Current research interests are very wide encompassing nonlinear dynamics to non-equilibrium systems broadly classified as complex systems.
Some are listed below.
For a complete list of publications: Click Here
Fractional Calculus, which deals with derivatives and integrals of fractional order, is useful in modeling scaling phenomena. In their original version these operators are non-local hence better suited to study asymptotic scaling. We are developing a local version of the calculus which is useful in characterizing the local scaling behavior as it exists in fractals.
We have initiated the development of nonlinear dynamical model of swaying of trees applicable even in the stormy conditions. Here a tree is modeled as an end-to-end connected segments with the nonlinear restoring forces taken into account. Till now we have carried out mostly theoretical studies and investigated nonlinear dynamical phenomena occurring in such systems. Future focus would be more on experimental verification of these aspects too.
Here we study coupled dynamical systems and the properties of the invariant measure and in particular its support. We find the value of the coupling parameter when the support of the measure shrinks to the synchronization manifold. This gives a precise value of the coupling parameter when the system undergoes the synchronizing transition. We have also studied the stationary density and found it to be multifractal.
Localized heating due to LASER, even if of low power, in a small fluid systems can give rise to interesting complex phenomena. It was an interesting experience to be involved in the theoretical understanding of two such experiments carried out in Tata Institute of Fundamental Research. One concerned with the formation of dendritic drying patterns in biological fluids and other had formation of vortices in a liquid droplet.
Does the learning dynamics decide the network structure? We studied the coupled map network with the Logistic map dynamics at the nodes and STDP like learning dynamics for the edges and demonstrated that the most of the edges in the network get pruned leading to a robust network with a broad degree distribution. Application of this idea to a Hodgkin-Huxley neuronal network gave rise to a network in an equivalent class of neuronal networks according to motif distribution.
We have defined new spaces which partially characterize the classical 2-microlocal spaces in a very simple manner. This new definition gives rise to an efficient algorithm to find this partial 2-microlocal frontier. This algorithm would be useful in detecting and characterizing oscillating behaviour in irregular signals arising in many fields. This algorithm can also determine the Holder exponents more accurately than other algorithms. Recently, this algorithm was added to the software FRACLAB being developed by INRIA.
A nontrivial symmetry was observed in numerical simulation of totally asymmetric simple exclusion process with spatially disordered jump rates. We studied this problem and found formally exact analytical expressions for the steady-state weights and the current. Using these expressions we showed that the magnitude of the steady state current remains invariant when the direction of all allowed jumps is reversed, a fact observed in the above mentioned numerical simulations.