Paper Citation Record · LEDGER

A Smoluchowski equation for a sheared suspension of frictionally interacting rods

As of 10 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 2 inbound Pith citation observations for arXiv:2512.19149.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2512.19149 v3

Coverage vector

measured 52 of 52 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-03T14:58:20.104977Z

measured 54 of 54 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T14:58:19.964701Z

measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

52 of 52 outbound references displayed

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External citation measurements

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Outbound references

Observation 172111f5-d0c8-4288-8dbd-7fa840609997 · outbound

This paper cites V.6 to calculate the dynamical equation for the order tensorQ.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods V.6 to calculate the dynamical equation for the order tensorQ

Reference 1

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Observation 0c692e55-5280-4c9e-bfe2-e2db93b65d63 · outbound

This paper cites Odijk, Polyelectrolytes near the rod limit, Journal of Polymer Science: Polymer Physics Edition15, 477 (1977).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Odijk, Polyelectrolytes near the rod limit, Journal of Polymer Science: Polymer Physics Edition15, 477 (1977)

Reference 2

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Observation 6e6650fb-d837-48b2-a1b7-4a8c155222a9 · outbound

This paper cites an unresolved cited work.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 3

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Observation 9743af5c-af80-43dc-8446-f68856c3ee17 · outbound

This paper cites This term can be evaluated using the following identity [40], ∫ ( ˆu ˆu− ˆI.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods This term can be evaluated using the following identity [40], ∫ ( ˆu ˆu− ˆI

Reference 4

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Observation 2d6d6d82-2705-4ab3-b8f4-2df2da701491 · outbound

This paper cites FRICTIONAL CONTRIBUTION TO THE STRESS We have thus-far constructed the Rayleighian on a per- particle basis.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods FRICTIONAL CONTRIBUTION TO THE STRESS We have thus-far constructed the Rayleighian on a per- particle basis

Reference 5

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Observation b33fd8f9-32a3-4dae-993c-d2d18aa17dc9 · outbound

This paper cites Bj¨ orkman, The nonlinear history of fibre flow research.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Bj¨ orkman, The nonlinear history of fibre flow research

Reference 6

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Observation 41051de9-5460-4705-bf99-324c56d18614 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 7

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Observation 3d9c26a5-a659-49ec-a059-a565c0f0543c · outbound

This paper cites an unresolved cited work.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 8

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Observation e711cb1b-bf6e-436d-ad3b-10ddf94d0cfd · outbound

This paper cites Fernandez, R.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Fernandez, R

Reference 9

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Observation 347a9ee8-54d6-40fb-9756-e0081fed9708 · outbound

This paper cites Lootens, H.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Lootens, H

Reference 10

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Observation 54520daa-ab66-4cce-bef2-2770797177f6 · outbound

This paper cites Wyart and M.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Wyart and M

Reference 11

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Observation 3ee78c6f-84a6-4c27-ac5b-6683d0d70581 · outbound

This paper cites Phan-Thien and A.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Phan-Thien and A

Reference 12

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Observation 33656b15-cd92-4033-922a-75674b77bfc0 · outbound

This paper cites Jeffery, The motion of ellipsoidal particles in a vis- cous fluid, Proc.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Jeffery, The motion of ellipsoidal particles in a vis- cous fluid, Proc

Reference 13

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 14

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Observation 6a0310fb-fac9-48ce-a1fb-6412fabf1557 · outbound

This paper cites A Smoluchowski equation for a sheared suspension of frictionally interacting rods.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods A Smoluchowski equation for a sheared suspension of frictionally interacting rods

Reference 15

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Observation ca4a6a73-fb52-43e8-9cd2-506c6c622095 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 16

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Observation b30e7b38-2555-4dbc-b5fc-3a54a7cab89a · outbound

This paper cites Folgar and C.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Folgar and C

Reference 17

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Observation f01e8866-3ccb-42aa-b10f-c4045df558d5 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 18

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Observation ab277656-a0d7-46c9-9e39-f893af1f504f · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 19

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Observation 8963a652-5bcc-4822-a682-5103c107338e · outbound

This paper cites Tseng, A constitutive equation for fiber suspen- sions in viscoelastic media, Physics of Fluids33, 071702 (2021).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Tseng, A constitutive equation for fiber suspen- sions in viscoelastic media, Physics of Fluids33, 071702 (2021)

Reference 20

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Observation 3063b725-4709-496c-aba1-eb9dc91c7131 · outbound

This paper cites Doi and S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Doi and S

Reference 21

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Observation e1ea3228-7b8c-47c3-a7d2-c708405bfc7c · outbound

This paper cites Doi, Onsager’s variational principle in soft matter, Journal of Physics-Condensed Matter23, 284118 (2011).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Doi, Onsager’s variational principle in soft matter, Journal of Physics-Condensed Matter23, 284118 (2011)

Reference 22

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Observation 85242a78-6e84-45ba-87ff-c2c14972d851 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 23

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Observation 71429ed1-5d71-49a1-9bbf-c2f150b17093 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 24

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Observation c542936d-95af-426d-ab42-ef5e7deef32f · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 25

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Observation 6cc08a15-4c9e-44e8-ab2b-5d100614085c · outbound

This paper cites Tapia, S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Tapia, S

Reference 26

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Observation 180e92b6-7b47-4c4d-8b85-fbf85b7feb30 · outbound

This paper cites Rathee, S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Rathee, S

Reference 27

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Observation 4d02fbb5-033a-4e8e-afe0-62549dc4869e · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 28

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Observation 2d42b80b-1c68-4f9d-8dbe-841446f769fe · outbound

This paper cites Singh, Hidden hierarchy in the rheology of dense sus- pensions, MRS Communications13, 971 (2023).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Singh, Hidden hierarchy in the rheology of dense sus- pensions, MRS Communications13, 971 (2023)

Reference 29

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Observation c16a6738-4bff-4a67-96ae-368727afb84f · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 30

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Observation 3ad48a9c-6651-4b9f-84c9-ba2233726e89 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 31

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Observation 860a6e40-8046-4d79-b4ff-84a01a2042e5 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 32

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Observation 20091027-46b7-4854-85d3-eb76bd009c62 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 33

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Observation 69a633a8-b639-4520-9760-0c4a72bec258 · outbound

This paper cites Toll and J.-A.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Toll and J.-A

Reference 34

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Observation d1251ab2-fb98-4224-859a-a16d649da3c5 · outbound

This paper cites Djalili-Moghaddam and S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Djalili-Moghaddam and S

Reference 35

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Observation c51b3429-5633-43f9-98f9-f7bac3376893 · outbound

This paper cites Bounoua, E.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Bounoua, E

Reference 36

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Observation 96136c2b-0234-4002-a7c4-3e2542be7da4 · outbound

This paper cites Doi and S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Doi and S

Reference 37

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Observation 2d3b07b5-f544-4c30-9164-8c90295df3cf · outbound

This paper cites Doi,Soft Matter Physics(Oxford University Press, Oxford, 2013).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Doi,Soft Matter Physics(Oxford University Press, Oxford, 2013)

Reference 38

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Observation 8f9e1da0-d2ed-4741-8cc9-92904d5b89c7 · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 39

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Observation b1835bb5-8ba7-4e54-9380-f6e2883c7675 · outbound

This paper cites Yamane, Y.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Yamane, Y

Reference 40

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

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Observation 20725fc4-b451-492f-97ba-55e8dd380607 · outbound

This paper cites Onsager, The effects of shape on the interaction of colloidal particles, Annals of the New York Academy of Sciences51, 627 (1949).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Onsager, The effects of shape on the interaction of colloidal particles, Annals of the New York Academy of Sciences51, 627 (1949)

Reference 42

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Observation e193c4bb-55bb-4a47-8bb3-0f19f957d2fa · outbound

This paper cites Toll, Packing mechanics of fiber reinforcements, Poly- mer Engineering and Science38, 1337 (1998).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Toll, Packing mechanics of fiber reinforcements, Poly- mer Engineering and Science38, 1337 (1998)

Reference 43

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Observation 764d7e5b-41c0-406d-8d3f-6030543afded · outbound

This paper cites Ferec, G.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Ferec, G

Reference 44

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Observation 025273d6-5bd2-45a5-bc48-186aa1df7ee3 · outbound

This paper cites Weinan and P.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Weinan and P

Reference 45

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Observation c91ce51b-cf0f-4374-bd12-99dc7b998f17 · outbound

This paper cites Demirkurt, D.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Demirkurt, D

Reference 46

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Observation f32b552f-57bf-46ac-8685-7c9fcfdfc303 · outbound

This paper cites Heussinger, Shear thickening in granular suspensions: Interparticle friction and dynamically correlated clusters, Physical Review E88, 050201 (2013).

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Heussinger, Shear thickening in granular suspensions: Interparticle friction and dynamically correlated clusters, Physical Review E88, 050201 (2013)

Reference 47

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Observation bb36b0e9-73cd-45bf-bbca-0f3542423891 · outbound

This paper cites Moghimi, J.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Moghimi, J

Reference 48

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Observation f37fe5ca-a09f-442f-aa5a-2223770f1e9d · outbound

This paper cites D’Amico, S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods D’Amico, S

Reference 49

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Observation dd197b12-c933-4232-a453-5d70152e1160 · outbound

This paper cites Kim and S.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Kim and S

Reference 50

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Observation 69a129b4-3505-4535-bb41-58ba0b4a58eb · outbound

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A Smoluchowski equation for a sheared suspension of frictionally interacting rods Unresolved cited work

Reference 51

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Observation 4cf7ac30-39d9-4765-a564-e85f9aa91075 · outbound

This paper cites Finally, the fullϵintegral in C.6 is ∫ L 2 − L 2 dϵi ∫ L 2 − L 2 dϵj∣ϵi∣(ϵi)2 = L5 32 .(C.10) Inserting C.10, C.9 and C.8 into C.6 (and invoking the definition of⟨⟩ j, Eq.

A Smoluchowski equation for a sheared suspension of frictionally interacting rods Finally, the fullϵintegral in C.6 is ∫ L 2 − L 2 dϵi ∫ L 2 − L 2 dϵj∣ϵi∣(ϵi)2 = L5 32 .(C.10) Inserting C.10, C.9 and C.8 into C.6 (and invoking the definition of⟨⟩ j, Eq

Reference 52

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Pith citing papers

Observation 6a0310fb-fac9-48ce-a1fb-6412fabf1557 · inbound