Positions

Positions available

PhD students and Post-doctoral Researchers

Positions are available for PhD students and post-doctoral researchers. The broad areas of research that is currently being pursued in the group are mentioned below. Please contact me directly for more information.

Students interested in pursuing MS are also welcome. Usually MS students will be working alongside a PhD student in the same topic.

Procedure:

Phd applicants need to apply through the formal application process using the institute portal. Selection of students is based on the departmental policies and procedure. Please write to me for more information.

Selection of post-doctoral researchers is usually through the Institute Post Doctoral Fellowship and requires submitting a proposal, that is prepared by the applicant in consultation with the mentor. please get in touch with me.

Ongoing Projects

Nonlinear dynamics: Problems involving a variety of nonlinear dynamical systems are being pursued in the group involving applications that range from vibration based energy harvesting, multi-physics problems like fluid structure interactions, as well as on non-smooth dynamical systems, such as impact problems leading to chattering in gears or fatigue damage due to flow induced vibrations in heat exchanger tubes. The focus on these studies is on understanding the physics associated with the dynamical behaviour and unravelling interesting phenomena and the route to bifurcations; please see the publication list for recent studies. The effects of uncertainties and noise in the dynamics of these systems is also investigated. Qualifications desired: Engineering/Physics/Mathematics background with a strong aptitude in differential equations, linear algebra and computations. Knowledge of solid mechanics, strength of materials and vibrations will be useful.
Stochasticity and noise induced transitions in spatio-temporal systems: Nonlinear dynamical models are highly sensitive to the model parameters that are estimated from observations having varying spatial resolutions. The uncertainties in modelling are incorporated into the mathematical models as noise. The effects of noise may lead to sudden and irreversible change in the system from one dynamical state to another, leading to sudden qualitative changes in the system dynamics, often leading to catastrophic events and are irreversible (example, limit cycle oscillations in rotor blades). It is of interest that these catastrophic events, classified as noise induced transitions, are predicted apriori for natural, biological and engineering systems. While studies on noise induced phenomena have been investigated for low order systems, similar studies on large ordered networked systems do not seem to have been addressed. This study will focus on the dynamical long term features of noise induced behaviour on large ordered networked models. Qualifications desired: Engineering/Physics/Mathematics background with a strong aptitude in differential equations, linear algebra and computations.
Dynamics of complex networked systems: Complex networked dynamical systems comprise of a large number of interconnected components, individually each of which behaves dynamically, with interactions that can be nonlinear and often stochastic in nature. The use of these type of models enables bypassing the traditional reductionist approach used in engineering and science, to investigate complex phenomena that otherwise are difficult to analyse. This includes a wide variety of phenomena ranging from natural systems (avalanche formation, flooding, earthquakes), technological and engineered systems (failures of power grids, collapse of structural systems), biological networks (networks of neurons, bronchial networks, metabolic networks), social networks (virality of fake news propagation, epidemics) and numerous others. Understanding the dynamics of such systems is crucial for predicting their behaviour, optimizing their performance, and designing interventions to influence their behaviour. Interesting dynamical phenomena include synchronization and chimeras and unravelling the routes to these states offer insights into the dynamics of these systems. Qualifications desired: Engineering/Physics/Mathematics background with a strong aptitude in differential equations, linear algebra and computations.
Data based low order models for nonlinear dynamical systems: The dynamics of many complex systems ranging from climate, financial markets, spread of fake news, growth of an epidemic or the changing traffic patterns are difficult to model using simple governing equations. However, with the abundance of measurement data, data-driven discovery of low order governing equations underlying a dynamical system is possible using measurement data and leveraging advances in sparsity techniques and machine learning. Qualifications desired: Engineering/Physics/Mathematics background with a strong aptitude in differential equations, linear algebra and computations.
Tensor decomposition techniques in learning: Tensors are multidimensional arrays and represent multi-parametered data in a variety of applications in signal processing, numerical linear algebra, data mining and graph analysis. Tensor decomposition techniques enable approximating high dimensional problems using low rank approximations, that enable breaking the curse of dimensionality and which have been shown to be more accurate and efficient than existing deep learning techniques. This study aims to explore on alternative tensor decomposition techniques that can have applications in a wide variety of problems, including in uncertainty quantification. Qualifications desired: Engineering/Physics/Mathematics background with a strong aptitude in linear algebra and computations.