Connecting the dots between Mathematics and Physics of the hydrodynamic instability known as Viscous Fingering (VF)
DST, Government of India, sanctioned a total outlay of Rs.14.63 lakhs to Dr Tapan Kumar Hota, Assistant Professor, Department of Mathematics, SRM University-AP, Andhra Pradesh, for pursuing research on “Mathematical analysis and Adjoint Based Stability for a Coupled Convection-Diffusion equation in Miscible Displacement”. Hydrodynamic Stability (Instability) is a study of an equilibrium point subject to small and/or medium disturbances. This assists in understanding several complicated natural phenomena such as fluid transition from laminar to turbulent, chemical mixing, formation of cloud, and others. The available stability analysis is unable to address the early-time evolution of the VF process. The early-time behaviour of the system helps us to choose the parameters that are responsible for the long-time behaviour of the coupled PDEs. To achieve the target, we need to address the linear stability of the system from the study of the singular-value-decomposition instead of traditional eigenvalue analysis. As the system is non-autonomous, the eigenvectors/eigenvalues may not be physically relevant. Further, it is required to confirm our linear stability analysis by mathematical analysis of the coupled non-linear PDEs.
‘The nonmonotonic viscosity profile when a high mobile fluid is displacing a less mobile fluid. There is a potentially unstable region, where the viscosity increases in the flow direction, followed in the downstream direction by a potentially stable region, where the viscosity decreases in the flow direction. The disturbance structure is computed using the singular-value decomposition of the propagator matrix. Reference: Hota & Mishra, Journal of Fluid Mech, Vol. 856, pp:552-579, 2018.’
Dr Tapan is keen on studying other branches of science to provide the correct mathematical approach to address the issues. His project will address one of the hydrodynamic instabilities known as viscous fingering (VF). It forms when a high mobile fluid displaces a low mobile fluid. It has enormous implications in the field of Chemical Engineering Science, Petroleum Engineering, Chromatography, and Oil Extraction process. He explains, “I will study this instability from a mathematician’s point of view, more precisely, to address the mathematical analysis of coupled partial differential equations (PDEs). The system that governs the VF is non-autonomous and there is no readily available stability analysis that can represent Physics, based on robust mathematical analysis. My aim is to connect the dots between mathematics and physics of the VF.”
Infrastructure and laboratory facilities are crucial to conduct research. Upon receiving approval from a prestigious organization like SERB (Science and Engineering Research Board), Govt. of India, Dr. Tapan is entitled to this unique opportunity to serve the scientific community. He divulges, “The award is not only a recognition to me but also to the SRM University, AP. The University will be more visible in the world of research and can attract more eminent scientists and researchers to make the University their second home.” Quoting Master Oogway, ‘Yesterday is history, Tomorrow is a mystery… Today is a gift, that’s why it is called present.’, Dr Tapan is eager to commence working on his project at the earliest, and looks forward to enjoying the process of accomplishing the task.
Department of Mathematics warmly welcomes Dr Prakash Kumar, newly joined Assistant Professor. Dr Prakash has completed his graduation from the University of Delhi. After that, he pursued his master’s and doctoral studies from the Indian Institute of Technology, Kharagpur. His research interests include-
- Mathematical models of different bioreactors consisting deformable porous scaffold to analyse the fluid flow and nutrient transport that support the cells to grow in the desired form.
- Fluid flow and deformation of the solid phase in the deformable porous medium using biphasic mixture equations.
Visit Dr Prakash’s faculty profile to know more about him.
Department of Mathematics, SRM University-AP organised a 3-day conference on Number Theory and Related Topics. The Conference was scheduled for July 30 – August 01, 2021. Distinguished speakers from IMSC Chennai, CMI-Chennai, IIT-Kanpur, Ropar, Indore, Gandhinagar and Delhi, IISER-Bhopal, Pune and Tirupati, Charles University, Prague, University of Zagreb, RKMVERI, Belur took part in the Conference and presented their work and ideas on Number Theory.
Modern number theory is connected with almost every other branch of mathematics. This Conference is dedicated to exploring different aspects of modern number theory, including modular forms, automorphic forms, representation theory, arithmetic geometry, special functions, diophantine approximations, quadratic forms etc. This Conference aims to encourage young aspiring mathematicians to get a flavour of the broad horizon of number theory.
For more information and to watch the lecture videos, please visit this site.
The Department of Mathematics is glad to announce that Dr Anirban Bose, Assistant Professor, has published an article, ‘Twisted conjugacy in linear algebraic groups II’ in the Q1 journal, Journal of Algebra. The paper was published in collaboration with Sushil Bhunia from Indian Institute of Science Education& Research, Mohali. The present work and its prequel “Twisted conjugacy in linear algebraic groups” are concerned with computing the number of orbits of a twisted conjugacy action of an algebraic group on itself. Dr Bose’s interests mainly lie studying the properties of groups of matrices.
Here’s the link to the article.