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- Dhagash Mehta, Jonathan D Hauenstein, Michael Kastner
- Physical review. E, Statistical, nonlinear, and…
- 2012

The stationary points of the potential energy function of the φ⁴ model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a globally convergent Newton-Raphson method. We analyze the properties of the stationary points, in particular with respect… (More)

- Dhagash Mehta, Tianran Chen, Jonathan D Hauenstein, David J Wales
- The Journal of chemical physics
- 2014

One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they all exhibit characteristic problems. Moreover, traditional methods can break down if the… (More)

—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 number of power systems contexts, most importantly in the context of direct methods for transient stability analysis and voltage stability assessment. We introduce a novel form of… (More)

- Michael Kastner, Dhagash Mehta
- Physical review letters
- 2011

The stationary points of the potential energy function V are studied for the ϕ4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of stationary points to the occurrence of thermodynamic phase transitions. We find that the phase transition potential energy… (More)

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical… (More)

Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find all of the equilibria for various choices of coupling constants K, natural frequencies, and on different graphs. We note… (More)

- Dhagash Mehta, Daniel A Stariolo, Michael Kastner
- Physical review. E, Statistical, nonlinear, and…
- 2013

We study the three-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial homotopy continuation method. On the basis of these stationary points, we analyze the complexity and other quantities… (More)

- Dhagash Mehta
- Physical review. E, Statistical, nonlinear, and…
- 2011

The stationary points (SPs) of a potential-energy landscape play a crucial role in understanding many of the physical or chemical properties of a given system. However, unless they are found analytically, no efficient method is available to obtain all the SPs of a given potential. We present a method, called the numerical polynomial-homotopy-continuation… (More)

- Lorenz von Smekal, Alexander Jorkowski, Dhagash Mehta, André Sternbeck
- 2008

The complete cancellation of Gribov copies and the Neuberger 0/0 problem of lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1), where the problem is a lattice artifact, there remain to be Gribov copies but their number is exponentially reduced. Moreover, there is no cancellation of copies there as the sign of the Faddeev-Popov… (More)

- Dhagash Mehta, André Sternbeck, Anthony G. Williams, Lorenz von Smekal
- 2007

We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S 1 → R for compact U(1) or the 3-sphere S 3 → R 3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact.… (More)