Elliptic functions and lattice sums for effective properties of heterogeneous materials
Sign Up to like & getrecommendations! Published in 2021 at "Continuum Mechanics and Thermodynamics"
DOI: 10.1007/s00161-021-00997-2
Abstract: Effective properties of fiber-reinforced composites can be estimated by applying the asymptotic homogenization method. Analytical solutions are possible for infinite long circular fibers based on the elliptic quasi-periodic Weierstrass Zeta function. This process leads to… read more here.
Keywords: functions lattice; properties heterogeneous; elliptic functions; sums effective ... See more keywords
Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions
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DOI: 10.1080/10652469.2017.1304938
Abstract: ABSTRACT Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the independent variable u is the argument of Jacobian… read more here.
Keywords: integrals incomplete; elliptic integrals; indefinite integrals; incomplete elliptic ... See more keywords
Buchstaber formal group and elliptic functions of small levels
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DOI: 10.1134/s0001434617070094
Abstract: In the paper, we suggest a method for finding relations concerning series defining the Buchstaber formal group. This method is applied to the cases in which the exponent of the group is an elliptic function… read more here.
Keywords: functions small; buchstaber formal; group; group elliptic ... See more keywords
A note on “Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G′/G)-expansion method including the generalized Riccati equation”
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DOI: 10.1140/epjp/s13360-020-00715-y
Abstract: Employing Jacobi elliptic functions and the so-called alternative ( $$ G^{\prime}/G $$ )-expansion method including the generalized Riccati equation, Tala-Tebue et al. (Eur Phys J Plus 129:136, 2014) derived exact solutions for a discrete nonlinear… read more here.
Keywords: expansion method; method including; including generalized; generalized riccati ... See more keywords