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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, An energy cascade finite volume scheme for a mixed 3- and 4- wave kinetic equation arising from the theory of finite-temperature trapped Bose gases , Arxiv, 2025.
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.
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