An Application of the Method of Lines to Multidimensional Free Boundary Problems

Multidimensional free boundary problems for elliptic and parabolicdifferential equations, among them one phase Stefan problems,are partially discretized with the method of lines. The multi-pointfree boundary problem for the resulting system of second orderordinary differential equations is solved iteratively with anSOR type iteration. At each step of this iteration a free boundaryproblem for a single ordinary differential equation must besolved for which an initial value technique is used. The methodcan effectively cope with quite general space and time dependentfree surface conditions.     

Modified Damped Least Squares: An Algorithm for Non-linear Estimation

A new method for non-linear regression is described and comparedto three other well-known methods for the non-linear least squaresproblem. Convergence theorems and computational results aregiven which indicate that the new method is more efficient andreliable than previously published methods.     

An outdoor investigation of the absorption degradation of single-junction amorphous silicon photovoltaic module due to localized heat/hot spot formation

This paper investigates the absorbance degradation of single-junction amorphous silicon (a-Si:H) photovoltaic (PV) module, due to the presence of localized heat. The decrease in optical density is a huge challenge due to the long-term degradation of PV modules. The reduction in solar cell optical density causes a decline in its conversion efficiency. This decreases the photogenerating current, hence reduces the effective efficiency of the PV device. An infrared thermography was used for mapping the module temperature profile. Fourier transform infrared spectroscopy (FTIR) was used for the absorption characterization. The rationale behind the outdoor deployment was to deduce a practical effect of hot spot formation on the module’s absorption ability. The results show a direct correlation between localized heat and the absorption degradation.     

Quantum states of hydrogen transfer and vibration in malonaldehyde

New ab initio results on the 21D potential energy surface of malonaldehyde and a quantum mechanical treatment of the hydrogen transfer motion and its interaction with all vibrations are presented. An explicit approximate reaction path, close to the minimum energy path but matching the reactive normal mode near equilibrium, allows one to predict the ground state tunnelling frequency even when using small basis sets. With a barrier of 1144 cm^?1 (3.27kcal mol-¹) the tunnelling splitting is predicted to be 22.0cm^?1 for the parent species and 3.8 cm^?1 for the species deuterated in the hydrogen bond, in good agreement with the observed values 21.6 and 2.9 cm^?1, respectively. Predicted energy levels for excited states of the hydrogen transfer motion and for the non-reactive vibrations suggest a re-examination of the vibrational spectra and an extension of the number of vibrational factors in the basis set to improve the results for the vibrationally excited states.