Numerical Integration of Weight Loss Curves for Kinetic Analysis

Research abounds in the literature on kinetic analyses using thermogravimetric (TG) runs. Many of these studies use approximations of integral or derivative forms of the kinetic law and all of them use programmed temperatures. In the present work, a numerical integration procedure was discussed and applied to different examples. We focused on materials presenting a single decomposition curve as well as other materials with more complex processes. Different examples were explored, and the methodology was applied to a number of wastes such as coffee husks, polystyrene and polyethylene. In all cases, the actual temperature measured by thermocouples close to the sample is used, and several runs are fitted using the same kinetic parameters, giving robustness to the results.

Numerical Integration of Weight Loss Curves for Kinetic Analysis

Research abounds in the literature on kinetic analyses using thermogravimetric (TG) runs. Many of these studies use approximations of integral or derivative forms of the kinetic law and all of them use programmed temperature, not the actual temperature measured by thermocouples close to the sample. In addition, it is common to conduct a single run in order to perform the calculation. Nevertheless, many authors consider that numerical methods should be used to analyse the kinetics of decomposition. In such cases, the actual temperature is used and, generally, several runs are fitted using the same kinetic parameters, giving robustness to the results. In the present work, a numerical integration procedure was discussed and applied to different examples. We focused on materials presenting a single decomposition curve as well as other materials with more complex processes. Different examples were explored, and the methodology was applied to a number of wastes such as coffee husks, polystyrene and polyethylene.

Uncertainties and Human Errors in the Design and Execution of Steel Structures

This paper contains a compilation of results from some 50 000 steel specimen tests and close to 5 000 measurements of the cross-sectional properties of rolled steel members. Based on the statistical distribution of these properties the statistical distribution of the sectional capacity of such steel members is evaluated using a numerical integration procedure. For standard structural steel members the variations of the strength properties are reasonably well-known and may be used in reliability assessment methods for the design of structures. However, it has been observed in many actual failures with steel structures that the cause of such failures normally is one gross human error, rather than a combination of “normal” variations in parameters affecting the actions and response of the structures. Another observation from failures experienced with steel structures is that gross human errors in execution are more critical than gross errors in the design process.

Evaluation of the Effective Temperature of Sunspots Using Molecular Parameters of AlF

The physical conditions of celestial objects can be analyzed using the spectrum of atoms or molecules present in the object. The present work focuses on the spectroscopic analysis of astrophysically significant molecule AlF. The evaluation of Franck-Condon (FC) factors andr-centroids is done by a numerical integration procedure using the suitable potential energy curves forC1Σ+-A1Σ+,b3Σ+-a3Πr,c3Σ-a3Πr, andf3Π-a3Πrband systems of AlF molecule. The intensity of various bands is discussed with the help of derived FC factors. The band degradation and the nature of potential energy curves are studied usingr-centroid values. The vibrational temperature of sunspot is estimated to be around 1220 ± 130 K which falls in the reported temperature range of cold sunspots.

Molecular parameters for the gas phase molecules SbO and SbP

Franck-Condon factors and r-centroids, which are very closely related to relative vibrational transition probabilities, were evaluated by the numerical integration procedure for the bands of the A2?3/2 - X2?3/2, C2? - X2?3/2 and D2? - X2? systems of the isotopic SbO molecule and for the B1? - X1?+ system of the isotopic SbP molecule, using a suitable potential.

Evaluation of astrophysically useful parameters for strontium monohydride and deuteride

The Franck-Condon factors and r-centroids which are very closely related to transition probabilities, have been evaluated by the more reliable numerical integration procedure for the band systems B2?-X2?, C2?-X2? and F2?-X2? of astrophysical molecules strontium monohydride and strontium deuteride using an adequate potential. The Franck-Condon factors are more intense, particularly for the ?? = 0 bands, for all the systems examined here. Thus the bands of the molecules are expected to be present in sunspot spectra, SC-stars, cool M-giant stars and other prominent astrophysical sources.

Hiemenz flow of a micropolar viscoelastic fluid in hydromagnetics

Boundary-layer equations are solved for the hydromagnetic problem of two-dimensional Hiemenz flow, for a micropolar, viscoelastic, incompressible, viscous, electrically conducting fluid, impinging perpendicularly onto a plane in the presence of a transverse magnetic field. The governing system of equations is first transformed into a dimensionless form. The resulting equations then are solved by using the Runge–Kutta numerical integration procedure in conjunction with shooting technique. Numerical solutions are presented for the governing momentum and angular-momentum equations. The proposed approximate solution, although simple, is nevertheless sufficiently accurate for the entire investigated range of values of the Hartman number. The effect of micropolar and viscoelastic parameters on Hiemenz flow in hydromagnetics is discussed.PACS No.: 46.35

SOLVING THE SCHRÖDINGER EQUATION FOR BOUND STATES WITH MATHEMATICA 3.0

Using Mathematica 3.0, the Schrödinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically. The corresponding program schroedinger.nb can be obtained from [email protected].

Franck-Condon Factors and R-Centroids for the Band System a1Π-X1Σ+ of the InH Molecule

The Franck-Condon factors (vibrational transition probabilities) and r-centroids have been evaluated by a numerical integration procedure for the bands of the a3Π1-X1Σ+ system of the InH molecule using a suitable potential.