Numerical solution of high dimensional stationary Fokker–Planck equations via tensor decomposition and Chebyshev spectral differentiation
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We present the measured Sunyaev-Zel'dovich (SZ) flux from 474 optically-selected MaxBCG clusters that fall within the Atacama Cosmology Telescope (ACT) Equatorial survey region. The ACT Equatorial region used in this analysis covers 510 square degrees and overlaps Stripe 82 of the Sloan Digital Sky Survey. We also present the measured SZ flux stacked on 52 X-ray-selected MCXC clusters that fall within the ACT Equatorial region and an ACT Southern survey region covering 455 square degrees. We find that the measured SZ flux from the X-ray-selected clusters is consistent with expectations. However, we find that the measured SZ flux from the optically-selected clusters is both significantly lower than expectations and lower than the recovered SZ flux measured by the Planck satellite. Since we find a lower recovered SZ signal than Planck, we investigate the possibility that there is a significant offset between the optically-selected brightest cluster galaxies (BCGs) and the SZ centers, to which ACT is more sensitive due to its finer resolution. Such offsets can arise due to either an intrinsic physical separation between the BCG and the center of the gas concentration or from misidentification of the cluster BCG. We find that the entire discrepancy for both ACT and Planck can be explained by assuming that the BCGs are offset from the SZ maxima with a uniform random distribution between 0 and 1.5 Mpc. In contrast, the physical separation between BCGs and X-ray peaks for an X-ray-selected subsample of MaxBCG clusters shows a much narrower distribution that peaks within 0.2 Mpc. We conclude that while offsets between BCGs and SZ peaks may be an important component in explaining the discrepancy, it is likely that a combination of factors is responsible for the ACT and Planck measurements. Several effects that can lower the SZ signal equally for both ACT and Planck, but not explain the difference in measured signals, include a larger percentage of false detections in the MaxBCG sample, a lower normalization of the mass-richness relation, radio or infrared galaxy contamination of the SZ flux, and a low intrinsic SZ signal. In the latter two cases, the effects would need to be preferentially more significant in the optically-selected MaxBCG sample than in the MCXC X-ray sample.
A new continuum model is formulated for dilute suspensions of swimming micro-organisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker-Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor sigma can be computed; Vc and D are required in the cell conservation equation, and sigma in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, lambda and epsilon; lambda is the ratio of the rotary diffusion time Dr-1 to the torque relaxation time B (balancing gravitational and viscous torques), while epsilon is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker-Planck equation exactly for epsilon = 0 (lambda arbitrary) and also obtain the first-order solution for small epsilon. Using experimental data on Vc and D obtained with the swimming alga, Chlamydomonas nivalis, in the absence of bulk flow, the epsilon = 0 results can be used to estimate the value of lambda for that species (lambda approximately 2.2; Dr approximately 0.13 s-1). The continuum model for small epsilon is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to sigma, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells' intrinsic swimming motions.
Environmental test facilities are not suitable in any case to comply with special or complex test requirements without modifications. Dedicated upgrades of the test facility and their subsystems with respect to the test requirements and specifications are often necessary. The Flight Model of the Planck Space Telescope was tested in the Large Space Simulator (LSS) of the ESTEC Test Centre. Main goals of the test were the verification of the deformation of the Telescope during thermal vacuum conditions at different temperature levels and the validation of the Thermal Model. The deformations of the telescope have been traced by two Videogrammetry canisters. In order to provide different view positions with respect to the PLANCK Telescope it was necessary to rotate the specimen by +/- 180deg. In addition very stringent requirements for the low temperature level of the thermal environment has lead to a comprehensive test set-up which was divided in four main elements: Dedicated support structure for the Videogrammetry canisters providing several DoF for adjustment. Structure to support three Infrared panels around the specimen. MLI curtain to cover the LSS 8m auxiliary chamber opening. System providing LN2 supply for the rotating PLANCK telescope cold panel. The design, manufacturing and integration of the necessary mechanical ground support to install for instance the canisters and to ensure the 180 rotation of the telescope under cold and high vacuum conditions was an extensive and important part of the entire test program. This paper will concentrate on the design issues, the implementation and verification of the MGSE provided for the Planck Space Telescope FM Videogrammetry Test in the LSS and the troubleshooting caused by a failure during the first rotation under cold conditions.
C II is one of the brightest emission lines from star-forming galaxies and is an excellent tracer for star formation. Recent work measured the C II emission line amplitude for redshifts 2 < z < 3.2 by cross-correlating Planck High Frequency Instrument emission maps with tracers of overdensity from the Baryon Oscillation Spectroscopic Sky Survey, finding I(CII)=6.6(sup +5.0, sub −4.8×10(exp 4) Jy/sr at 95per cent confidence level. In this paper, we present a refinement of this earlier work by improving the mask weighting in each of the Planck bands and the precision in the covariance matrix. We report a detection of excess emission in the 545 GHz Planck band separate from the cosmic infrared background (CIB) present in the 353–857 GHz Planck bands. This excess is consistent with redshifted C II emission, in which case we report b(CII)I(CII)=2.0(sup +1.2, sub −1.1×10(exp 5) Jy/sr at 95 per cent confidence level, which strongly favours many collisional excitation models of C II emission. Our detection shows strong evidence for a model with a non-zero C II parameter, though line intensity mapping observations at high spectral resolution will be needed to confirm this result.
An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.
The gyroresonance of electrons with parallel transverse cold plasma waves is considered, and the Fokker-Planck equation describing the evolution of the electron distribution function in the presence of a spectrum of turbulence is derived. A new resonance which produces a divergence in the Fokker-Planck coefficients is identified; it results when the electron is in gyroresonance with a wave that has a group velocity equal to the velocity of the electron along the magnetic field. Under the assumption of a power-law spectral density, the Fokker-Planck coefficients are calculated numerically, and their complicated momentum and pitch-angle dependence, as well as the influence of various approximations to the dispersion relation, gyroresonance condition, and spectral density are discussed. It is found that there is no resonance gap at any pitch angle as long as the full gyroresonance condition is used and waves propagating on both directions are present.
We analyze the time variation of microwave spectra and hard X-ray spectra of 1989 March 18, which are obtained from the Solar Array at the Owens Valley Radio Observatory (OVRO) and the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM), respectively. From this observation, it is noted that the hard X-ray spectra gradually soften over 50 - 200 keV on-and-after the maximum phase while the microwaves at 1 - 15 GHz show neither a change in spectral shape nor as rapid a decay as hard X-rays. This leads to decoupling of hard X-rays from the microwaves in the decay phase away from their good correlation seen in the initial rise phase. To interpret this observation, we adopt a view that microwave-emitting particles and hard X-ray particles are physically separated in an inhomogeneous magnetic loop, but linked via interactions with the Whistler waves generated during flares. From this viewpoint, it is argued that the observed decoupling of microwaves from hard X-rays may be due to the different ability of each source region to maintain high energy electrons in response to the Whistler waves passing through the entire loop. To demonstrate this possibility, we solve a Fokker-Planck equation that describes evolution of electrons interacting with the Whistler waves, taking into account the variation of Fokker-Planck coefficients with physical quantities of the background medium. The numerical Fokker-Planck solutions are then used to calculate microwave spectra and hard X-ray spectra for agreement with observations. Our model results are as follows: in a sronger field region, the energy loss by electron escape due to scattering by the waves is greatly enhanced resulting in steep particle distributions that reproduce the observed hard X-ray spectra. In a region with weaker fields and lower density, this loss term is reduced allowing high energy electrons to survive longer so that microwaves can be emitted there in excess of hard X-rays during the decay phase of the flare. Our results based on spectral fitting of a flare event are discussed in comparison with previous studies of microwaves and hard X-rays based on either temporal or spatial information.
Precise measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy will revolutionize cosmology. These measurements will discriminate between competing cosmological models and, if the standard inflationary scenario is correct, will determine each of the fundamental cosmological parameters with high precision. The astrophysics community has recognized this potential: the orbital experiments MAP and PLANCK, have been approved to measure CMB anisotropy. Balloon-borne experiments can realize much of this potential before these missions are launched. Additionally, properly designed balloon-borne experiments can complement MAP in frequency and angular resolution and can give the first realistic test of the instrumentation proposed for the high frequency instrument on PLANCK. The MAXIMA experiment is part of the MAXIMA/BOOMERANG collaboration which is doing balloon observations of the angular power spectrum of the Cosmic Microwave Background from l = 10 to l = 800. These experiments are designed to use the benefits of both North American and Antarctic long-duration ballooning to full advantage. We have developed several new technologies that together allow the power spectrum to be measured with unprecedented combination of angular resolution, beam throw, sensitivity, sky coverage and control of systematic effects. These technologies are the basis for the high frequency instrument for the PLANCK mission. Our measurements will strongly discriminate between models of the origin and evolution of structure in the universe and, for many models, will determine the value of the basic cosmological parameters to high precision.
We present cosmological constraints from a gravitational lensing mass map covering 9400 deg2 reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitude σ8 = 0.819 ± 0.015 at 1.8% precision, S 8 ≡σ 8 (Ω m>/sub>/0.3) 0.5 = 0.840 ± 0.028, and the Hubble constant H 0 = (68.3 ± 1.1) km s −1 Mpc −1 at 1.6% precision. A joint constraint with Planck CMB lensing yields σ 8 = 0.812 ± 0.013, S 8 ≡σ 8 (Ω m>/sub>/0.3) 0.5 = 0.831 ± 0.023, and H0 = (68.1 ± 1.0) km s −1 Mpc −1 . These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find that S 8 from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σ to 2.1σ. This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probing z ∼ 0.5–5 on mostly linear scales and galaxy lensing at z ∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑m ν < 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of cross-correlation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming ground-based CMB surveys.