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I am deeply interested in understanding the fundamental mechanics of materials at different length scales — from quantum to continuum, by mathematically modeling their behavior and employing numerical simulations.
Below are some glimpses of my research!
SPACE-TIME METAMATERIALS
SPACE-TIME METAMATERIALS
When material microstructures are allowed to vary in space as well as time, the design space is enriched due to the added degree of freedom of time. Thus, one gets even richer physics and even more exotic properties. In our recent work, we propose for the first time, space-time media with a tailored response to achieve energy conservation. This makes it possible to practically realize some previously impossible space-time media.
dog_V1.mp4It is well-known that in the presence of wave propagating through such space-time media, any time modulation of properties required energy be supplied to the system of energy be removed from the system. In some cases this energy exchange can be of exponential form and which makes it impractical to manufacture such materials. We propose am energy conserving temporal metasurface which has a tailored response.
Video: Temporal holograph of an image of Dog.
Two_Drops_StiffnessChange_2interface_V1.mp4Time holography
Time holography
Video: Waves propagating from an initial source, two Gaussian pulses, after encountering a time interface split into forward and backward propagating waves. The backward propagating waves reconstruct to create the image of the source at a later time. There is no energy exchange at the time interface, i.e., it is energy conserving.
NONLOCAL METAMATERIALS
NONLOCAL METAMATERIALS
Nonlocal interactions in phononic crystals can exhibit "Roton-like" points in their dispersion relations inside the first Brillouin zone, and open a door to exciting possibilities. My work, looks at multiband homogenization, dispersion customization, and wave-scattering in nonlocal phonic crystals.
We propose a multiband homogenization model that gives an effective dynamic PDE in real space along with effective jump conditions to be applied at the interface. The advantage of our technique is that it enables in solving initial value problems like that of impact wave propagation.
We provide a powerful analytical inverse design principle to customize the first 2 bands of the dispersion relation by employing non-local interactions in phononic crystals.
MULTIPHASE METAMATERIALS
MULTIPHASE METAMATERIALS
In two-phase quasi-static metamaterials we obtain bounds on fundamental quantities of interest. Using analytical and numerical investigations we also determine optimal microstrcuture designs that attain points on the bounds.
The ability to tune material resonances is extremely important. In one remarkable application, resonances in gold nanoshells were tuned to destroy cancer cells. Material resonances are often characterized by defining the material's Q-factor. In our work, we provide bounds on the extent to which such resonances can be tuned, i.e., our bounds correlate the absorption peaks in a metamaterial to its Q-factor.
Metamaterial architecture
Metamaterial architecture
Optimal microstructure found from numerical calculations corresponding to points C, D, and E on the bounds in left figure. It is the limiting case of a doubly coated ellipsoid where, the outer coating forms a laminate geometry and the inner coated ellipsoid is a tiny ellipsoidal inclusion
QUANTUM MATERIALS
QUANTUM MATERIALS
Kohn-Sham DFT
Kohn-Sham DFT
Geometry optimization of a water molecule using finite element method for density functional theory
Bond-breaking in dimers
Bond-breaking in dimers
Ground state density of the Carbon dimer in the bond-breaking regime, obtained from an all-electron self-consistent DFT calculation.
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