Journal Of Applied Mathematics Research Articles

A Hybrid Electrochemical Multi-Particle Model for Lithium-Ion Batteries

Over the years, physics-based models have proven to be effective tools in understanding the behavior of lithium-ion batteries, which is favorable for enhancing their design and performance. Among the various physics-based models, the Doyle-Fuller-Newman (DFN) model [1] has emerged as the most widely used model due to its ability to simulate battery behavior accurately. However, it has been observed that the DFN model performs poorly in the relaxation region after discharge, which might result in inaccurate battery simulations. The Multiple-Particle DFN (MP-DFN) model [2] has been proposed to address this issue. The MP-DFN model uses multiple electrode particle sizes to allow internal concentration heterogeneities, accurately capturing the slow diffusion processes. However, the MP-DFN model comes at a relatively high computational cost. The diffusion process within the solid electrode particles, typically modeled by Fick’s 2nd law, is the most computationally expensive part of the DFN model. Multiple particle sizes will increase the computational burden, leading to a longer calculation time. Padé approximations have been suggested to replace the commonly used finite difference method (FDM), reducing the computational burden [3]. However, this simplification may not work for larger particle sizes and/or low diffusion coefficients. To address these challenges, a Hybrid-Multiple-Particle DFN (HMP-DFN) model has been developed in this study. The model uses a combination of the FDM and Padé approximation for the various particle sizes in the electrodes. The scaled diffusion length [4] determines whether the FDM or Padé method for a specific particle in the electrode should be applied.A simulative comparison has been performed between MP-DFN, HMP-DFN, and Padé approximation using the fourth order for all particles (PMP-DFN) and the DFN with one particle size using the average value from the particle distribution. In this comparison, the MP-DFN model has been used as a reference as it is considered the most accurate. The main results are shown in Fig.1, which reveal that the DFN model gives the largest simulation errors, especially at the cut-off and relaxation parts. The PMP-DFN shows a relatively good agreement with the MP-DFN and is 60% faster in simulation time. However, relatively large errors can be observed at the beginning of discharge and in the relaxation region, resulting in a root mean square error (RMSE) of 0.4 mV and a maximum error of 8 mV. The HMP-DFN model shows remarkable accuracy in comparison to the MP-DFN model. It neglects the errors from the PMP-DFN model at the initial stage and decreases the error in the relaxation significantly, giving an RMSE below 0.06 mV, a maximum error below 1 mV, and a more than 40% faster simulation time in comparison to the MP-DFN model. Therefore, due to the decreased computation time with respect to the MP-DFN and the low simulation error, the HMP-DFN model is a suitable and practical tool for accurately simulating battery behavior and optimizing battery design.[1] M. Doyle, J. Newman, The use of mathematical modeling in the design of lithium/polymer battery systems, Electrochimica Acta. 40 (1995) 2191–2196, doi:10.1016/0013-4686(95)00162-8.[2] T.L. Kirk, C.P. Please, S.J. Chapman, Physical Modelling of the Slow Voltage Relaxation Phenomenon in Lithium-Ion Batteries, J. Electrochem. Soc. 168 (2021) 060554, doi:10.1149/1945-7111/ac0bf7.[3] G. Fan, K. Pan, M. Marcello, A comparison of model order reduction techniques for electrochemical characterization of Lithium-ion batteries, 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan (2015) 3922-3931, doi:10.1109/CDC.2015.7402829.[4] K. H. Chayambuka, G. Mulder, D. Danilov, P. Notten, A Hybrid Backward Euler Control Volume Method to Solve the Concentration-Dependent Solid-State Diffusion Problem in Battery Modeling, Journal of Applied Mathematics and Physics (2020), doi:10.4236/jamp.2020.86083. Fig. 1. Discharge voltage curves (1.5C) and corresponding relaxation parts simulated with various model types (a); the error curves of the comparison between the HMP-DFN, PMP-DFN, and DFN with the MP-DFN (b). Figure 1

The effect of pore-scale contaminant distribution on the reactive decontamination of porous media

AbstractA porous material that has been contaminated with a hazardous chemical agent is typically decontaminated by applying a cleanser solution to the surface and allowing the cleanser to react into the porous material, neutralising the agent. The agent and cleanser are often immiscible fluids and so, if the porous material is initially saturated with agent, a reaction front develops with the decontamination reaction occurring at this interface between the fluids. We investigate the effect of different initial agent configurations within the pore space on the decontamination process. Specifically, we compare the decontamination of a material initially saturated by the agent with the situation when, initially, the agent only coats the walls of the pores (referred to as the ‘agent-on-walls’ case). In previous work (Luckins et al., European Journal of Applied Mathematics, 31(5):782–805, 2020), we derived homogenised models for both of these decontamination scenarios, and in this paper we explore the solutions of these two models. We find that, for an identical initial volume of agent, the decontamination time is generally much faster for the agent-on-walls case compared with the initially saturated case, since the surface area on which the reaction can occur is greater. However for sufficiently deep spills of contaminant, or sufficiently slow reaction rates, decontamination in the agent-on-walls scenario can be slower. We also show that, in the limit of a dilute cleanser with a deep initial agent spill, the agent-on-walls model exhibits behaviour akin to a Stefan problem of the same form as that arising in the initially saturated model. The decontamination time is shown to decrease with both the applied cleanser concentration and the rate of the chemical reaction. However, increasing the cleanser concentration is also shown to result in lower decontamination efficiency, with an increase in the amount of cleanser chemical that is wasted.

Issue Information: ZAMM 6/2023

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 6 e202302009 ISSUE INFORMATIONFree Access Issue Information: ZAMM 6/2023 First published: 08 June 2023 https://doi.org/10.1002/zamm.202302009AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume103, Issue6June 2023e202302009 RelatedInformation

Contents

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 6 e202302010 CONTENTSFree Access Contents First published: 08 June 2023 https://doi.org/10.1002/zamm.202302010AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume103, Issue6June 2023e202302010 RelatedInformation

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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 5 e202302008 CONTENTSFree Access Contents First published: 07 May 2023 https://doi.org/10.1002/zamm.202302008AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume103, Issue5May 2023e202302008 RelatedInformation

Issue Information: ZAMM 5/2023

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 5 e202302007 ISSUE INFORMATIONFree Access Issue Information: ZAMM 5/2023 First published: 07 May 2023 https://doi.org/10.1002/zamm.202302007AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume103, Issue5May 2023e202302007 RelatedInformation

Issue Information: ZAMM 4/2023

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 4 e202302005 ISSUE INFORMATIONFree Access Issue Information: ZAMM 4/2023 First published: 10 April 2023 https://doi.org/10.1002/zamm.202302005AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume103, Issue4Special Issue: Mechanical Models in Electrodynamics – State of the ArtApril 2023e202302005 RelatedInformation

Contents

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 3 e202302002 CONTENTSFree Access Contents First published: 10 March 2023 https://doi.org/10.1002/zamm.202302002AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume103, Issue3March 2023e202302002 RelatedInformation

Issue Information: ZAMM 3/2023

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 103, Issue 3 e202302001 ISSUE INFORMATIONFree Access Issue Information: ZAMM 3/2023 First published: 10 March 2023 https://doi.org/10.1002/zamm.202302001AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume103, Issue3March 2023e202302001 RelatedInformation

Contents

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 102, Issue 5 e202202009 CONTENTSFree Access Contents First published: 09 May 2022 https://doi.org/10.1002/zamm.202202009AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume102, Issue5May 2022e202202009 RelatedInformation

Erratum to “Positive Solutions for a Class of Quasilinear Schrödinger Equations with Nonlocal Term” [Journal of Applied Mathematics and Physics (2022) 347-359

The original online version of this article (Liao, P., Ping, R. and Chen, S. (2022) Positive Solutions for a Class of Quasilinear Schr?dinger Equations with Nonlocal Term. Journal of Applied Mathematics and Physics, 10, 347-359. https://doi.org/10.4236/jamp.2022.102027) needs some further amendments and clarification.

Further results on LCD generalized Gabidulin codes

<abstract><p>Linear complementary dual (abbreviated LCD) generalized Gabidulin codes (including Gabidulin codes) have been recently investigated by Shi and Liu et al. (Shi et al. IEICE Trans. Fundamentals E101-A(9):1599-1602, 2018, Liu et al. Journal of Applied Mathematics and Computing 61(1): 281-295, 2019). They have constructed LCD generalized Gabidulin codes of length $ n $ over $ \mathbb{F}_{q^{n}} $ by using self-dual bases of $ \mathbb{F}_{q^{n}} $ over $ \mathbb{F}_{q} $ when $ q $ is even or both $ q $ and $ n $ are odd. Whereas for the case of odd $ q $ and even $ n $, whether LCD generalized Gabidulin codes of length $ n $ over $ \mathbb{F}_{q^{n}} $ exist or not is still open. In this paper, it is shown that one can always construct LCD generalized Gabidulin codes of length $ n $ over $ \mathbb{F}_{q^{n}} $ for the case of odd $ q $ and even $ n $.</p></abstract>

More Accurate Approximate Analytical Solution of Nonlinear Oscillators

A more accurate approximate analytical solution of nonlinear oscillator has been provided by using modified energy balance method. The results have been compared with those obtained by homotopy perturbation method (HPM) and a new homotopy perturbation method (NHPM). It has been observed that the results obtained by proposed method are better than those of HPM as well as its new version. Moreover the method provides better results than other existing methods. Cite as M. H. U. Molla, M. Z. Alam, Nazmul Sharif, & M. S. Alam. (2020). More Accurate Approximate Analytical Solution of Nonlinear Oscillators. Journal of Applied Mathematics and Statistical Analysis, 1(3), 1–7. http://doi.org/10.5281/zenodo.4311134

Exactness: A Generalized Approach to Solve 1st order 1st Degree Ordinary Differential Equations

Numerous sorts of 1 st order -1 st degree ordinary differential equation (ODE) are there along with their well-designed solution techniques depending on the assemblies of the equations. In this paper it is unveiled a single well-established solution procedure, exactness method, that can be used to solve all regular types of 1 st order- 1 st degree ODE. The transformation to exactness from the regular form has been demonstrated notionally and explicated with solved cases. Cite as Amena Ferdosui, M. Mostafizur Rahman, & Sajjadul Bari. (2020). Exactness: A Generalized Approach to Solve 1st order 1st Degree Ordinary Differential Equations. Journal of Applied Mathematics and Statistical Analysis, 1(3), 1–6. http://doi.org/10.5281/zenodo.4312261

Editorial

Celebrating the 100th anniversary of the founding of the ZAMM (Journal of Applied Mathematics and Mechanics) reasonably means that the focus of this year's issues is on some important persons and papers from the last century. This ZAMM jubilee is however an exceptional case: we celebrate this year during the COVID-19 pandemic that has partly paralyzed our ordinary and scientific life. With respect to this worldwide crisis, this issue features a special paper related to the pandemic titled “On build-up of epidemiologic models–development of a SEI3RSD model for the spread of SARS-CoV-2”. This paper was prepared by PD.Dr.rer.nat.habil. Michael Wolff, who is a retired scientist from the University of Bremen, Germany. The study investigates essential steps for the build-up of models for the description of the spread of infectious diseases. We have to recognize that the handling of any pandemic is not only a medical problem: beside medical and virologic concerns, economic, sociologic and many other aspects should be taken into account. The last one also includes mathematical points of view.

Evaluation of the Public Health Financing and National Health Insurance Scheme Policy in Nigeria

The inevitability of good healthcare system in national development depends on every government’s commitment in ensuring proper healthcare services to its populace. However, extant literature have focused on the effects of health care system financing without factoring the significance of its insurance scheme components. This study therefore evaluated the effect of public health financing on national health insurance scheme (NHIS) policy in Nigeria. Multistage (clustered and incident) sampling technique was employed to select the sample size of 399 individuals from a population of 113,853 residents of Ogbomoso North Local Government area. Primary data were collected using structured questionnaire which was administered on sampled respondents. Variables included income, education, settlement of patients’ bills, patient patronage, occupation, religion, and years of registration. Chi-square was used to assess the significance of public health financing on NHIS. Multiple regression analysis was used to analyze the effect of socio-cultural characteristics on NHIS adoption. The results showed that NHIS don’t settle their patients’ bill on time (42.9%). Also, patients’ patronage was low (10%) in most of NHIS accredited hospitals (57.1%). The analysis showed that p ublic health financing had effect on NHIS (χ 2 =14.000; p = 0.007). It was also revealed that socio-cultural characteristics such as education, income and sex had significant effect on NHIS adoption (R 2 = 0.624, F-ratio =15.344; p = 0.001). This study concluded that public health financing had effect on NHIS and that adoption of NHIS hinged on the socio-cultural characteristics. This study recommended that government should increase the awareness of NHIS so that larger population can benefit from it. Also, NHIS should ensure prompt payment of NHIS patients’ medical bills to encourage health facilities providers. Cite as Agboola, Oladayo Christiana, & Usman, Owolabi.A. (2020). Evaluation of the Public Health Financing and National Health Insurance Scheme Policy in Nigeria. Journal of Applied Mathematics and Statistical Analysis, 1(2), 1–7. http://doi.org/10.5281/zenodo.4067745

Editorial

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 100, Issue 10 e202002041 EDITORIALFree Access Editorial First published: 19 October 2020 https://doi.org/10.1002/zamm.202002041AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Lothar Collatz passed his first mathematics university exam in Berlin in 1933 supervised by Richard von Mises, who founded Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) in 1921. Since his graduation L. Collatz published short contributions [1-3] in ZAMM that summarized his presentations from the annual GAMM conferences. His first regular article appeared in ZAMM in 1935, right after the completion of his PhD [4]. In his long career (from obtaining his habilitation in 1937 in Karlsruhe, being a researcher in Karlsruhe and Darmstadt until 1943, when he received a professorship in Hannover and then from 1952 in Hamburg until his retirement 1978) he continuously published in ZAMM contributing over 35 articles. Lothar Collatz (1910–1990, photography by Elfriede Liebenow) His work had a major impact on the development of numerical mathematics, particularly by his supervision of 42 PhD students and his involvement in 24 habilitation procedures. Before he moved to Hamburg, all his positions were at Technical Universities. His research is closely related to applications of numerical mathematics in mechanics. Many of his contributions to ZAMM are directly motivated by specific computational engineering challenges for membranes, plates, and bars [2, 5-8] at a time well before the development of modern computers. His engagement for the collaboration of applied mathematics and mechanics was continuously embedded in his activities in GAMM: he was involved in both the organization and management of the GAMM society, especially as President from 1964 to 1966 [9]. With this issue's special anniversary article “Error bounds and enclosures: The development of numerical analysis and the impact of the contributions by Lothar Collatz” we celebrate and remember his work. REFERENCES 1Collatz, L.: Bemerkungen zur Fehlerabschätzung für das Differenzenverfahren bei partiellen Differentialgleichungen. J. Appl. Math. Mech. 13(1), 56– 57 (1933) Wiley Online LibraryGoogle Scholar 2Collatz, L.: Die Berechnung von Eigenschwingungen einer gleichseitig dreieckigen Membran mit Hilfe von Sechsecksnetzen. J. Appl. Math. Mech. 14(5), 315– 317 (1934) Wiley Online LibraryGoogle Scholar 3Collatz, L.: Eine Verallgemeinerung des Differenzenverfahrens für Differentialgleichungen. J. Appl. Math. Mech. 14(5), 350– 351 (1934) Google Scholar 4Collatz, L.: Über das Differenzenverfahren bei Anfangswertproblemen partieller Differentialgleichungen. J. Appl. Math. Mech. 16(4), 239– 247 (1936) Wiley Online LibraryGoogle Scholar 5Vdi, T.P., Collatz, L.: Über die Berechnung und Darstellung der Eigenfrequenzen homogener Maschinen mit Zusatzdrehmassen. J. Appl. Math. Mech. 18(3), 186– 194 (1938) Wiley Online LibraryGoogle Scholar 6Collatz, L.: Über Stabilität von Regelungen mit Nachlaufzeit. J. Appl. Math. Mech. 25(2), 60– 63 (1947) Wiley Online LibraryGoogle Scholar 7Collatz, L.: Das Mehrstellenverfahren bei Plattenaufgaben. J. Appl. Math. Mech. 30(11–12), 385– 388 (1950) Wiley Online LibraryGoogle Scholar 8Collatz, L.: Zur Stabilität des Differenzenverfahrens bei der Stabschwingungsgleichung. J. Appl. Math. Mech. 31(11–12), 392– 393 (1951) Wiley Online LibraryGoogle Scholar 9Ansorge, R.: Zum Tode von Lothar Collatz. J. Appl. Math. Mech. 71(7–8), 306– 308 (1991) Wiley Online LibraryGoogle Scholar Volume100, Issue10October 2020e202002041 This article also appears in:100th Jubilee of ZAMM Journal: Historical Anniversary Articles ReferencesRelatedInformation

Galerkin–Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures

This work deals with the modeling of nonsmooth vibro-impact motion of a continuous structure against a rigid distributed obstacle. Galerkin’s approach is used to approximate the solutions of the governing partial differential equations of the structure, which results in a system of ordinary differential equations. When these ordinary differential equations are subjected to unilateral constraints and velocity jump conditions, one must use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a computationally demanding task. Ivanov (Ivanov A 1993 “Analytical methods in the theory of vibro-impact systems”. Journal of Applied Mathematics and Mechanics 57(2): pp. 221–236.) proposed a nonsmooth transformation for a vibro-impacting multi-degree-of-freedom system subjected to a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. This nonsmooth transformation leads to sign function nonlinearities in the equations of motion. However, they can be easily accounted for during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions; however, he did not explore its application for simulating distributed collisions in spatially continuous structures. We adopt Ivanov’s transformation to deal with multiple unilateral constraints in spatially continuous structures. Also, imposing the velocity jump conditions exactly in the modal coordinates is nontrivial and challenging. Therefore, in this work, we use a modal-physical transformation to convert the system from modal to physical coordinates on a spatially discretized grid. We then apply Ivanov’s transformation on the physical system to simulate the vibro-impact motion of the structure. The developed method is demonstrated by modeling the distributed collision of a nonlinear string against a rigid distributed surface. For validation, we compare our results with the well-known penalty approach.

On the theory of plastic deformations and the residual stresses caused by them in the material

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 100, Issue 3 e202002019 SPECIAL ISSUE PAPER On the theory of plastic deformations and the residual stresses caused by them in the material HEINRICH HENCKY, HEINRICH HENCKY from Delft Translated from the German original: Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen, Z Angew Math Mech 4(1924):323–334 by O. Bruhns with kind support of B. Brechan and B. Nijboer. Certain misprints of Hencky's and a small mistake of minor importance in Eq. ( 4) and the respective consequences in subsequent relationships have been tacitly corrected in our translation.Search for more papers by this author HEINRICH HENCKY, HEINRICH HENCKY from Delft Translated from the German original: Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen, Z Angew Math Mech 4(1924):323–334 by O. Bruhns with kind support of B. Brechan and B. Nijboer. Certain misprints of Hencky's and a small mistake of minor importance in Eq. ( 4) and the respective consequences in subsequent relationships have been tacitly corrected in our translation.Search for more papers by this author First published: 07 May 2020 https://doi.org/10.1002/zamm.202002019 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume100, Issue3March 2020e202002019 This article also appears in:100th Jubilee of ZAMM Journal: Historical Anniversary Articles RelatedInformation

“The joy that engineers and mathematicians have come together.”1

“The joy that engineers and mathematicians have come together.”¹