The Influence of Crystal Anisotropy on the Characteristics of Solitary Waves in the Nonlinear Supratransmission Effect: Molecular Dynamic Modeling
Round 1
Reviewer 1 Report
The manuscript presents a very good work. However, I have some observations that may further improve the quality of the manuscript:-
- Addition of Graphical abstract may improve the presentation of work.
- Why only these planes were considered? Justification required.
- Check reference [30]. If there is any typing error.
- The author claims to find that nonlinear modes are mostly actively excited for all these crystal orientation options at frequencies close to the optical branch. This could be more defended and justified mainly with other experimental or theoretical methods.
- The authors should remember that the abstract and main text of a study is independent entities. Therefore, they should use abbreviations and the main text of a study is independent entities. Therefore, they should use Abbreviations and acronyms of terms both in the abstract and main text, use these abbreviations and acronyms when they are frequently used.
Language improvement tools may be used to improve the presentation of work.
Author Response
Subject: Response to Reviewer 1 Comments - Manuscript ID: computation-2559607
Thank you for your review of our manuscript titled "The Influence of Crystal Anisotropy on the Characteristics of Solitary Waves in the Nonlinear Supratransmission Effect: Molecular Dynamic Modeling" for Computation. We greatly appreciate your valuable comments and suggestions.
We have carefully addressed all of your feedback, and we are pleased to inform you that all modifications to the manuscript have been highlighted in yellow. Your insights have significantly improved the quality of our work.
Once again, thank you for your time and expertise.
Best regards,
Elena Korznikova
Head of the Laboratory "Metals and Alloys Under Extreme Impacts",
Ufa University of Science and Technology
[Manuscript ID: computation-2559607]
- Addition of Graphical abstract may improve the presentation of work.
We are pleased to inform you that the graphical abstract has been included.
- Why only these planes were considered? Justification required.
We have chosen planes that correspond to the densest crystallographic direction of the crystal. Densely packed planes are good for spreading delocalized nonlinear vibrations because a highly ordered medium allows certain wave functions to move unhindered throughout and achieve delocalization [Jakob, Rönnbäck. (2011). Spreading of wave packets in lattices with correlated disorder]. In the study of linear quasi-periodic structures, it has been observed that the coordinated motion of a large number of particles, known as collective excitations, can explain many properties of systems consisting of interacting molecules and atoms [doi: 10.1016/J.CNSNS.2014.09.028].
- Check reference [30]. If there is any typing error.
We have checked and the reference seem to be OK
Here it is in TEX format to be sure
title={Heat conduction in driven Frenkel-Kontorova lattices: Thermal pumping and resonance},
volume={81},
url={http://dx.doi.org/10.1103/PhysRevE.81.031124},
DOI={10.1103/physreve.81.031124},
number={3},
journal={Physical Review E},
publisher={American Physical Society (APS)},
author={Ai, Bao-quan and He, Dahai and Hu, Bambi},
year={2010},
month={Mar},
language={en}
- The author claims to find that nonlinear modes are mostly actively excited for all these crystal orientation options at frequencies close to the optical branch. This could be more defended and justified mainly with other experimental or theoretical methods.
Nonlinear modes are actively excited at frequencies close to the optical branch due to the strong nonlinear effects of self-confinement and intrinsic optical bistability induced by the reorientation of the atomic structure as it is shown in papers [https://doi.org/10.1016/j.cnsns.2021.106039, https://doi.org/10.1016/j.jmps.2021.104482, doi.org/10.1103/PhysRevE.95.022212]. Due to small spatial and time scale of the studied phenomenon at the moment it is not possible to apple experimental methods.
- The authors should remember that the abstract and main text of a study is independent entities. Therefore, they should use abbreviations and the main text of a study is independent entities. Therefore, they should use Abbreviations and acronyms of terms both in the abstract and main text, use these abbreviations and acronyms when they are frequently used.
Thank you for your comment. We have ensured that the abstract and the main text of our study are treated as independent entities, and as such, we have appropriately managed the use of abbreviations in each section to enhance clarity and readability.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This work studies nonlinear supratransmission (NST) effects
in crystals using the embedded atom method (EAM) of molecular
dynamics (MD). The solitary wave transmission in a
Pt3Al alloy is modeled. Disturbances along (100), (110),
and (111) planes are considered. Differences in wave
shapes depending on crystal direction are observed,
but a single analytical equation is derived to describe
all the wave shapes (eq. 3) using three fitted parameters.
This article is of interest to the solid-state physics
community and computational materials science. The approach
builds on prior works of the authors (e.g., refs 40-45, 51)
but contains some new developments. The presentation of
the method is brief but sufficient.
While this is considered to be a good work, some items are
still requested to be addressed in a revised version:
[1] The crystal structure of Pt3Al should be clearly stated.
What are the point & space groups? Is it FCC or BCC, or some
other cubic structure?
[2] There is some notational confusion about labeling of
crystal indices. For example, line 228, should the
favorable directions be <100> rather than {100}? The {.}
notation means families of planes, not directions, though
these can be interchanged in a regular cubic structure.
[3] It is recommended that a new Eq. 4 be added that expands
eq. 3 with the important new contribution of the paper:
epsilon = (lambda*q-V*t)/2.
[4] On line 69, it is stated that these effects are impossible
to detect in experiments. How can one be sure that the stated
NST effects really exist if they cannot be measured in real
experiments? Could they in fact be a simulation artefact?
[5] In eq. (2), the "exp" font is too small - it should not be
a subscript. Also, please confirm that the extreme exponent
of power 20 in the denominators is correct.
[6] In abstract line 16, the "3" in Pt3Al should be a
subscript. In line 173, there is a typo: "Pt3Alv".
[7] Formatting of references looks wrong. Too many terms
are italic. Only the journal titles should be italic font.
English is acceptable, though a proofreading is suggested to improve clarity.
Author Response
Subject: Response to Reviewer 2 Comments - Manuscript ID: computation-2559607
Thank you for your review of our manuscript titled "The Influence of Crystal Anisotropy on the Characteristics of Solitary Waves in the Nonlinear Supratransmission Effect: Molecular Dynamic Modeling" for Computation. We greatly appreciate your valuable comments and suggestions.
We have carefully addressed all of your feedback, and we are pleased to inform you that all modifications to the manuscript have been highlighted in yellow. Your insights have significantly improved the quality of our work.
Once again, thank you for your time and expertise.
Best regards,
Elena Korznikova
Head of the Laboratory "Metals and Alloys Under Extreme Impacts",
Ufa University of Science and Technology
[Manuscript ID: computation-2559607]
[1] The crystal structure of Pt3Al should be clearly stated.
What are the point & space groups? Is it FCC or BCC, or some other cubic structure?
Atoms in Pt3Al intermetallic compound are located on the sites of a FCC lattice and belong to Space Group Pm3m, point grout 221.
[2] There is some notational confusion about labeling of crystal indices. For example, line 228, should the favorable directions be <100> rather than {100}? The {.} notation means families of planes, not directions, though these can be interchanged in a regular cubic structure.
We are grateful to the Reviewer for the note and made the required corrections
[3] It is recommended that a new Eq. 4 be added that expands eq. 3 with the important new contribution of the paper: epsilon = (lambda*q-V*t)/2.
We are grateful to the Reviewer for the note and made the required corrections
[4] On line 69, it is stated that these effects are impossible to detect in experiments. How can one be sure that the stated NST effects really exist if they cannot be measured in real experiments? Could they in fact be a simulation artefact?
The effect of NST comes from the nonlinear nature of interatomic bonding ana cannot be related to the simulation artefact since they were observed in various nonlinear periodic systems including mechanical ones [doi: 10.1016/J.JSV.2016.10.041] and computational models with extremely different nonlinearity types and initial conditions excluding the possibility of the appearance of the common artefact. One can recall Nonlinear Supratransmission in Quartic Hamiltonian Lattices With Globally Interacting Particles and On-Site Potentials [doi: 10.1115/1.4048714], Gap soliton formation by nonlinear supratransmission in Bragg media doi: [10.1016/J.JSV.2016.10.041], energy transfer by NST mechanism in finite granular chains [doi: 10.1016/J.PHYSLETA.2004.05.054] .
[5] In eq. (2), the "exp" font is too small - it should not be a subscript. Also, please confirm that the extreme exponent of power 20 in the denominators is correct.
We are grateful to the Reviewer for the note and made the required corrections
[6] In abstract line 16, the "3" in Pt3Al should be a subscript. In line 173, there is a typo: "Pt3Alv".
We are grateful to the Reviewer for the note and made the required corrections
[7] Formatting of references looks wrong. Too many terms are italic. Only the journal titles should be italic font.
We are grateful to the Reviewer for the note and made the required corrections
Author Response File: Author Response.docx
Reviewer 3 Report
As attached file.
Comments for author File: 
Comments.pdf
Nil.
Author Response
Subject: Response to Reviewer 3 Comments - Manuscript ID: computation-2559607
Thank you for your review of our manuscript titled "The Influence of Crystal Anisotropy on the Characteristics of Solitary Waves in the Nonlinear Supratransmission Effect: Molecular Dynamic Modeling" for Computation. We greatly appreciate your valuable comments and suggestions.
We have carefully addressed all of your feedback, and we are pleased to inform you that all modifications to the manuscript have been highlighted in yellow. Your insights have significantly improved the quality of our work.
o
Once again, thank you for your time and expertise.
Best regards,
Elena Korznikova
Head f the Laboratory "Metals and Alloys Under Extreme Impacts",
Ufa University of Science and Technology
[Manuscript ID: computation-2559607]
This paper is interesting. However, some questions as follows should be clearly replied:
- As shown in Figs 2-5, why distributions of kinetic energy, instead of total energy (which includes kinetic and potential energy), per atom are used to describe the profiles of solitary wave in this study?
We agree with the Reviewer that any energy can be used for description. For the purposes of demonstration, kinetic energy has been chosen, as it serves as a measure of external influence and provides a more visually representative way of illustrating the propagation of thermal energy throughout the crystal.
- Generally, kinetic energy of an atom is related to its state of temperature. Why an initial temperature of 0 K, instead of, for example, room temperature, is imposed in this study?
The generation of solitary waves arises from the excitation of discrete breathers (high-amplitude nonlinear modes) in the vicinity of the impact zone. The non-zero temperature has an adverse effect on the excitation of discrete breathers. Thus, this study sets a temperature range for the initial conditions. The results show that the generated waves are capable of overcoming heating zones. However, examining their precise properties in this instance poses difficulty due to fluctuations in temperature. We appreciate the helpful feedback. The examination of thermal fluctuations is a potential path for further exploration of the solitary waves recorded in our research.
- How about the direction of harmonic oscillations applied in the first region (longitudinal or transverse wave)? And how to determine the required magnitude of the applied amplitude? (in this study, why being ranged from 0.03 to 0.3 angstroms?)
The directions of vibrations perpendicular to the selected ones will result in the manifestation of the supratransmission effect not as isolated waves, but as clusters of discrete breathers. This is a different extensive problem and we are working on it. In general, the NST phenomenon is quite complex and fundamental for nonlinear discrete systems. The issue of the threshold amplitude in such problems is analytically unsolvable, so the empirical approach was used. Concerning the calculational costs, due to the fact that calculations were performed on a supercomputer, the search of required amplitudes was conducted relatively quickly.
- As shown in Fig. 2(a), how to determine the profile of Pt-Al colored by yellow?
We have different series of atoms: in one case, it is pure Pt, in another, Al. Pt_Al is a row containing atoms of both types. Therefore, we have such a profile of energy distribution along this row.
We are grateful to the Reviewer for the note and made the required corrections
- How to determine the forbidden region in the spectrum in this study? Does it depend on crystalline orientations or the size of model cell?
The phonon spectrum of the crystal was computed using LAMMPS, which incorporates the requisite procedures and considers them in the Fourier transform autocorrelation functions of atomic displacement with time. For an in-depth examination of the calculation process, we direct readers to our prior work on this crystal (see reference 49 10.1134/S1063783419110416). This previous study provides more extensive information, but to avoid overcomplicating the present work, we refrain from including these details. The phonon spectrum comprises all modes supported by the crystal, and, for a defect-free crystal, it typically remains independent of the crystal's orientation or size. However, the Phonon DOS can be influenced by boundary conditions and structural defects. In this instance, we examined a stoichiometric À3B L10 crystal devoid of any defects. The boundary conditions were periodic along the X and Y axes.
- As shown in Fig. 4(a) for plane (100), why the highest peaks of wave at instant of 9, 10, and 11 ps occur and appear earlier than those at instant of 3-6 ps?
The excitation of the considered waves is a periodic process. After accumulating the next portion of energy on the localized modes near the impact zone, the next wave is emitted. Here, we observe higher peaks due to the overlay with thermal lattice oscillations. The evolution of subsequent peaks is similar to the first ones, but it is more challenging for numerical analysis due to cell heating.
- What is the physical meaning of displacement U written by Eq.(3)? Is it dimensionless?
You are correct, U is a dimensionless quantity that, being an exact solution of the discrete variational equations, can describe various physical parameters of the discrete system depending on the problem formulation. An explanation has been added to the text.
- Error in wording direction of plane:” Their velocity is higher than the speed of sound waves by 5-10%. For the propagation planes (110) and (111), the velocity was approximately 4.75 ×103 m/s. For the (110) propagation plane, the velocity was 4.45 × 103 m/s.”
We are grateful to the Reviewer for the note and made the required corrections
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The presented work is appropriate for the publication
Reviewer 2 Report
No more comments.
Reviewer 3 Report
Nil.
