Results for “PIC simulation” — Page 41

DOE OSTI2013

A RESOLVED DEBRIS DISK AROUND THE CANDIDATE PLANET-HOSTING STAR HD 95086

Recently, a new planet candidate was discovered on direct images around the young (10-17 Myr) A-type star HD 95086. The strong infrared excess of the system indicates that, similar to HR8799, β Pic, and Fomalhaut, the star harbors a circumstellar disk. Aiming to study the structure and gas content of the HD 95086 disk, and to investigate its possible interaction with the newly discovered planet, here we present new optical, infrared, and millimeter observations. We detected no CO emission, excluding the possibility of an evolved gaseous primordial disk. Simple blackbody modeling of the spectral energy distribution suggests the presence of two spatially separate dust belts at radial distances of 6 and 64 AU. Our resolved images obtained with the Herschel Space Observatory reveal a characteristic disk size of ∼6.''0 × 5.''4 (540 × 490 AU) and disk inclination of ∼25°. Assuming the same inclination for the planet candidate's orbit, its reprojected radial distance from the star is 62 AU, very close to the blackbody radius of the outer cold dust ring. The structure of the planetary system at HD 95086 resembles the one around HR8799. Both systems harbor a warm inner dust belt and a broad colder outer disk and giant planet(s) between the two dusty regions. Modeling implies that the candidate planet can dynamically excite the motion of planetesimals even out to 270 AU via their secular perturbation if its orbital eccentricity is larger than about 0.4. Our analysis adds a new example to the three known systems where directly imaged planet(s) and debris disks coexist.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗