Uncovering Oscillations, Complexity, and Chaos in Chemical Kinetics Using Mathematica

Ferreira, Márcia M. C.; Ferreira, Wilson Castro; Lino, Antonio C.S.; Porto, Maria Eugênia Garcia

doi:10.1021/ed076p861

Cited by 8 publications

(6 citation statements)

References 6 publications

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“…Despite being absent from most chemistry curricula (as surveyed by Novak), this representation is not completely unknown. For example, it is common to plot the concentrations of the time-oscillating species in the same plane to depict the evolution of the Lotka–Volterra reaction. , Similarly, the idea of “attainable region theory” in the chemical engineering literature uses a similar concentration vector representation to identify kinetic processes that reach sets of achievable compositions in a reactor …”

Section: Discussionmentioning

confidence: 99%

“…For example, it is common to plot the concentrations of the timeoscillating species in the same plane to depict the evolution of the Lotka−Volterra reaction. 14,15 Similarly, the idea of "attainable region theory" in the chemical engineering literature uses a similar concentration vector representation to identify kinetic processes that reach sets of achievable compositions in a reactor. 16 Figure 2 depicts an example a concentration space diagram of three stock solutions, denoted (a), (b), and (c) for a two-solute system.…”

Section: Prelude: Solution Mixing On a Number Linementioning

confidence: 99%

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Solution Mixing Calculations as a Geometry, Linear Algebra, and Convex Analysis Problem

Schrier

2021

J. Chem. Educ.

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Multicomponent solution calculations can be complicated for students and practiced chemists alike. This article describes how to simplify the calculations by representing a solution’s composition as a point in a “concentration space,” whose axes are the concentrations of each solute. The graphical representation of mixing processes in a concentration space diagram enables qualitative insights such as whether a mixture can be made from a set of stock solutions and the relative volume proportions needed, solely by visual inspection and without detailed calculation. The diagrams correspond to elementary linear algebra equations which facilitates the specification of quantitative calculations. The relationship of the solution mixing problem to convex analysis is discussed. Example applications of this approach to problems of calculating the composition following mixing, determining the volumes to use to create a specified mixture, selecting a set of stock solutions maximizing the number of possible unique mixtures that can be made, random experiment sampling, and common-ion effect problems are demonstrated.

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Section: Discussionmentioning

confidence: 99%

Section: Prelude: Solution Mixing On a Number Linementioning

confidence: 99%

Solution Mixing Calculations as a Geometry, Linear Algebra, and Convex Analysis Problem

Schrier

2021

J. Chem. Educ.

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“…The modules 3 consist of five initial exercises to assist students in understanding the concepts of: (1) first and 2 nd order reactions, (2) equilibrium, (3) rate-determining step, (4) steady-state approximation, (5) enzyme kinetics. The first example is a tutorial helping students learn about the Berkeley Madonna code.…”

Section: Modules and Pedagogiesmentioning

confidence: 99%

“…For example, for the first-order reaction, the conventional way of building the model looks like the following graph ( Figure- 2 It must be acknowledged that dynamic software other than Berkeley Madonna also has 'alias' like feature such as shadow variable in Vensim and ghost variable. 3 All reactions discussed in this manuscript refers to elementary step reactions that actually happen in the molecular level. Differential equations to represent the rate of appearance or disappearance can therefore be written as represented in each molecular elementary step reaction.…”

Section: First Order and 2 Nd Order Reactionmentioning

confidence: 99%

Teaching Kinetics through Differential Equations Constructed with a Berkeley Madonna(TM) Flow Chart Model

Chen¹

2018

JOCSE

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The alias feature of the Berkeley Madonna platform allows this author to create a chemical kinetics project manual for students, who create flow charts solving almost all kinetics problems using rate equations. The versatile and powerful platform allows students to explore any chemical kinetics problems, from simple (e.g. 1 st or 2 nd order kinetics) to complex (e.g. stratosphere ozone depletion, the Lotka-Volterra mechanism), bypassing complicated syntax that is required by most of powerful mathematical programs.This kinetics manual has been successfully implemented in Physical Chemistry at UW-Green Bay in the fall semester of 2017, with the students' success rate greater than 80%.

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“…Chaos phenomena also has other uses. For example, nonlinear circuits (Kandangath et al, 2007; Li et al, 2013), chemical reactions (Ferreira et al, 1999; Gaspard, 1999), power electronics (Ni et al, 2015; Wu et al, 2015), laser (Jiang and Huang, 2013) and robotics (Zang et al, 2016); study and research on its inherent characteristics and control are of particular importance. The control and synchronization of chaos has attracted many researchers’ attention over the past three decades, and it is still interesting to many others (Wei et al, 2015b, 2016).…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation and synchronization of hyper chaotic Lu system with disturbance input and uncertainty using two under-actuated control signals

Sabaghian

Balochian

2018

Transactions of the Institute of Measurement and Control

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In this paper, synchronization of two hyper chaotic Lu systems with unknown factors, such as uncertainty and disturbance, and less control signals with respect to system’s dimensions by applying an adaptive sliding mode controller is presented. In this research, firstly, an integral sliding mode controller is designed for synchronization of two hyper chaotic Lu systems with known parameters. Secondly, a controller is used to synchronize two hyper chaotic Lu systems with unknown parameters; in this case, unknown parameters are estimated using an adaptive rule. As a measure of performance, stability of the proposed control method is proved using the Lyapunov stability method. Numerical simulations validate the stabilization and synchronization.

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Uncovering Oscillations, Complexity, and Chaos in Chemical Kinetics Using Mathematica

Cited by 8 publications

References 6 publications

Solution Mixing Calculations as a Geometry, Linear Algebra, and Convex Analysis Problem

Solution Mixing Calculations as a Geometry, Linear Algebra, and Convex Analysis Problem

Teaching Kinetics through Differential Equations Constructed with a Berkeley Madonna(TM) Flow Chart Model

Parameter estimation and synchronization of hyper chaotic Lu system with disturbance input and uncertainty using two under-actuated control signals

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