On the use of universal relations in the modeling of transversely isotropic materials

A material is of coaxial type   if the Cauchy stress tensor T$\mathit{T}$ and the strain tensor B$\mathit{B}$ are coaxial for all deformations. Clearly a hyperelastic material is of coaxial type if and only if it is isotropic. Here we present a weaker definition of materials of coaxial type. Anisotropic materials may be of a coaxial type in a weak sense if for a given specific  B$\mathit{B}$ we have that TB=BT$\mathit{TB}=\mathit{BT}$. We denote these materials B$\mathit{B}$-coaxial. We show that for transverse isotropic materials weak coaxial constitutive equations may be characterized using universal relations. We discuss the impact of B$\mathit{B}$-coaxial materials in the modeling of soft tissues. We conclude that B$\mathit{B}$-coaxial materials are a strong evidence that in real world materials two anisotropic invariants are always necessary to model in a meaningful and correct way single fiber reinforced materials.     

Universality of a dynamical percolative approach to 1/f γ noise

A dynamical percolative model explaining the universality of 1/ f ^γ noise is reported. Exponents γ ranging from 0 to 2 are obtained under the hypothesis that noise originates from random switching events between two ON-OFF states in elemental parts (switchers) of a physical system. The usual noise behaviour with γ very close to 1 in an arbitrarily wide frequency range is obtained assuming a statistical distribution of switcher relaxation time τ proportional to τ ^-1 , as in McWhorter's model. The impact of these results with respect to recent self-organised criticality models is discussed. Received 6 November 2000 and Received in final form 22 May 2001     

Magnetoresistance anisotropy in a hexagonal lattice of Co antidots obtained by thermal evaporation

Patterned soft magnetic materials are eligible for use in magnetic random access memories. A hexagonal-lattice pattern of circular antidots was produced by optical lithography in a Co film. In order to test the effect of geometry on the local magnetisation configuration of such a structure, we performed room-temperature angle-resolved magnetisation measurements aimed to check the pinning of domain walls by the pattern's lattice. Magnetoresistance (MR) room-temperature measurements were performed at various angles between the magnetic field direction and the macroscopic electrical current vector, to clarify whether and how the local current density configuration affects the MR response. We found that the magnetoresistance is of anisotropic type (AMR) and has a local origin. Furthermore, the largely unsaturating behaviour of MR at high fields may be explained only by considering that tiny portions of the pattern constitute highly frustrated regions and align their magnetisation at rather high fields. A simplified model based on a local anisotropy term is shown to account for the experimental results for both M and MR.     

The Anti-Plane Shear Problem in Nonlinear Elasticity Revisited

A classical problem in the framework of nonlinear elasticity theory is the characterization of the materials that may sustain a pure state of anti-plane shear in the absence of body forces. This problem has been solved by Knowles and by Hill in the framework of isotropic and incompressible elasticity in the seventies. Here we provide a simpler and shorter proof of these classical results. Moreover, we extend these results to nonlinear elastodynamics and we provide some new special solutions.     

On universal relations in continuum mechanics

This paper is devoted to a systematic study of local universal relations in continuum mechanics. We show that it is possible to determine the complete set of independent universal relations whose characterization is obtained by linear universal rules. A historical review of the literature on the topic and various significant examples are given. Received: August 16, 1996     

Parametric resonance in non-linear elastodynamics

We show that finite amplitude shearing motions superimposed on an unsteady simple extension are admissible in any incompressible isotropic elastic material. We show that the determining equations for these shearing motions admit a general reduction to a system of ordinary differential equations (ODEs) in the remarkable case of generalized circularly polarized transverse waves. When these waves are standing and the underlying unsteady simple extension is composed of a harmonic perturbation of a static stretch it is possible to reduce the determining ODEs to linear or non-linear Mathieu equations. We use this property for a detailed study of the phenomenon of parametric resonance in non-linear elastodynamics.     

Length‐Dependent Charge Generation from Vertical Arrays of High‐Aspect‐Ratio ZnO Nanowires

Aqueous chemical growth of zinc oxide nanowires is a flexible and effective approach to obtain dense arrays of vertically oriented nanostructures with high aspect ratio. Herein we present a systematic study of the different synthesis parameters that influence the ZnO seed layer and thus the resulting morphological features of the free‐standing vertically oriented ZnO nanowires. We obtained a homogeneous coverage of transparent conductive substrates with high‐aspect‐ratio nanowire arrays (length/diameter ratio of up to 52). Such nanostructured vertical arrays were examined to assess their electric and piezoelectric properties, and showed an electric charge generation upon mechanical compressive stress. The principle of energy harvesting with these nanostructured ZnO arrays was demonstrated by connecting them to an electronic charge amplifier and storing the generated charge in a series of capacitors. We found that the generated charge and the electrical behavior of the ZnO nanowires are strictly dependent on the nanowire length. We have shown the importance of controlling the morphological properties of such ZnO nanostructures for optimizing a nanogenerator device.     

Mixed spectrum of correlated pulse sequences with application to linear atom chains

Line and continuous components of the power spectrum of a sequence of pulses with correlation between pulse shape and pulse separation interval are given. From these results the spectral properties of a diatomic chain are obtained straightforwardly.     

Quasisolutions as Group-Invariant Solutions for Partial Differential Equations

The group theoretical explanation is given of the quasisolution method for partial differential equations recently introduced by Rubel. The examples show that the group approach is simpler from the computational point of view.     

Using Symmetries à Rebours

We consider nonclassical symmetries of partial differential equations (PDEs) in dimensions. Given a th‐order ordinary differential equation in the unknown we are able to find the most general scalar PDE of a given order which can be reduced via a nonclassical symmetry to .