Parameter estimates in differential equation models for chemical kinetics

Winkel, Brian

doi:10.1080/0020739x.2010.500806

Cited by 11 publications

(6 citation statements)

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“…Students often encounter difficulties when studying differential equations used to understand the dynamics of a chemical system . Also, fitting of experimental data to complex kinetic models (e.g., beyond simple first- and second-order reactions) is rarely discussed in standard chemistry curricula .…”

Section: Introductionmentioning

confidence: 99%

“…5−7 Students often encounter difficulties when studying differential equations used to understand the dynamics of a chemical system. 8 Also, fitting of experimental data to complex kinetic models (e.g., beyond simple firstand second-order reactions) is rarely discussed in standard chemistry curricula. 9 In this regard, complex kinetic schemes are often simplified employing the steady-state approximation, a concept commonly taught in introductory physical chemistry courses.…”

Section: ■ Introductionmentioning

confidence: 99%

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Experience-Based Learning Approach to Chemical Kinetics: Learning from the COVID-19 Pandemic

et al. 2020

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Herein, we present an experience-based learning approach that uses the COVID-19 pandemics knowledge about virus spread and epidemics to establish an analogy between a simple epidemics modelthe SIR model (susceptible–infected–removed), and a second-order autocatalytic reaction with subsequent catalyst deactivation. Our approach provides a simple and engaging way for students to learn chemical kinetics from a current situation (the pandemic) while presenting them with programming tools to numerically solve any system of differential equations that may result from more complex chemical kinetic schemes. We include the option to fit experimental data to extract meaningful rate constants. Following Kolb’s cycle, we first establish the theoretical background of chemical kinetics and the SIR model and describe the analogy. Then, we propose the use of MATLAB and Python to numerically solve the system of differential equations associated with this model and plot the results showing the behavior of the system when changing the constants that describe the process, making the analogy with chemical kinetic constants. Finally, we fitted experimental data from the COVID-19 pandemic (up to early June 2020) to test the model and discuss the goodness of the fitting, the fitting parameters, and the utility of real kinetic data.

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Section: Introductionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Experience-Based Learning Approach to Chemical Kinetics: Learning from the COVID-19 Pandemic

et al. 2020

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“…As a result, the students achieve a low level of conceptual understanding of the models describing chemical kinetics. 3,5,9,10 The current literature on education considers reaction kinetics as understudied within Chemical Education Research, where traditional teaching practices remain. 5,11 Some efforts have been made to solve these difficulties, either by developing educational software, designing experiments to address the most bewildering concepts, or launching new pedagogical strategies.…”

Section: ■ Introductionmentioning

confidence: 99%

Analogy between Consecutive Reaction Kinetics and the Spread of COVID-19 as a Student-Centered Learning Approach

Almanza-Arjona

Durán–Álvarez

Fernández-Urtusástegui

et al. 2022

J. Chem. Educ.

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The reaction rate and rate law are chemical kinetics concepts that undergraduate students have difficulty understanding and applying in real life. A further challenge is the overall reaction rate of consecutive reactions. Herein we present a creative teaching practice using the analogy-based approach to exploit the similarities between the chemical kinetics of consecutive reactions involved in ethanol oxidation and the model employed to describe the COVID-19 outbreak. Students conducted the mathematical modeling using open online software. Fitting the epidemic data from four different countries during the first wave of the COVID-19 pandemic to the SIR model and comparing the results with the model of ethanol oxidation brought students insight into the effects of kinetic parameters and triggered a discussion on conceptual kinetic fundamentals. This teaching approach sets up an environment where students can build knowledge that accounts for their pandemic experience, fostering mathematical and computational skills along with data analysis and interpretation that promotes a deeper understanding of the phenomena implicated in the kinetics of consecutive reactions. Mathematical modeling activities are here to stay and will continue gaining relevance in undergraduate kinetics courses, even without the lockdown, therefore the development of these kinds of learning strategies is of high significance worldwide.

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“…However, such techniques have been used for estimating parameters of differential equations. For example, in [101] differential equations are promoted as an important tool in studying chemical reactions. Note that, the assumptions made for obtaining such equations are very similar to these made when building models for large population system using the mean-field approach.…”

Section: Differential Equation Modelmentioning

confidence: 99%

“…Note that, the assumptions made for obtaining such equations are very similar to these made when building models for large population system using the mean-field approach. The author of [101] proposes to use techniques based on squared error to estimate parameters of the obtained differential equations and presents evidence that this method works well for these equations. More advanced techniques for obtaining the parameters of differential equations were proposed.…”

Section: Differential Equation Modelmentioning

confidence: 99%

Model-checking mean-field models : algorithms & applications

Kolesnichenko¹

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Large systems of interacting objects are highly prevalent in today's world. Such system usually consist of a large number of relatively simple identical objects, and can be observed in many different field as, e.g., physics (interactions of molecules in gas), chemistry (chemical reactions), epidemiology (spread of the infection), etc. In this thesis we primarily address large systems of interacting objects in computer science, namely, computer networks. Analysis of such large systems is made difficult by the state space explosion problem, i.e., the number of states of the model grows exponentially with the number of interacting objects. In this thesis we tackle the state-space explosion problem by applying meanfield approximation, which was originally developed for models in physics, like the interaction of molecules in a gas. The mean-field method works by not considering the state of each individual object separately, but only their average, i.e., what fraction of the objects are in each possible state at any time. It allows to compute the exact limiting behaviour of an infinite population of identical objects, and this limiting behaviour is a good approximation, even when the number of objects is not infinite but sufficiently large. In this thesis we provide the theoretical background necessary for applying the mean-field method and illustrate the approach by a peer-to-peer Botnet case study. This thesis aims at formulating and analysing advanced properties of large systems of interacting objects using fast, efficient, and accurate algorithms. We propose to apply model-checking techniques to mean-field models. This allows (i) defining advanced properties of mean-field models, such as survivability, steady-state availability, conditional instantaneous availability using logic; and (ii) automatically checking these properties using model-checking algorithms. Existing model-checking logics and algorithms can not directly be applied to mean-field models since the model consist of two layers: the local level, describing the behaviour of a randomly chosen individual object in a large system, and the global level, which addresses the overall system of all viii interacting objects. Therefore, we motivate and define two logics, called Mean Field Continuous Stochastic Logic (MF-CSL), and Mean-Field Logic (MFL), for describing properties of systems composed of many identical interacting objects, on both the local and the global level. We present model-checking algorithms for checking both MF-CSL and MFL properties, and illustrated these algorithms using an extensive example on virus propagation in a computer network. We discuss the differences in the expressiveness of these two logics as well as their possible combination. Additionally, we combine the mean-field method with parameter fitting techniques in order to model real-world large systems, and obtain a better understanding of the behaviour of such systems. We explain how to build a mean-field model of the system, and how to estimate the corresponding parameter valu...

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Parameter estimates in differential equation models for chemical kinetics

Cited by 11 publications

References 0 publications

Experience-Based Learning Approach to Chemical Kinetics: Learning from the COVID-19 Pandemic

Experience-Based Learning Approach to Chemical Kinetics: Learning from the COVID-19 Pandemic

Analogy between Consecutive Reaction Kinetics and the Spread of COVID-19 as a Student-Centered Learning Approach

Model-checking mean-field models : algorithms & applications

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