90 citations · 1.1k across the 68 of their papers we have counts for
11 papers · 1 filter
Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points
Dhagash Mehta, Ciaran Hughes, Michael Kastner +1
The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary po…
Certified counting of roots of random univariate polynomials
Joseph Cleveland, Jeffrey Dzugan, Jonathan D. Hauenstein +5
A challenging problem in computational mathematics is to compute roots of a high-degree univariate random polynomial. We combine an efficient multiprecision implementation for solv…
Energy Landscape of the Finite-Size Mean-field 2-Spin Spherical Model and Topology Trivialization
Dhagash Mehta, Jonathan D. Hauenstein, Matthew Niemerg +2
Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical stud…
Exploring the Impact of Wind Penetration on Power System Equilibrium Using a Numerical Continuation Approach
Souvik Chandra, Dhagash Mehta, Aranya Chakrabortty
In this paper we investigate how the equilibrium characteristics of conventional power systems may change with an increase in wind penetration. We first derive a differential-algeb…
Numerical Polynomial Homotopy Continuation Method to Locate All The Power Flow Solutions
Dhagash Mehta, Hung Nguyen, Konstantin Turitsyn
The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a n…
Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
Jonathan D. Hauenstein, Rijun Huang, Dhagash Mehta +1
This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structu…