In living organisms chemical patterns determine mechanical heterogeneity ultimately leading to formation of complex shapes starting from a simple shape. In this project we will develop a computational framework to simulate this with the long term goal of finding the minimal ingredient to design an artificial tissue.

In this project, we will adapt the Rouse model, that describes the dynamics of a flexible polymer to account for different chromatin architecture. Specifically, we will develop a framework to study the signature of chromatin architecture in the dynamics of one or few segments in the polymer,

In this project, we will begin from the mechanics of flexible polymer popularly known as Rouse model. We will adapt this model to demonstrate different architecture of chromatin. Specifically, we will study in detail what are the signature of chromatin architecture dynamics of one or few beads carry. 

The project relates to pattern formation in a microfluidic network due to reacting and diffusing species. The objective is to estimate conditions under which Turing instabilities emerge in microfluidic networks. It involves mathematical modeling and computation. 

Reference: Van Gorder RA. 2021 A theory of pattern formation for reaction–diffusion systems on temporal networks. Proc.R.Soc.A477: 20200753. https://doi.org/10.1098/rspa.2020.0753 

We have developed a house-hold scale (16 litre), water purification device, based on nanoparticle-impregnated activated carbon (AC) composite, for disinfection of drinking water. It works by killing of microorganisms by metallic nanoparticles in the composite, whilst the AC part of the composite removes other organic and inorganic pollutants from water. This gives clean, drinking water, in our gravity-driven device, which does not need any electricity to flow water or kill microbes, as in a UV-lamp of a traditional filter, thereby saving energy.

Continuous monitoring of water quality parameters, like total dissolved solids, heavy metals, inorganic ions, organic pollutants etc.is an important measurement, to ascertain quality and use of a water body. This is critical for both a flowing water-stream (river, canal) or a stagnant water-pool, like a lake. To that end, in this project, one has to work with chemical reagants, which have been tested with both synthetic and field-water samples, for various species, like arsenic, fluoride, chromium, iron etc.

In this project, the student will model the deposition process of nanoparticles onto surface of hydrogel microbeads. The deposition and synthesis is based on droplet coalescence within a microchannel. The project will involve theory and simulations.

This project will model and simulate the a radial flow chromatographic column, which has advantages of high throughput over axial column chromatography. The project will benchmark with axial chromatography to compare their performances. 

The project involves developing a code for solving the Laplace equation with a free surface. The code will be used to simulate oceanic wave breaking under the potential flow approximation. Consider the project only if :

1. You are strong in maths & physics.

2. You are interested in programming & numerical computations.

   Reference:

   The deformation of steep surface waves on water - I. A numerical method of computation - Longuet-Higgins & Cokelet, Proc. Roy. Soc. 1976