Related papers: Indicative Surfaces for Crystal Optical Effects
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
In this note, we use crystalline methods and the Tate-conjecture to give a short proof that the Picard rank of an Enriques surface is equal to its second Betti number.
The refractive index of a y-cut SiO$_2$ crystal surface is reconstructed from polarization dependent soft X-ray reflectometry measurements in the energy range from 45 eV to 620 eV. Due to the anisotropy of the crystal structure in the (100)…
A third-order three-dimensional symmetric traceless tensor, called the \emph{octupolar} tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar \emph{potential}, a scalar-valued function generated…
The imaging problem of a specular reflector is revisited. Retaining terms through second order in the reflector surface expansion, we derive the form of the aberration-limiting aperture for arbitrary magnification assuming no bandwidth…
Image inpainting has made significant advances in recent years. However, it is still challenging to recover corrupted images with both vivid textures and reasonable structures. Some specific methods only tackle regular textures while losing…
In this study, we explore the geometric construction of the Klein bottle and the real projective plane ($\mathrm{RP}^2$) within the framework of tensor networks, focusing on the implementation of crosscap and rainbow boundaries. Previous…
We introduce colorings of oriented surface-links by biquasiles using marked graph diagrams. We use these colorings to define counting invariants and Boltzmann enhancements of the biquasile counting invariants for oriented surface-links. We…
The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam…
We construct examples of non-projective normal proper algebraic surfaces and discuss the pathological behaviour of their Neron-Severi group. Our surfaces are birational to the product of a projective line and a curve of higher genus.
Structural and optoelectronic properties of BaThO3 cubic perovskite are calculated using all electrons full potential linearized augmented plane wave (FP-LAPW) method. Wide and direct band gap, 5.7 eV, of the compound predicts that it can…
Metasurfaces provide the disruptive technology enabling miniaturization of complex cascades of optical elements on a plane. We leverage the benefits of such a surface to develop a planar integrated photonic beam collimator for on-chip…
This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments…
Here we present microscopic evidence of the persistence of uniaxial A-type antiferromagnetic order to the surface layers of MnBi$_2$Te$_4$ single crystals using magnetic force microscopy. Our results reveal termination-dependent magnetic…
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In…
Lithium niobate is a multi-functional material, which has been regarded as one of the most promising platform for the multi-purpose optical components and photonic circuits. Targeting at the miniature optical components and systems, lithium…
Surfaces of rutile-like RuO2, especially the most stable (110) surface, are important for catalysis, sensing and charge storage applications. Structure, chemical composition, and properties of the surface depend on external conditions.…
Regular $A_n$-, $B_n$- and $C_n$-crystals are edge-colored directed graphs, with ordered colors $1,2,...,n$, which are related to representations of quantized algebras $U_q(\mathfrak{sl}_{n+1})$, $U_q(\mathfrak{sp}_{2n})$ and…
We present a novel chiral sensing platform that combines a one-dimensional photonic crystal design with a birefringent surface defect. The platform sustains simultaneous transverse electric and transverse magnetic surface modes, which are…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…