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of load, which are linear or non-linear. Emphasis was placed on creating a mathematical model describing the two cases using an estimated algorithm to give a mathematical relationship between the load in terms of the length of the spring and the
. ( 2015 ) Numerical simulation analysis of a mathematical model of circadian pacemaker neurons . Appl. Math. 6 , 1214 – 1219 . 8. Szűcs , A
Abstract
Reading and co-workers introduced a new technique a few years ago called Modulated Differential Scanning Calorimetry or MDSC. Here the first part of a theoretical analysis for this technique is given. A simple mathematical model for modulated differential scanning calorimetry in the form of an ordinary differential equation is derived. The model is analysed to find the effect of a kinetic event in the form of a chemical reaction. Some possible sources of error are discussed. A more sophisticated version of the model allowing for spatial variation in a calorimeter is developed and it is seen how it can be reduced to the earlier model. Some preliminary work on a phase change is also presented.
Abstract
In this paper, pyrolysis characteristics of oil shale obtained from Huadian, China, are investigated by thermogravimetry method. The effect of operating conditions, such as particle size, heating rate on the pyrolysis process is analyzed, and kinetic parameters of pyrolysis at different heating rates are calculated using a two-stage Arrhenius model that is solved by the Freeman-Carroll method. On the basis of these experimental results and theoretical analysis, a mathematical model, fully suitable for the pyrolysis characteristics of oil shale, is developed: mass loss rate is described by a two-stage intrinsic kinetics equation for reducing the calculation error; pyrolytic heat value of volatile is contained in energy equation, and density equation is considered as well, due to the release of a large amount of volatiles in pyrolysis process. Thermogravimetric experimental data are used to validate the described models.
dimensional mathematical model of heat transmission of building structures (in Hungarian) Hungarian Research Found OTKA T 038336, 2006. William S. J. Engineering heat transfer , Second Edition, CRC Press, New
J. M. Gaidis 1988 Mathematical Model for Freeze-Thaw Durability of Concrete Journal of the American Ceramic Society 71 9 776
intermediate heat exchangers for the MTO process at the initial reaction stage is introduced in this study. A pseudo-homogeneous one-dimensional mathematical model is established and solved by the fourth-order Runge-Kutta integration method. Under the condition
Ecuadorian professional football league, whose annual season calendars have been drawn up since 2019 through a collaborative effort between league officials and our research team using mathematical models from the field of sports scheduling. Although the
This present work is modelling the three physiological stages of germination. The aim of modelling is to define within germination time the duration of the different stages and their temperature dependence. The periods follow Arrhenius-type relations with (average) activation energies typical for the given stages and according to the germination time as well. The germination time being different seed-by-seed can be considered a random variable of normal distribution according to the model. The result of the model was controlled by experimental data given by seed germination trials of the common reed ( Phragmites australis ) and in cases using those given on other seeds (rice, pea).
Some possible elementary reactions are not included in the classical mathematical models of thermal decomposition. For example, we can assume that in the thermal decompositions of simple carbonates a proportion of the O2− ions produced on the reaction interface can migrate into the interior of the reactant phase, since at this temperature there is some probability of CO2 exchange between an O2− and a neighbouring CO3 2− ion. A similar diffusion-type process can be assumed in a wide class of decomposition reactions. The present state of computer science makes it possible to show by mathematical modelling how this migration influences the TG curves of the simplest contracting-sphere-type reactions. The resulting extended contracting-sphere model can provide the induction and the acceleration period of the TG curves.
