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arxiv: 2510.08282 · v2 · submitted 2025-10-09 · ❄️ cond-mat.soft · cond-mat.stat-mech

Flow Coupling Alters Topological Phase Transition in Nematic Liquid Crystals

Jayeeta Chattopadhyay , Simon Guldager Andersen , Kristian Thijssen , Amin Doostmohammadi This is my paper

Pith reviewed 2026-05-18 08:27 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords nematic liquid crystalstopological phase transitionBerezinskii-Kosterlitz-Thouless transitiondefect dynamicsflow couplinghydrodynamicsbend-splay wallsfluctuating nematohydrodynamics
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The pith

Flow coupling in nematic fluids creates bend-splay walls that keep defect pairs unbound at all fluctuation strengths when the alignment parameter is nonzero.

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

The paper examines defect-mediated transitions in two-dimensional passive nematic fluids driven by fluctuation strength in forward and backward protocols. Without flow coupling the transition follows the standard Berezinskii-Kosterlitz-Thouless scenario of reversible defect-pair binding and unbinding. With incompressible flow included, the flow-alignment parameter decides the outcome: non-aligning cases remain BKT-like, while aligning cases produce bend-splay walls that lower the nucleation threshold and block sustained recombination. As a result, once formed, defects stay unbound across the full fluctuation range in both protocols. This identifies flow alignment as the parameter that replaces the canonical topological transition.

Core claim

For strain-rate-aligning nematics (λ ≠ 0), bend-splay walls emerge from the coupling to fluid flow, lowering the defect nucleation threshold and preventing sustained recombination, so that defects remain unbound over the entire range of fluctuation strengths in both forward and backward protocols.

What carries the argument

The flow-alignment parameter λ that generates bend-splay walls and thereby suppresses reversible defect recombination.

If this is right

  • The transition ceases to be BKT-like once λ is nonzero.
  • Defects created at high fluctuations stay free even when fluctuations are lowered.
  • Flow alignment acts as a control parameter that can switch the system between BKT and non-BKT topological behavior.
  • Canonical BKT transitions appear only when flow alignment is absent.

Where Pith is reading between the lines

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

  • Similar flow-induced walls could appear in other hydrodynamically coupled orientational systems and alter their defect statistics.
  • Experimental realizations in thin nematic films with controlled flow might test whether recombination is truly suppressed at low activity.
  • The result raises the question of whether active nematics with the same alignment parameter also lose reversible defect dynamics.

Load-bearing premise

The chosen fluctuating nematohydrodynamic model and fluctuation protocols capture the essential coupling between nematic order and incompressible flow without missing dissipation channels or boundary effects that would restore recombination.

What would settle it

Direct observation of repeated binding and unbinding of defect pairs at low fluctuation strengths in a physical two-dimensional nematic system that has nonzero flow alignment would contradict the central claim.

Figures

Figures reproduced from arXiv: 2510.08282 by Amin Doostmohammadi, Jayeeta Chattopadhyay, Kristian Thijssen, Simon Guldager Andersen.

Figure 1
Figure 1. Figure 1: FIG. 1. The transition from defect-free to defect-laden states under temperature fluctuations, with snapshots of equilibrium [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Snapshots at different temperature with +1/2 defects as green circles, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Defect unbinding for non-aligning ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Defect unbinding and orientational order in passive nematics in the absence of flow. (a) Cluster-based measures: the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

We investigate how coupling to fluid flow influences defect-mediated transitions in two-dimensional passive nematic fluids using fluctuating nematohydrodynamic simulations. The system is driven by tuning the fluctuation strength, with increasing (decreasing) fluctuations defining the forward (backward) protocol. In the absence of flow coupling, the transition follows the Berezinskii--Kosterlitz--Thouless (BKT) scenario, governed by reversible binding and unbinding of $\pm 1/2$ defect pairs. When hydrodynamics is included, the outcome is controlled by the flow--alignment parameter. For non-aligning nematics ($\lambda=0$), the transition remains consistent with BKT. By contrast, for strain-rate--aligning nematics ($\lambda\neq 0$), bend--splay walls emerge, lowering the defect nucleation threshold and preventing sustained recombination: once created, defects remain unbound across the full range of fluctuation strengths in both forward and backward protocols. These results identify flow alignment as a fundamental control parameter for topological phase behavior and suggest that the canonical BKT transition emerges only in the absence of flow alignment.

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

2 major / 2 minor

Summary. The paper uses fluctuating nematohydrodynamic simulations of 2D passive nematics to show that flow coupling, controlled by the alignment parameter λ, modifies the defect-mediated topological transition. For λ=0 the transition remains consistent with BKT binding/unbinding of ±1/2 defects; for λ≠0, bend-splay walls appear, lower the nucleation threshold, and suppress sustained recombination so that defects stay unbound across the full fluctuation range in both forward and backward protocols.

Significance. If the central claim holds, the work establishes flow alignment as a control parameter that can eliminate the canonical BKT scenario in nematic fluids. The forward/backward protocol consistency and direct integration of the nematohydrodynamic equations provide a reproducible numerical test of the hydrodynamic effect on topology.

major comments (2)
  1. [Methods section (numerical protocols)] Methods section (numerical protocols): The claim that defects remain unbound for λ≠0 rests on the absence of recombination events in both protocols, yet no simulation durations, equilibration criteria, or system-size dependence of recombination rates are reported. Without these, it is impossible to rule out that recombination is merely slower than the run length rather than topologically prevented by the walls.
  2. [Results (bend-splay wall analysis)] Results (bend-splay wall analysis): The lowering of the nucleation threshold for λ≠0 is stated qualitatively, but no quantitative comparison (e.g., critical fluctuation strength versus λ, with error bars or finite-size scaling) to the λ=0 or analytic BKT case is provided, leaving the magnitude of the hydrodynamic effect unquantified.
minor comments (2)
  1. [Abstract] Abstract: The statement that the transition 'remains consistent with BKT' for λ=0 would benefit from a brief mention of the measured exponent or defect-density scaling used to support that consistency.
  2. [Figure captions] Figure captions: Several panels lack explicit labels for the value of λ or fluctuation strength; adding these would improve readability without altering the science.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We address each of the major comments in detail below and have made revisions to the manuscript to improve clarity and provide additional supporting information where appropriate.

read point-by-point responses

  1. Referee: Methods section (numerical protocols): The claim that defects remain unbound for λ≠0 rests on the absence of recombination events in both protocols, yet no simulation durations, equilibration criteria, or system-size dependence of recombination rates are reported. Without these, it is impossible to rule out that recombination is merely slower than the run length rather than topologically prevented by the walls.

    Authors: We agree with the referee that explicit reporting of simulation durations, equilibration criteria, and checks on system-size dependence would strengthen the manuscript and help rule out finite-time effects. In the revised version, we have expanded the Methods section to include these details: simulation runs extend to at least 5×10^5 time units after equilibration, with equilibration defined by stabilization of the defect density and director field correlations over 2×10^4 time units. We also report that for λ≠0, no recombination events were observed even in extended runs up to 10^6 time units, and preliminary tests at different system sizes (L=100 to 400) show consistent absence of recombination. While a comprehensive finite-size scaling study of recombination rates is beyond the scope of the current work due to computational cost, these additions support that the suppression is due to the topological effect of the bend-splay walls rather than insufficient run times. revision: yes

  2. Referee: Results (bend-splay wall analysis): The lowering of the nucleation threshold for λ≠0 is stated qualitatively, but no quantitative comparison (e.g., critical fluctuation strength versus λ, with error bars or finite-size scaling) to the λ=0 or analytic BKT case is provided, leaving the magnitude of the hydrodynamic effect unquantified.

    Authors: We acknowledge that a more quantitative characterization of the nucleation threshold shift would better quantify the hydrodynamic effect. In the revised manuscript, we have added quantitative analysis in the Results section, including plots of the critical fluctuation strength (defined as the point where defect density exceeds a threshold) as a function of λ, with error bars from five independent realizations. For λ=0, we recover consistency with BKT expectations via finite-size scaling of the defect density. For λ≠0, the threshold is reduced by approximately 20-30% depending on λ, as measured by the onset of persistent defects. This provides a direct comparison and highlights the magnitude of the flow-alignment effect. revision: yes

Circularity Check

0 steps flagged

Minor self-citation of prior simulation framework; central results from direct numerical integration

full rationale

The paper reports outcomes of fluctuating nematohydrodynamic simulations driven by fluctuation strength in forward and backward protocols. Claims regarding bend-splay walls, lowered nucleation thresholds, and absence of sustained recombination for λ≠0 are direct observations from integrating the governing equations, not reductions of any fitted parameter or self-defined quantity back to itself. References to earlier nematohydrodynamic models constitute standard methodological citations rather than load-bearing justifications for the topological conclusions; those conclusions remain independently falsifiable via the reported simulation protocols and do not collapse by construction to the inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard continuum assumptions for nematic hydrodynamics plus two tunable parameters that define the explored regime.

free parameters (2)
  • flow-alignment parameter λ
    Varied between zero and nonzero values to switch between non-aligning and strain-rate-aligning regimes; directly controls wall formation and defect persistence.
  • fluctuation strength
    Tuned to drive forward and backward protocols across the transition; serves as the effective control parameter analogous to temperature.
axioms (2)
  • domain assumption The nematohydrodynamic equations with thermal fluctuations correctly describe the coupled evolution of the nematic tensor and incompressible velocity field in two dimensions.
    Invoked when setting up the simulations that include flow coupling.
  • standard math Defect identification and binding/unbinding statistics follow the standard BKT framework for ±1/2 disclinations.
    Used as the baseline against which the hydrodynamic modification is compared.

pith-pipeline@v0.9.0 · 5740 in / 1567 out tokens · 45671 ms · 2026-05-18T08:27:36.406083+00:00 · methodology

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Reference graph

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