Low Momentum Classical Mechanics with Effective Quantum Potentials

A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a smoothed potential both of them constructed from the classical potential. The exact solution of the approximated theory in one spatial dimension is found. The concept of effective transmission and reflection coefficients for effective quantum potentials is proposed and discussed in comparison with an analogous quantum statistical mixture problem. The results are applied to the case of a square barrier.Comment: 4 figure

Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem

Relativistic Klein-Gordon-Maxwell multistream model for quantum plasmas

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluid-like version of the Klein-Gordon-Maxwell system. The one and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known non-relativistic results. In both the one and two-stream cases, steady-state solutions reduce the model to a set of coupled nonlinear ordinary differential equations, which can be numerically solved, yielding a manifold of nonlinear periodic and soliton structures. The validity conditions for the applicability of the model are addressed

The dust SED in the dwarf galaxy NGC 1569: Indications for an altered dust composition?

We discuss the interpretation of the dust SED from the mid-infrared to the millimeter range of NGC 1569. The model developed by D\'esert et al. (1990) including three dust components (Polyaromatic Hydrocarbons, Very Small Grains and big grains) can explain the data using a realistic interstellar radiation field and adopting an enhanced abundance of VSGs. A simple three-temperature model is also able to reproduce the data but requires a very low dust temperature which is considered to be unlikely in this low-metallicity starburst galaxy. The high abundance of Very Small Grains might be due to large grain destruction in supernova shocks. This possibility is supported by ISO data showing that the emission at 14.3 $\mu$m, tracing VSGs, is enhanced with respect to the emission at 6.7 $\mu$m and 850 $\mu$m in regions of high star formation.Comment: 4 pages, conference proceedings paper, "The Spectral Energy Distribution of Gas-Rich Galaxies: Confronting Models with Data", Heidelberg, 4-8 Oct. 2004, eds. C.C. Popescu & R.J. Tuffs, AIP Conf. Ser., in pres

Jacobi Structures in R3\mathbb{R}^3

The most general Jacobi brackets in $\mathbb{R}^3$ are constructed after solving the equations imposed by the Jacobi identity. Two classes of Jacobi brackets were identified, according to the rank of the Jacobi structures. The associated Hamiltonian vector fields are also constructed

On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

The ionization structure of the Orion nebula: Infrared line observations and models

Observations of the (O III) 52 and 88 micron lines and the (N III) 57 micron line have been made at 6 positions and the (Ne III) 36 micron line at 4 positions in the Orion Nebula to probe its ionization structure. The measurements, made with a -40" diameter beam, were spaced every 45" in a line south from and including the Trapezium. The wavelength of the (Ne III) line was measured to be 36.013 + or - 0.004 micron. Electron densities and abundance ratios of N(++)/O(++) have been calculated and compared to other radio and optical observations. Detailed one component and two component (bar plus halo) spherical models were calculated for exciting stars with effective temperatures of 37 to 40,000K and log g = 4.0 and 4.5. Both the new infrared observations and the visible line measurements of oxygen and nitrogen require T sub eff approx less than 37,000K. However, the double ionized neon requires a model with T sub eff more than or equal to 39,000K, which is more consistent with that inferred from the radio flux or spectral type. These differences in T sub eff are not due to effects of dust on the stellar radiation field, but are probably due to inaccuracies in the assumed stellar spectrum. The observed N(++)/O(++) ratio is almost twice the N(+)/O(+) ratio. The best fit models give N/H = 8.4 x 10 to the -5 power, O/H = 4.0 x 10 to the -4 power, and Ne/H = 1.3 x 10 to the -4 power. Thus neon and nitrogen are approximately solar, but oxygen is half solar in abundance. From the infrared O(++) lines it is concluded that the ionization bar results from an increase in column depth rather than from a local density enhancement

General Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

We report on a set of long-term general-relativistic three-dimensional (3D) multi-group (energy-dependent) neutrino-radiation hydrodynamics simulations of core-collapse supernovae. We employ a full 3D two-moment scheme with the local M1 closure, three neutrino species, and 12 energy groups per species. With this, we follow the post-core-bounce evolution of the core of a nonrotating $27$-$M_\odot$ progenitor in full unconstrained 3D and in octant symmetry for $\gtrsim$$380\,\mathrm{ms}$. We find the development of an asymmetric runaway explosion in our unconstrained simulation. We test the resolution dependence of our results and, in agreement with previous work, find that low resolution artificially aids explosion and leads to an earlier runaway expansion of the shock. At low resolution, the octant and full 3D dynamics are qualitatively very similar, but at high resolution, only the full 3D simulation exhibits the onset of explosion.Comment: Accepted to Ap