PULSEDYN—A dynamical simulation tool for studying strongly nonlinear chains

Abstract

We introduce PULSEDYN, a particle dynamics program written in C++, to solve the equations of motion of many-body nonlinear systems in one dimension. PULSEDYN contains a suite of commonly used potentials (Fermi–Pasta–Ulam–Tsingou, Toda, Morse and Lennard-Jones) and solvers (velocity-Verlet and Gear 5th order predictor–corrector) for particle dynamics. PULSEDYN is designed to perform scientifically accurate simulations using these calculations. For accessing the built-in features of PULSEDYN, no knowledge of programming is expected, apart from the creation of a parameter file using predefined commands for running the executable. Therefore, simulations for research projects can be performed with minimal code writing using PULSEDYN. PULSEDYN is distributed under the GNU GPL v3 license and the source code and the executable are available on Github. The writing style emphasizes organization and legibility. Therefore, we anticipate that it would serve as a good template for users who may wish to adapt the code to their specific needs. In this manuscript, we first discuss PULSEDYN and its features in detail. Then, we show results reproduced from literature using PULSEDYN for the following cases (i) Soliton propagation and collisions in the (integrable) Toda lattice (ii) Recurrence phenomena, decay of localized excitations and solitary wave collision in the Fermi–Pasta–Ulam–Tsingou lattice and (iii) Solitary wave propagation in the Morse and Lennard-Jones lattices. Finally, we present a new result on a problem of fundamental historical importance using PULSEDYN. We show by means of explicit specific heat calculations, that in the limit of strong nonlinearity, the quartic Fermi–Pasta–Ulam–Tsingou system approaches equipartition at late times. Program summaryProgram Title: PULSEDYNProgram Files doi:http://dx.doi.org/10.17632/fc8483t7jz.1Licensing provisions: GNU General Public License 3 (GPL)Programming Language: C++Supplementary Material: user manual, documentationNature of problem: We solve a Newtonian particle dynamics problem in one dimension for a variety of commonly used nonlinear manybody systems. The goal is that the user should be able to run scientifically accurate simulations with minimal effort. Benchmarking should also be easy to perform by different users running simulations across different platforms.Solution method: The code uses a parameter file interface with a set of commands for a range of pre-built functionalities. By providing the code and the needed parameter file to the user we hope to make scientifically accurate simulations easier to perform. We provide the Gear 5th order predictor–corrector algorithm as well as the velocity-Verlet algorithm and the following potentials — the Toda potential, Morse Potential, Lennard-Jones Potential and a polynomial potential up to 4th order. To make benchmarking consistent we release the software as open source and free to distribute.