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arxiv: 2605.29552 · v1 · pith:ATKSNIOOnew · submitted 2026-05-28 · ❄️ cond-mat.soft

Emergence of Dynamical Anisotropy induced by Demixing in a Binary System with Differential Diffusivity under an External Potential

Rashmi Trivedi , Subhajit Paul , Sumanta Kundu , Sunita Kumari This is my paper

Pith reviewed 2026-06-29 01:01 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords demixingbinary mixturedifferential diffusivityexternal potentialhexatic orderdynamical anisotropypercolating bandpacking fraction
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The pith

An external potential expands demixing in a binary mixture of particles with different diffusivities and produces direction-dependent motion through percolating bands.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a binary system of particles that differ in their diffusion rates and are placed in a one-dimensional spatially varying external potential. It shows that the potential widens the range of packing fractions where the particles separate into distinct bands, with slower particles clustering near potential minima and displaying stronger local ordering. This separation produces a connected band structure and makes long-time particle motion faster or slower depending on the direction relative to the potential. In the absence of the potential the same mixture shows neither the expanded demixing nor the directional bias in transport.

Core claim

In simulations of a binary mixture with differential diffusivity under a spatially varying external potential, demixing occurs across a broader interval of packing fractions than without the potential. The less diffusive particles form bands near the potential minima that exhibit pronounced hexatic order. Mean-squared displacements of the two species differ markedly along the potential direction but remain normally diffusive in the transverse direction for both species. The arrangement produces a percolating band and a clear dynamical anisotropy that is absent when the external potential is removed.

What carries the argument

The spatially varying external potential acting on particles that differ in diffusivity, which drives directional band formation and anisotropic transport.

If this is right

  • Demixing persists over a wider interval of packing fractions when the potential is present.
  • Slower particles inside the bands near potential minima show stronger hexatic order.
  • A connected percolating band appears that is absent without the potential.
  • Long-time motion becomes sub-diffusive for cold particles and diffusive for hot particles along the potential axis, while both remain normally diffusive perpendicular to it.
  • Non-Gaussian displacement statistics appear that reflect the spatial separation of the two species.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same mechanism could be used to steer segregation in confined granular or cellular systems by tuning the shape or strength of an external field.
  • The transverse normal diffusion suggests that anisotropy is strictly aligned with the potential gradient and could be reversed by rotating the field direction.
  • The percolating band may act as a transport channel whose permeability changes with packing fraction, offering a route to density-controlled filtering in soft-matter devices.

Load-bearing premise

The demixing, ordering, and anisotropy arise specifically from the combination of the particles' differing diffusivities and the chosen one-dimensional external potential.

What would settle it

Running the same simulations with equal diffusivities for both species or with the external potential turned off and finding no percolating band or directional difference in long-time motion.

Figures

Figures reproduced from arXiv: 2605.29552 by Rashmi Trivedi, Subhajit Paul, Sumanta Kundu, Sunita Kumari.

Figure 1
Figure 1. Figure 1: FIG. 1. Typical steady-state snapshots of the binary system with particles having two different diffusivities (blue marking the “cold” and red [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Demixing parameter (DP) of the binary mixture system for different values of packing fraction [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Representative snapshots marking the hexatic order cor [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Mean-squared-displacement (MSD) of “hot” and “cold” tagged particle corresponding to [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Typical trajectories of a few “hot” particles after the system [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. MSDs [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Normalized distributions of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Mean-squared displacement [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Spatial arrangment of hot ( [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Representative trajectories of the center-of-mass (cm), [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Normalized distributions [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

Spontaneous demixing in active matter is a ubiquitous phenomenon that is crucial for numerous living processes ranging from bacterial swarming to sorting of cells in dense tissues. Here, we systematically investigate the effect of spatially varying potential acting along one direction and packing fraction on the binary mixture of particles with different diffusivities. Our results indicate that the presence of an external potential promotes demixing over a larger range of packing fractions, while also fostering a more pronounced 'hexatic order' within the bands of less diffusive "cold") particles formed near the minima of the potential. The mean-squared displacements (MSD) of "cold" and "hot" particles in different directions exhibit a distinct behavior. In contrast to the long-time sub-diffusive behavior of the "cold" particles, the "hot" ones display diffusive nature following an intermediate plateau. However, in the direction transverse to the applied potential, both types of particles undergo normal diffusion. Furthermore, interesting non-Gaussian characteristics are observed, corresponding to the spatial distribution of the displacement of "hot" and "cold" particles. Interestingly, our results reveal the formation of a 'percolating band', and the emergence of such dynamic anisotropy is not observed in the absence of an external potential. These aspects are highly relevant to the dynamics of various systems-including densely packed tissues, bacterial motility in confined spaces, and granular segregation in the pharmaceutical industry.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates the emergence of dynamical anisotropy in a binary mixture of particles with different diffusivities under a spatially varying external potential using molecular dynamics simulations. It claims that the external potential promotes demixing over a larger range of packing fractions, enhances hexatic order in the bands of less diffusive 'cold' particles, results in anisotropic mean squared displacements (sub-diffusive for cold particles and diffusive for hot particles along the potential direction, with normal diffusion transverse to it), non-Gaussian displacement distributions, and the formation of a percolating band leading to dynamic anisotropy that is absent without the external potential.

Significance. If the simulation results are robust, the work demonstrates a mechanism by which an external potential can induce directional dependence in particle dynamics through demixing in systems with heterogeneous diffusivity. This is relevant to understanding cell sorting in tissues, bacterial motility, and granular segregation. The inclusion of a control simulation without the potential provides a clear baseline for attributing the anisotropy to the potential. The study is simulation-based with no machine-checked proofs or parameter-free derivations noted.

major comments (1)
  1. The provided abstract and text do not detail the simulation methodology, such as the explicit form of the external potential, the diffusivity values for 'cold' and 'hot' particles, the particle interaction model, time step, system size, or criteria for data analysis and error estimation. This is a load-bearing issue because all central claims (demixing range, hexatic order, MSD behaviors, percolating band) rely on these simulation outcomes.
minor comments (2)
  1. The term 'hexatic order' is placed in quotes; if this refers to the standard six-fold bond orientational order parameter, it should be defined or referenced explicitly.
  2. The abstract would benefit from mentioning the range of packing fractions simulated and any quantitative measures of the demixing or anisotropy.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed feedback. We agree that explicit simulation methodology is essential for reproducibility and will add a dedicated Methods section in the revision.

read point-by-point responses

  1. Referee: The provided abstract and text do not detail the simulation methodology, such as the explicit form of the external potential, the diffusivity values for 'cold' and 'hot' particles, the particle interaction model, time step, system size, or criteria for data analysis and error estimation. This is a load-bearing issue because all central claims (demixing range, hexatic order, MSD behaviors, percolating band) rely on these simulation outcomes.

    Authors: We agree that the manuscript as submitted does not provide sufficient methodological detail. In the revised version we will insert a new Methods section that explicitly states the functional form of the external potential, the numerical values of diffusivity for cold and hot particles, the form of the interparticle potential, the integration time step, the system sizes employed, and the procedures used for computing MSD, hexatic order parameters, and error bars (including the number of independent runs and any block-averaging protocol). These additions will directly underpin the reported demixing range, ordering, and dynamical anisotropy. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper reports direct outputs from molecular dynamics simulations of a binary mixture with differential diffusivity under a spatially varying external potential. Key claims (enlarged demixing regime, hexatic order in cold-particle bands, direction-dependent MSD, non-Gaussian displacements, percolating band, and dynamic anisotropy) are obtained by comparing simulation runs with and without the potential across packing fractions. No analytical derivation chain, self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or described results. All quantities are computed from particle trajectories in the model; the zero-potential control is an independent simulation, not a circular input.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be extracted from the provided text.

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    2023