96 citations · 97 across the 6 of their papers we have counts for
6 papers
A direct approach to computing the non-interacting kinetic energy functional
Dharamveer Kumar, Amuthan A. Ramabathiran
The non-interacting kinetic energy functional, , plays a fundamental role in Density Functional Theory (DFT), but its explicit form remains unknown for arbitrary -rep…
Size-Dependent Power Laws for Edge Dislocations in Nickel Superalloys: A Molecular Dynamics Study
Divyeshkumar A. Mistry, Amuthan A. Ramabathiran
We present computational evidence using MD simulations of a size effect for the critical resolved shear stress (CRSS) of edge dislocation motion in nickel superalloys. We model the…
Analysis of quasi-planar defects using the Thomas--Fermi--von Weizsäcker model
Dharamveer Kumar, Amuthan A. Ramabathiran
We analyze the convergence of the electron density and relative energy with respect to a perfect crystal of a class of volume defects that are compactly contained along one directi…
Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs
Amuthan A. Ramabathiran, Prabhu Ramachandran
There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are…
SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs
Amuthan A. Ramabathiran, Prabhu Ramachandran
We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting…
An iterative scheme for the generalized Peierls-Nabarro model based on the inverse Hilbert transform
Amuthan A. Ramabathiran
A new semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls-Nabarro model. The numerical method developed here exploits certain basic proper…