Obituary: Jang Bahadur Shukla

By Arni S.R. Srinivasa Rao, Peeyush Chandra, Balaram Dubey, Ram Naresh, Mini Ghosh, and Sunita Gakkhar

Jang Bahadur (J.B.) Shukla passed away on March 15, 2023, at the age of 86. His inspiring, innovative research and energetic leadership spanned more than 65 years of mathematical modeling and explored topics such as air pollution, fluid mechanics, population dynamics, and disease spread.

Jang Bahadur was born on January 13, 1937, in the city of Balrampur in Uttar Pradesh, India. He received both an undergraduate and master’s degree in mathematics from the University of Lucknow in 1955 and 1957 respectively, and earned his Ph.D. from the Indian Institute of Technology Kanpur (IITK) in 1964 under the guidance of Jagat Narain Kapur, who was one of the finest mathematicians in India after the country gained independence from British colonial rule. After serving as a professor of mathematics at IITK, Jang Bahadur left this position in 2000 to become a professor at the LNM Institute of Information Technology (LNMIIT) in Jaipur. He later worked at the Bhabha Group of Institutions in Kanpur.

Jang Bahadur’s Ph.D. thesis determined important properties for two viscous fluids between two plates, which combine to form a nonhomogeneous mixture that moves in the positive direction between the plates (see Figure 1). He later extended these results to axially symmetric self-superposable hydromagnetic flows and axially symmetric force-free fields, both of which have practical utility for blood flow in arteries and veins. Jang Bahadur conducted theoretical derivations to understand surface roughness and its impact on the lubrication of fluids, which consequently inspired laboratory experiments. He also expanded upon the original works of Kapur and Prabhu Lal Bhatnagar to advance the velocity and directional pressure properties of nonhomogeneous mixture fluids [1], which shed light on rainfall and climatic conditions.

The Oseen and Stokes expansions play a fundamental role when two incompressible viscous fluids flow at a velocity \(V\) [6]. This calculation involves two important quantities: the Oseen space variable with \(V\) and the Stokes variables that use \(\gamma\) as the kinematic coefficient. With a characteristic body length \(L\), the Reynolds number \(R\) is then defined as

\[R = \frac{LV}{\gamma}.\tag1\]

One can then use \(R\) to asymptotically express the nondimensional velocity via the Oseen and Stokes expansions. Jang Bahadur and his students contributed significantly to hydrodynamic lubrication theory in this context.

Jang Bahadur was the first researcher in India to conduct a study of mathematical models for synovial joint lubrication. In 1972, he and his collaborators presented a paper on the “Tribological Study of Diseased Human Joints” at the First World Conference in Industrial Tribology, which took place in New Delhi [8]. Jang Bahadur also coauthored a “Generalized Reynolds Equation for Stochastic Lubrication and its Application” in 1975 [2] and contributed to roughness effects in bearings with “A New Theory of Lubrication for Rough Surfaces” in 1978 [7]. He introduced the notion of peripheral layers near the wall for blood flow in arteries and organized a research group that focused on biofluid flows.

In separate efforts, Jang Bahadur and his collaborators developed innovative mathematical models for the removal of water pollution and control of air pollution [3-5, 10-12]. Air pollution is one of the most challenging problems that plague post-industrialized societies. The discharge of gaseous and particulate matter from various household, agricultural, industrial, and vehicular emission sources contribute to high levels of atmospheric pollution throughout the world. Jang Bahadur recognized the importance of modeling these scenarios; his contributions to the dispersion of air pollutants from a time-dependent point source—and its application to methyl isocyanate leakage from the Union Carbide factory in Bhopal—is particularly well-noted. 

Jang Bahadur also initiated and modeled the concept of planting “green belts” around ground-based sources of pollutants and near receptors in order to limit the effects of pollution. His novel analysis explored the reduction of air pollutant concentration due to the presence of green belts, which can protect historical monuments and other important sites. Jang Bahadur also proposed several mathematical models to study the role of removal mechanisms in the environment, including the conversion of primary pollutants to secondary species, precipitation scavenging, and artificial rain. In addition, he used modeling and analysis to demonstrate the critical role of environmental factors in the spread of infectious diseases. Jang Bahadur and his students introduced several novel situations in which environmentally degraded regions of the world could contribute to the spread of viruses and investigated possible mitigation of such scenarios [3, 4, 11].

To synthesize contemporary applications, Jang Bahadur organized the International Symposium on Mathematical Modelling of Ecological, Environmental and Biological Systems at IITK in 1985 [9]. He was always eager to share his research findings at conferences or with colleagues and visitors at any time. Jang Bahadur constantly promoted the application of mathematical models in real-world situations and passionately encouraged young modelers to work on practically relevant projects.

To strengthen mathematical modeling in India and increase its practical utility, Jang Bahadur founded the Indian Society for Mathematical Modeling and Computer Simulation (ISMMACS) in 1998. In 2022, ISMMACS and Amity University Lucknow organized an international conference and workshop to honor Jang Bahadur on the occasion of his 85th birthday. The three-day event recognized Jang Bahadur’s mentorship of three generations of mathematical modelers while at IITK, LNMIIT, and the Bhabha Group of Institutions. Jang Bahadur participated in the festivities virtually and enjoyed the company of his former students, collaborators, and other long-term friends and family.

Jang Bahadur received numerous prestigious awards throughout his professional life, including the Federation of Indian Chambers of Commerce & Industry Award in 1980, the Shanti Swarup Bhatnagar Prize for Science and Technology in 1982, and the Distinguished Service Award in Mathematical Sciences from Vijnana Parishad of India in 1997.

In addition to academic leadership in mathematical modeling, Jang Bahadur had a good sense of humor and an easily approachable personality. His benevolent disposition and unquestionable willingness to help others—especially with research—were much admired. He will be sorely missed.

---

Acknowledgments: We thank Prawal Sinha (retired professor from IITK), Alok K. Agrawal (Amity University Lucknow), and Arvind K. Misra (Banaras Hindu University, Varanasi) for their contributions to and help with this article.

References
[1] Bhatnagar, P.L., & Verma, P.D. (1957). On superposable flows. Proc. Indian Acad. Sci., 45, 281-292.
[2] Christensen, H., Shukla, J.B., & Kumar, S. (1975). Generalized Reynolds equation for stochastic lubrication and its application. J. Mech. Eng. Sci., 17(5), 262-270.
[3] Ghosh, M., Chandra, P., Sinha, P., & Shukla, J.B. (2004). Modelling the spread of carrier-dependent infectious diseases with environmental effect. Appl. Math. Comput., 152(2), 385-402.
[4] Ghosh, M., Chandra, P., Sinha, P., & Shukla, J.B. (2005). Modelling the spread of bacterial disease: Effect of service providers from an environmentally degraded region. Appl. Math. Comput., 160(3), 615-647.
[5] Goyal, A., Sanghi, R., Misra, A.K., & Shukla, J.B. (2013). A modeling study on the role of fungi in removing inorganic pollutants. Math. Biosci., 244(2), 116-124.
[6] Lin, Z. (1990). The asymptotic expansion of solutions for the Navier-Stokes equations with large parameters. J. Partial Differ. Equ., 3(2), 41-54.
[7] Shukla, J.B. (1978). A new theory of lubrication for rough surfaces. Wear, 49(1), 33-42.
[8] Shukla, J.B., Chandra, P., & Srivastava, R.C. (1972). Tribological study of diseased human joints. In Proceedings of the first world conference in industrial tribology (paper no. C4.1). New Delhi, India.
[9] Shukla, J.B., Hallam, T.G., & Capassco, V. (Eds.). (1987). Mathematical modelling of environmental and ecological systems. In Developments in environmental modeling (Vol. 11). Amsterdam, the Netherlands: Elsevier Science.
[10] Shukla, J.B., Maitri, V., & Misra, A.K. (2017). Effect of global warming on sea level rise: A modeling study. Ecol. Complex., 32, 99-110.
[11] Singh, S., Shukla, J.B., & Chandra, P. (2005). Modelling and analysis of the spread of malaria: Environmental and ecological effects. J. Biol. Syst., 13(1), 1-11.
[12] Sundar, S., Naresh, R., Misra, A.K., & Shukla, J.B. (2009). A nonlinear mathematical model to study the interactions of hot gases with cloud droplets and raindrops. Appl. Math. Model., 33(7), 3015-3024.

Arni S.R. Srinivasa Rao ([email protected]) is a professor and director of the Laboratory for Theory and Mathematical Modeling in the Medical College of Georgia and a professor in the Department of Mathematics at Augusta University in the U.S. Peeyush Chandra is a retired professor from the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur in India. Balaram Dubey is a professor in the Department of Mathematics at the Birla Institute of Technology and Science, Pilani in India. Ram Naresh is a professor in the Department of Mathematics at Harcourt Butler Technical University, Kanpur in India. Mini Ghosh is a professor in the Department of Mathematics within the School of Advanced Sciences at Vellore Institute of Technology, Chennai in India. Sunita Gakkhar is a professor emerita in the Department of Mathematics at the Indian Institute of Technology Roorkee in India.