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Brief profile: I am an Assistant Professor in the Department of Mathematics at Thapar Institute of Engineering and Technology (TIET), Patiala, Punjab, India. Before joining TIET, I was a postdoctoral researcher at the Chair for Dynamics, Control, Machine Learning, and Numerics - Alexander von Humboldt Professorship in the Department of Mathematics at Friedrich-Alexander Universität, Germany, lead by Prof. Enrique Zuazua. I defended my PhD thesis in June 2024 at the National Institute of Technology Tiruchirappalli in India under the supervision of Dr. Jitraj Saha.
Prior to pursuing my PhD, I earned a Bachelor of Science degree in Mathematics (Honors) from Midnapore College, affiliated with Vidyasagar University, from 2011 to 2014. I then continued at Vidyasagar University, enrolling in the M.Sc. in Applied Mathematics program, and completed my master's degree in 2016. Following my M.Sc., I obtained a Bachelor of Education degree from the same university. My commitment to academic excellence is reflected in my achievements, including passing national-level examinations such as GATE and NET-JRF in 2019-2020.
Broad area of my research: My research focuses on the mathematical and numerical analysis of integrodifferential equations, particularly in the context of particulate processes such as aggregation and fragmentation. These processes occur in a variety of natural phenomena and are also crucial in different engineering sectors. A well-known application of particulate processes includes the production of instant coffee powder, the manufacturing of pharmaceutical tablets and capsules, and the grinding of minerals from their ores. In my study, I aim to incorporate physically realistic kinetic rates for particle aggregation and fragmentation into standard models and then examine various mathematical aspects of the resulting solutions.
Existence, Non-existence, and Uniqueness Analysis: I am dedicated to the analysis of solutions to the coagulation fragmentation models exploring existence, non-existence, and uniqueness characteristics.
Asymptotic Analysis: My research also delves into the asymptomatic behavior of these solutions, whether they reach equilibrium or remain in a non-equilibrium state. I am particularly interested in investigating properties such as gelation and shattering.
Numerical Approximation: To complement the theoretical investigations, I am involved in developing numerical schemes utilizing sectional methods, including finite volume, fixed pivot technique, etc. My work also encompasses a thorough convergence analysis of these numerical approximations.
Recent Articles:
Arijit Das, Minh-Binh Tran. Numerical schemes for a fully nonlinear coagulation-fragmentation model coming from wave kinetic theory, Proceeding of the Royal Society A: Mathematical, Physical and Engineering Science, Volume 481, Article 20250197, 2025.
Arijit Das, Jitraj Saha. Approximate solutions to the nonlinear hyperbolic population balance equation: Convergence, error estimates and numerical simulations, Accepted for publication in Zeitschrift für angewandte Mathematik und Physik (ZAMP), Volume 75, Article 125, 2024.
Arijit Das, Jitraj Saha. Trend to equilibrium solution for the discrete Safronov-Dubovskiĭ aggregation equation with forcing, Accepted for publication in Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Volume 155(3), Pages 869-892, 2023.
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