SciPost Submission Page
Boundary layers, transport and universal distribution in boundary driven active systems
by Pritha Dolai, Arghya Das
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Arghya Das · Pritha Dolai |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202506_00052v1 (pdf) |
| Date submitted: | June 27, 2025, 6:36 p.m. |
| Submitted by: | Arghya Das |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We discuss analytical results for a run-and-tumble particle (RTP) in one dimension in presence of boundary reservoirs. It exhibits 'kinetic boundary layers', nonmonotonous distribution, current without density gradient, diffusion facilitated current reversal and optimisation on tuning dynamical parameters, and a new transport effect in the steady state. The spatial and internal degrees of freedom together possess a symmetry, using which we find the eigenspectrum for large systems. The eigenvalues are arranged in two bands which can mix in certain conditions resulting in a crossover in the relaxation. The late time distribution for large systems is obtained analytically; it retains a strong and often dominant 'active' contribution in the bulk rendering an effective passive-like description inadequate. A nontrivial 'Milne length' also emerges in the dynamics. Finally, a novel universality is proposed in the absorbing boundary problem for dynamics with short-ranged colored noise. Active processes driven by active reservoirs may thus provide a common physical ground for diverse and new nonequilibrium phenomena.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We thank you and the editorial team for processing the paper. We thank the referees for their valuable and constructive comments which helped in improving the manuscript. Specifically, we made a number of rearrangements and included some explanations which we believe make the results and their implications clearer and the paper better readable. The implications of the steady state results in Eqs. (7)-(9) are now restructured with added explanations under three paragraph headings. The plots in Fig. 2 are changed. And some of the calculational details are moved to the Appendix. We however decided to keep the main formalism and the discussion on the symmetry in the main text. All the major changes are enlisted below.
We also uploaded a detailed response to each comment raised by the referees separately. The revised manuscript is now uploaded.
With regards,
Pritha Dolai, Arghya Das
List of changes
- In the abstract, ''violation of Fourier’s law'' is replaced with ''current without density gradient'', and the ''Seebeck-like effect'' is replaced with ''a new transport effect''. These changes are incorporated throughout the main text also.
- ''Two species of particles'' is replaced with ''particles with different orientations''.
- The ''Milne length'' is defined in the introduction. 4.After Eq. (9) the significance of different quantities like $D_e,\mu,M$ are mentioned.
- The plots in Figure 2 have been changed. Now we have added plots of the density and magnetisation profiles for two values of $\omega$ (tumble rate) with same boundary conditions. The caption is modified accordingly.
- The implications of the steady state profiles and current, Eqs. (7)-(9), are restructured into three major paragraphs. The content is also rewritten with added explanations and clarifications.
- In the section (3.1) the simulatin scheme for the steady state with zero boundary magnetisations is added.
- In section (4), a subsection title ''Formalism'' is added (now subsection 4.1). Coefficients $\alpha$ are now replaced with $\beta$.
- The calculation details of the correction terms in $\lambda_n$ and the coefficients $\beta$ are now moved to the Appendix (now Appendices C and D).
- Tile of section (5) is updated to ''Proposed universality...''. The text is also slightly modified, and the ''Boundary layers'' and ''$P_{\rm BM}$'' are now defined.
- Part of the ''Conclusion'' section is rephrased and elaborated.
- A new appendix (now Appendix A) for a brief discussion on the boundary magnetisation control is added. The form of the large time distribution of underdamped passive particle in presence of absorbing boundary is explicitly added (now in Appendix E).
- References 41,48,64,65 are added.
Major changes are in blue. This apart, minor polishing is done throughout the manuscript.
Current status:
Reports on this Submission
Report #2 by Goncalo Antunes (Referee 2) on 2025-7-30 (Invited Report)
- Cite as: Goncalo Antunes, Report on arXiv:scipost_202506_00052v1, delivered 2025-07-30, doi: 10.21468/SciPost.Report.11668
Report
I have only some small gripes left that I would like to see addressed.
Requested changes
1) - If the authors do not want to use adimensional quantities or physical units for their plots, a paragraph at the start of the results section (or potentially included in the figure captions) should be included stating that arbitrary units are used. Nonetheless, I must stress that stating all lengths in units of channel length and times in units of typical time between tumble (for example) is a very natural (and informative) way of defining units. Presenting results in such a way greatly facilitates understanding of the parameter values chosen as well as comparison with experiments.
2) The caption of Fig. 3 as currently written leaves a possibility of confusion: while the 10^ 4 factor is present in both graph label and caption, a reader may be left confused whether the 10^ 4 factor should be applied two times or just once (in order to get the real values). I would suggest that in the caption of Fig. 3, the phrase inside parenthesis should be re-written as (Note that in both panels the y-axis ...). The inclusion of "Note that" makes it clearly that this sentence is merely calling for attention to the 10^4 factor in the graph axis.
3) In section 4.2, text is split into non-numbered sub-sections labelled with "spectrum for o_x = 1 (even sector)" and "spectrum for o_x = −1 (odd sector):". This choice of formatting is awkward as it is not used in the rest of the paper, and does not immediately pop-out as sub-section titles (instead blending in with the rest of the text). The authors should either upgrade these subsections to proper numbered subsections, or get rid of them entirely (instead distinguishing the two cases directly in the text, rather than using subsection titles).
Recommendation
Ask for minor revision
Report
Recommendation
Ask for minor revision
Comment: ''The concerns that were raised in my previous report were satisfyingly addressed by the authors. I also appreciate that they now speculate on possible magnetisation control mechanisms, however the clarity of the writing in Appendix A should be improved. I am happy to recommend publication of the manuscript, conditional on this last adjustment.''
Reply: We thank the referee for the suggestion and recommendation for publication. Appendix A is revised and hope it is clearer now.
Author: Arghya Das on 2025-08-25 [id 5758]
(in reply to Report 2 by Goncalo Antunes on 2025-07-30)Comment: ''I thank the authors for their answers to my questions. Most of the issue I had with the previous iteration of the paper have been resolved and I believe the quality of the manuscript has greatly improved.
I have only some small gripes left that I would like to see addressed.''
Reply: We thank the referee for the positive response and constructive suggestions, which we have incorporated. Our pointwise reply to the comments are as follows.
Comment: ''1) - If the authors do not want to use adimensional quantities or physical units for their plots, a paragraph at the start of the results section (or potentially included in the figure captions) should be included stating that arbitrary units are used. Nonetheless, I must stress that stating all lengths in units of channel length and times in units of typical time between tumble (for example) is a very natural (and informative) way of defining units. Presenting results in such a way greatly facilitates understanding of the parameter values chosen as well as comparison with experiments.''
Reply: We acknowledge the general advantages of using dimensionless quantities, and we did consider it. An issue is, in that case two parameters, e.g. system size and tumble rate, have to be fixed at a value $1$ and remaining parameters becoming a combination of these. In our case this is not a very suitable position. For example, the current reversal or some other features emerging with changing tumble rate will then have to be discussed in terms of other parameters in a rather contrived manner. We prefer to avoid it and continue with dimensional quantities of unspecified units, as long as it is consistently used.
Now we have mentioned of the use of arbitrary units in the ''Model'' section, and provided an example of the units to be used in a specific case.
Comment: ''2) The caption of Fig. 3 as currently written leaves a possibility of confusion: while the $10^4$ factor is present in both graph label and caption, a reader may be left confused whether the $10^4$ factor should be applied two times or just once (in order to get the real values). I would suggest that in the caption of Fig. 3, the phrase inside parenthesis should be re-written as (Note that in both panels the y-axis ...). The inclusion of "Note that" makes it clearly that this sentence is merely calling for attention to the $10^4$ factor in the graph axis.''
Reply: The required change is made.
Comment: '' 3) In section 4.2, text is split into non-numbered sub-sections labelled with ''spectrum for $o_x = 1$ (even sector)'' and ''spectrum for $o_x = −1$ (odd sector):''. This choice of formatting is awkward as it is not used in the rest of the paper, and does not immediately pop-out as sub-section titles (instead blending in with the rest of the text). The authors should either upgrade these subsections to proper numbered subsections, or get rid of them entirely (instead distinguishing the two cases directly in the text, rather than using subsection titles).''
Reply: We agree with the suggestion and have now removed the paragraph headers.