An <i>O</i>(<i>N</i>) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; Qin, Jian; Karpeev, Dmitry; Hernández-Ortiz, Juan P.; Pablo, Juan; Heinonen, Olle

doi:10.1063/1.4960436

Cited by 15 publications

(18 citation statements)

References 48 publications

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“…The logarithmic divergence, although being cut at small gap separation, still plagues numerical calculations in practice. 18 This type of crossover behavior has been confirmed in a study on dielectric spherical dimers using the image method. 19 The limiting value of the capacitance 2 ln ǫ r as well as the crossover is also consistent with the analytically known result between a conducting sphere and a dielectric plane.…”

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confidence: 66%

Exact polarization energy for clusters of contacting dielectrics

Lian¹,

Qin²

2021

Preprint

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The induced surface charges appear to diverge when dielectric particles form close contacts. Resolving this singularity numerically is prohibitively expensive because high spatial resolution is needed. We show that the strength of this singularity is logarithmic in both inter-particle separation and dielectric permittivity. A regularization scheme is proposed to isolate this singularity, and to calculate the exact cohesive energy for clusters of contacting dielectric particles. The results indicate that polarization energy stabilizes clusters of open configurations when permittivity is high, in agreement with the behavior of conducting particles, but stabilizes the compact configurations when permittivity is low.

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confidence: 66%

Exact polarization energy for clusters of contacting dielectrics

Lian¹,

Qin²

2021

Preprint

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“…The proposed strategy could be extended to more complex systems containing electrostatically charged granular particles. For example, using a recently developed parallel O(N ) numerical solver for electrostatic polarization interactions among arbitrary-shaped particles 21 , the evolutionary optimization strategy could be applied to determine charges not only of spherical particles, but also on arbitrarily-shaped particles with uniform or nonuniform surface charge distributions, and including rotational motion. The proposed strategy could also be used to determine the charges of particles in micro-or nanofluid environments by coupling the strategy with a recently developed parallel O(N ) Stokes' solver for hydrodynamically interacting objects in general geometries 44 .…”

Section: Discussionmentioning

confidence: 99%

“…The induced surface charge density (σ pol ) on every particle is calculated using COPSS (https://bitbucket.org/COPSS/copsspolarization-public) 21 . We obtain excellent agreement between the simulated and experimental trajectories of the particles.…”

Section: Application To Experimental Trajectoriesmentioning

confidence: 99%

Evolutionary strategy for inverse charge measurements of dielectric particles

Jiang

Lee

et al. 2018

The Journal of Chemical Physics

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We report a computational strategy to obtain the charges of individual dielectric particles from experimental observation of their interactions as a function of time. This strategy uses evolutionary optimization to minimize the difference between trajectories extracted from the experiment and simulated trajectories based on many-particle force fields. The force fields include both Coulombic interactions and dielectric polarization effects that arise due to particle-particle charge mismatch and particle-environment dielectric contrast. The strategy was applied to systems of free falling charged granular particles in a vacuum, where electrostatic interactions are the only driving forces that influence the particles' motion. We show that when the particles' initial positions and velocities are known, the optimizer requires only an initial and final particle configuration of a short trajectory in order to accurately infer the particles' charges; when the initial velocities are unknown and only the initial positions are given, the optimizer can learn from multiple frames along the trajectory to determine the particles' initial velocities and charges. While the results presented here offer a proof-of-concept demonstration of the proposed ideas, the proposed strategy could be extended to more complex systems of electrostatically charged granular matter.

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“…Furthermore, many materials interfaces are characterized by a discontinuity in the permittivity, resulting in induced surface polarization charges. This induced charge may significantly affect the ionic distributions [21,22,23,24,25,26] and dynamics [27,28,29], so that developing efficient methods for modeling spatially varying dielectrics has received considerable research attention [30,31,32,33,34,35,36]. Whereas this is typically costly, the special situation of planar interfaces (as well as systems that can be approximated as such) can be treated highly efficiently and accurately via the wellknown image-charge method (ICM) [37].…”

Section: Introductionmentioning

confidence: 99%

HSMA: An O(N) electrostatics package implemented in LAMMPS

Liang,

Yuan,

2021

Preprint

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We implement two recently developed fast Coulomb solvers, HSMA3D [J. Chem. Phys. 149 (8) ( 2018) 084111] and HSMA2D [J. Chem. Phys. 152 (13) (2020) 134109], into a new user package HSMA for molecular dynamics simulation engine LAMMPS. The HSMA package is designed for efficient and accurate modeling of electrostatic interactions in 3D and 2D periodic systems with dielectric effects at the O(N) cost. The implementation is hybrid MPI and OpenMP parallelized and compatible with existing LAMMPS functionalities. The vectorization technique following AVX512 instructions is adopted for acceleration. To establish the validity of our implementation, we have presented extensive comparisons to the widely used particle-particle particle-mesh (PPPM) algorithm in LAMMPS and other dielectric solvers. With the proper choice of algorithm parameters and parallelization setup, the package enables calculations of electrostatic interactions that outperform the standard PPPM in speed for a wide range of particle numbers.

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An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

Cited by 15 publications

References 48 publications

Exact polarization energy for clusters of contacting dielectrics

Exact polarization energy for clusters of contacting dielectrics

Evolutionary strategy for inverse charge measurements of dielectric particles

HSMA: An O(N) electrostatics package implemented in LAMMPS

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