Multiferroic magnetoelectric materials, which simultaneously exhibit ferroelectricity and ferromagnetism, have recently stimulated a sharply increasing number of research activities for their scientific interest and significant technological promise in the novel multifunctional devices. Natural multiferroic single-phase compounds are rare, and their magnetoelectric responses are either relatively weak or occurs at temperatures too low for practical applications. In contrast, multiferroic composites, which incorporate both ferroelectric and ferri-/ferromagnetic phases, typically yield giant magnetoelectric coupling response above room temperature, which makes them ready for technological applications. This review of mostly recent activities begins with a brief summary of the historical perspective of the multiferroic magnetoelectric composites since its appearance in 1972. In such composites the magnetoelectric effect is generated as a product property of a magnetostrictive and a piezoelectric substance. A...

Multiferroic magnetoelectric composites: Historical perspective, status, and future directions

Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

The phonon is the physical particle representing mechanical vibration and is responsible for the transmission of everyday sound and heat. Understanding and controlling the phononic properties of materials provides opportunities to thermally insulate buildings, reduce environmental noise, transform waste heat into electricity and develop earthquake protection. Here I review recent progress and the development of new ideas and devices that make use of phononic properties to control both sound and heat. Advances in sonic and thermal diodes, optomechanical crystals, acoustic and thermal cloaking, hypersonic phononic crystals, thermoelectrics, and thermocrystals herald the next technological revolution in phononics.

Sound and heat revolutions in phononics

1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

In nanoscaled solids, the mathematical behavior of a curved interface between two different phases with interface stress effects can be described by the generalized Young-Laplace equations [T. Young, Philos. Trans. R. Soc. London 95, 65 (1805); P. S. Laplace, Traite de Mechanique Celeste (Gauthier-Villars, Paris, 1805), Vol. 4, Supplements au Livre X]. Here we present a geometric illustration to prove the equations. By considering a small element of the curved thin interface, we model the interface stresses as in-plane stresses acting along its edges, while on the top and bottom faces of the interface the tractions are contributed from its three-dimensional bulk neighborhood. With this schematic illustration, simple force balance considerations will give the Young-Laplace equations across the interface. Similar procedures can be applied to conduction phenomena. This will allow us to reconstruct one type of imperfect interfaces, referred to as highly conducting interfaces.

http://ir.lib.ncku.edu.tw/bitstream/987654321/51156/2/3010600101021.pdf

Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

Stress fields in composites with coated inclusions

Poisson's ratio for isotropic elastic materials is bounded between -1 and 1 / 2 . It is shown that Poisson's ratio for anisotropic elastic materials can have an arbitrarily large positive or negative value under the prerequisite of positive definiteness of strain energy density. The large Poisson's ratio for cubic materials is physically realistic because the strains are bounded.

/pdf/poisson-s-ratio-for-anisotropic-elastic-materials-can-have-3axen8nu2d.pdf

Poisson's ratio for anisotropic elastic materials can have no bounds

We explore the possibility to cloak a region in curvilinearly anisotropic background materials in the context of conductivity. Materials with curvilinear anisotropy possess constant properties in specific curvilinear coordinate. For cylindrically and spherically anisotropic solids, the cloak center and the origin of material coordinate are generally not collocated. We show that in combination with a rigid-body translation from the cloak center to the material origin, the previous coordinate transformation procedure remains applicable. But now the transformed material specifications depend on the position of cloak center. The validity of the cloak parameters is verified by finite element simulations.

Cloak for curvilinearly anisotropic media in conduction

T he existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas L evin 's results [ Mechanics of Solids 2 , 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.

Tungyang Chen

Papers

Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

Stress fields in composites with coated inclusions

Poisson's ratio for anisotropic elastic materials can have no bounds

Cloak for curvilinearly anisotropic media in conduction

On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media