Mathematical Modeling of Heavy Metal Transport in Soil

This monograph provides a comprehensive mathematical framework for modeling heavy metal transport in soil. Drawing on advection-diffusion equations, exponential decay models, and advanced numerical techniques, the book bridges theoretical mathematics with practical applications in environmental science and policy. Through detailed derivations, simulations, and case studies it demonstrates how predictive models can forecast plume migration, optimize remediation, and quantify climate change impacts. Key innovations include stochastic uncertainty analysis, machine learning integration for parameter estimation, and scalable frameworks for site-to-regional assessments. The text explores real-world implications, from cost reductions in cleanup (up to 31% savings) to environmental justice considerations, equipping readers with tools to mitigate risks to human health and ecosystems. Intended for environmental scientists, mathematicians, engineers, and policymakers, this work synthesizes decades of research while proposing forward-looking scenarios, such as microplastic-metal interactions and real-time sensor assimilation. With rigorous analytical solutions, computational efficiency (O (n log n) complexity), and interdisciplinary connections to hydrogeology and soil chemistry, it offers a robust toolkit for sustainable soil management. Ultimately, the book transforms abstract equations into actionable strategies for a cleaner planet, emphasizing mathematics as a language of environmental hope and stewardship.

Dr. Busayamas Pimpunchat is an Assistant Professor in Applied Mathematics at the Industrial Mathematics Research Group (IMRG), Department of Mathematics, School of Sciences, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Thailand. Her expertise spans *applied mathematics, data analytics, financial modelling, and risk management, with strong emphasis on real-world applications in **finance, insurance, and environmental systems. Her research in *financial specialization* focuses on *credit risk modelling, expected credit loss (ECL) calculation, and actuarial-based financial management, particularly for financial management and debt-related companies. She has applied **stochastic processes, probability models, and machine learning techniques* to support decision-making under uncertainty and regulatory compliance. In addition, she has contributed to projects involving the *calculation of contribution rates* for employers and employees under Thailand’s *Workmen’s Compensation Fund*, integrating actuarial principles with policy and labour risk assessment.
Beyond finance, her work includes *environmental and pollution modelling, as well as **artificial intelligence and data science applications* such as Support Vector Machines (SVM) and deep learning models. She has held several leadership roles in academic and analytics centers and received the *Hope Award* from Kyushu University, Japan. Her interdisciplinary research bridges *mathematics, finance, insurance, and public policy*, financial mathematics in in PDE, delivering practical and sustainable solutions for industry and society.

Dr. V. Govindan is an Associate Professor in the Department of Mathematics at Hindustan Institute of Technology and Science, Chennai, India, with over 16 years of teaching and research experience. His expertise includes stability of functional and differential equations, fractional differential equations, and nanofluid dynamics. He holds a PhD from Periyar University (2017) on functional equations in defined in Various normed spaces, an MPhil (2009), MSc (2006), and BSc (2004) from the same institution. Dr. V.Govindan has authored 243 research articles (162 in Scopus/SCIE), with 1413 Google Scholar citations, an h-index of 16, and two patent. He has served as a Visiting Professor at KMITL, Thailand (2025), and held positions at DMI St. John the Baptist University, Malawi (2020-2023), and Sri Vidya Mandir Arts & Science College, India (2009-2020).He received the Best researcher award in the international conference at Dubai (2023) ,he received the young scientist award in the international conference at University of Malaya, Malaysia (2024) ,and he received the Sri Ramanujan best researcher award at Thammasat University ,Thailand (2025). Passionate about mentoring and interdisciplinary research, he reviews for journals and has organized many conferences on mathematical modelling.

Dr. N. Avinash is an Assistant Professor in the Department of Mathematics at Sacred Heart College (Autonomous), Tirupattur, India, with 9 years of professional experience. Specializing in fractional calculus, difference equations, and epidemic modeling, he has a PhD in Difference Equations (viva-voce 2025) from Sacred Heart College, MSc (2016) from S.T. Hindu College, and BSc (2014) from Lekshmipuram College. He has published 11 papers in SCIE/Scopus-indexed journals on topics like COVID-19 and monkeypox models, authored 3 books, and holds 1 patent on team interaction analysis. Dr. Avinash has 12 communicated papers, serves as a peer reviewer for Scientific Reports (13 manuscripts), and has organized 3 conferences/workshops. He has attended 27 conferences and 17 FDPs, earning awards like All India Rank 75 in CSIR-NET and a Lifetime Membership in AARM. Proficient in LaTeX, Maple, SPSS, and AI tools, he focuses on translating research into practical applications for public health.

Dr. Mustafa Inc is a Full Professor in the Department of Mathematics at Firat University, Elazig, Turkey, since 2013. His research interests include approximate solutions of PDEs and ODEs, fractional dynamics, numerical and analytical methods for differential equations, optical solitons, nonlinear optics, Lie symmetry analysis, and stability analysis. He holds a PhD (2002), MSc (1997), and BSc (1992) in Mathematics from Firat University. Dr. Inc has supervised 9 PhD theses, authored 493 articles with 16,000 citations and an h-index of 52, and reviews for over 30 international journals. He served as Associate Professor (2009-2013), Assistant Professor (2003-2009), and Visiting Professor at Biruni University (2021-2023). Recognized for his contributions to applied mathematics and environmental.