[Funded by SERB: Govt. of India: 2016-2019; Project Investigator - S. Jayanthi]

We investigate in detail the underlying spin-dynamics associated with time-dependent Hamiltonians by developing theoretical models in complex spin systems (1H-14N, 1H-35Cl etc.). In a recent work, published in Journal of Magnetic Resonance we employed matrix logarithm and Floquet theory to compute numerically the effective Hamiltonian associated to a time-dependent problem in solid state Nuclear Magnetic Resonance, Cross-Polarization under fast Magic Angle Spinning (MAS) and Double Cross Polarization under fast MAS.

In this work, a novel experiment using selective longitudinal Cross Polarization is proposed and demonstrated that enhances the sensitivity and resolution of homonuclear NOESY correlations by targeting selected 1H–15N spin pairs.The enhanced signal sensitivity (~ 2-5) as well as access to both 15N–1H and 1H–1H NOESY dimensions can greatly facilitate RNA assignments and secondary structure determinations, as demonstrated with the analysis of genome fragments derived from the SARS-CoV-2 virus.

Improvement of heteronuclear transfers through J-driven cross polarization (J-CP), which transfers polarization by spin-locking the coupled spins under Hartmann-Hahn conditions. J-CP provides certain immunity against chemical exchange and other T2-like relaxation effects, a behavior that is examined in depth by both Liouville-space numerical and analytical derivations describing the transfer efficiency.

Figure: Numerical vs analytical solutions for J-CP as a function of contact time.

A way to obtain artifact-free correlations between labile sites as well as between labile and non-labile sites – the extended Hadamard scheme, and its performance corroborated with a series of RNA-based measurements in SARS-CoV2 RNA Fragments.

The onset of turbulence is often related to the randomness of background movement, for instance, structural vibrations, magnetic fields, and other environmental disturbances. One way to model this is to consider randomly forced Navier-Stokes equations. The stochastic forcing that is added to the deterministic Navier-Stokes equation models the influence of the random environment on the fluid in fully developed turbulence.

The graph embedding is the process of representing the graph in a vector space using properties of the graphs. The existing graph embeddings rely mostly on a single property of graphs for data representation which is found to be inappropriate to capture all the characteristics of the data. Hence we designed graph embedding using multi-view approach, where each view is an embedding of the graph using a graph property. The input space of multi-view learning is then taken as the direct sum of the subspaces in which the graph embedding lie.

A problem in affine algebraic geometry asks the following.

Problem 1. Let R be a ring containing Q, A an A2-fibration over R and D : A → A a fixed point free R-LND. Does D have a slice?

The mathematical model of fluid flow problems consists of coupled nonlinear partial differential equations, and hence obtaining analytical solutions or even closed-form solutions will be very difficult. Moreover, their numerical simulation in complicated scenarios (such as domains with diverse types of boundary and transmission conditions) remains far from trivial. Therefore, in collaboration with Prof. Ricardo Ruiz-Baier ( Monash University Australia), Prof.

The aim of underlying research work is to achieve higher-order uniformly convergent numerical approximation to the solutions of a class of singularly perturbed parabolic partial differential equations (PDEs). These types of model problems can be viewed, for instance, as the unsteady Navier-Stokes equation with large Reynolds number; and generally possess boundary layers.