An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model
Round 1
Reviewer 1 Report
The authors investigated the motion of interacting atoms in one-dimension using the Frenkel-Kontorova model. I think that this article can be publishable in Electronics, but the following revisions are necessary before publication.
1. Before Eq. (1)
The authors wrote that "The FK model for a ... is". However, from this word, it is difficult to know the meaning of "Phi" appeared in Eq. (1) for readers. For this reason, the authors should revise this sentence or an explanation for "Phi" is necessary.
2. After Eq. (1)
The author wrote that the first term in Eq. (1) is "potential function". In my opinion, some explanation about this function may be necessary, because the second term in Eq. (1) is also a kind of potential. Notice that readers are not always specialist in this field.
3. An equation given after Eq. (1)
Outer ( ) is unnecessary and the size of the inner ( ) is too small. In addition, I recommend to change the style of "cos" being roman letters instead of italic one. I also recommend that you revise subsequent equations regarding this comment.
4. Before Eq. (2)
A revision of the sentence "One treats the FK model ... but often with an additional linear tensile force of amount mu" may be necessary. Although the authors wrote as "but often with an additional linear tensile force of amount mu" in the last part of this sentence, mu already appears in Eq. (2).
5. Figure caption of Fig. 1 and other places
In the representation 2/3as, it is not clear whether this expression means 2/(3as) or 2as/3. Regarding this, the authors should revise it.
6. Line 56 and other places
The authors wrote “Equ. (4)” and, in other places, they wrote “Eq. (7)”(for example, see line 170). The authors should unify these representations. I recommend to revise as “Equ. -> Eq.”
7. Line 63
The sentence “We conclude a kind of” may be incomplete.
8. Line 73
vise versa -> vice versa
9. An equation before line 93, and line 137
I recommend that the authors revise the word “new” and “mod” being roman letters.
Author Response
Reviewer #1
The authors investigated the motion of interacting atoms in one-dimension
using the Frenkel-Kontorova model. I think that this article can be
publishable in Electronics, but the following revisions are necessary
before publication.
ANSWER: We agree.
1. Before Eq. (1)
The authors wrote that "The FK model for a ... is". However, from this word,
it is difficult to know the meaning of "Phi" appeared in Eq. (1) for
readers. For this reason, the authors should revise this sentence or an
explanation for "Phi" is necessary.
ANSWER: We have corrected the gap. Phi is still replaced by U.
2. After Eq. (1)
The author wrote that the first term in Eq. (1) is "potential function".
In my opinion, some explanation about this function may be necessary,
because the second term in Eq. (1) is also a kind of potential. Notice
that readers are not always specialist in this field.
ANSWER: We have used the hint; thanks for the help.
3. An equation given after Eq. (1)
Outer ( ) is unnecessary and the size of the inner ( ) is too small. In
addition, I recommend to change the style of "cos" being roman letters
instead of italic one. I also recommend that you revise subsequent equations
regarding this comment.
ANSWER: We have corrected the form.
4. Before Eq. (2)
A revision of the sentence "One treats the FK model ... but often with an
additional linear tensile force of amount mu" may be necessary. Although the
authors wrote as "but often with an additional linear tensile force of
amount mu" in the last part of this sentence, mu already appears in Eq. (2).
ANSWER: We have corrected the order of the description; thanks for the help.
5. Figure caption of Fig. 1 and other places
In the representation 2/3as, it is not clear whether this expression means
2/(3as) or 2as/3. Regarding this, the authors should revise it.
ANSWER: We have corrected the form into 2a_s/3.
6. Line 56 and other places
The authors wrote "Equ. (4)" and, in other places, they wrote "Eq.(7)" (for
example, see line 170). The authors should unify these representations.
I recommend to revise as "Equ. -> Eq."
ANSWER: We have corrected the form equally into Eq.
7. Line 63
The sentence “We conclude a kind of” may be incomplete.
ANSWER: We have completed the sentence.
8. Line 73
vise versa -> vice versa
ANSWER: We have corrected the form.
9. An equation before line 93, and line 137
I recommend that the authors revise the word "new" and "mod" being roman
letters.
ANSWER: We have corrected the form of both words.
Thanks to the rewiewer for the many hints.
Reviewer 2 Report
The paper is a well-written contribution, devoted to the important problem.
The paper is publishable after the minor revision.
Remarks:
1. In the text: "In Fig. 4 right we depict the result of the twist map used with the two correct initial points, u1 = 0.368 584 657 086 779 5 and u2 = 4.701 493 064 798 507, of the optimized structure".
I do not like such endless lines of figures, which have no physical meaning. Physical scientific methodology should be kept in the physical paper, from the mathematical point of view the statement: "In Fig. 4 right we depict the result of the twist map used with the two correct initial
points, "u1 = 0.368 584 657 086 779 5 and u2 = 4.701 493 064 798 507, of the optimized structure", has a sense, from the physical point of view the statement is senseless and absurd; no physical measurement can provide such an exaggerated accuracy. The problem is usual for the mathematical papers devoted to modeling of physical papers. This point definitely should be addressed under the revision.
2. I will be happy to see in the revised version of the paper the physical exemplifications of the discussed model.
Author Response
reviewer #2
The paper is a well-written contribution, devoted to the important problem.
The paper is publishable after the minor revision.
Remarks:
1. In the text: "In Fig. 4 right we depict the result of the twist map used
with the two correct initial points, u1 = 0.368 584 657 086 779 5 and
u2 = 4.701 493 064 798 507, of the optimized structure".
I do not like such endless lines of figures, which have no physical meaning.
Physical scientific methodology should be kept in the physical paper, from
the mathematical point of view the statement: "In Fig. 4 right we depict the
result of the twist map used with the two correct initial
points, "u1 = 0.368 584 657 086 779 5 and u2 = 4.701 493 064 798 507, of the
optimized structure", has a sense, from the physical point of view the
statement is senseless and absurd; no physical measurement can provide such
an exaggerated accuracy. The problem is usual for the mathematical papers
devoted to modeling of physical papers. This point definitely should be
addressed under the revision.
ANSWER: We have shorten the two numbers to 3 places.
2. I will be happy to see in the revised version of the paper the physical
exemplifications of the discussed model.
ANSWER: We mainly discuss the non-applicability of the twist map.
Of course then a physical example is not possible. However, we give a
contradiction to many papers which apply in a non-correct way 'results'
of the twist map. See page 8, Chapter Discussion.
Thanks to the rewiewer for the hint 1.
Reviewer 3 Report
The paper is a discussion about the use of the twist map for the finite Frenkel-Kontorova model. The paper does not contain any significant results to be published in any journal. Therefore, I cannot recommend it for publication in Electronics.
Author Response
reviewer #3
The paper is a discussion about the use of the twist map for the finite
Frenkel-Kontorova model. The paper does not contain any significant results
to be published in any journal. Therefore, I cannot recommend it for
publication in Electronics.
ANSWER: We have a contradictory meaning.
Round 2
Reviewer 1 Report
The aythors revised the manuscript according to my comment. Now I recommend the publication of this work in Electronics.
Reviewer 3 Report
As I wrote earlier, the paper is not rigorously well written. For example, Theorem (see line 65-68) is not a Theorem. It seems the authors do not know what is Theorem is meant. Moreover, the paper does not contain any new results.
