Characterization of the symmetry class of an elasticity tensor using polynomial covariants

We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is the cornerstone of the theory of elasticity and a toy model for linear constitutive laws in physics. The novelty is that these conditions are written using polynomial covariants. As a corollary, we deduce that the symmetry classes are affine algebraic sets, a result which seems to be new. Meanwhile, we have been lead to produce a minimal set of 70 generators for the covariant algebra of a fourth-order harmonic tensor and introduce an original generalized cross-product on totally symmetric tensors. Finally, using these tensorial covariants, we produce a new minimal set of 294 generators for the invariant algebra of the elasticity tensor.

Characterization of Pure Face-Shear Strain in Piezoelectric α-Tellurium Dioxide (α-TeO2)

Paratellurite, also known as α-tellurium dioxide, is a ceramic that is primarily employed for its interesting optical properties. However, this material’s crystal structure belongs to the 422 symmetry class that allows a unique piezoelectric behavior to manifest itself: deformation in pure face-shear. This means that crystal symmetry necessitates the piezoelectric tensor to have only a single non-zero coefficient, d123 = d14: such unique behavior has the potential to enable novel gyroscopic sensors and high-precision torsional microelectromechanical systems (MEMS) actuators, as pure face-shear can be used to induce pure torsion. Although α-TeO2 is one of the few known materials belonging to this symmetry class, considerable uncertainty in its single piezoelectric coefficient exists, with the few reported literature values ranging from 6.13 to 14.58 pC/N; this large uncertainty results from the difficulty in using conventional piezoelectric characterization techniques on paratellurite, limiting measurements to indirect methods. The novel applications that would be enabled by the adoption of this extraordinary material are frustrated by this lack of confidence in the literature. We therefore leverage, for the first time, a first-principles analytical physical model with electrochemical impedance spectroscopy (EIS) to determine, directly, the lone piezoelectric coefficient d123 = d14 = 7.92 pC/N.

Distances of Stiffnesses to Symmetry Classes

For a given elastic stiffness tetrad an algorithm is provided to determine the distance of this particular tetrad to all tetrads of a prescribed symmetry class. If the particular tetrad already belongs to this class then the distance is zero and the presentation of this tetrad with respect to the symmetry axes can be obtained. If the distance turns out to be positive, the algorithm provides a measure to see how close it is to this symmetry class. Moreover, the closest element of this class to it is also determined. This applies in cases where the tetrad is not ideal due to scattering of its measurement. The algorithm is entirely algebraic and applies to all symmetry classes, although the isotropic and the cubic class need a different treatment from all other classes.

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

Symmetry Classes and Matrix Representations of the 2D Flexoelectric Law

We determine the different symmetry classes of bi-dimensional flexoelectric tensors. Using the harmonic decomposition method, we show that there are six symmetry classes. We also provide the matrix representations of the flexoelectric tensor and of the complete flexoelectric law, for each symmetry class.

Probing depth and lateral variations of upper-mantle seismic anisotropy from full-waveform inversion of teleseismic body-waves

SUMMARY While seismic anisotropy can potentially provide crucial insights into mantle dynamics, 3-D imaging of seismic anisotropy is still a challenging problem. Here, we present an extension of our regional full-waveform inversion method to image seismic anisotropy in the lithosphere and asthenosphere from teleseismic P and S waveforms. The models are parametrized in terms of density and the 21 elastic coefficients of the fourth-order elasticity tensor. The inversion method makes no a priori assumptions on the symmetry class or on the orientation of the symmetry axes. Instead, the elasticity tensors in the final models are decomposed with the projection method. This method allows us to determine the orientation of the symmetry axes and to extract the contributions of each symmetry class. From simple synthetic experiments, we demonstrate that our full-waveform inversion method is able to image complex 3-D anisotropic structures. In particular, the method is able to almost perfectly recover the general orientation of the symmetry axis or complex layered anisotropic models, which are both extremely challenging problems. We attribute this success to the joint exploitation of both P and S teleseismic waves, which constrain different parts of the elasticity tensor. Another key ingredient is the pre-conditioning of the gradient with an approximate inverse Hessian computed with scattering integrals. The inverse Hessian is crucial for mitigating the artefacts resulting from the uneven (mostly vertical) illumination of teleseismic acquisitions.