SciPost Submission Page
HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance
by Jan Košata, Javier del Pino, Toni L. Heugel, Oded Zilberberg
This is not the latest submitted version.
|As Contributors:||Jan Košata · Javier del Pino|
|Date submitted:||2022-02-03 16:26|
|Submitted by:||del Pino, Javier|
|Submitted to:||SciPost Physics|
HarmonicBalance.jl is a publicly available Julia package designed to simplify and solve sys- tems of periodic time-dependent nonlinear ordinary differential equations. Time dependence of the system parameters is treated with the harmonic balance method, which approximates the system’s behaviour as a set of harmonic terms with slowly-varying amplitudes. Under this approximation, the set of all possible steady-state responses follows from the solution of a polynomial system. In HarmonicBalance.jl, we combine harmonic balance with contemporary implementations of symbolic algebra and the homotopy continuation method to numerically determine all steady-state solutions and their associated fluctuation dynamics. For the ex- ploration of involved steady-state topologies, we provide a simple graphical user interface, allowing for arbitrary solution observables and phase diagrams. HarmonicBalance.jl is a free software available at https://github.com/NonlinearOscillations/HarmonicBalance.jl.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2022-4-4 (Invited Report)
- The article is well written. It is a good pedagogical introduction to the topic of nonlinear resonators.
- It represents a good manual for the potential users of the software package.
- The literature about the topic is not complete.
- At conceptual level, it does not introduce any novelty. The package performs standard numerical methods and approximations that are commonly used by the experts in the field.
- The target system is also not clear. It is not clear what are the scientific motivations and research interests in investigating a large number of N coupled resonators instead of a few of them (N=1, 2 ,3) or many harmonic components of a single resonator.
(see attached file)
Anonymous Report 1 on 2022-3-21 (Invited Report)
1 - Very well written, provides a very clear review of the relevant subjects.
2 - The presented software package is very useful
1 - Scientific novelty is quite low, package does not introduce any new tools or apply them in a novel manner.
See attached file.