Bound on global error of the fast multipole method for Helmholtz equation in 2-D

This paper analyze the global error of the fast multipole method(FMM) for two-dimensional Helmholtz equation. We first propose the global error of the FMM for the discretized boundary integral operator. The error is caused by truncating Graf's addition theorem, according to the limiting forms of Bessel and Neumann functions, we provide sharper and more precise estimates for the truncations of Graf's addition theorem. Finally, using the estimates we derive the explicit bound and convergence rate for the global error of the FMM for Helmholtz equation, numerical experiments show that the results are valid. The method in this paper can also be applied to the FMM for other problems such as potential problems, elastostatic problems, Stokes flow problems and so on

Treating Coulomb exchange contributions in relativistic mean field calculations: why and how

The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow 'mock up' the effects of meson-induced exchange terms by adjusting the meson-nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this note, we show that the Coulomb exchange effects can be easily included with a good accuracy in a perturbative approach. Therefore, it would be desirable for future relativistic EDF models to incorporate Coulomb exchange effects, at least to some order of perturbation.Comment: 3 pages, 1 figure, Proceedings of the 20th Nuclear Physics Workshop "Marie & Pierre Curie", Kazimierz, Poland, 25-29 September, 201

Identifying Influential Users Of Micro-Blogging Services: A Dynamic Action-Based Network Approach

In this paper, we present a dynamic model to identify influential users of micro-blogging services. Micro-blogging services, such as Twitter, allow their users (twitterers) to publish tweets and choose to follow other users to receive tweets. Previous work on user influence on Twitter, concerns more on following link structure and the contents user published, seldom emphasizes the importance of interactions among users. We argue that, by emphasizing on user actions in micro-blogging platform, user influence could be measured more accurately. Since micro-blogging is a powerful social media and communication platform, identifying influential users according to user interactions has more practical meanings, e.g., advertisers may concern how many actions – buying, in this scenario – the influential users could initiate rather than how many advertisements they spread. By introducing the idea of PageRank algorithm, innovatively, we propose our model using action-based network which could capture the ability of influential users when they interacting with micro-blogging platform. Taking the evolving prosperity of micro-blogging into consideration, we extend our action-based user influence model into a dynamic one, which could distinguish influential users in different time periods. Simulation results demonstrate that our models could support and give reasonable explanations for the scenarios that we considered

New effective interactions in RMF theory with non-linear terms and density-dependent meson-nucleon coupling

New parameter sets for the Lagrangian density in the relativistic mean field (RMF) theory, PK1 with nonlinear sigma- and omega-meson self-coupling, PK1R with nonlinear sigma-, omega- and rho-meson self-coupling and PKDD with the density-dependent meson-nucleon coupling, are proposed. They are able to provide an excellent description not only for the properties of nuclear matter but also for the nuclei in and far from the valley of beta-stability. For the first time in the parametrization of the RMF Lagrangian density, the center-of-mass correction is treated by a microscopic way, which is essential to unify the description of nuclei from light to heavy regions with one effective interaction.Comment: 22 pages, 16 EPS figures, RevTeX

Deep Neural Network Representation of Density Functional Theory Hamiltonian

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern research of material science. Here we study the crucial problem of representing DFT Hamiltonian for crystalline materials of arbitrary configurations via deep neural network. A general framework is proposed to deal with the infinite dimensionality and covariance transformation of DFT Hamiltonian matrix in virtue of locality and use message passing neural network together with graph representation for deep learning. Our example study on graphene-based systems demonstrates that high accuracy ($\sim$meV) and good transferability can be obtained for DFT Hamiltonian, ensuring accurate predictions of materials properties without DFT. The Deep Hamiltonian method provides a solution to the accuracy-efficiency dilemma of DFT and opens new opportunities to explore large-scale materials and physics.Comment: 5 pages, 4 figure

Evolution of Nuclear Shell Structure due to the Pion Exchange Potential

The evolution of nuclear shell structure is investigated for the first time within density-dependent relativistic Hartree-Fock theory and the role of $\pi$-exchange potential is studied in detail. The energy differences between the neutron orbits \Lrb{\nu1h_{9/2},\nu 1i_{13/2}} in the N=82 isotones and between the proton ones \Lrb{\pi1g_{7/2},\pi1h_{11/2}} in the Z=50 isotopes are extracted as a function of neutron excess $N-Z$. A kink around $Z = 58$ for the N=82 isotones is found as an effect resulting from pion correlations. It is shown that the inclusion of $\pi$-coupling plays a central role to provide realistic isospin dependence of the energy differences. In particular, the tensor part of the $\pi$-coupling has an important effect on the characteristic isospin dependence observed in recent experiments.Comment: 4 pages and 4 figure