相关论文: Shadow boundary effects in hybrid numerical-asympt…
The Helmholtz equation arises in the study of electromagnetic radiation, optics, acoustics, etc. In spherical coordinates, its general solution can be written as a spherical harmonic series which satisfies the radiation condition at…
We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and the weak feature size of the real part of an equidimensional and smooth algebraic variety using the variety's defining…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…
Light scattering from self-affine homogeneous isotropic random rough surfaces is studied using the ray-optics approximation. Numerical methods are developed to accelerate the first-order scattering simulations from surfaces represented as…
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the standard output least-squares formulation where the…
This study builds on a recent paper by Lai et al [Appl. Comput. Harmon. Anal., 2018] in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal…
The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental discovery…
Transport equations for heavy inertial particles in turbulent boundary layers may be derived from an underlying phase-space probability density function (PDF) equation. These equations, however, are unclosed, and the standard closure…
We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The mean idea is to take advantage of the fact that such structures are dissipative and…
The Kirchhoff approximation (K-A) to calculate the acoustic backscattering of a complex structure can be evaluated using a discretized version of its surface (i.e. a $\textit{mesh}$). From the computational viewpoint, the most accesible…
Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…
The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely…
We develop a multidimensional coupled channel method suitable for studying the interplay of bound state resonance and phonon assisted scattering of inert gas atoms from solid surfaces in one, two and three dimensions. This enables us to get…
We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate…
Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The…
We investigate the far-field optical resonances of individual dimer nanoantennas using confocal scattering spectroscopy. Experiments on a single-antenna array with varying arm lengths and interparticle gap sizes show large spectral shifts…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…