arXiv subjects

Wei Cai

Publications and source records attributed to Wei Cai.

At least 127 records · Page 7Linked to original sources

arXiv2020

Fast multipole method for 3-D Laplace equation in layered media

In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free space component and four types of reaction field components, and the latter can be associated with the potential of a polarization source defined for each type. New multipole expansions (MEs) and local expansions (LEs), as well as the multipole to local (M2L) translation operators are derived for the reaction components, based on which the FMMs for reaction components are then proposed. The resulting FMM for charge interactions in layered media is a combination of using the classic FMM for the free space components and the new FMMs for the reaction field components. With the help of a recurrence formula for the run-time computation of the Sommerfeld-type integrals used in M2L translation operators, pre-computations of a large number of tables are avoided. The new FMMs for the reaction components are found to be much faster than the classic FMM for the free space components due to the separation of equivalent polarization charges and the associated target charges by a material interface. As a result, the FMM for potential in layered media costs almost the same as the classic FMM in the free space case. Numerical results validate the fast convergence of the MEs for the reaction components, and the O(N) complexity of the FMM with a given truncation number p for charge interactions in 3-D layered media.

math.NA↗

arXiv2020

Unveiling the secrets of the mid-infrared Moon

The Moon's optical characteristics in visible and long-wavelength infrared (LWIR) have long been observed with our eyes or with instruments. What the mid-infrared (MIR) Moon looks like is still a mystery. For the first time we present detailed appearance of the MIR Moon observed by a high-resolution geostationary satellite and reveal the essence behind its appearance. The appearance of the MIR Moon is opposite to its normal visible appearance. In addition the MIR Moon shows limb darkening. Both the absolute and the relative brightness distribution of the MIR lunar disk changes with the solar incidence angle. The signatures of the MIR Moon are controlled by both the reflection and emission of the lunar surface. We also show first-ever brightness temperature maps of the lunar disk without needing a mosaic, which better show the temperature variation across the lunar disk. They reveal that the relationship between brightness temperature and solar incidence angle i is cos1/bi, and the power parameter is smaller than the Lambertian temperature model of cos1/4i observed for lunar orbit-based measurements. The slower decrease of the brightness temperature when moving away from the sub-solar point than the Lambertian model is due to topographic effects. The brightness temperature is dominated by albedo and the solar incidence angle and influenced by the topography. Our results indicate that the Moon in the MIR exhibits many interesting phenomena which were previously unknown, and contains abundant information about lunar reflection and thermal emission for future study.

astro-ph.EP↗

arXiv2020

Optically Addressed Spatial Light Modulator based on Nonlinear Metasurface

Spatial light modulators (SLMs) are devices for modulating amplitude, phase or polarization of a light beam on demand. Such devices have been playing an indispensable inuence in many areas from our daily entertainments to scientific researches. In the past decades, the SLMs have been mainly operated in electrical addressing (EASLM) manner, wherein the writing images are created and loaded via conventional electronic interfaces. However, adoption of pixelated electrodes puts limits on both resolution and efficiency of the EASLMs. Here, we present an optically addressed SLM based on a nonlinear metasurface (MS-OASLM), by which signal light is directly modulated by another writing beam requiring no electrode. The MS-OASLM shows unprecedented compactness and is 400 nm in total thickness benefitting from the outstanding nonlinearity of the metasurface. And their subwavelength feature size enables a high resolution up to 250 line pairs per millimeter, which is more than one order of magnitude better than any currently commercial SLMs. Such MS-OASLMs could provide opportunities to develop the next generation of high resolution displays and all-optical information processing technologies.

physics.optics↗

arXiv2020

Fast Multipole Method for 3-D Linearized Poisson-Boltzmann Equation in Layered Media

In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media [1,2], using an extension of the Funk-Hecke formula for pure imaginary wave number. Moreover, a recurrence formula is provided for the run-time computation of the Sommerfeld-type integrals used in the FMM algorithm. Due to the similarity between Helmholtz and linearized PB equation, the recurrence formula can also be used for the FMM of Helmholtz equation in layered media with minor changes as mentioned in [1] . Numerical results validate that the FMM for interactions of charges under screen's potentials in layered media has the same accuracy and CPU complexity as the classic FMM for charge interactions in free space.

math.NA↗

arXiv2020

Topological origin of strain induced damage of multi-network elastomers by bond breaking

Elastomers that can sustain large reversible strain are essential components for stretchable electronics. The stretchability and mechanical robustness of unfilled elastomers can be enhanced by introducing easier-to-break cross-links, e.g. through the multi-network structure, which also causes stress-strain hysteresis indicating strain-induced damage. However, it remains unclear whether cross-link breakage follows a predictable pattern that can be used to understand the damage evolution with strain. Using coarse-grained molecular dynamics and topology analyses of the polymer network, we find that bond-breaking events are controlled by the evolution of the global shortest path length between well-separated cross-links, which is both anisotropic and hysteretic with strain. These findings establish an explicit connection between the molecular structure and the macroscopic mechanical behavior of elastomers, thereby providing guidelines for designing mechanically robust soft materials.

cond-mat.soft↗

arXiv2019

EdgeToll: A Blockchain-based Toll Collection System for Public Sharing of Heterogeneous Edges

Edge computing is a novel paradigm designed toimprove the quality of service for latency sensitive cloud applications. However, the state-of-the-art edge services are designedfor specific applications, which are isolated from each other.To better improve the utilization level of edge nodes, publicresource sharing among edges from distinct service providersshould be encouraged economically. In this work, we employ thepayment channel techniques to design and implement EdgeToll,a blockchain-based toll collection system for heterogeneous public edge sharing. Test-bed has been developed to validate theproposal and preliminary experiments have been conducted todemonstrate the time and cost efficiency of the system.

cs.DC↗

arXiv2019

A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems

In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common DNNs often achieve convergence in the low frequency range first, and a series of moderately-sized DNNs are constructed and trained for selected high frequency ranges. With the help of phase shifts in the frequency domain, each of the DNNs will be trained to approximate the function's higher frequency content over a specific range at the the speed of convergence as in the low frequency range. As a result, the proposed PhaseDNN is able to convert high frequency learning to low frequency one, allowing a uniform learning to wideband functions. The PhaseDNN will then be applied to find the solution of high frequency wave equations in inhomogeneous media through both differential and integral equation formulations with least square residual loss functions. Numerical results have demonstrated the capability of the PhaseDNN in learning high frequency functions and oscillatory solutions of interior and exterior Helmholtz equations.

cs.LG↗

arXiv2019

A Note on StiffDNN -- a DNN for Stiff Dynamic Systems

In this note, we will present a specially designed deep neural network (DNN), which will target components of the solution of different time rate individually through perspective of the Laplace s-transform of the solution. Each segment of s-frequency range will be approximated by a small size DNN separately after a reference central rate is factored out, leaving the rest of the frequencies confined within a short range of rates, and allowing fast and uniform learning by normal DNN.

eess.SP↗

arXiv2019

What Is the Fractional Laplacian?

The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for a given application. The Riesz (or integral) definition, for example, admits a nonlocal boundary condition, where the value of a function u(x) must be prescribed on the entire exterior of the domain in order to compute its fractional Laplacian. In contrast, the spectral definition requires only the standard local boundary condition. These differences, among others, lead us to ask the question: "What is the fractional Laplacian?" We compare several commonly used definitions of the fractional Laplacian (the Riesz, spectral, directional, and horizon-based nonlocal definitions), and we use a joint theoretical and computational approach to examining their different characteristics by studying solutions of related fractional Poisson equations formulated on bounded domains. In this work, we provide new numerical methods as well as a self-contained discussion of state-of-the-art methods for discretizing the fractional Laplacian, and we present new results on the differences in features, regularity, and boundary behaviors of solutions to equations posed with these different definitions. We present stochastic interpretations and demonstrate the equivalence between some recent formulations. Through our efforts, we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications.

math.NA↗

arXiv2019

Multi-scale Deep Neural Networks for Solving High Dimensional PDEs

In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs. Numerical results on high dimensional function fitting and solutions of high dimensional PDEs, using loss functions with either Ritz energy or least squared PDE residuals, have validated the increased power of multi-scale resolution and high frequency capturing of the proposed MscaleDNN.

cs.LG↗

arXiv2019

Fast Multipole Method For 3-D Helmholtz Equation In Layered Media

In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for the Helmholtz equation, which satisfies the transmission conditions at material interfaces, is decomposed into a free space component and four types of reaction field components arising from wave reflections and transmissions through the layered media. The proposed algorithm is a combination of the classic FMM for the free space component and FMMs specifically designed for the four types reaction components, made possible by new multipole expansions (MEs) and local expansions (LEs) as well as the multipole-to-local translation (M2L) operators for the reaction field components. { Moreover, equivalent polarization source can be defined for each reaction component based on the convergence analysis of its ME. The FMMs for the reaction components, implemented with the target particles and equivalent polarization sources, are found to be much more efficient than the classic FMM for the free space component due to the fact that the equivalent polarization sources and the target particles are always separated by a material interface.} As a result, the FMM algorithm developed for layered media has a similar computational cost as that for the free space. Numerical results validate the fast convergence of the MEs and the $O(N)$ complexity of the FMM for interactions of low-frequency wave sources in 3-D layered media.

math.NA↗

arXiv2019

A Path Integral Monte Carlo Method based on Feynman-Kac Formula for Electrical Impedance Tomography

A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain electrical potentials. The forward problem is an important part for iterative algorithms of the inverse problem of EIT, which has attracted continual interest due to its applications in medical imaging and material testing of materials. By simulating reflecting Brownian motion with walk-on-sphere techniques and calculating its corresponding local time, we are able to obtain accurate voltage-to-current map for the conductivity equation with mixed boundary conditions for a 3-D spherical object with eight electrodes. Due to the local property of the PIMC method, the solution of the map can be done locally for each electrode in a parallel manner.

math.NA↗

arXiv2019

Rhythm Dungeon: A Blockchain-based Music Roguelike Game

Rhythm Dungeon is a rhythm game which leverages the blockchain as a shared open database. During the gaming session, the player explores a roguelike dungeon by inputting specific sequences in time to music rhythm. By integrating smart contract to the game program, the enemies through the venture are generated from other games which share the identical blockchain. On the other hand, the player may upload their characters at the end of their journey, so that their own character may appear in other games and make an influence. Rhythm Dungeon is designed and implemented to show the potential of decentralized gaming experience, which utilizes the blockchain to provide asynchronous interactions among massive players.

cs.MM↗

arXiv2019

A Security Case Study for Blockchain Games

Blockchain gaming is an emerging entertainment paradigm. However, blockchain games are still suffering from security issues, due to the immature blockchain technologies and its unsophisticated developers. In this work, we analyzed the blockchain game architecture and reveal the possible penetration methods of cracking. We scanned more than 600 commercial blockchain games to summarize a security overview from the perspective of the web server and smart contract, respectively. We also conducted three case studies for blockchain games to show detailed vulnerability detection.

cs.CR↗

arXiv2019

Blockchain Games: A Survey

With the support of the blockchain systems, the cryptocurrency has changed the world of virtual assets. Digital games, especially those with massive multi-player scenarios, will be significantly impacted by this novel technology. However, there are insufficient academic studies on this topic. In this work, we filled the blank by surveying the state-of-the-art blockchain games. We discuss the blockchain integration for games and then categorize existing blockchain games from the aspects of their genres and technical platforms. Moreover, by analyzing the industrial trend with a statistical approach, we envision the future of blockchain games from technological and commercial perspectives.

cs.DC↗

arXiv2019

Exponential convergence for multipole and local expansions and their translations for sources in layered media: 2-D acoustic wave

In this paper, we will first give a derivation of the multipole expansion (ME) and local expansion (LE) for the far field from sources in general 2-D layered media and the multipole-to-local translation (M2L) operator by using the generating function for Bessel functions. Then, we present a rigorous proof of the exponential convergence of the ME, LE, and M2L for 2-D Helmholtz equations in layered media. It is shown that the convergence of ME, LE, and M2L for the reaction field component of the Green's function depends on a polarized distance between the target and a polarized image of the source.

math.NA↗

arXiv2019

PhaseDNN - A Parallel Phase Shift Deep Neural Network for Adaptive Wideband Learning

In this paper, we propose a phase shift deep neural network (PhaseDNN) which provides a wideband convergence in approximating a high dimensional function during its training of the network. The PhaseDNN utilizes the fact that many DNN achieves convergence in the low frequency range first, thus, a series of moderately-sized of DNNs are constructed and trained in parallel for ranges of higher frequencies. With the help of phase shifts in the frequency domain, implemented through a simple phase factor multiplication on the training data, each DNN in the series will be trained to approximate the target function's higher frequency content over a specific range. Due to the phase shift, each DNN achieves the speed of convergence as in the low frequency range. As a result, the proposed PhaseDNN system is able to convert wideband frequency learning to low frequency learning, thus allowing a uniform learning to wideband high dimensional functions with frequency adaptive training. Numerical results have demonstrated the capability of PhaseDNN in learning information of a target function from low to high frequency uniformly.

eess.SP↗

arXiv2019

Taylor expansion based fast Multipole Methods for 3-D Helmholtz equations in Layered Media

In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's function are developed. A key component of the first algorithm is an efficient algorithm based on discrete complex image approximation and recurrence formula for the calculation of the layered media Green's function and its derivatives, which are given in terms of Sommerfeld integrals. The second algorithm uses symmetric derivatives in the Taylor expansion to reduce the size of precomputed tables for the derivatives of layered media Green's function. Numerical tests in layered media have validated the accuracy and O(N) complexity of the proposed algorithms.

math.NA↗