274 research outputs found
An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling
A new approach to the kinetic simulation of plasmas in complex geometries,
based on the Particle-in- Cell (PIC) simulation method, is explored. In the two
dimensional (2d) electrostatic version of our method, called the Arbitrary
Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are
carried out in 2d on a uniform grid on the unit square logical domain, and
mapped to a nonuniform boundary-fitted grid on the physical domain. As the
resulting logical grid equations of motion are not separable, we have developed
an extension of the semi-implicit Modified Leapfrog (ML) integration technique
to preserve the symplectic nature of the logical grid particle mover. A
generalized, curvilinear coordinate formulation of Poisson's equations to solve
for the electrostatic fields on the uniform logical grid is also developed. By
our formulation, we compute the plasma charge density on the logical grid based
on the particles' positions on the logical domain. That is, the plasma
particles are weighted to the uniform logical grid and the self-consistent mean
electrostatic fields obtained from the solution of the logical grid Poisson
equation are interpolated to the particle positions on the logical grid. This
process eliminates the complexity associated with the weighting and
interpolation processes on the nonuniform physical grid and allows us to run
the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201
Quantifying the structural stability of simplicial homology
The homology groups of a simplicial complex reveal fundamental properties of
the topology of the data or the system and the notion of topological stability
naturally poses an important yet not fully investigated question. In the
current work, we study the stability in terms of the smallest perturbation
sufficient to change the dimensionality of the corresponding homology group.
Such definition requires an appropriate weighting and normalizing procedure for
the boundary operators acting on the Hodge algebra's homology groups. Using the
resulting boundary operators, we then formulate the question of structural
stability as a spectral matrix nearness problem for the corresponding
higher-order graph Laplacian. We develop a bilevel optimization procedure
suitable for the formulated matrix nearness problem and illustrate the method's
performance on a variety of synthetic quasi-triangulation datasets and
transportation networks.Comment: 25 pages, 9 figure
Plasmonic properties and energy flow in rounded hexahedral and octahedral nanoparticles
The resonant plasmonic properties of small dual rounded nano-scatterers are numerically investigated. A set of Drude-like, silver hexahedral and octahedral structures are studied and compared with a reference spherical particle through a numerical surface integral equation technique. Surface, near field, Poynting field and streamline distributions are presented illustrating novel plasmonic features arising from the complex shapes of the nanoparticles, while several designing rules are described. These qualitative observations can be used appropriately towards sensing, sorting, harvesting, and radiation control
applications
- …