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arXiv 2022年

作者： Huang, Heqing Overvig, Adam C. Xu, Yuan Malek, Stephanie C. Tsai, Cheng-Chia Alù, Andrea Yu, Nanfang Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Photonics Initiative Advanced Science Research Center City University of New York New YorkNY10031 United States Physics Program Graduate Center of the City University of New York New YorkNY10016 United States

Metasurfaces have been rapidly advancing our command over the many degrees of freedom of light within compact, lightweight devices. However, so far, they have mostly been limited to manipulating light in free space. Grating couplers provide the opportunity of bridging far-field optical radiation and in-plane guided waves, and thus have become fundamental building blocks in photonic integrated circuits. However, their operation and degree of light control is much more limited than metasurfaces. Metasurfaces integrated on top of guided wave photonic systems have been explored to control the scattering of light off-chip with enhanced functionalities – namely, point-by-point manipulation of amplitude, phase or polarization. However, these efforts have so far been limited to controlling one or two optical degrees of freedom at best, and to device configurations much more complex compared to conventional grating couplers. Here, we introduce leaky-wave metasurfaces, which are based on symmetry-broken photonic crystal slabs that support quasi-bound states in the continuum. This platform has a compact form factor equivalent to the one of conventional grating couplers, but it provides full command over amplitude, phase and polarization (four optical degrees of freedom) across large apertures. We present experimental demonstrations of various functionalities for operation at λ = 1.55 μm based on leaky-wave metasurfaces, including devices for phase and amplitude control at a fixed polarization state, and devices controlling all four optical degrees of freedom. Our results merge the fields of guided and free-space optics under the umbrella of metasurfaces, exploiting the hybrid nature of quasi-bound states in the continuum, for opportunities to advance in disruptive ways imaging, communications, augmented reality, quantum optics, LIDAR and integrated photonic systems. © 2022, CC BY.

关键词： Guided electromagnetic wave propagation

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The Jacobi theta distribution

arXiv

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arXiv 2021年

作者： Bastian, Caleb Deen Rempala, Grzegorz A. Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Division of Biostatistics The Ohio State University ColumbusOH United States Department of Mathematics The Ohio State University ColumbusOH United States Department of Chemistry Princeton University PrincetonNJ United States

We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the positive reals, has a single positive parameter, is unimodal, positively skewed, and leptokurtic. Its cumulative distribution and density functions are expressed in terms of the Jacobi theta function. We describe asymptotic and log-normal approximations, inference, and a few applications of such distributions to *** Codes 60E05, 60G57 © 2021, CC BY.

关键词： Laplace transforms

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A NEW CLASS OF DISTANCES ON COMPLEX PROJECTIVE SPACES

arXiv

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arXiv 2023年

作者： Bistron, Rafal Eckstein, Michal Friedland, Shmuel Miller, Tomasz Życzkowski, Karol Institute of Theoretical Physics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Krakow Poland Doctoral School of Exact and Natural Sciences Jagiellonian University Poland Department of Mathematics Statistics and Computer Science University of Illinois at Chicago ChicagoIL60607-7045 United States Copernicus Center for Interdisciplinary Studies Jagiellonian University Krakow Poland Center for Theoretical Physics Polish Academy of Science Warsaw Poland

The complex projective space (ℂn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the 'earth mover problem'. We show that this construction leads to a quantity satisfying the triangle inequality, which yields a true distance on complex projective space belonging to the family of quantum 2-Wasserstein distances. © 2023, CC BY.

关键词： Earth (planet)

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Surrogate approximation of the grad-shafranov free boundary problem via stochastic collocation on sparse grids

arXiv

引用

arXiv 2021年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Courant Institute of Mathematical Sciences New York University Department of Mathematics The University of Arizona

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. The use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over *** Codes 65C30, 65C05, 65N35, 65N99, 65Z05 Copyright © 2021, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Simulated Diffusion Spreadability for Characterizing the Structure and Transport Properties of Two-Phase Materials

SSRN

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SSRN 2023年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences The Institute for Advanced Study PrincetonNJ08540 United States

Time-dependent diffusion processes between phases are ubiquitous in physical, chemical, and biological materials. Examples of such materials include composite materials, porous materials, cellular solids, polymer blends, colloids, gels, and biological materials. The recently developeddiffusion spreadability, S(t), provides a direct link between time-dependent interphase diffusive transport and the microstructure of two-phase materials across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)];thus making S(t) a powerful dynamic means for classifying all statistically homogeneous microstructures, spanning from anti-hyperuniform to hyperuniform. It was shown that the small-, intermediate-, and long-time behaviors of S(t) are directly determined by the small-, intermediate-, and large-scale structural features of the material. Moreover, the spreadability can be applied as a physical-property based tool for microstructural characterization in the absence of or as supplement to scattering information. In this work, we develop a computationally efficient algorithm for ascertaining s(t) directly from digitized representations of material microstructures via random-walk techniques. Our algorithm computes the time-dependent local walker concentration field c(x, t), a quantity not previously examined in the context of the spreadability, enabling us to compute the entropy production rate s(t) of the associated diffusion process which is a quantity related to the rate of dissipation. We also derive exact analytical expressions for s(t), and find that hyperuniform materials have smaller dissipation than any nonhyperuniform materials. Lastly, we use our algorithm to compute, for the first time, the more general case of the spreadability in which the phase diffusion coefficients are distinct and provide a method for extracting the effective diffusion coefficient of the two-phase material from such data. We apply our algorithm to a variety of two- and three-dimensional s

关键词： Microstructure

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Spatio-temporal characterization of non-linear forcing in turbulence

arXiv

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arXiv 2023年

作者： Huang, Yuting Toedtli, Simon S. Chini, Gregory P. McKeon, Beverley J. Graduate Aerospace Laboratories California Institute of Technology PasadenaCA91125 United States Department of Mechanical Engineering Johns Hopkins University BaltimoreMD21218 United States Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering Stanford University StanfordCA94305 United States

The quadratic convection term in the incompressible Navier-Stokes equations is considered as a non-linear forcing to the linear operator, and it is studied in the Fourier domain through the analysis of interactions between triadically compatible wavenumber-frequency triplets. Interaction coefficients are proposed to quantify the contribution to the forcing by each pair of triplets and are computed using data from direct numerical simulations of a turbulent channel at Reτ ≈ 550. The coefficients show the importance of interactions involving streamwise large scales. The regions of non-linear interactions permitted under the quasi-linear (QL) and generalized quasi-linear (GQL) assumptions are shown to be significant contributors to the forcing and increasing the number of GQL-large scales is shown to monotonically increase the total forcing captured, providing a possible reason for the success of QL and GQL simulations. The tools presented are expected to be useful for improving modeling of the nonlinearity, especially in QL, GQL, and resolvent analyses, and understanding the amplitude modulation mechanism relating large-scale fluctuations to the modulation of near-wall structures. Copyright © 2023, The Authors. All rights reserved.

关键词： Turbulence

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Deep potentials for materials science

材料展望（英文）

引用

材料展望（英文） 2022年第2期 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople's Republic of China AI for Science Institute BeijingPeople's Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople's Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople's Republic of China AI for Science Institute BeijingPeople's Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople's Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China International Digital Economy Academy(IDEA) ShenzhenPeople's Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network

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A deep potential model with long-range electrostatic interactions

arXiv

引用

arXiv 2021年

作者： Zhang, Linfeng Wang, Han Muniz, Maria Carolina Panagiotopoulos, Athanassios Z. Car, Roberto Weinan, E. DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. © 2021, CC BY.

关键词： Electrostatics

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Aedes-AI: Neural network models of mosquito abundance

arXiv

引用

arXiv 2021年

作者： Kinney, Adrienne C. Current, Sean Lega, Joceline Interdisciplinary Program in Applied Mathematics The University of Arizona TucsonAZ85721 United States Department of Mathematics The University of Arizona TucsonAZ85721 United States Department of Epidemiology and Biostatistics The University of Arizona TucsonAZ85721 United States BIO5 Institute The University of Arizona TucsonAZ85721 United States Department of Computer Science and Engineering The Ohio State University ColumbusOH43202 United States

We present artificial neural networks as a feasible replacement for a mechanistic model of mosquito abundance. We develop a feed-forward neural network, a long short-term memory recurrent neural network, and a gated recurrent unit network. We evaluate the networks in their ability to replicate the spatiotemporal features of mosquito populations predicted by the mechanistic model, and discuss how augmenting the training data with time series that emphasize specific dynamical behaviors affects model performance. We conclude with an outlook on how such equation-free models may facilitate vector control or the estimation of disease risk at arbitrary spatial scales. © 2021, CC BY-NC-ND.

关键词： Feedforward neural networks

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Hidden Independence in Unstructured Probabilistic Models 31

Hidden Independence in Unstructured Probabilistic Models

引用

31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, A of A 2020

作者： Pearson, Antony Lladser, Manuel E. Department of Applied Mathematics University of Colorado BoulderCO United States Iq Biology Program BioFrontiers Institute University of Colorado BoulderCO United States University of Colorado BoulderCO United States

ISBN: (纸本)9783959771474

We describe a novel way to represent the probability distribution of a random binary string as a mixture having a maximally weighted component associated with independent (though not necessarily identically distributed) Bernoulli characters. We refer to this as the latent independent weight of the probabilistic source producing the string, and derive a combinatorial algorithm to compute it. The decomposition we propose may serve as an alternative to the Boolean paradigm of hypothesis testing, or to assess the fraction of uncorrupted samples originating from a source with independent marginal distributions. In this sense, the latent independent weight quantifies the maximal amount of independence contained within a probabilistic source, which, properly speaking, may not have independent marginal distributions. 2012 ACM Subject Classification mathematics of computing Probabilistic representations;mathematics of computing Dimensionality reduction;mathematics of computing Discrete mathematics. © 2020 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH Dagstuhl Publishing. All rights reserved.

关键词： Bayesian networks

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