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There is only a handful of scanning techniques that can provide surface topography at nanometre resolution. At the same time, there are no methods that are capable of non-invasive imaging of the three-dimensional surface topography of a…
Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior…
Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD). Previously, there has been…
In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a couple of non-linear telegraph equation and a parabolic equation. Proposed strategy…
Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective…
In Graph Theory a number of results were devoted to studying the computational complexity of the number modulo 2 of a graph's edge set decompositions of various kinds, first of all including its Hamiltonian decompositions, as well as the…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a…
In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…
Remarkable optical and electrical properties of two-dimensional (2D) materials, such as graphene and transition-metal dichalcogenide (TMDC) monolayers, offer vast technological potential for novel and improved optoelectronic nanodevices,…
Topological photonic insulators show promise for applications in compact integrated photonic circuits due to their ability to transport light robustly through sharp bendings. The number of topological edge states relies on the difference…
We introduce a deterministic approach to edge detection and image segmentation by formulating pseudo-Boolean polynomials on image patches. The approach works by applying a binary classification of blob and edge regions in an image based on…
We study electromagnetic scattering and subsequent plasmonic excitations in periodic grids of graphene ribbons. To address this problem, we develop an analytical method to describe the plasmon-assisted absorption of electromagnetic…
Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has…
We introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented…
Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths.…
A novel type of one-dimensional (1D) photonic crystal formed by the array of periodically located stacks of alternating graphene and dielectric stripes embedded into a background dielectric medium is proposed. The wave equation for the…
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…
Ptychography is a promising phase retrieval technique for label-free quantitative phase imaging. Recent advances in phase retrieval algorithms witnessed the development of spectral methods, in order to accelerate gradient descent…
The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…