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A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It…
Designing nanophotonic structures traditionally grapples with the complexities of discrete parameters, such as real materials, often resorting to costly global optimization methods. This paper introduces an approach that leverages…
Efficiently coupling light from optical fibers into photonic integrated circuits is a key step toward practical photonic devices. While a notable coupling can be achieved by out of plane couplers such as grating couplers, their basic planar…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence X-Ray fluorescence data set in…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
3D additive manufacturing enables the fabrication of nanophotonic structures with subwavelength features that control light across macroscopic scales. Gradient-based optimization offers an efficient approach to design these complex and…
A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…
The accurate calculation of guided electromagnetic modes in optical nanofibres is critical for applications in nanophotonics, from quantum interfaces to vectorial light sensing. Standard textbook methods rely on solving a $4\times4$ matrix…
We introduce a new general framework for the approximation of evolution equations at low regularity and develop a new class of schemes for a wide range of equations under lower regularity assumptions than classical methods require. In…
The Fourier Basis Density Model (FBM) was recently introduced as a flexible probability model for band-limited distributions, i.e. ones which are smooth in the sense of having a characteristic function with limited support around the…
Hierarchical biomaterials embody nature's intricate design principles, offering advanced functionalities through the complex, multi-level organization of their molecular and nanosized building blocks. However, the comprehensive…
We employ polarization tomography to characterize the modal properties of a dielectric nanocavity with sub-wavelength mode confinement. Our analysis of reflection spectra shows that the Fano-lineshape depends strongly on the polarization in…
We consider the system of partial differential equations stemming from the time discretization of the two-field formulation of the Biot's model with the backward Euler scheme. A typical difficulty encountered in the space discretization of…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface.…
Freeform optical components offer significant compactization of multi-lens systems, as well as advanced manipulation of light that is not possible with traditional systems. However, their fabrication relies on machining processes that are…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
This paper extends the author's previous two-dimensional work with Ou and LeVeque to high-resolution finite volume modeling of systems of fluids and poroelastic media in three dimensions, using logically rectangular mapped grids. A method…
We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be…