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A. Frank

Publications and source records attributed to A. Frank.

105 records · Page 6Linked to original sources
arXiv1997

Effects of Cooling on the Propagation of Magnetized Jets

We present multi-dimensional simulations of magnetized radiative jets appropriate to Young Stellar Objects. Magnetized jets subject to collisionally excited radiative losses have not, as yet, received extensive scrutiny. The purpose of this letter is to articulate the propagation dynamics of radiative MHD jets in the context of the extensive jet literature. Most importantly, we look for morphological and kinematic diagnostics that may distinguish hydrodynamic protostellar jets from their magnetically dominated cousins. Our simulations are axisymmetric (2.5-D). A toroidal B_phi field geometry is used. Our models have high sonic Mach numbers (Ms approx 10), but lower fast mode Mach number (Mf approx 5). This is approximately the case for jets formed via disk-wind or X-wind models - currently the consensus choice for launching and collimating YSO jets. Time-dependent radiative losses are included via a coronal cooling curve. Our results demonstrate that the morphology and propagation characteristics of strongly magnetized radiative jets can differ significantly from jets with weak fields. In particular the formation of nose-cones via post-shock hoop stresses leads to narrow bow shocks and enhanced bow shock speeds. In addition, the hoop stresses produce strong shocks in the jet beam which constrasts with the relatively unperturbed beam in radiative hydrodynamic jets. Our simulations show that pinch modes produced by magnetic tension can strongly effect magnetized protostellar jets.

astro-ph↗
arXiv1997

A symmetry adapted approach to vibrational excitations in atomic clusters

An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na$^+_n$ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be$_4$, H$_3^+$, Be$_3$ and Na$_3^+$ clusters.

physics.chem-ph↗
arXiv1997

A comparison between algebraic models of molecular spectroscopy

We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in previous versions of the vibron model, in which the Hamiltonian is expressed in terms of Casimir operators and their products. The inclusion of these new interactions leads to reliable spectroscopic predictions. As an example we study the vibrational excitations of the methane molecule, and compare our results with those obtained in other algebraic models.

physics.chem-ph↗
arXiv1997

Symmetry-adapted algebraic description of stretching and bending vibrations of ozone

The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U(2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O_3 and 18 O_3 yields a r.m.s. deviation of 2.5 and 1.0 1/cm, respectively.

chem-ph↗
arXiv1997

Analytically Solvable Mean-Field Potential for Stable and Exotic Nuclei

Slater determinants built from the single-particle wave functions of the analytically solvable Ginocchio potential are used to approximate the self-consistent Hartree-Fock solutions for the ground states of nuclei. The results indicate that the Ginocchio potential provides a good parametrization of the nuclear mean field for a wide range of nuclei, including those at the limit of particle stability.

nucl-th↗
arXiv1997

Comment on ``Boson-realization model for the vibrational spectra of tetrahedral molecules''

An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry adapted algebraic approach based on U(2) algebras.

physics.chem-ph↗
arXiv1996

A symmetry-adapted algebraic approach to molecular spectroscopy

We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have identified interaction terms that were absent in previous formulations of the vibron model. The inclusion of these new interactions leads to reliable spectroscopic predictions. We illustrate the method for the D_3h triatomic molecules, H_3^+, Be_3 and Na_3, and the T_d molecules, Be_4 and CH_4.

physics.chem-ph↗
arXiv1996

Application of a symmetry-adapted algebraic model to the vibratioinal spectrum of methane

The stretching and bending vibrations of methane are studied in the framework of a symmetry-adapted algebraic model. The model is based on the realization of the one-dimensional Morse potential in terms of a $U(2)$ algebra. For the 44 observed energies we obtain a fit with a r.m.s. deviation of 1.16 cm$^{-1}$ which is an order of magnitude more accurate than previous algebraic calculations.

physics.chem-ph↗
arXiv1996

Transition from the Seniority to the Anharmonic Vibrator Regime in Nuclei

A recent analysis of experimental energy systematics suggests that all collective nuclei fall into one of three classes -- seniority, anharmonic vibrational, or rotational -- with sharp phase transitions between them. We investigate the transition from the seniority to the anharmonic vibrator regime within a shell model framework involving a single large j-orbit. The calculations qualitatively reproduce the observed transitional behavior, both for U(5) like and O(6) like nuclei. They also confirm the preeminent role played by the neutron-proton interaction in producing the phase transition.

nucl-th↗
arXiv1996

A general algebraic model for molecular vibrational spectroscopy

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.

chem-ph↗
arXiv1996

A Symmetry Adapted Approach to Molecular Spectroscopy: The Anharmonic Oscillator Symmetry Model

We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and configuration space formulations, by means of which new interactions are found in the algebraic model, leading to reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules and the ${\cal T}_d$ Be-cluster.

chem-ph↗
arXiv1995

Algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei

We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single-particle degrees of freedom in an application to elastic and inelastic proton scattering from $^{195}$Pt.

nucl-th↗
arXiv1994

Principle Based Semantics for HPSG

The paper presents a constraint based semantic formalism for HPSG. The advantages of the formlism are shown with respect to a grammar for a fragment of German that deals with (i) quantifier scope ambiguities triggered by scrambling and/or movement and (ii) ambiguities that arise from the collective/distributive distinction of plural NPs. The syntax-semantics interface directly implements syntactic conditions on quantifier scoping and distributivity. The construction of semantic representations is guided by general principles governing the interaction between syntax and semantics. Each of these principles acts as a constraint to narrow down the set of possible interpretations of a sentence. Meanings of ambiguous sentences are represented by single partial representations (so-called U(nderspecified) D(iscourse) R(epresentation) S(tructure)s) to which further constraints can be added monotonically to gain more information about the content of a sentence. There is no need to build up a large number of alternative representations of the sentence which are then filtered by subsequent discourse and world knowledge. The advantage of UDRSs is not only that they allow for monotonic incremental interpretation but also that they are equipped with truth conditions and a proof theory that allows for inferences to be drawn directly on structures where quantifier scope is not resolved.

cmp-lg↗