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A splash in a one-dimensional cold gas
by Subhadip Chakraborti, Abhishek Dhar and P. L. Krapivsky
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Subhadip Chakraborti · Abhishek Dhar · Paul Krapivsky |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202204_00001v2 (pdf) |
| Date accepted: | 2022-08-18 |
| Date submitted: | 2022-07-15 08:55 |
| Submitted by: | Chakraborti, Subhadip |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.
Author comments upon resubmission
We thank both the referees for their constructive criticisms, to which we provide a response in the particular sections. We are
submitting a revised manuscript where we have made some changes in response to the comments of the referees. All
changes are marked in blue in the revised manuscript.
Regards,
Subhadip Chakraborti, Abhishek Dhar and P. L. Krapivsky
List of changes
All changes are marked in blue in the revised manuscript. Here is a list of major changes.
1) We have displayed Eq. (1) for better visibility.
2) We have added a new paragraph in the introduction and a sentence in the conclusion which describes the importance of this paper and explains why it is of more general relevance, and has implications beyond the specific case treated in this paper.
3) We have added few lines in Sec (2) to describe the interaction of the particles in detail.
4) We have explained the origin of Eq. (6) from dimensional analysis just before it.
5) We have explicitly mentioned that G, V and Z are three scaling functions.
6) We have modified Fig. (3) and plotted them on the same time range.
7) Modified the caption of Fig. (4).
8) Updated the arrangement of figures in Figs. (5) and (6) for better visibility.
9) We have added two new references.
10) We have polished the paper throughout to make it more clear and to response to some of the issues raised by the referees.
Published as SciPost Phys. 13, 074 (2022)
Reports on this Submission
Report
The authors have successfully addressed all the comments and questions raised in my previous report. The new version of the paper is now clearer and, as I said in my previous report, the results described here are very interesting and relevant for a broad community of physicists interested in the transport properties of low dimensional systems. For these reasons I recommend the publication of the current version of the manuscript in SciPost.