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Abstract Transformation optics has formulated a versatile framework to mold the flow of light and tailor its spatial characteristics at will. Despite its huge success in bringing scientific fiction (such as invisibility cloaking) into reality, the coordinate transformation often yields extreme material parameters unfeasible even with metamaterials. Here, we demonstrate a new transformation paradigm based upon the invariance of the eigenspectra of the Hamiltonian of a physical system, enabled by supersymmetry. By creating a gradient-index metamaterial to control the local index variation in a family of isospectral optical potentials, we demonstrate broadband continuous supersymmetric transformation in optics, on a silicon chip, to simultaneously transform the transverse spatial characteristics of multiple optical states for arbitrary steering and switching of light flows. Through a novel synergy of symmetry physics and metamaterials, our work provides an adaptable strategy to conveniently tame the flow of light with full exploitation of its spatial degree of freedom.
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A finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in NiTi single crystals
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Multigroup discriminant analysis is an important supervised learning technique in the classification framework, with applications in various disciplines. Its objective is to approximate underlying class distributions based on data attributes or features. After the class distributions are estimated, the classification task can be readily carried out for data points with unknown labels. Linear discriminant analysis (LDA) as well as quadratic discriminant analysis (QDA) are statistical procedures widely utilized by practitioners due to their practicality and generally good performance. Both procedures rely on the assumption of normally distributed classes and can be affected by deviations from multivariate normality. To address this model deficiency, we propose an extension of LDA and QDA that relies on the idea of transformation and can readily accommodate asymmetry and skewness in data classes. Through the set of simulation studies and applications to real-life data sets, we demonstrate that the developed technique is promising as it demonstrates superior performance over competitors in a variety of cases.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1016/j.ijplas.2021.102957
