On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation

The TDPAC study of the Ni-5 at.% Hf alloy

16th International Conference on Solid Compounds of Transition Elements, July 26-31, Dresden, Germany, 2008

On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation

Epigenetic signature of early trauma: differences in the FKBP5 DNA methylation levels among psychotic patients, their healthy siblings and controls

30th Congress of the European-College-of-Neuropsychopharmacology (ECNP), Sep 02-05, 2017, Paris, Franc

Representativity of Air Quality Control in Limited Number of Grid Points

In this study, we point to loss of accuracy in representing a field of air pollution concentration due to reduction of number of monitoring points or changes in their location. Using a Gaussian-type diffusion model, a high resolution concentration field was generated from 17 points representing the actual distribution of possible pollution sources. The starting grid consisted of 90 601 points. Then we reduced number of points by two orders of magnitude, forming the grid of 961 points. After that, the second reduction to 36 points was performed, still forming a regular grid. Finally, we had 16 points whose positions are in a qualitative agreement with the actual distribution of sampling stations in the area