Sverker Edvardsson

Role of the electrostatic model in calculating rare-earth crystal-field parameters

The Sternheimer method is used to derive shielding parameters and antishielding factors for the whole series of rare earths using relativistic wavefunctions. It is found that the shielding parameter σ2 of the 4f electronic shell is decreased compared to earlier calculations. The σ4 and σ6 parameters are calculated for the first time for all rare-earth ions. In all cases, they are found to be small. The influence of the various calculated parameters on the crystal-field parameters for the cases Nd:LiYF4 and Pr:LiYF4 is studied. Present corrections result in ab initio crystal-field parameters that are in excellent agreement with experimentally fitted phenomenological parameters. The nuclear antishielding factors γ∞ are found to essentially agree with earlier findings. These are also found to agree with some early experiments. The various wavefunctions used are derived from a relativistic Desclaux code. These are more external compared to standard Hartree–Fock wavefunctions.

An atomic program for energy levels of equivalent electrons: lanthanides and actinides

A program written in C is presented to carry out brute force calculations in order to derive energy levels for an equivalent electronic configuration. Relativistic effects are partly neglected except for the spin-orbit interaction. Since the main relativistic effects are indirect, i.e. causing a contraction of the core which in turn causes the outer shells to expand, they are included to a high degree through the use of appropriate Slater integrals. The program is especially useful for primarily unfilled f-shells of the rare-earth or actinide ions. Modifications of the program to include spin−spin, spin−other orbit, Breit interaction etc. is straight forward. The program is also general in the sense that there is no need to find out or generate any Racah coefficients of fractional parentage. The complete energy matrix is diagonalized with all operators interacting simultaneously thus allowing mixing of all quantum numbers. This result in all energy eigenvalues and eigenvectors that in turn for example are partly responsible for the polarized dipole, quadrupole, … transitions within the unfilled shell. Free ion configuration interaction is accounted for through the use of standard CI operators. The Stark splitting can be studied via the standard crystal field Hamiltonian. Magnetic field influence on the energy levels may also be studied.

Accurate spin axes and solar system dynamics: climatic variations for the Earth and Mars

Celestial mechanical simulations from a purely classical point of view of the whole solar system, including our Moon and the Mars moons { Phobos and Deimos { are carried out for 2 millions of years before present. Within the classical approximation, the results are derived at a very high level of accuracy. Eects from general relativity for a number of variables are investigated and found to be small. For climatic studies of about 1 Myr, general relativity can safely be ignored. Three dierent and independent integrations schemes are used in order to exclude numerical anomalies. The converged results from all methods are found to be in complete agreement. For verication, a number of properties such as spin axis precession, nutation, and orbit inclination for Earth and Mars have been calculated. Times and positions of equinoxes and solstices are continously monitored. As also observed earlier, the obliquity of the Earth is stabilized by the Moon. On the other hand, the obliquity of Mars shows dramatic variations. Climatic influences due to celestial variables for the Earth and Mars are studied. Instead of using mean insolation as in the usual applications of Milankovitch theory, the present approach focuses on the instantaneous solar radiation power (insolation) at each summer solstice. Solar radiation power is compared to the derivative of the icevolume and these quantities are found to be in excellent agreement. Orbital precessions for the inner planets are studied as well. In the case of Mercury, it is investigated in detail.

Energy level and oscillator strength calculations for Er3+:Y2O3: A molecular dynamics based study

Abstract A molecular dynamics (MD) based approach is being developed to calculate energies and oscillator strengths for RE ions in various solid/liquid/amorphous inorganic compounds. In this connection, the complete 364×364 energy matrix for the Er 3+ (4f 11 ) electrons has been diagonalized for different MD-generated environments. The importance of MD is emphasized. Configuration interaction (CI) effects are included in constructing the energy matrix, since these have a significant influence on the derived absorption spectrum. The A tp parameters have been calculated by direct summation over 100 multipole-expanded environments generated with MD. The various polarizabilities and shielding parameters used have been calculated by ab initio methods. The derived energies and eigenvectors have been used to compute the oscillator strengths and the corresponding spectra. Both electric-dipole and inhomogeneous dielectric mechanisms have been considered in the oscillator strength calculation. The calculated Stark splittings and oscillator strengths for the Stark–Stark level transitions agree well with experiment for Er 3+ :Y 2 O 3 . The best agreement is obtained when consistent multipole contributions are included in the converged calculated crystal field. The method described above is important in predicting a priori laser related properties (radiative lifetimes, etc.) for potential host materials.

Fisher: a program for the detection of H/ACA snoRNAs using MFE secondary structure prediction and comparative genomics -- assessment and update.

BackgroundThe H/ACA family of small nucleolar RNAs (snoRNAs) plays a central role in guiding the pseudouridylation of ribosomal RNA (rRNA). In an effort to systematically identify the complete set of rRNA-modifying H/ACA snoRNAs from the genome sequence of the budding yeast, Saccharomyces cerevisiae, we developed a program – Fisher – and previously presented several candidate snoRNAs based on our analysis [1].FindingsIn this report, we provide a brief update of this work, which was aborted after the publication of experimentally-identified snoRNAs [2] identical to candidates we had identified bioinformatically using Fisher. Our motivation for revisiting this work is to report on the status of the candidate snoRNAs described in [1], and secondly, to report that a modified version of Fisher together with the available multiple yeast genome sequences was able to correctly identify several H/ACA snoRNAs for modification sites not identified by the snoGPS program [3]. While we are no longer developing Fisher, we briefly consider the merits of the Fisher algorithm relative to snoGPS, which may be of use for workers considering pursuing a similar search strategy for the identification of small RNAs. The modified source code for Fisher is made available as supplementary material.ConclusionOur results confirm the validity of using minimum free energy (MFE) secondary structure prediction to guide comparative genomic screening for RNA families with few sequence constraints.

System Dynamics of the Open-Draw With Web Adhesion: Particle Approach

In the present work we propose a particle approach, which is designed to treat complex mechanics and dynamics of the open-draw sections that are still present in many of todays paper machines. First, known steady-state continuous solutions are successfully reproduced. However, it is shown that since the boundary conditions depend on the solution itself, the solutions for web strain and web path in the open-draw section are generally time-dependent. With a certain set of system parameters, the nonsteady solutions are common. A temporal fluctuation of Youngs modulus, for example, destabilizes the system irreversibly, resulting in the continuous growth of web strain, i.e., break. Finally we exemplify with some strategic draw countermeasures how to prevent a dangerous evolution in the web strain.

The Use of Cl Calculated Polarizabilities to Study Rare-Earth CFP Dependencies in the Laser Host RE:YLF

It has earlier been shown that the Sternheimer method is appropriate in deriving crystal field parameters (CFP) for Pr3+ and Nd3+ doped in YLF or Nd3+ in YAG. In this connection, the dipole (αD) and quadrupole (αQ) polarizabilities for the whole rare-earth (RE) series will be presented. These are needed for the self consistent lattice summations performed. The various rare-earth wavefunctions needed for the computations are derived from the well known relativistic full Hartree-Fock code by R. D. Cowan. The main CFP behaviour for the various RE dopants in YLF are seen to agree fairly well with the experimentally fitted parameters. Covalency effects are, as expected, observed to be more important for higher order parameters. It is also seen that the contribution to the crystal field due to covalency is approximately constant for a given Btp. This observation is also supported by calculations of Newman. The shielding, nuclear antishielding factors and radial integrals for the whole RE series are also presented.

A study of vibrational modes in Na+ beta -alumina by molecular dynamics simulation

The vibrational properties of crystalline Na+ beta -alumina (Na1.22Al11O17.11) have been studied using the molecular dynamics simulation technique. The vibrational density of states was calculated from the velocity autocorrelation function, and the infrared spectrum from the dipole-dipole autocorrelation function. Knowledge of the vibrations in different crystallographic directions for the different atomic species facilitates the assignment of spectral peaks. The sodium in-plane vibrations are 59, 88 and 112 cm-1, and the out-of-plane vibrations are at 146 cm-1. The stoichiometric compound is also studied, and in this case the sodium in-plane vibrations are at 80 cm-1 and the out-of-plane vibrations at 140 cm-1. The density of states is used to calculate thermodynamic properties: heat capacity, entropy and internal and free energy. The values obtained at 300 K are Cnu =410 J K-1 mol-1, Snu =300 J K-1 mol-1, U=370 kJ mol-1 and F=280 kJ mol-1. The heat capacity and entropy values are in good agreement with experiment, and thus strongly support the empirical force field used in the simulation.

Soap-film coating: High-speed deposition of multilayer nanofilms

The coating of thin films is applied in numerous fields and many methods are employed for the deposition of these films. Some coating techniques may deposit films at high speed; for example, ordinary printing paper is coated with micrometre-thick layers of clay at a speed of tens of meters per second. However, to coat nanometre thin films at high speed, vacuum techniques are typically required, which increases the complexity of the process. Here, we report a simple wet chemical method for the high-speed coating of films with thicknesses at the nanometre level. This soap-film coating technique is based on forcing a substrate through a soap film that contains nanomaterials. Molecules and nanomaterials can be deposited at a thickness ranging from less than a monolayer to several layers at speeds up to meters per second. We believe that the soap-film coating method is potentially important for industrial-scale nanotechnology.

The Dynamical Functional Particle Method: An Approach for Boundary Value Problems

The present work is concerned with new ideas of potential value for solving differential equations. First, a brief introduction to particle methods in mechanics is made by revisiting the vibrating string. The full case of nonlinear motion is studied and the corresponding nonlinear differential equations are derived. It is suggested that the particle origin of these equations is of more general interest than usually considered. A novel possibility to develop particle methods for solving differential equations in a direct way is investigated. The dynamical functional particle method (DFPM) is developed as a solution method for boundary value problems. DFPM is based on the concept of an interaction functional as a dynamical force field acting on quasi particles. The approach is not limited to linear equations. We exemplify by applying DFPM to several linear Schrodinger type of problems as well as a nonlinear case. It is seen that DFPM performs very well in comparison with some standard numerical libraries. In all cases, the convergence rates are exponential in time.