On applications of Herglotz-Nevanlinna functions in material sciences. II: Extended applications and generalized theory. (English) Zbl 1500.74059

Ou, Miao-Jung Yvonne; Luger, Annemarie

Español, Malena I. (ed.) et al., Research in mathematics of materials science. Cham: Springer. Assoc. Women Math. Ser. 31, 461-499 (2022).

Summary: Part II of the review article focuses on the applications of Herglotz-Nevanlinna functions in material sciences. It presents a diverse set of applications with details and the role of Herglotz-Nevanlinna functions clearly pointed out. This chapter is concluded by a collection of existent generalizations of the class of Herglotz-Nevanlinna functions that are motivated by potential applications.
For Part I, see [the authors, ibid. 433–459 (2022; Zbl 1501.74067)].
For the entire collection see [Zbl 1495.74001].

MSC:

74S70	Complex-variable methods applied to problems in solid mechanics
74A40	Random materials and composite materials
74Q20	Bounds on effective properties in solid mechanics
74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Keywords:

matrix-valued Herglotz-Nevanlinna function; two-phase composite; bound on effective property; permeability tensor; porous material

Citations:

Zbl 1501.74067

References:

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