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The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…
The variational autoencoder (VAE) is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other…
A flexible and efficient method for fully vectorial modal analysis of 3D dielectric optical waveguides with arbitrary 2D cross-sections is proposed. The technique is based on expansion of each modal component in some a priori defined…
Blending of galaxies has a major contribution in the systematic error budget of weak lensing studies, affecting photometric and shape measurements, particularly for ground-based, deep, photometric galaxy surveys, such as the Rubin…
Vector beams are inhomogeneously polarized optical fields with nonseparable, quantum-like correlations between their polarisation and spatial components, and hold tremendous promise for classical and quantum communication across various…
Various methods have been introduced to measure the orbital angular momentum (OAM) of light, from fork holograms to Dove prism interferometers, from tilted lenses to triangular apertures - each with their own benefits and limitations. Here…
Cubic to tetragonal distortion in spinel compounds have been a contentious issue for last two decades. Different groups have proposed different mechanisms to understand such a distortion in these spinels, which are: (i) spin lattice…
Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, one can hope to detect out-of-distribution (abnormal) latent vectors, but several issues arise when…
Measuring the Doppler broadening of the positron annihilation radiation or the angular correlation between the two annihilation gamma quanta reflects the momentum distribution of electrons seen by positrons in the material.Vacancy-type…
This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…
We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely,…
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…
This paper demonstrates that a simple modification of the variational autoencoder (VAE) formalism enables the method to identify and classify rotated and distorted digits. In particular, the conventional objective (cost) function employed…
Optical Coherence Tomography (OCT) is an emerging medical imaging modality for luminal organ diagnosis. The non-constant rotation speed of optical components in the OCT catheter tip causes rotational distortion in OCT volumetric scanning.…
The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…
We explore the separability of point sets in the plane by a restricted-orientation convex hull, which is an orientation-dependent, possibly disconnected, and non-convex enclosing shape that generalizes the convex hull. Let $R$ and $B$ be…
The equilibrium code, VMEC, is used to study external kinks in low $\beta$ tokamaks and $l=2$ stellarators. The applicability of the code when modelling nonlinear MHD effects is explored in an attempt to understand and predict how the…
This paper studies the straight skeleton of polyhedra in three dimensions. We first address voxel-based polyhedra (polycubes), formed as the union of a collection of cubical (axis-aligned) voxels. We analyze the ways in which the skeleton…