Three things that are ubiquitous around us are vibrations (dynamics), randomness (uncertainty and fluctuations) and complexity (nonlinearity, coupled systems). My primary research interests lie where they all converge. A topic wise summary of my research is provided below, with links to respective publications.
Climate systems are intricate, complex, stochastic and nonlinear, typically they involve multiple spatial and temporal scales too. This also means that lower and intermediate order models can conveniently capture dynamics at select gross scales and help us in obtaining physical insights into climate. This is in contrast to large climate models used to predict weather and climate. Understanding the nonlinear dynamics of such models, primarily for Indian summer monsoon, is the focus of this study. Additionally, I am working on extending these understandings to urban climate, and how cities and climate affect each other.
Ref: S Krishna Kumar, Ashwin K Seshadri, Model hierarchies and bifurcations in QE monsoon models - EGU General Assembly Conference Abstracts, 2023
S Krishna Kumar, Ashwin K Seshadri, Bifurcations In Convective QE Based Lower Order Models Of South Asian Monsoon - AGU Fall Meeting Abstracts, 2021
S. Krishna Kumar and Ashwin K Seshadri, Origins and suppression of bifurcation phenomena in lower-order monsoon models, Earth System Dynamics, (under review)
Karthik Murthy, S. Krishna Kumar and Ashwin K Seshadri, Effect of current global warming trends on temperature-sensitive tri-trophic interactions , (close to submission)
Most physical systems- astrophysical, biological and mechanical- are nonlinear in at least certain regimes of their operation. Non-linearity brings in a variety of post-instability behaviour not captured by linear models of these systems. While deterministic nonlinear models capture the 'bifurcations' in the system behaviour with parametric variation, real systems are beset with parametric as well as non-parametric random fluctuations or 'noise'. Such stochastic scenarios have been found to exhibit phenomena otherwise unexpected, e.g., noise induced shift in bifurcation point and noise induced intermittency. Our investigations into the emergence of intermittency due to flow velocity fluctuations in fluid-elastic systems have revealed the predominant role the noise correlation plays in the appearance of intermittency. Further exploration of these ideas, for a class of simple and generic one-dimensional maps (e.g., logistic map or tent map), has yielded analytical conditions on onset and disappearance of intermittency due to parametric or multiplicative noise. Higher noise correlation has been found to yield wider regimes of intermittency and these regimes are found to be co-terminus with regimes of 'phenomenological bifurcations' defined on the basis of structural changes in stationary densities.
Ref: J. Venkatramani, S. Krishna Kumar, Sunetra Sarkar, Sayan Gupta (2017), Physical mechanism of intermittency route to aeroelastic flutter,Journal of Fluids and Structures, Vol.75, pp 9-26.
S. Krishna Kumar, Sunetra Sarkar, Sayan Gupta (2019), Multiplicative noise induced intermittency in maps, International Journal of Non-linear Mechanics, Vol. 117, 103251 .
S. Krishna Kumar, Sunetra Sarkar, Sayan Gupta (2020), Intermittency in a cantilever plate in randomly fluctuating fluid flow , Journal of Fluids and Structures, Vol. 90, 102855.
Aging infrastructure, often in remote or inaccessible locations, needs monitoring on regular basis to avoid material and human losses. This is implemented using sensors, which are prone to a variety of faults. Such faults can also occur biological monitoring sensors. Detection of these faults and distinguishing them from structural damage, in reasonable computational time, is a hard task. Analysing a multi-sensor data in short time for detecting the faults is central to the success of online wireless structural health monitoring. This however leads to a combinatorial menace, as one does not know the number and position of these faults a priori. I was part of efforts to resolve this using evolutionary optimization algorithms like Genetic Algorithm, adaptive Dfferential Evolution and variants of Particle Swarm Optimization along with data analysis concepts like Principal Component Analysis, Observability and controllability etc. I also developed a simple multi-level search algorithm as an alternative to optimization techniques whose run time cannot be ascertained apriori. A GUI-based MATLAB toolbox for performing sensor validation through various algorithms was also developed. Some of these efforts were also extended to the problem of optimal sensor placement.
Ref: A. Rama Mohan Rao, K. Lakshmi, S. Krishna Kumar (2015), Detection of delamination in laminated composites with limited measurements combining PCA and dynamic QPSO, Advances in Engineering Software, 86, 85-106.
A. Rama Mohan Rao, S. Krishna Kumar, K. Lakshmi (2014), A Sensor Fault Detection Algorithm for Structural Health Monitoring Using Adaptive Differential Evolution, International Journal for Computational Methods in Engineering Science and Mechanics, 15(3), 282-293.
A. Rama Mohan Rao, K. Lakshmi, S. Krishna Kumar (2014), A generalized optimal sensor placement technique for structural health monitoring and system identification, Procedia Engineering, 86, 529-538 (First International Conference on Structural Integrity (ICONS) 2014).
A. Rama Mohan Rao, S. Krishna Kumar, K. Lakshmi (2012), Sensor fault detection in large sensor networks using PCA with a multi-level search algorithm, Structural Durability & Health Monitoring, 8(3), 271-294.
Fluttering flags, aircraft wings, vocal cord and many other physical systems involve fluid- structure interaction. I am interested in the dynamical behaviour of such systems, with applications like energy harvesting. I explore the effects of upstream flow fluctuations and vibrations of flexible structures. Flow fluctuations have been found to cause intermittency before the onset of sustained oscillations. It has been seen that the time scales of the flow fluctuations affect the appearance and nature of intermittency. Numerical simulations using unsteady lumped vortex model of a flexible cantilever plate and experiments on a cylinder-plate system have confirmed the ubiquitous presence of intermittency. Conditions for onset and disappearance of intermittency, obtained through study of simple physical systems like 1-d maps, have been applied to yield bounds of intermittent regime for vibrating flexible plate and to study the effect of fluctuation time scales.
Ref: J. Venkatramani, S. Krishna Kumar, Sunetra Sarkar, Sayan Gupta (2017), Physical mechanism of intermittency route to aeroelastic flutter,Journal of Fluids and Structures, Vol.75, pp 9-26.
S. Krishna Kumar, Sayan Gupta, Sunetra Sarkar (2017), Intermittent Oscillations of Elastic structure in Fluctuating Axial Fluid Flow,9th European Nonlinear Dynamics Conference, Budapest University of Technology and Economics, Budapest, Hungary, 25-30 June 2017.
S. Krishna Kumar, Chandan Bose, Shaikh Faruque Ali, Sunetra Sarkar, Sayan Gupta (2018), Investigations on a vortex induced vibration based energy harvester, Applied Physics Letters, 111.24 (2017): 243903.
S. Krishna Kumar, Sunetra Sarkar, Sayan Gupta (2020), Intermittency in a cantilever plate in randomly fluctuating fluid flow , Journal of Fluids and Structures, Vol. 90, 102855.
Ambient energy harvesting, mainly to power wireless sensor nodes in health monitoring applications, have been developed over years for various energy sources like vehicle vibrations, wind effects etc. I work on developing robust vortex induced vibration harvesters. A flexible body, placed downstream of a bluff body like a circular cylinder vibrates due to the vortex shedding occurring in the cylinder wake. Experimental investigations on a model energy harvester has shown that harvester efficiency is greatly affected by the gap between the cylinder and plate. Further, the fluctuating flow in cylinder wake is found to cause intermittent plate vibrations, which affects the harvester performance.
Ref: S. Krishna Kumar, Chandan Bose, Shaikh Faruque Ali, Sunetra Sarkar, Sayan Gupta (2018), Investigations on a vortex induced vibration based energy harvester, Applied Physics Letters, 111.24 (2017): 243903.
S. Krishna Kumar, Sunetra Sarkar, Sayan Gupta (2020), Vibration energy harvesting in fluctuating fluid flows, In: Mukhopadhyay A., Sen S., Basu D., Mondal S. (eds) Dynamics and Control of Energy Systems. Energy, Environment, and Sustainability. Springer, Singapore.