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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.
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Submission summary
| Authors (as registered SciPost users): | Jan Košata · Javier del Pino |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202202_00005v1 (pdf) |
| Code repository: | https://github.com/NonlinearOscillations/HarmonicBalance.jl |
| Date submitted: | 2022-02-03 16:26 |
| Submitted by: | del Pino, Javier |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 3) on 2022-4-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202202_00005v1, delivered 2022-04-04, doi: 10.21468/SciPost.Report.4854
Strengths
- 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.
Weaknesses
- 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.
Report
(see attached file)
Report #1 by Anonymous (Referee 4) on 2022-3-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202202_00005v1, delivered 2022-03-21, doi: 10.21468/SciPost.Report.4739
Strengths
1 - Very well written, provides a very clear review of the relevant subjects.
2 - The presented software package is very useful
Weaknesses
1 - Scientific novelty is quite low, package does not introduce any new tools or apply them in a novel manner.
Report
See attached file.
Author: Javier del Pino on 2022-05-17 [id 2480]
(in reply to Report 1 on 2022-03-21)Response can be found in attached .pdf.
Author: Javier del Pino on 2022-05-16 [id 2476]
(in reply to Report 2 on 2022-04-04)Response can be found in the attached .pdf.
Attachment:
response_to_referee2.pdf
Anonymous on 2022-05-23 [id 2504]
(in reply to Javier del Pino on 2022-05-16 [id 2476])I read the reply and the authors satisfactorily answered to most of my criticism.
In a first reading, I had an oversight on some functionalities already implemented in the code.
I am still a bit sceptic about the relevance for experimental systems with an increasing number of resonator modes but I agree that the work can be published on SciPost Codebases.