scholarly journals SOLVING INVERSE PROBLEM OF CHEMICAL KINETICS WITH USE OF CUBIC SPLINES

2020 ◽  
Vol 63 (7) ◽  
pp. 61-66
Author(s):  
Nikolay I. Kol'tsov
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Chemical Kinetics ◽  
Good Accuracy ◽  
Cubic Splines ◽  
Rate Of Change ◽  
Reference Points ◽  
Additional Advantage ◽  
Instantaneous Rate ◽  
Relaxation Curves

A simple effective method for solving the inverse problem of chemical kinetics based on non-stationary experiments for multistage reactions occurring in an isothermal reactor of ideal mixing is described. The idea of the method is based on taking into account the distinctive features (informativeness) of different fragments of relaxation curves for chemical reactions with arbitrary (non-monotonic) kinetics and their as accurate approximation as possible. For this purpose, non-linear (cubic) splines are used to describe different informative fragments of relaxation curves, which allow to approximate and interpolate experimental data as accurately as possible. An additional advantage of cubic splines, from the point of view of the implementation of the described method, is their continuity at all given points up to and including second-order derivatives (smoothness). This allows us to calculate with good accuracy not only the concentration of reagents, but also the instantaneous rate of change at any time. The consequence of this is the possibility of a sufficiently accurate solution of the inverse problem based on the data of non-stationary experiments. The correctness of the mathematical model used and the stability of the method were tested using variations of the original data. An example of using the method for determining the intervals of physical values of the rate constants of the stages of a two-stage reaction is given. The influence of the method of selecting the reference points (structure) of the spline and measurement errors (noise) of experimental data on the error of determining the speed constants of the stages is estimated. The efficiency of application and good accuracy of the method for solving the inverse problem of chemical kinetics of multistage reactions occurring in non-gradient systems with taking into account of noise is shown.

Numerical simulation of a catalytic reaction dynamics in a kinetic region

1984 ◽  
Vol 49 (1) ◽  
pp. 170-178 ◽  
Author(s):  
Karel Klusáček
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Catalytic Reaction ◽  
Reaction Dynamics ◽  
Methanol Dehydration ◽  
Balance Equations ◽  
Kinetic Region ◽  
Lumped Parameters ◽  
Relaxation Curves ◽  
Calculation Procedures

The method of numerical simulation of a catalytic system dynamics with lumped parameters is reported. Appropriate balance equations have been derived and suitable calculation procedures are discussed. Numerical example of simulation of the catalytic methanol dehydration dynamics is presented and calculated relaxation curves are compared with experimental data obtained earlier.

scholarly journals A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

2018 ◽  
Vol 11 (4) ◽  
pp. 2339-2367 ◽  
Author(s):  
Michael V. Klibanov ◽  
Nikolay A. Koshev ◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen ◽  
Aaron Brettin ◽  
...  
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Numerical Method ◽  
Coefficient Inverse Problem ◽  
Single Measurement

scholarly journals Convolution and deconvolution: two mathematical tools to help performing tests in research and industry

2021 ◽  
Vol 12 ◽  
pp. 6
Author(s):  
Jean-Pierre Fanton
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Electrical Energy ◽  
Integral Transforms ◽  
Physical Measurement ◽  
Photographic Images ◽  
Test Standards ◽  
Energy Networks ◽  
The Third ◽  
The Subject

The concepts of convolution and deconvolution are well known in the field of physical measurement. In particular, they are of interest in the field of metrology, since they can positively influence the performance of the measurement. Numerous mathematical models and computer developments dedicated to convolution and deconvolution have emerged, enabling a more efficient use of experimental data; this in sectors as different as biology, astronomy, manufacturing and energy industries. The subject finds today a new topicality because it has been made accessible to a large public for applications such as processing photographic images. The purpose of this paper is to take into account some recent evolutions such as the introduction of convolution methods in international test standards. Thus, its first part delivers a few reminders of some associated definitions. They concern linear systems properties, and integral transforms. If convolution, in most cases, does not create major calculation problems, deconvolution on the contrary is an inverse problem, and as such needs more attention. The principles of some of the methods available today are exposed. In the third part, illustrations are given on recent examples of applications, belonging to the domain of electrical energy networks and photographic enhancement.

scholarly journals Higher Education in VUCA-World: New Metaphor of University

2019 ◽  
Vol 5 (2) ◽  
pp. 31
Author(s):  
Tatiana V. Korsakova
Keyword(s):  
Rate Of Change ◽  
Reference Points ◽  
Organizational Systems ◽  
Modern World ◽  
Dynamic Changes ◽  
The World ◽  
Organizational Ties ◽  
State Of Affairs ◽  
The University ◽  
Current Reality

In the 21st century universities cannot survive if they simply support an established state of affairs because the modern world is described by the following relation: the rate of change tends to infinity; the transition interval tends to zero. This leads to the fact that universities cannot rest on their laurels and not change. The university that cannot construct new organizational ties loses its magnitude forever. The article describes the specific features of the new reality which are of great importance for building modern organizational systems in universities. Reference points have been being identified and that allows presenting the direction of development that meets the new requirements of the modern world to people, processes, technologies, structures, and systems accordingly to the university. Analysis of the selected reference points leads to the conclusion that in the conditions of dynamic changes and uncertainty of the world the concrete way of the vision of the university’s situation is to see it as if in the light of the modern world. A metaphor is presented, which is based on a comparison of the university internal world with the current reality. It is expressed by the acronym VUCA.

scholarly journals Kinematic parameters of goats walking on different slopes and biomimetic walking mechanisms

2017 ◽  
Author(s):  
Fu Zhang ◽  
Yafei Wang ◽  
Wei Wang ◽  
Keyword(s):  
Experimental Data ◽  
Theoretical Basis ◽  
High Speed ◽  
Rate Of Change ◽  
Kinematic Parameters ◽  
High Speed Video ◽  
Experimental Image ◽  
Displacement Speed ◽  
Walking Mechanism ◽  
Uphill Walking

A comparative analysis of the kinematic parameters of a goat on different slopes was conducted to study the kinematic parameters of goats on different slopes with walking mechanics. The uphill walking processes on different slopes (0°, 5°, 10°, 15°, 20°, 25° and 30°) were recorded by a high speed video system (VRI Phantom M110). The experimental image results were processed and analyzed using PCC and MATLAB software. The kinematic parameters were obtained from the goat walking on different slopes; these parameters are the changes of centroid with displacement, speed with time, and acceleration with time. As the gradient in the uphill process increases, the range of centroid fluctuation ranges from 0.079 to 0.59 and the rate of change ranges from 0.4 to 2.2 m/s, while the acceleration of the goat slope decreases. The present research can provide theoretical basis and experimental data for the design of a biomimetic agricultural slope walking mechanism.

Solving the inverse problem for aggregation in activated sludge flocculation using a population balance framework

2007 ◽  
Vol 56 (6) ◽  
pp. 95-103 ◽  
Author(s):  
I. Nopens ◽  
N. Nere ◽  
P.A. Vanrolleghem ◽  
D. Ramkrishna
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Particle Size ◽  
Activated Sludge ◽  
Predictive Power ◽  
Population Balance ◽  
Model Structure ◽  
Forward Simulation ◽  
Floc Size

Many systems contain populations of individuals. Often, they are regarded as a lumped phase, which might, for some applications, lead to inadequate model predictive power. An alternative framework, Population Balance Models, has been used here to describe such a system, activated sludge flocculation in which particle size is the property one wants to model. An important problem to solve in population balance modelling is to determine the model structure that adequately describes experimentally obtained data on for instance, the time evolution of the floc size distribution. In this contribution, an alternative method based on solving the inverse problem is used to recover the model structure from the data. In this respect, the presence of similarity in the data simplifies the problem significantly. Similarity was found and the inverse problem could be solved. A forward simulation then confirmed the quality of the model structure to describe the experimental data.

Modelling Choice Decision Time

1980 ◽  
Vol 24 (1) ◽  
pp. 76-79
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Reaction Time ◽  
Choice Reaction Time ◽  
Memory Search ◽  
Decision Time ◽  
Rate Of Change ◽  
Search Process ◽  
Exponential Law ◽  
Choice Decision

A power/exponential law of choice reaction time is proposed as an alternative to the classical Hick-Hyman's law and the Sternberg's law of memory search. A reanalysis of some experimental data, including those by Hick, Hyman and Sternberg, indicates that this alternative law provides at least as good fits to experimental data as do the Hick-Hyman's and Sternberg's laws. Some important implications of this finding are pointed out concerning the rate of change of information and the nature of the memory search process for the Sternberg's paradigm.

Sign in / Sign up

Export Citation Format

Share Document