Quantum number dimensional scaling analysis for excited states of multielectron atoms

A new dimensional scaling method for the calculation of excited states of multielectron atoms is introduced. By including the principle and orbital quantum numbers in the dimension parameter, we obtain an energy expression for excited states including high angular momentum states. The method is tested on He, Li, and Be. We obtain good agreement with more orthodox quantum mechanical treatments even in the zeroth order.Comment: Submitted to Physical Review A, 13 pages, 6 Table

Fragments of ML Decidable by Nested Data Class Memory Automata

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument

On the Asymmetric Longitudinal Oscillations of a Pikelner's Model Prominence

We present analytical and numerical models of a normal-polarity quiescent prominence that are based on the model of Pikelner (Solar Phys. 1971, 17, 44 ). We derive the general analytical expressions for the two-dimensional equilibrium plasma quantities such as the mass density and a gas pressure, and we specify magnetic-field components for the prominence, which corresponds to a dense and cold plasma residing in the dip of curved magnetic-field lines. With the adaptation of these expressions, we solve numerically the 2D, nonlinear, ideal MHD equations for a Pikelner's model of a prominence that is initially perturbed by reducing the gas pressure at the dip of magnetic-field lines. Our findings reveal that as a result of pressure perturbations the prominence plasma starts evolving in time and this leads to the antisymmetric magnetoacoustic--gravity oscillations as well as to the mass-density growth at the magnetic dip, and the magnetic-field lines subside there. This growth depends on the depth of magnetic dip. For a shallower dip, less plasma is condensed and vice-versa. We conjecture that the observed long-period magnetoacoustic-gravity oscillations in various prominence systems are in general the consequence of the internal pressure perturbations of the plasma residing in equilibrium at the prominence dip.Comment: 24 Pages; 16 Figures; Solar Physic

New analytical and numerical models of solar coronal loop: I. Application to forced vertical kink oscillations

Aims. We construct a new analytical model of a solar coronal loop that is embedded in a gravitationally stratified and magnetically confined atmosphere. On the basis of this analytical model, we devise a numerical model of solar coronal loops. We adopt it to perform the numerical simulations of its vertical kink oscillations excited by an external driver. Methods. Our model of the solar atmosphere is constructed by adopting a realistic temperature distribution and specifying the curved magnetic field lines that constitute a coronal loop. This loop is described by 2D, ideal magnetohydro- dynamic equations that are numerically solved by the FLASH code. Results. The vertical kink oscillations are excited by a periodic driver in the vertical component of velocity, acting at the top of the photosphere. For this forced driver with its amplitude 3 km/s, the excited oscillations exhibit about 1.2 km/s amplitude in their velocity and the loop apex oscillates with its amplitude in displacement of about 100 km. Conclusions. The newly devised analytical model of the coronal loops is utilized for the numerical simulations of the vertical kink oscillations, which match well with the recent observations of decay-less kink oscillations excited in solar loops. The model will have further implications on the study of waves and plasma dynamics in coronal loops, revealing physics of energy and mass transport mechanisms in the localized solar atmosphere.Comment: 6 Pages; 5 Figures; A&

Three-dimensional numerical simulation of magnetohydrodynamic-gravity waves and vortices in the solar atmosphere

With the adaptation of the FLASH code we simulate magnetohydrodynamic-gravity waves and vortices as well as their response in the magnetized three-dimensional (3D) solar atmosphere at different heights to understand the localized energy transport processes. In the solar atmosphere strongly structured by gravitational and magnetic forces, we launch a localized velocity pulse (in horizontal and vertical components) within a bottom layer of 3D solar atmosphere modelled by initial VAL-IIIC conditions, which triggers waves and vortices. The rotation direction of vortices depends on the orientation of an initial perturbation. The vertical driver generates magnetoacoustic-gravity waves which result in oscillations of the transition region, and it leads to the eddies with their symmetry axis oriented vertically. The horizontal pulse excites all magnetohydrodynamic-gravity waves and horizontally oriented eddies. These waves propagate upwards, penetrate the transition region, and enter the solar corona. In the high-beta plasma regions the magnetic field lines move with the plasma and the temporal evolution show that they swirl with eddies. We estimate the energy fluxes carried out by the waves in the magnetized solar atmosphere and conclude that such wave dynamics and vortices may be significant in transporting the energy to sufficiently balance the energy losses in the localized corona. Moreover, the structure of the transition region highly affects such energy transports, and causes the channelling of the propagating waves into the inner corona.Comment: 11 Pages, 12 Figures, Accepted for the publication in MNRA

Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels

We present simulation results of the impulsively generated linear and non-linear Alfv\'en waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic (MHD) equations to obtain the temporal signatures of the small (linear) and large-amplitude (non-linear) Alfv\'en waves in the model atmosphere of expanding open magnetic field configuration (e.g., coronal funnels) by considering a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfv\'en waves at different heights in the coronal funnel, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfv\'en waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfv\'en waves show that they can contribute only to the plasma dynamics and heating of the funnel-like magnetic flux-tubes associated with the polar coronal holes.Comment: 16 pages of the text and 3 figure