Redistribution Function Research Articles

Study on the solutions of the Sunyaev-Zeldovich effect for clusters of galaxies

Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the formal solutions in three different representation forms for the Sunyaev-Zeldovich effect. By expanding the formal solution in the operator representation in powers of both the derivative operator and electron velocity, we derive a formal solution that is equivalent to the Fokker-Planck expansion approximation. We extend the present formalism to the kinematical Sunyaev-Zeldovich effect. The properties of the frequency redistribution functions are studied. We find that the kinematical Sunyaev-Zeldovich effect is described by the redistribution function related to the electron pressure. We also solve the rate equations numerically. We obtain the exact numerical solutions, which include the full-order terms in powers of the optical depth.

Resonance line radiative transfer for hot atom coronae using Kappa distributions

Hot atomic populations are an important component of the planetary exospheres. Usually, radiative transfer models describing the scattering of light by moving atoms assume that these populations have a Maxwellian velocity distribution. However, the velocity distributions of the hot populations could actually have some more extended wings. Popular velocity distributions often used in plasma physics and recently proposed to describe neutral planetary environments are Kappa velocity function distributions. In this paper, following the work of Hummer [Non-coherent scattering: I The redistribution functions with Doppler broadening. R Astron. Soc Month Not 1962;125:21] and Cranmer [Non-Maxwellian redistribution in solar coronal Lyα emission. Astrophys J 1998;508:925–39], we calculate the frequency redistribution functions of radiation scattered by moving atoms with Kappa velocity distribution. We also present a detailed study of a radiative transfer model taking into account Kappa velocity distribution functions, for integer and semi-integer values of κ. We apply this theory to a model of Jupiter hydrogen corona containing 0.1% column density of hot hydrogen to quantify the spectroscopic and imaging differences between Kappa velocity distributions and bi-Maxwellian velocity distributions. When assuming a Kappa velocity distribution with κ=2 for the hot population, intensity increases of ∼40% occur at the bright limb and ∼15% on the disk compared with the same calculations done using a Maxwellian velocity distribution. The line profile differs slightly from a Maxwellian distribution on the disk and at the bright limb, but the difference is larger above the limb. Kappa distributions used to study the Jovian atmosphere are speculative and further studies are needed to link the formation of the hot exospheric populations to the Kappa velocity distributions.

Analytical study on the Sunyaev-Zeldovich effect for clusters of galaxies

Starting from a covariant formalism of the Sunyaev-Zeldovich effect for the thermal and nonthermal distributions, we derive the frequency redistribution function identical to Wright's method assuming the smallness of the photon energy (in the Thomson limit). We also derive the redistribution function in the covariant formalism in the Thomson limit. We show that two redistribution functions are mathematically equivalent in the Thomson limit, which is fully valid for the cosmic microwave background photon energies. We will also extend the formalism to the kinematical Sunyaev-Zeldovich effect. With the present formalism we will clarify the situation for the discrepancy existed in the higher-order terms of the kinematical Sunyaev-Zeldovich effect.

Modeling of the radiation transfer under partial frequency redistribution

A model is developed of the resonance radiation transfer under partial redistribution over frequencies. The media’s condition is described via the rate population balance equations for the two-level atom. The spectral intensity of the scattered radiation is calculated according to the stationary transfer equation. The light scattering by the atoms is modeled by a linear combination of the angle-averaged redistribution functions, RII and RIII. The obtained integro-differential equation system is solved numerically taking into account the radiation transfer in a cylindrical gas containing volume. The influence is investigated of the partial frequency redistribution on the sodium atom resonance line (λ = 589 nm) profile as well as on the efficient vapor afterglow duration depending on its optical thickness.

Statistical evaluation of the flux cross-calibration of the XMM-Newton EPIC cameras

The second XMM-Newton serendipitous source catalogue, 2XMM, provides the ideal data base for performing a statistical evaluation of the flux cross-calibration of the XMM-Newton European Photon Imaging Cameras (EPIC). We aim to evaluate the status of the relative flux calibration of the EPIC cameras on board XMM-Newton (MOS1, MOS2, and pn) and investigate the dependence of the calibration on energy, position in the field of view of the X-ray detectors, and lifetime of the mission. We compiled the distribution of flux percentage differences for large samples of 'good quality' objects detected with at least two of the EPIC cameras. The mean offset of the fluxes and dispersion of the distributions was then found by Gaussian fitting. Count rate to flux conversion was performed with a fixed spectral model. The impact on the results of varying this model was investigated. Excellent agreement was found between the two EPIC MOS cameras to better than 4% from 0.2 keV to 12.0 keV. MOS cameras register 7-9% higher flux than pn below 4.5 keV and 10-13% flux excess above 4.5 keV. No evolution of the flux ratios is seen with time, except at energies below 0.5 keV, where we found a strong decrease in the MOS to pn flux ratio with time. This effect is known to be due to a gradually degrading MOS redistribution function. The flux ratios show some dependence on distance from the optical axis in the sense that the MOS to pn flux excess increases with off-axis angle. Furthermore, in the 4.5-12.0 keV band there is a strong dependence of the MOS to pn excess flux on the azimuthal-angle. These results strongly suggest that the calibration of the Reflection Grating Array (RGA) blocking factors is incorrect at high energies. Finally, we recommend ways to improve the calculation of fluxes in future versions of XMM-Newton source catalogues.

Tax Competition, Public Good Provision, and Income Redistribution

This paper considers a tax competition model in which regional government activities include income redistribution as well as public good provision. To incorporate the regional government function of income redistribution, we extend the tax system from the stylized proportional capital income tax to the linear capital income tax with a uniform lump-sum grant: the revenue collected from capital taxation in each region is used not only to provide the regional public good but also to offer a uniform lump-sum grant to each individual in the region. In contrast to Hoyt's (1991) finding that the extent to which public goods are undersupplied is monotonically increasing in the number of competing regions, we show that, regardless of the number of competing regions, all heterogeneous individuals concur with each other on the first-best provision of public goods; on the other hand, the size of income redistribution is monotonically decreasing in the number of competing regions.

Numerical investigation of the escape factor of lithium and sodium vapour at partial frequency redistribution

The method of numerical simulation was used to study the effective lifetime of the excited level of the resonance transition in sodium and lithium vapour. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved with the equation of radiation transfer. The Biberman–Holstein escape factor was calculated as a function of the optical thickness of vapour for different geometries of the luminescing gas and different models of the frequency redistribution functions. The dependence of the escape factor on the optical thickness investigated experimentally by Romberg and Kunze (J. Quant. Spectrosc. Radiat. Transfer. 1988 39 99) is discussed.

An analytical model for the Ly α redistribution function in conditions of tokamak edge plasmas

Radiation redistribution is investigated for applications to magnetic fusion studies. An analytical model, suitable for Monte Carlo simulations of radiative transfer, is developed for the redistribution function of the resonance line of hydrogen isotopes. The model retains Zeeman and Stark effects in the atom's rest frame and in the impact approximation. The Zeeman effect is shown to play a major role on redistribution. Discussions are given on consequences of the Doppler effect in the laboratory frame.

La démocratie radicale de Jürgen Habermas

Résumé Jürgen Habermas est sans doute l’intellectuel dont les écrits ont eu la plus grande influence politique en Europe depuis une vingtaine d’années. Parmi ses nombreux ouvrages, Droit et Démocratie est probablement le plus important à cet égard. Dans ce livre, Habermas expose sa conception de la démocratie, et plus largement de la politique. Il y pose les fondements théoriques de ce qu’il nomme une « démocratie radicale », une démocratie qui ne serait plus fondée sur les droits naturels de l’homme, mais sur ce qu’Habermas appelle le principe de discussion. Une telle démocratie lui semble désormais indispensable pour pouvoir combiner les libertés individuelles de la tradition libérale avec les fonctions redistributrices assurées par l’État providence. Le présent article se propose d’examiner la solidité des fondations de cette « démocratie radicale » qu’Habermas appelle de ses vœux.

Quantitative live-cell analysis of microtubule-uncoupled cargo-protein sorting in the ER

The sorting and concentration of cargo proteins within ER exit sites (ERESs) is a fundamental function of the secretory machinery. The mechanism by which peripheral coat complexes and their small GTPase effectors mediate this function with export membrane domains is only partially understood. The secretory-machinery-mediated sorting to ERESs is a process that counters the entropy-driven even distribution of membrane proteins within organellar membranes. Here, for the first time, we quantified the dynamic properties of GFP-VSVG sorting to ERESs in living cells by uncoupling it from later translocation steps using microtubule depolymerization. The dynamics of the ER to ERES redistribution of cargo proteins was quantified in single cells by measuring changes in fluorescence-intensity variance after shift to the permissive temperature. Cargo concentration within ERESs continued in cells overexpressing the GTP-locked ARF1Q71L or in the presence of brefeldin A. In the absence of COPI and microtubules, ERESs transformed from tubulovesicular to spherical membranes that actively accumulated secretory cargo and excluded ER-membrane markers. We found sorting to ERESs to be a slow and diffusion-unlimited process. Our findings exclude COPI, and identify the COPII protein complex to be directly involved in the secretory cargo sorting and redistribution functions of ERESs.

Why There Was No ‘Marshall Plan’ for Eastern Europe and Why This Still Matters

Starting with an overview of the design and impact of the original Marshall Plan, this article explores the question of why the EC/EU failed to set in motion a similar project for Eastern Europe—purposefully targeted massive foreign aid conditioned upon cooperation among the recipient countries that could have encouraged productive investment and regional integration. Three elements of the Marshall Plan played a crucial role in the making of post-war economic miracle in Western Europe—regional integration that laid the basis for self-sustaining growth, a developmental state, and a balance between free market policies and social cohesion. It was the absence of these three elements from the Western strategy for Eastern Europe that made the latter relapse to its peripheral status. Indeed, precisely the opposite pattern was transplanted onto this region—economic fragmentation, the progressive withdrawal of the state from various redistributive and social functions thus effectively limiting its role to that of a guardian of the free market, and an organization of social forces that favoured economic liberalism at the expense of social cohesion. Salient features of the contemporary Eastern European capitalism are high share of foreign ownership of industrial and financial assets, large and growing dependence on capital imports, and trade dependence.

The Hanle effect

Context. It has been shown for the weak-field Hanle effect that the Stokes parameters I, Q, and U can be represented by a set of six cylindrically symmetrical functions. The proof relies on azimuthal Fourier expansions of the radiation field and of the Hanle phase matrix. It holds for a plane-parallel atmosphere and scattering processes that can be described by a redistribution matrix where redistribution in frequency is decoupled from angle redistribution and polarization. Aims. We give a simpler and more general proof of the Stokes parameter decomposition using powerful new tools introduced for polarimetry, in particular the Landi Degl'Innocenti spherical tensors T Κ Q(i, Ω). Methods. The elements of the Hanle phase matrix are written as a sum of terms that depend separately on the magnetic field vector and the directions Ω and Ω' of the incoming and scattered beams. The dependence on Ω and Ω' is expressed in terms of the spherical tensors T Κ Q (i, Ω) where i refers to the Stokes parameters (i = 0,..., 3). A multipolar expansion in terms of the T K Q,(Ω) is then established for the source term in the transfer equation for the Stokes parameters. Results. We show that the Stokes parameters have a multipolar expansion that can be written as I i (ν,Ω) =1Σ KQ τΚ Q (i,Ω)l K Q )(ν,θ) (K = 0,1, 2, -K ≤ Q < +K) where the I Q K are nine cylindrically symmetrical, irreducible tensors, θ being the inclination of Ω with respect to the vertical in the atmosphere. The proof is generalized to frequency-dependent phase matrices. It is applied both to partial frequency redistribution with angle-averaged scalar frequency redistribution functions and to complete frequency redistribution with the Hanle effect in the line core and Rayleigh scattering in the wings. Non-LTE transfer equations for the I Q K and integral equations for the associated source functions S Κ Q are established. Formal vectors and matrices constructed with I Q K , S K Q , and τ K Q are introduced in order to present the results in a compact matrix notation. In particular, a simple factorized form is proposed for the Hanle phase matrix.

Reflexive Democracy: Political Equality and the Welfare State

Reflexive Democracy: Political Equality and the Welfare State. By Kevin Olson. Cambridge, MA: MIT Press, 2006. 288p. $35.00.Recent work on the welfare state has largely focused on the role of welfare programs in state economies—their redistributive functions and their role in managing incentives for work. Reflexive Democracy marks a much-needed shift in focus, offering an analysis and then a reconstruction of the relationship between welfare programs and citizen participation.

Hanle‐Zeeman Redistribution Matrix. I. Classical Theory Expressions in the Laboratory Frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Effective deexcitation time of lithium vapor

The method of numerical simulation was used to study the effective deexcitation time of the resonance transition in lithium vapor at the wavelength λ = 670.776 nm. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved along with the equation of radiation transfer. The light scattering by an atom was simulated by a linear combination of the angle-averaged frequency distribution functions R II and R III. The Biberman-Holstein escape factor was calculated as a function of the optical thickness of lithium vapor for different geometries of the luminescing gas and different models of the frequency redistribution functions.

The H Lyman- α emission line from the upper atmosphere of Jupiter: Parametric radiative transfer study and comparison with data

This study uses the adding-doubling radiative transfer method in which we take into account the curvature effect of the planetary atmosphere in order to test the sensitivity of the jovian Ly- α emission line in relation to H column density, eddy diffusion coefficient, frequency redistribution function for photon scattering, temperature vertical profile, and an added hot atomic H layer on the top of the atmosphere. We also focus here on developing new diagnostic tools that will help us to obtain more confidently the underlying thermospheric structure of Jupiter. First, using the brightness distribution for specific wavelength bands as proposed by Ben Jaffel et al. [Ben Jaffel, L., Magnan, C., Vidal-Madjar, A., 1988. Astron. Astrophys. 204, 319–326], we show that the spatial thickness of the atomic H layer above the homopause level can be measured directly as the separation between the vertical positions of respectively the line core and line wing optical limbs. This thickness also constrains the [ H ] column and the value K H of the eddy diffusion coefficient at the homopause level at the disc location under consideration. We also propose to refine the value of K H and [ H ] , respectively, at a specific planetary latitude, using the Q ratio of the limb peak brightness to the intensity from other regions over the planetary disc. Finally, the relationship between the disc brightness distribution from specific wavelength bands of the emission line and the temperature gradient in the thermosphere is demonstrated, thus providing an accurate tool to access this key information from high resolution observations. Quick, preliminary comparisons with some existing HTS/STIS data show the H layer thickness at auroral latitudes ( ∼ 1700 km ) is much smaller than at equatorial latitudes ( ∼ 3900 km ). These results strongly support the existence of a gradient in both H density and K H versus latitude, with higher values of K H at high latitudes and higher values of the H density at the equatorial regions. Such a small H layer thickness at auroral latitudes is consistent with a high mixing in the atmosphere that brings the hydrocarbons upwards, reducing consequently the column of hydrogen that scatters photons. These preliminary results show the strength of the proposed approach and open new horizons to use strong resonant emission lines at high resolution as a diagnostic for the state and structure of planetary upper atmospheres.

Ridging, strength, and stability in high‐resolution sea ice models

In multicategory sea ice models the compressive strength of the ice pack is often assumed to be a function of the potential energy of pressure ridges. This assumption, combined with other standard features of ridging schemes, allows the ice strength to change dramatically on short timescales. In high‐resolution (∼10 km) sea ice models with a typical time step (∼1 hour), abrupt strength changes can lead to large internal stress gradients that destabilize the flow. The unstable flow is characterized by large oscillations in ice concentration, thickness, strength, velocity, and strain rates. Straightforward, physically motivated changes in the ridging scheme can reduce the likelihood of abrupt strength changes and improve stability. In simple test problems with flow toward and around topography, stability is significantly enhanced by eliminating the threshold fraction G* in the ridging participation function. Use of an exponential participation function increases the maximum stable time step at 10‐km resolution from less than 30 min to about 2 hours. Modifying the redistribution function to build thinner ridges modestly improves stability and also gives better agreement between modeled and observed thickness distributions. Allowing the ice strength to increase linearly with the mean ice thickness improves stability but probably underestimates the maximum stresses.

The Extension of Social Security Coverage in Developing Countries

We investigate the dynamic general equilibrium effects of introducing a social assistance program to elderly informal sector workers in developing countries. We find that the extension of such “retirement benefits” in environments with lacking private sector risk-sharing mechanisms results in welfare increases and relatively minor efficiency losses. Our results suggest that welfare gains attributed to the insurance and redistribution function of the social assistance program dominate welfare losses from distortionary effects of pension payments.

On the relevance of Compton scattering for the soft X-ray spectra of hot DA white dwarfs

We re-examine the effects of Compton scattering on the emergent spectra of hot DA white dwarfs in the soft X-ray range. Earlier studies have implied that sensitive X-ray observations at wavelengths $\lambda < 50$ \AA might be capable of probing the flux deficits predicted by the redistribution of electron-scattered X-ray photons toward longer wavelengths. We adopt two independent numerical approaches to the inclusion of Compton scattering in the computation of pure hydrogen atmospheres in hydrostatic equilibrium. One employs the Kompaneets diffusion approximation formalism, while the other uses the cross-sections and redistribution functions of Guilbert. Models and emergent spectra are computed for stellar parameters representative of HZ 43 and Sirius B, and for models with an effective temperature $T_{\rm eff} = 100 000$ K. The differences between emergent spectra computed for Compton and Thomson scattering cases are completely negligible in the case of both HZ 43 and Sirius B models, and are also negligible for all practical purposes for models with temperatures as high as $T_{\rm eff} = 100 000$ K. Models of the soft X-ray flux from these stars are instead dominated by uncertainties in their fundamental parameters.

Theoretical study of partial frequency redistribution function in irradiated, moving atmospheres of close binary components

We have studied the effects of partial frequency redistribution function with angle-averaged R II-A in irradiated and moving atmospheres of close binary components. We have considered the atmospheric extension of the primary component to be twice the radius of the primary component in a close binary system. We have considered two cases: (i) when the atmosphere is at rest and (ii) when the atmosphere is moving. In both the cases, we have computed the line profiles along the line of sight for a given optical depth. The irradiation from the secondary component is assumed to be one, five and 10 times the self-radiation. The line fluxes in the line of sight are calculated by using the total source functions due to self-radiation of the primary component and due to the irradiation from the secondary component. We have noted double-peaked emission lines in the case of a static medium and a reduction of emission peaks in the case of velocity field.