Pith. sign in

REVIEW 1 major objections 47 references

Collective phases in overdamped magnetic self-propelled spherocylinders

T0 review · 1 major / 0 minor · reviewed 2026-06-26 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Elongated particles with separated magnetic monopoles tune through gas, flock, chain, vortex and dimer phases via two adjustable parameters.

desk verdict The dumbbell monopole model adds a geometric torque lever that maps out new phases in magnetic spherocylinders, but the paper asserts rather than demonstrates that point-dipole versions cannot reach the same states. read the letter →

arxiv 2606.19498 v1 pith:57UHWRLH submitted 2026-06-17 cond-mat.soft cond-mat.stat-mech

Francisca Guzmán-Lastra , Néstor Sepúlveda This is my paper · ORCID
classification cond-mat.softcond-mat.stat-mech
keywords magneticactivematterself-propelledspherocylinderscollectivephasesdumbbellmodeloverdampeddynamicsphasediagramstericandtorque
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper examines the collective dynamics of overdamped self-propelled spherocylinders whose magnetic interactions are represented by two opposite monopoles placed a distance ℓ apart along each particle's long axis. Varying this separation together with overall dipole strength produces a sequence of states that includes a disordered gas, polar flocks, chains, vortex-aligned configurations, and locked dimers. A reader would care because the two parameters map directly onto the physical length and magnetization of real cylindrical particles, supplying a concrete experimental route to select among coherent states in magnetic active matter.

What carries the argument

dumbbell monopole model of separation ℓ that supplies an explicit geometric lever arm for magnetic torque on elongated particles

What would settle it

Simulations or experiments that replace the separated monopoles with true point dipoles at the particle center and still recover the full sequence of gas, flock, chain, vortex and dimer phases would falsify the claim that distributed charge is required.

Watch

Extended reading notes

Core claim

Particle elongation combined with a dumbbell distribution of magnetic charge supplies a minimal, experimentally accessible pair of tuning knobs that let the system traverse a landscape of collective states—gas, polar flock, chain, vortex-alignment, and locked-dimer phases—by letting magnetic torque compete with steric alignment in a geometry inaccessible to point-dipole or disk models.

Load-bearing premise

The dumbbell monopole model with separation ℓ introduces a geometric lever arm for magnetic torque that competes with steric alignment in a manner inaccessible to point-dipole or disk models.

Editorial extensions

If this is right

  • Independent control of monopole separation and dipole strength is sufficient to select among five distinct collective phases.
  • The dumbbell representation remains well-defined at short range where point-dipole approximations break down.
  • The resulting phase diagram supplies design rules for self-organized magnetic microswimmers and active colloidal assemblies.
  • Steric and magnetic torques can be balanced through particle aspect ratio and magnetization without additional external fields.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Real cylindrical magnets of controllable length and magnetization should be able to traverse the same phase sequence in laboratory realizations.
  • The locked-dimer state may provide a route to stable, magnetically bound clusters that could be harvested for larger-scale assembly.
  • Extending the same two-parameter scan to three dimensions or to particles with different aspect ratios would test how robust the reported states remain.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 0 minor

Summary. The manuscript presents a two-dimensional simulation study of overdamped self-propelled spherocylinders whose magnetic interactions are modeled as dumbbell monopoles of strength ±Q separated by distance ℓ along the particle axis. By independently varying ℓ and Q (parameters that map to experimental magnet geometry and magnetization), the authors report a sequence of collective phases—gas, polar flock, chain, vortex-alignment, and locked-dimer—arising from the competition between magnetic torque (enabled by the geometric lever arm of the dumbbell) and steric alignment. The central claim is that particle elongation combined with distributed magnetic charge supplies a minimal, experimentally accessible set of tuning knobs unavailable to point-dipole or disk models.

Significance. If the reported phases are shown to be inaccessible under equivalent point-dipole treatments on the same spherocylinder geometry, the work would supply a concrete, minimal-parameter route to controlling coherent states in magnetic active matter and would directly inform the design of self-organized magnetic microswimmers and colloidal assemblies. The mapping of ℓ and Q to laboratory quantities is a practical strength.

major comments (1)
  1. [Abstract / Model section] Abstract and model description: the assertion that the dumbbell-monopole geometry produces phases (vortex-alignment, locked-dimer) inaccessible to point-dipole or disk models is load-bearing for the central claim, yet the manuscript provides no side-by-side simulations of an equivalent point-dipole treatment on the identical spherocylinder shape and propulsion parameters. Without such comparisons it is impossible to determine whether the observed states require the explicit lever arm of the dumbbell or could arise from finite-size or higher-multipole effects already present in elongated point-dipole particles.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive critique. The major comment correctly identifies a gap in our presentation of the central claim. We address it below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / Model section] Abstract and model description: the assertion that the dumbbell-monopole geometry produces phases (vortex-alignment, locked-dimer) inaccessible to point-dipole or disk models is load-bearing for the central claim, yet the manuscript provides no side-by-side simulations of an equivalent point-dipole treatment on the identical spherocylinder shape and propulsion parameters. Without such comparisons it is impossible to determine whether the observed states require the explicit lever arm of the dumbbell or could arise from finite-size or higher-multipole effects already present in elongated point-dipole particles.

    Authors: We agree that the absence of direct comparisons weakens the load-bearing assertion in the abstract and model section. The dumbbell construction supplies an explicit geometric lever arm for torque that is absent when the same total dipole moment is placed at the particle center. However, without side-by-side runs it remains possible that finite-size effects or higher multipoles already present in elongated point-dipole spherocylinders could produce similar states. In the revised manuscript we will add a dedicated comparison section (or supplementary figure) that repeats the full phase diagram using a point-dipole interaction on identical spherocylinder geometry, propulsion speed, and packing fraction. These new simulations will be used to test whether the vortex-alignment and locked-dimer phases survive or disappear under the point-dipole treatment. The abstract and model description will be updated to reflect the outcome of this test. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: simulation study with independent numerical exploration

full rationale

The paper is a purely numerical simulation study of overdamped self-propelled spherocylinders using a dumbbell monopole model. No equations, fitted parameters, or predictions are presented that reduce by construction to inputs, self-citations, or ansatzes. Central claims about accessible phases rest on direct variation of monopole separation ℓ and dipole strength Q in simulations, with no load-bearing derivations or uniqueness theorems invoked. The work is self-contained against external benchmarks as a parameter-sweep exploration.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the dumbbell model being a valid short-range representation and on numerical exploration of parameter space; no independent evidence or machine-checked elements are described.

free parameters (2)
  • monopole separation ℓ
    Independently varied to map onto cylindrical magnet geometry; controls lever arm for torque.
  • dipole strength Q
    Independently varied to control magnetization strength.
assumptions (2)
  • domain assumption Overdamped dynamics in two dimensions
    Standard modeling choice for colloidal active matter at low Reynolds number, invoked to justify the simulation framework.
  • ad hoc to paper Dumbbell monopole model accurately captures magnetic torque competition with steric alignment
    Introduced in the abstract as the key modeling choice enabling new phases.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Collective phases in overdamped magnetic self-propelled spherocylinders." pith.science (2026). https://pith.science/paper/57UHWRLH

@misc{pith2026260619498,
  author       = {Pith},
  title        = {Pith review of: Collective phases in overdamped magnetic self-propelled spherocylinders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/57UHWRLH}},
  note         = {Machine review of arXiv:2606.19498}
}
abstract

We study the collective dynamics of self-propelled spherocylinders carrying magnetic dipole moments in two dimensions. Magnetic interactions are modeled as two opposite monopoles $\pm Q$ separated by a distance $\ell$ along the particle director, a dumbbell model that remains well-defined at short range and introduces an explicit geometric lever arm for the magnetic torque. This approach, combined with the elongated particle geometry, produces a torque that competes with steric alignment in a manner inaccessible to point-dipole or disk models. By independently varying monopole separation and dipole strength (parameters that map directly onto the geometry and magnetization of cylindrical magnets) we show that the system navigates a rich landscape of collective states: gas, polar flock, chain, vortex-alignment, and locked-dimer phases. Our results establish that particle elongation and distributed magnetic charge together provide a minimal, experimentally accessible set of tuning knobs for controlling coherent states in magnetic active matter, with direct implications for the design of self-organized magnetic microswimmers and active colloidal assemblies.

Figures

Figures reproduced from arXiv: 2606.19498 by the authors.

Figure 1
Figure 1. FIG. 1: Two interacting self-propelled spherocylinders [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Steady-state configurations at Π [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4: Phase diagram in the Π [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (2 more)
Figure 3
Figure 3. Figure 3: FIG. 3: Dimensionless two-particle contact energies [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Cluster size scale [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 2 canonical work pages

  1. [1]

    ,(7) ¯εblocked =− 2Π2 3 1 2 − 1p 9Π2 1 + 4 ! .(8) Both vanish at Π 1 = 0 and are linear in Π 2 (Fig. 3). The ratio R(Π1)≡ |¯εblocked| |¯εchain| = 5(25−9Π 2 1) 9Π2 1 1 2 − 1p 9Π2 1 + 4 ! (9) isindependent ofΠ 2 and decreases monotonically from R≈7.4 at Π 1 = 0.17 toR≈1.3 at Π 1 = 1.17. This inde- pendence is the key to reading the phase diagram: the en- er...

  2. [2]

    The mechanics and statistics of active matter.Annual Review of Condensed Matter Physics, 1(Volume 1, 2010):323–345, 2010

    Sriram Ramaswamy. The mechanics and statistics of active matter.Annual Review of Condensed Matter Physics, 1(Volume 1, 2010):323–345, 2010

    2010

  3. [3]

    The 2025 motile active matter roadmap.Journal of Physics: Condensed Matter, 37(14):143501, 2025

    Gerhard Gompper, Howard A Stone, Christina Kurzthaler, David Saintillan, Fernado Peruani, Dmitry A Fedosov, Thorsten Auth, Cecile Cottin- Bizonne, Christophe Ybert, Eric Cl´ ement, et al. The 2025 motile active matter roadmap.Journal of Physics: Condensed Matter, 37(14):143501, 2025

    2025

  4. [4]

    Novel type of phase transi- tion in a system of self-driven particles.Phys

    Tam´ as Vicsek, Andr´ as Czir´ ok, Eshel Ben-Jacob, Inon Cohen, and Ofer Shochet. Novel type of phase transi- tion in a system of self-driven particles.Phys. Rev. Lett., 75:1226–1229, Aug 1995

    1995

  5. [5]

    M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha. Hydrodynamics of soft active matter.Rev. Mod. Phys., 85:1143–1189, Jul 2013

    2013

  6. [6]

    Nonequilibrium clustering of self-propelled rods.Phys

    Fernando Peruani, Andreas Deutsch, and Markus B¨ ar. Nonequilibrium clustering of self-propelled rods.Phys. Rev. E, 74:030904(R), Sep 2006

    2006

  7. [7]

    Self-propelled rods exhibit a phase-separated state characterized by the presence of active stresses and the ejection of polar clusters.Physical Review E, 92(1):012322, 2015

    Sebastian Weitz, Andreas Deutsch, and Fernando Pe- ruani. Self-propelled rods exhibit a phase-separated state characterized by the presence of active stresses and the ejection of polar clusters.Physical Review E, 92(1):012322, 2015

    2015

  8. [8]

    Large-scale pat- terns in a minimal cognitive flocking model: Incidental leaders, nematic patterns, and aggregates.Phys

    Lucas Barberis and Fernando Peruani. Large-scale pat- terns in a minimal cognitive flocking model: Incidental leaders, nematic patterns, and aggregates.Phys. Rev. Lett., 117:248001, Dec 2016

    2016

Show all 47 references
  1. [9]

    Collective dynamics and pair-distribution func- tion of active brownian ellipsoids in two spatial dimen- sions.Communications Physics, 7(1):238, 2024

    Stephan Br¨ oker, Michael te Vrugt, and Raphael Wit- tkowski. Collective dynamics and pair-distribution func- tion of active brownian ellipsoids in two spatial dimen- sions.Communications Physics, 7(1):238, 2024

    2024

  2. [10]

    Wensink, J¨ orn Dunkel, Sebastian Heiden- reich, Knut Drescher, Raymond E

    Henricus H. Wensink, J¨ orn Dunkel, Sebastian Heiden- reich, Knut Drescher, Raymond E. Goldstein, Hartmut L¨ owen, and Julia M. Yeomans. Meso-scale turbulence in living fluids.Proceedings of the National Academy of Sciences, 109(36):14308–14313, 2012

    2012

  3. [11]

    Active turbulence.Annual Review of Condensed Matter Physics, 13(1):143–170, 2022

    Ricard Alert, Jaume Casademunt, and Jean-Fran¸ cois Joanny. Active turbulence.Annual Review of Condensed Matter Physics, 13(1):143–170, 2022

    2022

  4. [12]

    Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence.Soft Matter, 18(33):6179– 6191, 2022

    Arne W Zantop and Holger Stark. Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence.Soft Matter, 18(33):6179– 6191, 2022

    2022

  5. [13]

    Shape anisotropy governs organization of active rods: Swarming, turbulence, flocking, and jamming.Sci- ence, 392(6794):202–206, 2026

    Yogesh Shelke, Anpuj Nair S, and Hanumantha Rao Vu- tukuri. Shape anisotropy governs organization of active rods: Swarming, turbulence, flocking, and jamming.Sci- ence, 392(6794):202–206, 2026

    2026

  6. [14]

    Mag- netotactic bacteria in a droplet self-assemble into a rotary motor.Nature Communications, 10(1):5082, 2019

    Benoit Vincenti, Gabriel Ramos, Maria Luisa Cordero, Carine Douarche, Rodrigo Soto, and Eric Clement. Mag- netotactic bacteria in a droplet self-assemble into a rotary motor.Nature Communications, 10(1):5082, 2019

    2019

  7. [15]

    Destabilization of a flow focused suspension of magne- totactic bacteria.Physical Review Fluids, 1(5):053203, 2016

    Nicolas Waisbord, Christopher T Lef` evre, Lyd´ eric Boc- quet, Christophe Ybert, and C´ ecile Cottin-Bizonne. Destabilization of a flow focused suspension of magne- totactic bacteria.Physical Review Fluids, 1(5):053203, 2016

    2016

  8. [16]

    Phases of active matter composed of multicellular magnetotactic bacteria near a hard surface.Physical Review Fluids, 7(5):053102, 2022

    Alexander Petroff, Alejandra Rosselli-Calderon, Ben Roque, and Pradeep Kumar. Phases of active matter composed of multicellular magnetotactic bacteria near a hard surface.Physical Review Fluids, 7(5):053102, 2022

    2022

  9. [17]

    Dongdong Jin and Li Zhang. Collective behaviors of magnetic active matter: Recent progress toward reconfigurable, adaptive, and multifunctional swarm- ing micro/nanorobots.Accounts of Chemical Research, 55(1):98–109, 2021

    2021

  10. [18]

    Magnetic active matter based on helical propulsion.Accounts of chemical research, 51(11):2689– 2698, 2018

    Pranay Mandal, Gouri Patil, Hreedish Kakoty, and Am- barish Ghosh. Magnetic active matter based on helical propulsion.Accounts of chemical research, 51(11):2689– 2698, 2018

    2018

  11. [19]

    Winkler, Gerhard Gompper, Igor S

    Gaˇ sper Kokot, Shibananda Das, Roland G. Winkler, Gerhard Gompper, Igor S. Aranson, and Alexey Snezhko. Active turbulence in a gas of self-assembled spin- ners.Proceedings of the National Academy of Sciences, 114(49):12870–12875, 2017

    2017

  12. [20]

    Aran- son

    Andreas Kaiser, Alexey Snezhko, and Igor S. Aran- son. Flocking ferromagnetic colloids.Science Advances, 3(2):e1601469, 2017

    2017

  13. [21]

    Emergence of reconfig- urable wires and spinners via dynamic self-assembly.Sci- entific reports, 5(1):9528, 2015

    Gasper Kokot, David Piet, George M Whitesides, Igor S Aranson, and Alexey Snezhko. Emergence of reconfig- urable wires and spinners via dynamic self-assembly.Sci- entific reports, 5(1):9528, 2015

    2015

  14. [22]

    Dy- namical self-assembly of dipolar active brownian particles in two dimensions.Soft Matter, 16(9):2208–2223, 2020

    Guo-Jun Liao, Carol K Hall, and Sabine HL Klapp. Dy- namical self-assembly of dipolar active brownian particles in two dimensions.Soft Matter, 16(9):2208–2223, 2020

    2020

  15. [23]

    Collective dynamics of dipolar self-propelled particles

    N Vanesse, E Opsomer, G Lumay, and N Vandewalle. Collective dynamics of dipolar self-propelled particles. Physical Review E, 108(2):024608, 2023

    2023

  16. [24]

    Emergent hydrodynamic bound states between magnetically powered micropropellers.Science advances, 4(1):eaap9379, 2018

    Fernando Martinez-Pedrero, Eloy Navarro-Argem´ ı, An- tonio Ortiz-Ambriz, Ignacio Pagonabarraga, and Pietro Tierno. Emergent hydrodynamic bound states between magnetically powered micropropellers.Science advances, 4(1):eaap9379, 2018

    2018

  17. [25]

    Recent advances in anisotropic magnetic colloids: realization, assembly and applications.Physical chemistry chemical physics, 16(43):23515–23528, 2014

    Pietro Tierno. Recent advances in anisotropic magnetic colloids: realization, assembly and applications.Physical chemistry chemical physics, 16(43):23515–23528, 2014

    2014

  18. [26]

    Aranson, and Alexey Snezhko

    Koohee Han, Gaˇ sper Kokot, Oleh Tovkach, Andreas Glatz, Igor S. Aranson, and Alexey Snezhko. Emergence of self-organized multivortex states in flocks of active rollers.Proceedings of the National Academy of Sciences, 117(18):9706–9711, 2020

    2020

  19. [27]

    Simulations of struc- ture formation by confined dipolar active particles.Soft Matter, 16(46):10537–10547, 2020

    Vitali Telezki and Stefan Klumpp. Simulations of struc- ture formation by confined dipolar active particles.Soft Matter, 16(46):10537–10547, 2020

    2020

  20. [28]

    Emergent vortices and phase separation in systems of chiral active particles with dipolar interactions.Soft Matter, 17(28):6833–6847, 2021

    Guo-Jun Liao and Sabine HL Klapp. Emergent vortices and phase separation in systems of chiral active particles with dipolar interactions.Soft Matter, 17(28):6833–6847, 2021

    2021

  21. [29]

    Fission and fusion scenarios for mag- netic microswimmer clusters.Nature Communications, 7(1):13519, 2016

    Francisca Guzm´ an-Lastra, Andreas Kaiser, and Hart- mut L¨ owen. Fission and fusion scenarios for mag- netic microswimmer clusters.Nature Communications, 7(1):13519, 2016

    2016

  22. [30]

    Transport and assem- bly of magnetic surface rotors.ChemNanoMat, 7(8):881– 893, 2021

    Pietro Tierno and Alexey Snezhko. Transport and assem- bly of magnetic surface rotors.ChemNanoMat, 7(8):881– 893, 2021

    2021

  23. [31]

    Swimming with magnets: from bio- logical organisms to synthetic devices.Physics Reports, 789:1–54, 2019

    Stefan Klumpp, Christopher T Lef` evre, Mathieu Bennet, and Damien Faivre. Swimming with magnets: from bio- logical organisms to synthetic devices.Physics Reports, 789:1–54, 2019

    2019

  24. [32]

    Emergent pattern formation of active magnetic suspensions in an external field.New Journal of Physics, 22(10):103007, 2020

    Fabian R Koessel and Sara Jabbari-Farouji. Emergent pattern formation of active magnetic suspensions in an external field.New Journal of Physics, 22(10):103007, 2020

    2020

  25. [33]

    Controlling 7 stability and transport of magnetic microswimmers by an external field.Europhysics Letters, 125(2):28001, 2019

    Fabian R Koessel and Sara Jabbari-Farouji. Controlling 7 stability and transport of magnetic microswimmers by an external field.Europhysics Letters, 125(2):28001, 2019

    2019

  26. [34]

    Patterns of active dipolar particles in external magnetic fields.Physical Re- view E, 112(6):065422, 2025

    Vitali Telezki and Stefan Klumpp. Patterns of active dipolar particles in external magnetic fields.Physical Re- view E, 112(6):065422, 2025

    2025

  27. [35]

    Modulation of nonequilibrium structures of active dipolar particles by an external field.Physical Review E, 112(6):065402, 2025

    Baptiste Parage and Sara Jabbari-Farouji. Modulation of nonequilibrium structures of active dipolar particles by an external field.Physical Review E, 112(6):065402, 2025

    2025

  28. [36]

    Dy- namics of magnetic self-propelled particles in a harmonic trap.arXiv preprint arXiv:2403.02569, 2024

    Pamela Mu˜ noz Obreque, Oscar Garrido, Diego Romero, Hartmut L¨ owen, and Francisca Guzm´ an-Lastra. Dy- namics of magnetic self-propelled particles in a harmonic trap.arXiv preprint arXiv:2403.02569, 2024

    2024

  29. [37]

    Fluidiza- tion induced by magnetic interactions in confined active matter.Physical Review E, 113(5):055413, 2026

    Marco Musacchio, Markus Felber, Matteo Paoluzzi, An- drea Gnoli, Andrea Puglisi, and Luca Angelani. Fluidiza- tion induced by magnetic interactions in confined active matter.Physical Review E, 113(5):055413, 2026

    2026

  30. [38]

    Bioinspired magnetic active matter and the physical limits of magnetotaxis.arXiv preprint arXiv:2111.04889, 2021

    N´ estor Sep´ ulveda, Francisca Guzm´ an-Lastra, Miguel Carrasco, Bernardo Gonz´ alez, Eugenio Hamm, and Andr´ es Concha. Bioinspired magnetic active matter and the physical limits of magnetotaxis.arXiv preprint arXiv:2111.04889, 2021

    2021 arXiv

  31. [39]

    Magnetic monopoles in spin ice.Nature, 451(7174):42–45, 2008

    Claudio Castelnovo, Roderich Moessner, and Shivaji L Sondhi. Magnetic monopoles in spin ice.Nature, 451(7174):42–45, 2008

    2008

  32. [40]

    Macroscopic magnetic frustration.Physical review let- ters, 109(25):257203, 2012

    Paula Mellado, Andres Concha, and L Mahadevan. Macroscopic magnetic frustration.Physical review let- ters, 109(25):257203, 2012

    2012

  33. [41]

    The influence of shape anisotropy on the mi- crostructure of magnetic dipolar particles.Soft Matter, 9(29):6594–6603, 2013

    Sofia Kantorovich, Elena Pyanzina, and Francesco Sciortino. The influence of shape anisotropy on the mi- crostructure of magnetic dipolar particles.Soft Matter, 9(29):6594–6603, 2013

    2013

  34. [42]

    De- signing hysteresis with dipolar chains.Physical review letters, 120(15):157202, 2018

    Andr´ es Concha, David Aguayo, and Paula Mellado. De- signing hysteresis with dipolar chains.Physical review letters, 120(15):157202, 2018

    2018

  35. [43]

    See Supplemental Material at [URL will be inserted by publisher] for details of the numerical methods, addi- tional figures, and supplementary analyses

  36. [44]

    Soft magnetic microrobots with remote sensing and communication ca- pabilities.Nature Communications, 16(1):10489, 2025

    Quan Gao, Minsoo Kim, Denis Von Arx, Elric Zhang, Xinzhi Zhang, Hao Ye, Christian Vogt, Claas Ehmke, Dianne Corsino, Federica Catania, et al. Soft magnetic microrobots with remote sensing and communication ca- pabilities.Nature Communications, 16(1):10489, 2025

    2025

  37. [45]

    Nature-inspired miniaturized magnetic soft robotic swimmers.Applied Physics Reviews, 11(2), 2024

    Ratnadeep Pramanik, RWCP Verstappen, and PR Onck. Nature-inspired miniaturized magnetic soft robotic swimmers.Applied Physics Reviews, 11(2), 2024

    2024

  38. [46]

    Active dipole clusters: From helical motion to fission

    Andreas Kaiser, Katarina Popowa, and Hartmut L¨ owen. Active dipole clusters: From helical motion to fission. Physical Review E, 92(1):012301, 2015

    2015

  39. [47]

    Pro- gramming structural and magnetic anisotropy for tai- lored interaction and control of soft microrobots.Com- munications Engineering, 3(1):7, 2024

    Yimo Yan, Chao Song, Zaiyi Shen, Yuechen Zhu, Xingyu Ni, Bin Wang, Michael G Christiansen, Stavros Stavrakis, Juho S Lintuvuori, Baoquan Chen, et al. Pro- gramming structural and magnetic anisotropy for tai- lored interaction and control of soft microrobots.Com- munications En...

    2024

Pith tools

Reviewed June 26, 2026 · model on record in the stance chip above.