The fractional d'Alembert's formulas

Li, Chenggang; Li, Miao; Piskarev, Sergey; Meerschaert, Mark M.

doi:10.1016/j.jfa.2019.108279

Cited by 6 publications

(1 citation statement)

References 35 publications

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“…In this paper, hairiness on the fabric is treated as elastic thin rod. According to non-linear dynamics characteristics of hairiness during fabric pilling, following the principles of mechanical balance and energy conservation, the non-linear dynamic mechanics model is established by using D'Alembert theory (Li et al, 2019). At the same time, the FEM is adopted to simulate hairiness behavior during fabric pilling.…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling and simulating pilling of polyester fabric

Xiao

2022

IJCST

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PurposeThe paper aims to build a finite element simulation model for pilling of polyester hairiness on the fabric to study the effects of hairiness performance on pilling and reveal pilling mechanisms.Design/methodology/approachThe finite element simulation model of pilling of polyester hairiness was established by ABAQUS. Polyester hairiness was treated as elastic thin rod, which was divided by two-node linear three-dimensional truss element. The effects of hairiness elastic modulus, hairiness friction coefficient and hairiness diameter on frictional dissipation energy, strain energy and kinetic energy produced by pilling have been studied. The analysis solution values were compared with the finite element simulation results, which was used to verify finite element simulation.FindingsThe paper provides new insights about how to reveal pilling mechanisms of polyester hairiness with different performance. Comparing finite element simulation results with analysis solutions shows that the fitness is greater than 0.96, which verifies finite element simulation. Larger hairiness elastic modulus gives rise to higher friction dissipation energy and strain energy of hairiness but lower kinetic energy. Increasing friction coefficient enhances friction dissipation and strain energy of hairiness. However, kinetic energy decreases with the increase of friction coefficient. Hairiness diameter also has an important effect on hairiness entanglement and pilling. Increasing hairiness diameter can decrease friction dissipation energy but enhance strain energy and kinetic energy.Research limitations/implicationsFinite element simulation was verified by analysis solutions. The solutions include friction dissipation energy, strain energy and kinetic energy, which cannot measured b experiment. Therefore, researchers are encouraged to simulate pilling to obtain pilling grades, which be compared with experiment results.Originality/valuePilling of polyester hairiness was simulated by ABAQUS. This method makes pilling process visualization, and pilling mechanisms was revealed from non-linear dynamics.

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Section: Introductionmentioning

confidence: 99%

Finite element modeling and simulating pilling of polyester fabric

Xiao

2022

IJCST

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Anomalous Random Flights and Time-Fractional Run-and-Tumble Equations

Angelani,

De Gregorio,

Garra

et al. 2024

J Stat Phys

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Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.

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