Related papers: Parametrically Constrained Geometry Relaxations fo…

We extend the relaxation mechanism to the Elementary Goldstone Higgs framework. Besides studying the allowed parameter space of the theory we add the minimal ingredients needed for the framework to be phenomenologically viable. The very…

This paper presents a new hybridizable discontinuous Galerkin (HDG) method for linear elasticity on general polyhedral meshes, based on a strong symmetric stress formulation. The key feature of this new HDG method is the use of a special…

We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…

Plasmons, collective excitations of electrons in solids, are associated with strongly confined electromagnetic fields, with wavelengths far below the wavelength of photons in free space. This strong confinement promises the realization of…

Hybridizable \(H(\textrm{div})\)-conforming finite elements for symmetric tensors on simplices with barycentric refinement are developed in this work for arbitrary dimensions and any polynomial order. By employing barycentric refinement and…

The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…

Inverse design algorithms are the basis for realizing high-performance, freeform nanophotonic devices. Current methods to enforce geometric constraints, such as practical fabrication constraints, are heuristic and not robust. In this work,…

While the design of always new metamaterials with exotic static and dynamic properties is attracting deep attention in the last decades, little effort is made to explore their interactions with other materials. This prevents the conception…

Losses in metamaterials render the applications of such exotic materials less practical unless an efficient way of reducing them is found. We present two different techniques to reduce ohmic losses at both lower and higher frequencies,…

This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally…

Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…

Inspired by geometrically frustrated magnetic systems, we present the optical response of three cases of hexagonal lattices of plasmonic nanoelements. All of them were designed using a metal-insulator-metal configuration to enhance…

Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and the general form of the underlying balance law model, we perform a detailed…

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…

One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered…

For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…

Introduction of a twist between layers of two-dimensional materials which leads to the formation of a moir\'e pattern is an emerging pathway to tune the electronic, vibrational and optical properties. The fascinating properties of these…

A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases…

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

We propose a relax-and-round approach combined with a greedy search strategy for performing complex lattice basis reduction. Taking an optimization perspective, we introduce a relaxed version of the problem that, while still nonconvex, has…