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I am currently a postdoc/visiting scientist at the Courant Institute, New York University, 
working with Mike Shelley and Jun Zhang, in the Applied Math Lab (AML). 
I am studying biomechanics of locomotion, specifically locomotion of C elegans in structured environments. 

(A comprehensive database about various aspects of C elegans biology is at Wormbase)

My earlier reasearch as a postdoc at MIT in Gareth McKinley's Lab was in 

non-Newtonian fluid dynamics, specifically viscoelastic jets.  

(A very instructive set of videos about Newtonian, and non-Newtonian fluid dynamics is available here.)

(A good resource for rheology is the Society of Rheology, SOR.)

Prior to this, I was a graduate student at Duke University, Department of Physics, 
working with Professor Bob Behringer on granular systems.

Research:

1.    Bio-fluid Dynamics and Bio-Mechanics: Locomotion of C. elegans in structured environments

The focus of my current research is to understand low Reynolds number locomotion 

of microorganisms. Undulatory locomotion of microorganisms in complex environments is 

ubiquitous in nature. For example, a sperm moving through mucus, or a Spirochaete moving 

through tissue. Microorganisms navigate complex environments consisting of fluids and 

obstacles, negotiating hydrodynamic effects and geometrical constraints. 

Some of the key questions are: 

What role do hydrodynamics and geometrical constraints play? Do these obstacles help or hinder 

their motion? 

To gain insights into these questions, I am studying undulating locomotion of C. elegans in 

PDMS micro-pillar arrays filled with buffer solution. Such a setup allows systematic control over 

geometric constraints, and along with hydrodynamic simulations, determines the role of 

hydrodynamic contributions. 

We have found that the nematode (L ~ 1 mm), while swimming between the pillars, employs a number 

of different locomotory strategies depending on the lattice spacing (q: [0.380 - 0.700] mm). 

Instead of being hindered by the obstacles, it can utilize them to push off and gain speed. 

These regimes of enhanced locomotion depend on the lattice spacing scaled by the length of 

the nematode. In addition, we also observe changes in frequency, velocity, curvature, and the gait 

of the worm as a function of the scaled lattice spacing. Our experimental approach, in conjunction with 

modeling and simulations (Eric Keaveny and Mike Shelley), allow us to disentangle the effects of 

geometry and hydrodynamics on end behavior. We find that the simulations not only reproduce 

locomotory strategies of the real nematode, but also match the experimental measurements of enhanced 

velocity quantitatively. Combining experiments and simulations, we can now establish a regime map of 

changes in locomotory strategies of an undulating swimmer in structured media

2.    Granular Physics: (Advisor: Bob Behringer, Duke University, Physics)

The focus of my graduate research was on understanding the statistical properties of dense, dry 

granular systems under isotropic compression and pure shear. The key feature of granular 

systems is the heterogeneous network of contact forces called the “force-chain” network. 

Understanding these force networks and their spatial correlations is a fundamental goal of 

granular mechanics. Although knowledge of inter-grain contact forces is indispensable 

for a complete understanding of the system, they are exceedingly difficult to measure 

non-destructively in a realistic granular system. I developed a novel method to measure 

both the normal and tangential components of contact forces, in bulk samples, at the grain scale [1]. 

We visualized the stresses by using birefringent circular disks and solved the inverse problem 

of finding the contact forces producing the observed stress patterns. Figure shows an experimental 

image (left) of sheared granular system, and the corresponding "best-fit" image obtained after finding 

the contact forces.

3.    Non-Newtonian Fluid Dynamics: Jetting of Viscoelastic Fluids (Advisor: Gareth McKinley, Mech. E. MIT)

Viscoelastic jets with moderate elasticities exhibit a rich array of complex nonlinear dynamics: 

the buckling instability of a steady jet resulting in periodic coiling, and a transition from periodic 

to quasi-periodic dynamics, followed by a transition to multi-frequency, chaotic dynamics. Beyond 

this regime, the jet dynamics smoothly crosses over to exhibit a spectacular ``leaping shampoo" or the 

Kaye effect. We created a regime map of the dynamics of the jet in terms of viscous, elastic, 

gravitational, and inertial effects, allowing us to connect rheology of the fluids to the changes in the 

dynamics of the jets. We examined different dynamical regimes in terms of scaling variables, which 

depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid 

properties (elasto-gravity number). This approach allowed us to unify diverse phenomena like dripping, 

coiling, and leaping jets, as a sequence of transitions in the parameter space of scaled flow rate and scaled 

height. 

Fluids with higher elasticities predominantly tend to exhibit folding motions (linear oscillations) 

instead of circular coiling. There is also an absence of any ``leaping shampoo" effect, and at larger 

heights, the jet ruptures as it cannot sustain the elastic stresses. The regime map of the dynamics for 

high elasticity fluids was also established along the same lines.

Preprints:

1.   Trushant Majmudar, Matthieu Varagnat, and Gareth McKinley, “Nonlinear Dynamics
      of coiling in Viscoelastic Jets”, To be submitted to Phys. Fluids (2010).
        PDF of the paper

2.   Matthieu Varagnat, Trushant Majmudar, and Gareth McKinley, “The folding dynamics in 
      axi-symmetric jets of surfactant fluids”, To be submitted to J. non-Newt. Fluid Mech. (2010).
        PDF of the Paper 

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