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A generalised distributed-order Maxwell model

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Luis Ferrás, Maria Luisa Morgado, Magda Rebelo

Classical Physics · Submitted 10 Feb 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Blumen, Hierarchical analogues to fractional relaxation equations, Journal of Physics A: Mathematical and General 26 (1993) 5057-50] and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen.

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arXiv ID2202.05878 (version 1)
Pith IDWFLHLA4G, Pith's permanent record of this paper and its review
CitationLuis Ferr\'as, Magda Rebelo, Maria Luisa Morgado. "A generalised distributed-order Maxwell model." arXiv:2202.05878 (2022). https://pith.science/paper/WFLHLA4G
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,931 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.18 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this work we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented in [H. Schiessel, A. Blumen, Hierarchical analogues to fractional relaxation equations, Journal of Physics A: Mathematical and General 26 (1993) 5057-50] and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional, and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus, and the creep compliance for specific weighting functions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this work we present a generalised viscoelastic model using distributed-order derivatives. contribution 1.00 0.92 0.18 asserted 1.00
s1 The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. method 0.82 0.70 0.07 asserted 1.00
s2 The new model generalises the fractional viscoelastic model presented in [H. Schiessel, A. contribution 0.71 0.35 0.10 asserted 0.98
s3 Blumen, Hierarchical analogues to fractional relaxation equations, Journal of Physics A: Mathematical and General 26 (1993) 5057-50] and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. contribution 0.55 0.45 0.27 asserted 0.88
s4 We discuss the connection between classical, fractional, and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. contribution 0.84 0.84 0.10 asserted 0.98
s5 We also derive the relaxation modulus, the storage and loss modulus, and the creep compliance for specific weighting functions. result 0.52 0.96 0.15 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this work we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented in [H. Schiessel, A. Blumen, Hierarchical analogues to fractional relaxation equations, Journal of Physics A: Mathematical and General 26 (1993) 5057-50] and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional, and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus, and the creep compliance for specific weighting functions.

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