A new method of calculation of parameters of enthalpy relaxation models is proposed. Regression analysis treatment compares the experimental and calculated values of relaxation enthalpy. The experimental values of relaxation enthalpy are obtained by numerical integration of the difference between the two DSC curves. Contrary to the overall shape of the DSC curve the integral values are not affected by particular heat flow conditions during the DSC experiment. The Narayanaswamy's numerical model based on the Kohlrausch—William—Watts relaxation function was used to calculate the theoretical values of relaxation enthalpy. The application of the proposed method on the DSC experimental data of enthalpy relaxation of As2Se3 is shown.
Authors:T. Wanjun, L. Yuwen, Z. Hen, W. Zhiyong, and W. Cunxin
A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic
parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical
calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with
several published approximate formulae, this new one is much superior to all other approximations and is the most suitable
solution for the evaluation of kinetic parameters from TG experiments.
The mathematical evaluation of the activation
energy, E, of non-isothermal degradation
reactions is usually made using the Ozawa/Flynn–Wall isoconversion principle
and involves the numerical resolution of a set of integrals without closed
form solution, which are solved by polynomial approximation or by numeric
integration. In the present work, the isoconversion principle, originally
described and maintained until now as an algebraic problem, was written as
a set of ordinary differential equations (ODEs). The individual ODEs obtained
are integrated by numeric methods and are used to estimate the activation
energy of simulated examples. A least square error (LSE) objective function
using the introduced ODEs was written to deal with multiple heating rate CaCO3
thermal decomposition TG experiments.
Authors:E. L. Dorval, M. A. Arribére, S. Ribeiro Guevara, I. M. Cohen, A. J. Kestelman, R. A. Ohaco, M. S. Segovia, A. N. Yunes, and M. Arrondo
We have measured the cross sections, averaged over a 235U fission neutron spectrum, for the two high threshold reactions: 75As(n,p)75mGe and 75As(n,2n)74As. The measured averaged cross sections are 0.292±0.022 mb, referred to the 3.95±0.20 mb standard for the 27Al(n,p)27Mg averaged cross section, and 0.371±0.032 mb referred to the 111±3 mb standard for the 58Ni(n,p)58m+gCo averaged cross section, respectively. The measured averaged cross sections were also evaluated semi-empirically by numerically
integrating experimental differential cross section data extracted for both reactions from the current literature. The calculations
were performed for four different representations of the thermal-neutron-induced 235U fission neutron spectrum. The calculated cross sections, though depending on analytical representation of the flux, agree
with the measured values within the estimated uncertainties.
Authors:Hai-Qing Zhang, Bang-Fa Ni, Wei-Zhi Tian, Gui-Ying Zhang, Dong-Hui Huang, Cun-Xiong Liu, Cai-Jin Xiao, Peng Nie, and Hong-Chao Sun
An expression of γ-ray efficiency for large samples is proposed based on numerical integration of efficiencies over compositional
point sources. The widely used expression on radial variation of HPGe efficiency for point source originally proposed by Noguchi
et al. (Int J Appl Radiat Isot 32:17–22, 1980 [<cite>1</cite>]) was amended and a new expression was proposed. A comparison between the two expressions indicates that the newly proposed
expression brings about an obvious improvement, and Self-absorption correction for a voluminous source is also given out by
using the EID principle. The functional relationship between HPGe efficiency for γ-rays from a point source and the spatial
position of the source was established. The results of this study can be applied in order to determine γ attenuation effects
of unknown bulky samples with various shapes and materials.
Being interested in (rotation-)invariant pseudodifferential equations of satellite problems corresponding to spherical orbits, we are reasonably led to generating kernels that depend only on the spherical distance, i.\,e., in the language of modern constructive approximation form spherical radial basis functions. In this paper approximate identities generated by such (rotation-invariant) kernels which are additionally locally supported are investigated in detail from theoretical as well as numerical point of view. So-called spherical difference wavelets are introduced. The wavelet transforms are evaluated by the use of a numerical integration rule, that is based on Weyl's law of equidistribution. This approximate formula is constructed such that it can cope with millions of (satellite) data. The approximation error is estimated on the orbital sphere. Finally, we apply the developed theory to the problems of satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG).
Temperature-modulated calorimetry (TMC) allows the experimental evaluation of the kinetic parameters of the glass transition
from quasi-isothermal experiments. In this paper, model calculations based on experimental data are presented for the total
and reversing apparent heat capacities on heating and cooling through the glass transition region as a function of heating
rate and modulation frequency for the modulated differential scanning calorimeter (MDSC). Amorphous poly(ethylene terephthalate)
(PET) is used as the example polymer and a simple first-order kinetics is fitted to the data. The total heat flow carries
the hysteresis information (enthalpy relaxation, thermal history) and indications of changes in modulation frequency due to
the glass transition. The reversing heat flow permits the assessment of the first and higher harmonics of the apparent heat
capacities. The computations are carried out by numerical integrations with up to 5000 steps. Comparisons of the calculations
with experiments are possible. As one moves further from equilibrium, i.e. the liquid state, cooperative kinetics must be
used to match model and experiment.
The temperature-dependence of the electrical resistance of Al-Zn 78 wt.% was measured during linear cooling of the samples in the range of eutectoidal decomposition. The resulting resistancevs. temperature curves were analysed by:deriving the temperature-dependence of the volume fractionx(T) of theη precipitate;fitting the theoretical functionx(T)=xh(T)+xc(T) following from numerical integration of the reaction rate equations for the simultaneously occurring homogeneous (H) and cellular (C) precipitation processes.