electrochemical oscillations

Co-Authorship I hereby declare that this thesis incorporates material that is result of joint research, as follows: Chapters 2 and 3 of the thesis was co-authored and under the supervision of Dr. Jichang Wang. In all cases, the key ideas, primary contributions, experimental designs, data analysis, interpretation, and writing were performed by the author. Dr. Jichang Wang provided contributions through feedback, revisions, and discussion to the manuscripts. I am aware of the University of Windsor Senate Policy on Authorship and I certify that I have properly acknowledged the contribution of other researchers to my thesis, and have obtained written permission from each of the co-author(s) to include the above material(s) in my thesis. I certify that, with the above qualification, this thesis, and the research to which it refers, is the product of my own work. II. Previous Publication This thesis includes 2 original papers that have been previously published/submitted for publication in peer reviewed journals, as follows: Thesis Chapter Publication title/full citation Publication status* Chapter 2 Bifurcations Induced by the Size of Glassy Carbon Electrodes during the Electrochemical Oxidation of Bisulfite. 2019.

The nonlinear dynamics of an oscillatory Ni electrodissolution-hydrogen ion reduction system are explored in a multi-electrode anode-single cathode system. A mathematical analysis of the charge balance equations reveals that the coupling scheme is similar to dynamical quorum sensing, where the number of anode wires a ects a parameter related to the population density. In a parameter region where the large population exhibits stationary behavior, with su ciently strong coupling (with small individual resistances attached to the anode wires), synchronized oscillations emerge abruptly with decreasing the number of anodes. Therefore, an "inverse" dynamical quorum sensing takes place. With weak coupling the transition is gradual. The experiments are supported by numerical simulation of a kinetic model of the process. The results thus show that the description of nontrivial cathode-anode interactions in the form of dynamical quorum sensing provides an e cient way of analyzing the dynamical response of complex, interacting electrochemical reactions.

This paper synergize the newly discovered generalised geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper also illustrates the concept of the “TRIADS of Metallic Means”.  The Metallic Means and their TRIADS can be geometrically substantiated, in an intriguing manner, as described in this paper.

This paper introduces certain new geometric aspects of the Metallic Ratios. Each Metallic Ratio is observed to be closely associated with a special right triangle, which provides the precise fractional expression of that Ratio. This work explicates the geometric substantiation of Metallic Ratio, on basis of the right angled triangle which is the quintessential form of that particular ratio.

This paper introduces the concept of special right angled triangles those epitomize the different Metallic Ratios. These right triangles not only have the precise Metallic Means embedded in all their geometric features, but they also provide the most accurate geometric substantiation of all Metallic Means. These special right triangles manifest the corresponding Metallic Ratios more holistically than the regular pentagon, octagon or tridecagon, etc

This paper introduces the perfect complementary relationship between the 3-4-5 Pythagorean triangle and the 1:2: right-angled triangle. The classical geometric intimacy between these two right triangles not only provides for the ultimate geometric substantiation of Golden Ratio, but it also reveals the fundamental Pi: Phi correlation (π: φ), with an extreme level of precision, and which is firmly based upon the classical geometric principles.

The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means.

This paper introduces the perfect complementary relationship between the 3-4-5 Pythagorean triangle and the 1:2: right-angled triangle. The classical geometric intimacy between these two right triangles not only provides for the ultimate geometric substantiation of Golden Ratio, but it also reveals the fundamental Pi: Phi correlation (π: φ), with an extreme level of precision, and which is firmly based upon the classical geometric principles.

This paper introduces the perfect complementary relationship between the 3-4-5 Pythagorean triangle and the 1:2: √5 right-angled triangle. The classical geometric intimacy between these two right triangles not only provides for the ultimate geometric substantiation of Golden Ratio, but it also reveals the fundamental Pi: Phi correlation (π: φ), with an extreme level of precision, and which is firmly based upon the classical geometric principles.

This paper synergizes the newly discovered geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper also illustrates the concept of the "TRIADS of Metallic Means". The Metallic Means and their TRIADS can be geometrically substantiated, in an intriguing manner, as described herein.

This paper introduces the unique geometric features of 1:2:√5 right triangle, which is observed to be the quintessential form of Golden Ratio (φ). The 1:2:√5 triangle, with all its peculiar geometric attributes described herein, turns out to be the real 'Golden Ratio Triangle' in every sense of the term. This special right triangle also reveals the fundamental Pi:Phi (π:φ) correlation, in terms of precise geometric ratios, with an extreme level of precision. Further, this 1:2:√5 triangle is found to have a classical geometric relationship with 3-4-5 Pythagorean triple. The perfect complementary relationship between1:2:√5 triangle and 3-4-5 triangle not only unveils several new aspects of Golden Ratio, but it also imparts the most accurate π:φ correlation, which is firmly premised upon the classical geometric principles. Moreover, this paper introduces the concept of special right triangles; those provide the generalised geometric substantiation of all Metallic Means.

This paper introduces the perfect complementary relationship between the 3-4-5 Pythagorean triangle and the 1:2: √5 right-angled triangle. The classical geometric intimacy between these two right triangles not only provides for the ultimate geometric substantiation of Golden Ratio, but it also reveals the fundamental Pi: Phi correlation (π: φ), with an extreme level of precision, and which is firmly based upon the classical geometric principles.

The series arrangement of identical electrolytic cells having copper anodes and chloride electrolyte is found to
demonstrate an extremely asymmetric and reciprocally oscillating voltage drop across the series of these coupled cells.
The origin of this phenomenon is attributed to the presence of different extents of cuprous oxide phase on surfaces of
the anodes of different cells, in the series. Such series arrangement of multiple electrolytic cells introduces a novel
phenomenon of the non-linear temporal behaviour of coupled cells. Most importantly, such configuration proves the
very existence of adsorbed Cu2O on surface of copper anode, in acidic chloride media. And hence, it signifies the
important role of Cu2O in the electro-dissolution mechanism of copper anode, even at lower pH values.