Dr. Atul Anurag

About Me

I am working as a Visiting Assistant Professor of Mathematics at the Ramapo College of New Jersey. I received my Bachelor’s degree in Mathematics in 2015 from Ramjas College, University of Delhi, and a Master’s degree in Applied Mathematics in 2017 from the National Institute of Technology, Warangal, Telangana.
I earned my Ph.D. in Applied Mathematics in 2025 from the Department of Mathematical Sciences, New Jersey Institute of Technology, where I was advised by Dr. Roy Goodman.

The Global Phase Plane Analysis of Three Vortex Interactions
The Global Phase Plane Analysis of Three Vortex Interactions

Apr 23, 2025
Dr. Atul Anurag

About Me I am working as a Visiting Assistant Professor of Mathematics at the Ramapo College of New Jersey. I received my Bachelor’s degree in Mathematics in 2015 from Ramjas College, University of Delhi, and a Master’s degree in Applied Mathematics in 2017 from the National Institute of Technology, Warangal, Telangana.

Apr 23, 2025
The Global Phase Space of the Three-Vortex Interaction System
The Global Phase Space of the Three-Vortex Interaction System

We derive a symplectic reduction of the evolution equations for a system of three point vortices and use the reduced system to succinctly explain a kind of bifurcation diagram that has appeared in the literature in a form that was difficult to understand and interpret. The reduction proceeds in two steps: a reduction to Jacobi coordinates and a Lie-Poisson reduction.

Apr 22, 2025
Global Phase Plane Analysis of the three-vortex problem
Global Phase Plane Analysis of the three-vortex problem

Nov 1, 2024
The Phase Space of the Three-Vortex Problem
The Phase Space of the Three-Vortex Problem

Jun 24, 2024
A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering
A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering

We use Jacobi coordinates and Nambu brackets to derive a new representation of the motion of three vortices which, unlinke all previous reductions, introduces no singularities into the system. We use this to study the scattering of dipoles by stationary vortices.

Jun 6, 2024
Point Vortex Dipole Scattering
Point Vortex Dipole Scattering

Oct 20, 2023
Generalization of Leapfrogging Orbits of Point Vortices
Generalization of Leapfrogging Orbits of Point Vortices

Jul 20, 2023