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At least 91 records · Page 5

Global weak solutions for a nonlocal multispecies Fokker–Planck–Landau system

The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker–Planck–Landau system for plasmas in the three-dimensional whole space is shown. The Fokker–Planck–Landau system is a simplification of the Landau equations assuming a linearized, velocity-independent, and isotropic kernel. The resulting equations depend nonlocally and nonlinearly on the moments of the distribution functions via the multispecies local Maxwellians. Furthermore, the existence proof is based on a three-level approximation scheme, energy and entropy estimates, as well as compactness results, and it holds for both soft and hard potentials.

97 MATHEMATICS AND COMPUTING↗

Fokker-Planck equations for charged-particle transport in random fields.

The Fokker-Planck equations for charged-particle dynamics are rederived, extending somewhat the elegant discussion of Hasselmann and Wibberenz. It is shown that the usual results are obtae and the conclusions in many cases are correct over a very broad range in energy. In particular, the rate for pitch-angle scattering may be accurately given down to energies much lower than previously thought. Recent claims that these Fokker-Planck equations are in general incorrect are thus shown to be in error.

Jokipii, J. R.↗

Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

Englert, G. W.↗

A sequence solution to the Fokker-Planck equation.

In this paper a new approach to nonlinear system analysis based on the Fokker-Planck equation is developed. The development begins as a modification of the parametrix method of partial differential equation theory and provides a sequence solution to the multidimensional time-varying Fokker-Planck equation. This sequence is simplified for the case where only a steady-state solution or a solution for the variance of a particular combination of states is desired. Equations are presented in a form suitable for obtaining numerical results using a digital computer.

Mayfield, W. W.↗

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

Fisk, L. A.↗

Mirroring within the Fokker-Planck formulation of cosmic ray pitch angle scattering in homogeneous magnetic turbulence

The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field.

Goldstein, M. L.↗

Fokker-Planck equations for charged-particle transport with a discussion of some higher-order effects

A derivation of the Fokker-Planck equation, based on the central limit theorem, is presented which clearly illustrates the conditions for its validity. It is reiterated that previous use of the Fokker-Planck equation in cosmic-ray transport is correct. Higher-order effects associated with magnetic mirroring and field line random walk at low energies are discussed heuristically.

Jokipii, J. R.↗

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximations yield the same integral for the Fokker-Planck coefficient for the pitch-angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For small pitch angles, the errors in previous evaluations are fortuitously of minor importance. For large pitch angles, however, these errors become more significant; and for pitch angles of 90 deg, the actual Fokker-Planck coefficient contains a delta function which has been overlooked in the past. The implications of these corrections on the possibility of relating cosmic-ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

Fisk, L. A.↗

Mirroring in the Fokker-Planck coefficient for cosmic-ray pitch-angle scattering in homogeneous magnetic turbulence

The Fokker-Planck coefficient for pitch-angle scattering, appropriate for cosmic rays in homogeneous stationary magnetic turbulence is computed without making any specific assumptions concerning the statistical symmetries of the random field. The Fokker-Planck coefficient obtained can be used to compute the parallel diffusion coefficient for high-energy cosmic rays propagating in the presence of strong turbulence, or for low-energy cosmic rays in the presence of weak turbulence. Because of the generality of magnetic turbulence allowed for in the analysis, special interplanetary magnetic field features, such as discontinuities or particular wave modes, can be included rigorously.

Goldstein, M. L.↗

Fokker-Planck response of stochastic satellites

The present investigation is concerned with the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The study of pointing accuracies requires a knowledge of the rates of error growth over and above any criteria for the asymptotic stability of the satellites. For this reason the investigation is oriented toward the determination of the statistical properties of the responses of the satellites. The geometries of the satellites are considered stochastic so as to have a phenomenological model of the motions of the flexible structural elements of the satellites. A widely used method of solving stochastic equations is the Fokker-Planck approach where the equations are assumed to define a Markoff process and the transition probability densities of the responses are computed directly as a function of time. The Fokker-Planck formulation is used to analyze the response vector of a rigid satellite.

Huang, T. C.↗

[Probing Planck-scale Physics with a Ne-21/He-3 Zeeman Maser]

The Ne-21/He-3 Zeeman maser is a recently developed device which employs co-located ensembles of Ne-21 and He-3 atoms to provide sensitive differential measurements of the noble gas nuclear Zeeman splittings as a function of time, thereby greatly attenuating common-mode systematic effects such as uniform magnetic field variations. The Ne-21 maser will serve as a precision magnetometer to stabilize the system's static magnetic field, while the He-3 maser is used as a sensitive probe for violations of CPT and Lorentz symmetry by searching for small variations in the 3He maser frequency as the spatial orientation of the apparatus changes due to the rotation of the Earth (or placement on a rotating table). In the context of a general extension of the Standard Model of particle physics, the Ne-21/He-3 maser will provide the most sensitive search to date for CPT and Lorentz violation of the neutron: better than 10(exp -32) GeV, an improvement of more than an order of magnitude over past experiments. This exceptional precision will offer a rare opportunity to probe physics at the Planck scale. A future space-based Ne-21/He-3 maser or related device could provide even greater sensitivity to violations of CPT and Lorentz symmetry, and hence to Planck-scale physics, because of isolation from dominant systematic effects associated with ground-based operation, and because of access to different positions in space-time.

Source record↗

Gravitation and Special Relativity from Compton Wave Interactions at the Planck Scale: An Algorithmic Approach

In this paper space is modeled as a lattice of Compton wave oscillators (CWOs) of near- Planck size. It is shown that gravitation and special relativity emerge from the interaction between particles Compton waves. To develop this CWO model an algorithmic approach was taken, incorporating simple rules of interaction at the Planck-scale developed using well known physical laws. This technique naturally leads to Newton s law of gravitation and a new form of doubly special relativity. The model is in apparent agreement with the holographic principle, and it predicts a cutoff energy for ultrahigh-energy cosmic rays that is consistent with observational data.

Blackwell, William C., Jr.↗

The Planck Sorption Cooler: Using Metal Hydrides to Produce 20 K

The Jet Propulsion Laboratory has built and delivered two continuous closed cycle hydrogen Joule-Thomson (JT) cryocoolers for the ESA Planck mission, which will measure the anisotropy in the cosmic microwave background. The metal hydride compressor consists of six sorbent beds containing LaNi4.78Sn0.22 alloy and a low pressure storage bed of the same material. Each sorbent bed contains a separate gas-gap heat switch that couples or isolates the bed with radiators during the compressor operating cycle. ZrNiHx hydride is used in this heat switch. The Planck compressor produces hydrogen gas at a pressure of 48 Bar by heating the hydride to approx.450 K. This gas passes through a cryogenic cold end consisting of a tube-in-tube heat exchanger, three pre-cooling stages to bring the gas to nominally 52 K, a JT value to expand the gas into the two-phase regime at approx.20 K, and two liquid - vapor heat exchangers that must remove 190 and 646 mW of heat respectively.

hydrogen storage materials↗

Simultaneous Planck, Swift, and Fermi Observations of X-Ray and gamma-Ray Selected Blazars

We present simultaneous Planck, Swift, Fermi, and ground-based data for 105 blazars belonging to three samples with flux limits in the soft X-ray, hard X-ray, and -ray bands, and we compare our results to those of a companion paper presenting simultaneous Planck and multi-frequency observations of 104 radio-loud northern active galactic nuclei selected at radio frequencies. While we confirm several previous results, our unique data set has allowed us to demonstrate that the selection method strongly influences the results, producing biases that cannot be ignored. Almost all the BL Lac objects have been detected by Fermi Large Area Telescope (LAT), whereas 30 to 40% of the flat-spectrum radio quasars (FSRQs) in the radio, soft X-ray, and hard X-ray selected samples are still below the gamma ray detection limit even after integrating 27 months of Fermi-LAT data. The radio to sub-millimetre spectral slope of blazars is quite flat, with [alpha] approximately 0 up to about 70 GHz, above which it steepens to [alpha] approximately -0.65. BL Lacs have significantly flatter spectra than FSRQs at higher frequencies. The distribution of the rest-frame synchrotron peak frequency (v(sup IC) (sub (PEAK)), ranges from 10(sup 21) to 10(sup 22) HZ. The distribution of the rest-frame synchrotron peak frequency (v(sup s)(sub peak)) in the spectral energy distribution (SED) of FSRQs is the same in all the blazar samples with (v(sup s)(sub peak) = 10(sup 13:1 plus or minus 0.1) Hz, while the mean inverse-Compton peak frequency,(v(sup IC)(sub peak) ranges from 10(sup 21) to 10(sup 22) Hz. The distributions of v(sup S)(sub peak) and of v(sup IC)(sub peak) of BL Lacs are much broader and are shifted to higher energies than those of FSRQs; their shapes strongly depend on the selection method. The Compton dominance of blazars ranges from less than 0.2 to nearly 100, with only FSRQs reaching values larger than about 3. Its distribution is broad and depends strongly on the selection method, with gamma-ray selected blazars peaking at approximately 7 or more, and radio-selected blazars at values close to 1, thus implying that the common assumption that the blazar power budget is largely dominated by high-energy emission is a selection effect. A comparison of our multi-frequency data with theoretical predictions shows that simple homogeneous SSC models cannot explain the simultaneous SEDs of most of the gamma-ray detected blazars in all samples. The SED of the blazars that were not detected by Fermi-LAT may instead be consistent with SSC emission. Our data challenge the correlation between bolometric luminosity and v(sup S)(sub peak) predicted by the blazar sequence.

Giommi, P.↗

Discovery of a Giant Radio Halo in a New Planck Galaxy Cluster PLCKG171.9-40.7

We report the discovery of a giant radio halo in a new, hot, X-ray luminous galaxy cluster recently found by Planck, PLCKG171.9-40.7. The radio halo was found using Giant Metrewave Radio Telescope observations at 235 MHz and 610 MHz, and in the 1.4 GHz data from a NRAO Very Large Array Sky Survey pointing that we have reanalyzed. The diffuse radio emission is coincident with the cluster X-ray emission, has an extent of approx.1 Mpc and a radio power of approx. 5×10(exp 24)W/Hz at 1.4 GHz. Its integrated radio spectrum has a slope of alpha approx. = 1.8 between 235 MHz and 1.4 GHz, steeper than that of a typical giant halo. The analysis of the archival XMMNewton X-ray data shows that the cluster is hot (approx. 10 keV) and disturbed, consistent with X-ray selected clusters hosting radio halos. This is the first giant radio halo discovered in one of the new clusters found by Planck.

Giacintucci, Simona↗

Measuring the Redshift Dependence of The Cosmic Microwave Background Monopole Temperature With Planck Data

We study the capability of Planck data to constrain deviations of the cosmic microwave background (CMB) blackbody temperature from adiabatic evolution using the thermal Sunyaev-Zeldovich anisotropy induced by clusters of galaxies. We consider two types of data sets depending on how the cosmological signal is removed: using a CMB template or using the 217 GHz map. We apply two different statistical estimators, based on the ratio of temperature anisotropies at two different frequencies and on a fit to the spectral variation of the cluster signal with frequency. The ratio method is biased if CMB residuals with amplitude approximately 1 microK or larger are present in the data, while residuals are not so critical for the fit method. To test for systematics, we construct a template from clusters drawn from a hydro-simulation included in the pre-launch Planck Sky Model. We demonstrate that, using a proprietary catalog of X-ray-selected clusters with measured redshifts, electron densities, and X-ray temperatures, we can constrain deviations of adiabatic evolution, measured by the parameter α in the redshift scaling T (z) = T0(1 + z)(sup 1−alpha), with an accuracy of sigma(sub alpha) = 0.011 in the most optimal case and with sigma alpha = 0.018 for a less optimal case. These results represent a factor of 2-3 improvement over similar measurements carried out using quasar spectral lines and a factor 6-20 with respect to earlier results using smaller cluster samples.

cosmic background radiation↗

The Planck Mission

Planck, scheduled for launch in 2007, will be the third space mission to observe the cosmic microwave background (CMB). Two cryogenic instruments and an off-axis telescope will provide an unprecedented combination of sensitivity, angular resolution, and frequency coverage. Planck is designed to measure the temperature anisotropies of the CMB to limits set not by the instruments, but rather by the Universe itself. In addition, it will measure the E-type polarization of the CMB, and provide all-sky surveys at nine frequencies between 30 and 857GHz.

cosmic↗

Strong detection of the CMB lensing and galaxy weak lensing cross-correlation from ACT-DR4, Planck Legacy, and KiDS-1000

We measured the cross-correlation between galaxy weak lensing data from the Kilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the Planck Legacy survey. We used two samples of source galaxies, selected with photometric redshifts, (0.1 < z(B) < 1.2) and (1.2 < z(B) < 2), which produce a combined detection significance of the CMB lensing and weak galaxy lensing cross-spectrum of 7.7σ. With the lower redshift galaxy sample, for which the cross-correlation was detected at a significance of 5.3σ, we present joint cosmological constraints on the matter density parameter, Ω(m), and the matter fluctuation amplitude parameter, σ(8), marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration as well as the intrinsic alignment of galaxies. We find our measurement to be consistent with the best-fitting flat ΛCDM cosmological models from both Planck and KiDS-1000. We demonstrate the capacity of CMB weak lensing cross-correlations to set constraints on either the redshift or shear calibration by analysing a previously unused high-redshift KiDS galaxy sample (1.2 < z(B) < 2), with the cross-correlation detected at a significance of 7σ. This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.

Naomi Clare Robertson↗