arXiv subjects

Wei Cai

Publications and source records attributed to Wei Cai.

At least 109 records · Page 6Linked to original sources

arXiv2021

Free energy calculation of crystalline solids using normalizing flow

Taking advantage of the advances in generative deep learning, particularly normalizing flow, a framework, called Boltzmann Generator, has recently been proposed for the purpose of generating equilibrium atomic configurations from the canonical ensemble and determining the associated free energy. In this work, we revisit Boltzmann Generator to motivate the construction of the loss function from the statistical mechanical point of view, and to cast the training of the neural networks in a purely unsupervised manner that requires no samples of the atomic configurations from the equilibrium ensemble. We further show that the normalizing flow framework furnishes a reference thermodynamic system, very close to the real thermodynamic system under consideration, that is suitable for the well-established free energy perturbation methods to determine accurate free energy of solids. We then apply the normalizing flow to two problems: temperature-dependent Gibbs free energy of perfect crystal and formation free energy of monovacancy defect in a model system of diamond cubic Si. The results obtained from the normalizing flow are shown to be in good agreement with that obtained from independent well-established free energy methods.

cond-mat.stat-mech↗

arXiv2021

Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses

In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network (DNN) utilizes a multiple scaling technique to convert high frequency function to lower frequency functions before using a DNN to learn a specific range of frequency of the function. The multi-scale concept is integrated into the DeepONet which is based on a universal approximation theory of nonlinear operators. The resulting multi-scale DeepONet is shown to be effective to represent building seismic response operator which maps oscillatory seismic excitation to the oscillatory building responses.

math.NA↗

arXiv2021

Infrared full-Stokes polarimetry by parametric up-conversion

Polarimetry aims to measure polarization information of an optical field, providing a new freedom to enhance performance of optical metrology. Furthermore, the polarimetry in infrared (IR) range holds a promise for a wide range of academic and industrial applications because the IR light relates to unique spectral signatures of various complex chemicals. However, a primary challenge in IR applications remains lacking efficient detectors. Motivated by such a constraint, we present in this paper a nonlinear up-conversion full-Stokes IR Retrieval Polarimetry (IRP) that is able to decipher the IR polarization using a well-commercial and high-performance visible light detector. Assisted by a nonlinear sum-frequency generation (SFG) process in a lithium niobate thin film, the polarization states of the IR light are encoded into the visible SF wave. Based on a Stokes-Mueller formalism developed here, the IR polarization is successfully retrieved from SF light with high precision, and polarization imaging over the targets with either uniform or non-uniform polarization distributions are demonstrated. Our results form a fresh perspective for the design of novel advanced up-conversion polarimeter for a wide range of IR metrological applications.

physics.optics↗

arXiv2021

An Incentive Mechanism for Sustainable Blockchain Storage

Miners in a blockchain system are suffering from ever-increasing storage costs, which in general have not been properly compensated by the users' transaction fees. This reduces the incentives for the miners' participation and may jeopardize the blockchain security. We propose to mitigate this blockchain insufficient fee issue through a Fee and Waiting Tax (FWT) mechanism, which explicitly considers the two types of negative externalities in the system. Specifically, we model the interactions between the protocol designer, users, and miners as a three-stage Stackelberg game. By characterizing the equilibrium of the game, we find that miners neglecting the negative externality in transaction selection cause they are willing to accept insufficient-fee transactions. This leads to the insufficient storage fee issue in the existing protocol. Moreover, our proposed optimal FWT mechanism can motivate users to pay sufficient transaction fees to cover the storage costs and achieve the unconstrained social optimum. Numerical results show that the optimal FWT mechanism guarantees sufficient transaction fees and achieves an average social welfare improvement of 33.73\% or more over the existing protocol. Furthermore, the optimal FWT mechanism achieves the maximum fairness index and performs well even under heterogeneous-storage-cost miners.

cs.GT↗

arXiv2021

Metaverse for Social Good: A University Campus Prototype

In recent years, the metaverse has attracted enormous attention from around the world with the development of related technologies. The expected metaverse should be a realistic society with more direct and physical interactions, while the concepts of race, gender, and even physical disability would be weakened, which would be highly beneficial for society. However, the development of metaverse is still in its infancy, with great potential for improvement. Regarding metaverse's huge potential, industry has already come forward with advance preparation, accompanied by feverish investment, but there are few discussions about metaverse in academia to scientifically guide its development. In this paper, we highlight the representative applications for social good. Then we propose a three-layer metaverse architecture from a macro perspective, containing infrastructure, interaction, and ecosystem. Moreover, we journey toward both a historical and novel metaverse with a detailed timeline and table of specific attributes. Lastly, we illustrate our implemented blockchain-driven metaverse prototype of a university campus and discuss the prototype design and insights.

cs.MM↗

arXiv2021

Correlative image learning of chemo-mechanics in phase-transforming solids

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (e.g., due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. In this work, we developed a generalizable, physically-constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li$_X$FePO$_4$, a technologically-relevant battery positive electrode material. We uncovered the functional form of composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 $\leq$ X $\leq$ 1), including inside the thermodynamically-unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

cond-mat.mtrl-sci↗

arXiv2021

FBSDE based Neural Network Algorithms for High-Dimensional Quasilinear Parabolic PDEs

In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs), which are related to the FBSDEs by the Pardoux-Peng theory. The algorithms rely on a learning process by minimizing the pathwise difference between two discrete stochastic processes, defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively. The proposed algorithms are shown to generate DNN solutions for a 100-dimensional Black--Scholes--Barenblatt equation, accurate in a finite region in the solution space, and has a convergence rate similar to that of the Euler--Maruyama discretization used for the FBSDEs. As a result, a Richardson extrapolation technique over time discretizations can be used to enhance the accuracy of the DNN solutions. For time oscillatory solutions, a multiscale DNN is shown to improve the performance of the FBSDE DNN for high frequencies.

math.NA↗

arXiv2021

Linearized Learning Methods with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions

In this paper, we present linearized learning methods to accelerate the convergence of training for stationary nonlinear Navier-Stokes equations. To solve the stationary nonlinear Navier-Stokes (NS) equation, we integrate the procedure of linearization of the nonlinear convection term in the NS equation into the training process of multi-scale deep neural network approximation of the NS solution. Four forms of linearizations are considered. After a benchmark problem, we solve the highly oscillating stationary flows utilizing the proposed linearized learning with multi-scale neural network for complex domains. The results show that multiscale deep neural network combining with the linearized schemes can be trained fast and accurately.

math.NA↗

arXiv2021

Active plasmon interference control on ultrafast time scales by free electrons

Interference between light waves is one of the widely known phenomena in physics, which is widely used in modern optics, ranging from precise detection at the nanoscale to gravitational-wave observation. Akin to light, both classical and quantum interferences between surface plasmon polaritons (SPPs) have been demonstrated. However, to actively control the SPP interference within subcycle in time (usually less than several femtoseconds in the visible range) is still missing, which hinders the ultimate manipulation of SPP interference on ultrafast time scale. In this paper, the interference between SPPs launched by a hole dimer, which was excited by a grazing incident free electron beam without direct contact, was manipulated through both propagation and initial phase difference control. Particularly, using cathodoluminescence spectroscopy, the appearance of higher-order interference orders was obtained through propagation phase control by increasing separation distances of the dimer. Meanwhile, the peak-valley-peak evolution at a certain wavelength through changing the accelerating voltages was observed, which originates from the initial phase difference control of hole launched SPPs. In particular, the time resolution of this kind of control is shown to be in the ultrafast attosecond (as) region. Our work suggests that fast electron beams can be an efficient tool to control polarition interference in subcycle temporal scale, which can be potentially used in ultrafast optical processing or sensing.

physics.optics↗

arXiv2021

Radial stellar populations of AGN-host dwarf galaxies in SDSS-IV MaNGA survey

Based on MaNGA integral field unit (IFU) spectroscopy we search 60 AGN candidates, which have stellar masses $M_{\star}\leqslant5\times10^{9}$$M_{\odot}$ and show AGN ionization signatures in the BPT diagram. For these AGN candidates, we derive the spatially resolved stellar population with the stellar population synthesis code STARLIGHT and measure the gradients of the mean stellar age and metallicity. We find that the gradients of mean stellar age (metallicity) of individual AGN-host dwarfs are diverse in 0-0.5 Re, 0.5-1 Re and 0-1 Re. However, the overall behavior of the mean stellar age (metallicity) profiles tend to be flat, as the median values of the gradients are close to zero. We further study the overall behavior of the mean stellar age (metallicity) by plotting the co-added radial profiles for the AGN sample and compare with a control sample with similar stellar mass. We find that the median values of light-weighted mean stellar ages of AGN sample are as old as 2-3 ~Gyr within 2 Re,which are about 4-7 times older than those of the control sample. Meanwhile, most of the AGN candidates are low-level AGNs, as only eight sources have L[OIII]>$10^{39.5}$~erg~s$^{-1}$. Hence, the AGNs in dwarf galaxies might accelerate the evolution of galaxies by accelerating the consumption of the gas, resulting in an overall quenching of the dwarf galaxies, and the AGNs also become weak due to the lack of gas. The median values of mass-weighted mean stellar age of both samples within 2 $Re$ are similar and as old as about 10~Gyr, indicating that the stellar mass is mainly contributed by old stellar populations.The gradients of co-added mean stellar metallicity for both samples tend to be negative but close to zero, and the similar mean stellar metallicity profiles for both samples indicate that the chemical evolution of the host galaxy is not strongly influenced by the AGN.

astro-ph.GA↗

arXiv2021

Electro-Optic Lithium Niobate Metasurfaces

Many applications of metasurfaces require an ability to dynamically change their properties in time domain. Electrical tuning techniques are of particular interest, since they pave a way to on-chip integration of metasurfaces with optoelectronic devices. In this work, we propose and experimentally demonstrate an electro-optic lithium niobate (EO-LN) metasurface that shows dynamic modulations to phase retardation of transmitted light. Quasi-bound states in the continuum (QBIC) are observed from our metasurface. And by applying external electric voltages, the refractive index of the LN is changed by Pockels EO nonlinearity, leading to efficient phase modulations to the transmitted light around the QBIC wavelength. Our EO-LN metasurface opens up new routes for potential applications in the field of displaying, pulse shaping, and spatial light modulating.

physics.optics↗

arXiv2020

Stellar Populations of a Sample of Optically Selected AGN-host Dwarf Galaxies

In this paper we present our studies on the stellar populations and star formation histories (SFHs) for the Reines et al. sample of 136 dwarf galaxies which host active galactic nuclei (AGNs), selected from the Sloan Digital Sky Survey Data Release 8. We derive stellar populations and reconstruct SFHs for these AGN-host dwarfs using the stellar population synthesis code STARLIGHT. Our results suggest that these AGN-host dwarfs have assembled their stellar masses within a narrow period of time with the stellar mass-weighted ages in the range of $10^9-10^{10}$yr, but show a wide diversity of SFHs with the luminosity-weighted stellar ages in the range of $10^7-10^{10}$yr. The old population ($t>10^9$yr) contributes most to the galaxy light for the majority of the sample; the young population ($t<10^8$yr) also appears in significant but widely varying fractions, while the intermediate-age population ($10^8 10^{39}$erg s$^{-1}$, indicating that there is a physical connection between star formation and AGN activities in these dwarf galaxies.

astro-ph.GA↗

arXiv2020

Multi-scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

In this paper, we study a multi-scale deep neural network (MscaleDNN) as a meshless numerical method for computing oscillatory Stokes flows in complex domains. The MscaleDNN employs a multi-scale structure in the design of its DNN using radial scalings to convert the approximation of high frequency components of the highly oscillatory Stokes solution to one of lower frequencies. The MscaleDNN solution to the Stokes problem is obtained by minimizing a loss function in terms of L2 normof the residual of the Stokes equation. Three forms of loss functions are investigated based on vorticity-velocity-pressure, velocity-stress-pressure, and velocity-gradient of velocity-pressure formulations of the Stokes equation. We first conduct a systematic study of the MscaleDNN methods with various loss functions on the Kovasznay flow in comparison with normal fully connected DNNs. Then, Stokes flows with highly oscillatory solutions in a 2-D domain with six randomly placed holes are simulated by the MscaleDNN. The results show that MscaleDNN has faster convergence and consistent error decays in the simulation of Kovasznay flow for all four tested loss functions. More importantly, the MscaleDNN is capable of learning highly oscillatory solutions when the normal DNNs fail to converge.

math.NA↗

arXiv2020

Resonantly tunable second harmonic generation from lithium niobate metasurfaces

Second harmonic generation (SHG) is a coherent nonlinear phenomenon that plays an important role in laser color conversion. Lithium niobate (LN), which features both a large band gap and outstanding second-order nonlinearities, acts as an important optical material for nonlinear frequency conversion covering a wide spectral range from ultraviolet to mid-infrared. Here we experimentally demonstrate LN metasurfaces with controllable SHG properties. Distinct enhancements for the SHG efficiency are observed at Mie-resonances. And by changing the geometric parameters thus the resonances of the metasurfaces, we manage to selectively boost the SHG efficiency at different wavelengths. Our results would pave a way for developing with high flexibility the novel compact nonlinear light sources for applications, such as biosensing and optical communications.

physics.optics↗

arXiv2020

Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to a problem of learning about lower frequency functions, and the compact support activation functions facilitate the separation of frequency contents of the target function to be approximated by corresponding DNNs. As a result, the MscaleDNNs achieve fast uniform convergence over multiple scales. The proposed MscaleDNNs are shown to be superior to traditional fully connected DNNs and be an effective mesh-less numerical method for Poisson-Boltzmann equations with ample frequency contents over complex and singular domains.

physics.comp-ph↗

arXiv2020

A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media

A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the Maxwell's Green's functions into independent TE and TM components, each satisfying a Helmholtz equation, and decompose the elastic wave Green's function into the S-wave and the P-wave components. In addition, a derived vector basis formulation is applied to the case for acoustic wave sources from a non-viscous fluid layer.

math-ph↗

arXiv2020

Exponential convergence for multipole and local expansions and their translations for sources in layered media: three-dimensional Laplace equation

In this paper, we prove the exponential convergence of the multipole and local expansions, shifting and translation operators used in fast multipole methods (FMMs) for 3-dimensional Laplace equations in layered media. These theoretical results ensure the exponential convergence of the FMM which has been shown by the numerical results recently reported in [9]. As the free space components are calculated by the classic FMM, this paper will focus on the analysis for the reaction components of the Green's function for the Laplace equation in layered media. We first prove that the density functions in the integral representations of the reaction components are analytic and bounded in the right half complex plane. Then, using the Cagniard-de Hoop transform and contour deformations, estimate for the remainder terms of the truncated expansions is given, and, as a result, the exponential convergence for the expansions and translation operators is proven.

math.NA↗

arXiv2020

Dislocation Density-Based Plasticity Model from Massive Discrete Dislocation Dynamics Database

We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each slip system, and, equivalently, an exponential dependence of the plastic shear strain rate on the resolved shear stress. Hence the proposed generalized Taylor relation subsumes the Orowan relation for plastic flow. The DDD data also calls for a correction to the Kocks-Mecking model of dislocation multiplication to account for the increase of dislocation density on slip systems with negligible plastic shear strain rate. This is accomplished by allowing the multiplication rate on each slip system to include contributions from the plastic strain rates of the two coplanar slip systems. The resulting constitutive model successfully captures the strain hardening rate dependence on the loading orientation as predicted by the DDD simulations, which is also consistent with existing experiments.

cond-mat.mtrl-sci↗