresis is a consequence of the feedback of the Overhauser field on the nuclear spin cooling rate. A semi-classical model describing the coupled nuclear and electron spin dynamics successfully explains the observed hysteresis but leaves open questions for the low field behaviour of the nuclear spin polarization.Comment: 7 pages, 4 figure

Orbital Decay of the PSR J0045-7319/B Star Binary System: Age of Radio Pulsar and Initial Spin of Neutron Star

Recent timing observations of PSR J0045-7319 reveal that the neutron star/B star binary orbit is decaying on a time scale of |\Porb/\dot\Porb|=0.5 Myr, shorter than the characteristic age ($\tau_c=3$ Myr) of the pulsar (Kaspi et al.~1996a). We study mechanisms for the orbital decay. The standard weak friction theory based on static tide requires far too short a viscous time to explain the observed \dot\Porb. We show that dynamical tidal excitation of g-modes in the B star can be responsible for the orbital decay. However, to explain the observed short decay timescale, the B star must have some significant retrograde rotation with respect to the orbit --- The retrograde rotation brings lower-order g-modes, which couple much more strongly to the tidal potential, into closer ``resonances'' with the orbital motion, thus significantly enhancing the dynamical tide. A much less likely possibility is that the g-mode damping time is much shorter than the ordinary radiative damping time. The observed orbital decay timescale combined with a generic orbital evolution model based on dynamical tide can be used as a ``timer'', giving an upper limit of $1.4$ Myr for the age of the binary system since the neutron star formation. Thus the characteristic age of the pulsar is not a good age indicator. Assuming standard magnetic dipole braking for the pulsar and no significant magnetic field decay on a timescale \lo 1 Myr, the upper limit for the age implies that the initial spin of the neutron star at birth was close to its current value.Comment: AASTeX, 9 pages, 3 ps figures. ApJ Letters, in pres

Radiative transitions of the helium atom in highly magnetized neutron star atmospheres

Recent observations of thermally emitting isolated neutron stars revealed spectral features that could be interpreted as radiative transitions of He in a magnetized neutron star atmosphere. We present Hartree-Fock calculations of the polarization-dependent photoionization cross sections of the He atom in strong magnetic fields ranging from 10^12 G to 10^14 G. Convenient fitting formulae for the cross sections are given as well as related oscillator strengths for various bound-bound transitions. The effects of finite nucleus mass on the radiative absorption cross sections are examined using perturbation theory.Comment: 14 pages, 7 figures. Minor changes. MNRAS in pres

On the Implementation of Efficient Channel Filters for Wideband Receivers by Optimizing Common Subexpression Elimination Methods

No abstract availabl

Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344