Estimating the size of the cosmic-ray halo using particle distribution moments

Context: Particle transport in many astrophysical problems can be described either by the Fokker–Planck equation or by an equivalent system of stochastic differential equations. Aims: It is shown that the latter method can be applied to the problem of defining the size of the cosmic-ray galactic halo. Methods: Analytical expressions for the leading moments of the pitch-angle distribution of relativistic particles are determined. Particle scattering and escape are analyzed in terms of the moments. Results: In the case of an anisotropic distribution, the first moment leads to an expression for the halo size, identified with the particle escape from the region of strong scattering. Previous studies are generalized by analyzing the case of a strictly isotropic initial distribution. A new expression for the variance of the distribution is derived, which illustrates the anisotropization of the distribution. Conclusions: Stochastic calculus tools allow one to analyze physically motivated forms for the scattering rate, so that a detailed realistic model can be developed

Poorly characterized phases in C2M carbonaceous chondrites : proposed structures and significance

Poorly characterized phases (PCP's) may constitute up to 30 volume percent of some C2M carbonaceous chondrite matrices [1] and are an important key to an understanding of matrix evolution. PCPs are usually fine-grained (<lµm in size), and are difficult to characterize by conventional optical or X-ray techniques [2]. Fuchs et al. [2] introduced the term PCP in their detailed description of Fe-S-Ni-0 phases in the matrix of Murchison. Ramdohr [3] described a similar Fe-S-C phase with trace amounts of Ni in five carbonaceous chondrites and proposed that this mineral has a layer structure. Both the Fe-S-Ni-0 and Fe-S-Ni-C phases have similar optical properties and are conveniently described by the generic term PCP [1]. On the basis of recent high resolution electron microscopy (HREM) studies [4-9], we propose that these PCP's form at least two ordered, stable structures based upon alternating sequences of mackinawite- and brucite- (or amakinite-) type layers

Comparative Analysis of Non-thermal Emissions and Study of Electron Transport in a Solar Flare

We study the non-thermal emissions in a solar flare occurring on 2003 May 29 by using RHESSI hard X-ray (HXR) and Nobeyama microwave observations. This flare shows several typical behaviors of the HXR and microwave emissions: time delay of microwave peaks relative to HXR peaks, loop-top microwave and footpoint HXR sources, and a harder electron energy distribution inferred from the microwave spectrum than from the HXR spectrum. In addition, we found that the time profile of the spectral index of the higher-energy (\gsim 100 keV) HXRs is similar to that of the microwaves, and is delayed from that of the lower-energy (\lsim 100 keV) HXRs. We interpret these observations in terms of an electron transport model called {\TPP}. We numerically solved the spatially-homogeneous {\FP} equation to determine electron evolution in energy and pitch-angle space. By comparing the behaviors of the HXR and microwave emissions predicted by the model with the observations, we discuss the pitch-angle distribution of the electrons injected into the flare site. We found that the observed spectral variations can qualitatively be explained if the injected electrons have a pitch-angle distribution concentrated perpendicular to the magnetic field lines rather than isotropic distribution.Comment: 32 pages, 12 figures, accepted for publication in The Astronomical Journa

Towards a complete inventory of stratospheric dust particles, with implications for their classification

Several investigators have recently proposed classification schemes for stratospheric dust particles [1-3]. In addition, extraterrestrial materials within stratospheric dust collections may be used as a measure of micrometeorite flux [4]. However, little attention has been given to the problems of the stratospheric collection as a whole. Some of these problems include: (a) determination of accurate particle abundances at a given point in time; (b) the extent of bias in the particle selection process; (c) the variation of particle shape and chemistry with size; (d) the efficacy of proposed classification schemes and (e) an accurate determination of physical parameters associated with the particle collection process (e.g. minimum particle size collected, collection efficiency, variation of particle density with time). We present here preliminary results from SEM, EDS and, where appropriate, XRD analysis of all of the particles from a collection surface which sampled the stratosphere between 18 and 20km in altitude. Determinations of particle densities from this study may then be used to refine models of the behavior of particles in the stratosphere [5]

Numerical simulations of chromospheric hard X-ray source sizes in solar flares

X-ray observations are a powerful diagnostic tool for transport, acceleration, and heating of electrons in solar flares. Height and size measurements of X-ray footpoints sources can be used to determine the chromospheric density and constrain the parameters of magnetic field convergence and electron pitch-angle evolution. We investigate the influence of the chromospheric density, magnetic mirroring and collisional pitch-angle scattering on the size of X-ray sources. The time-independent Fokker-Planck equation for electron transport is solved numerically and analytically to find the electron distribution as a function of height above the photosphere. From this distribution, the expected X-ray flux as a function of height, its peak height and full width at half maximum are calculated and compared with RHESSI observations. A purely instrumental explanation for the observed source size was ruled out by using simulated RHESSI images. We find that magnetic mirroring and collisional pitch-angle scattering tend to change the electron flux such that electrons are stopped higher in the atmosphere compared with the simple case with collisional energy loss only. However, the resulting X-ray flux is dominated by the density structure in the chromosphere and only marginal increases in source width are found. Very high loop densities (>10^{11} cm^{-3}) could explain the observed sizes at higher energies, but are unrealistic and would result in no footpoint emission below about 40 keV, contrary to observations. We conclude that within a monolithic density model the vertical sizes are given mostly by the density scale-height and are predicted smaller than the RHESSI results show.Comment: 19 pages, 9 figures, accepted for publication in Ap

Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details

In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of Quantum Mechanics. This epoch-making paper is generally regarded as being difficult to follow, perhaps partly because Heisenberg provided few clues as to how he arrived at the results which he reported. Here we give details of calculations of the type which, we suggest, Heisenberg may have performed. We take as a specific example one of the anharmonic oscillator problems considered by Heisenberg, and use our reconstruction of his approach to solve it up to second order in perturbation theory. We emphasize that the results are precisely those obtained in standard quantum mechanics, and suggest that some discussion of the approach - based on the direct computation of transition amplitudes - could usefully be included in undergraduate courses in quantum mechanics.Comment: 24 pages, no figures, Latex, submitted to Am. J. Phy

Story Based Learning: A Student Centred Practice-Oriented Learning Strategy

Story based learning (SBL) has evolved as a way to promote quality in nursing education by assisting faculty to develop a student-centred learning environment. SBL is a teaching/learning strategy that also strengthens learners’ capacities to provide quality nursing care. Health professional education has been identified as a key contributor to advancing quality care. Key documents identify the pillars of quality health professional education as client–centred care, inter-professional education, teamwork and collaborative learning, knowledge mobilization and evidence-based practice, awareness of the limits of one’s knowledge as a foundation for reflective practice and life-long learning, and mastery of a field of practice. SBL incorporates elements of problem-based learning, case method teaching, and narrative pedagogy. The student-centred orientation of SBL aligns with the philosophical principles of client-centred nursing: respect for lived experience, participatory dialogue, and critical appraisal of health–related contexts. After providing an overview of SBL, we discuss the power of stories to engage learners in focused practice learning. We show how SBL sensitizes learners to: identify learning needs, develop information literacy, and recognize ethical, personal, interpersonal, and health team issues. We address how SBL fosters collaborative and participatory learning. Through a nursing lens learners using SBL identify a focus for nursing action, a process for negotiating nursing care, and appropriate nursing supports. The SBL process concludes with learners reflecting on what they have learned about learning and nursing. SBL is designed to develop in learners a habit of mind for clinical reasoning, reflective practice, and the delivery of quality nursing care. _________________ L’apprentissage au moyen de récits (AMR) est devenu une manière de favoriser la qualité de la formation en sciences infirmières en amenant le corps professoral à créer un environnement d’apprentissage centré sur l’étudiant(e). L’AMR est une stratégie d’enseignement et d’apprentissage qui renforce également les capacités des apprenants à offrir des soins infirmiers de qualité. La formation des professionnels de la santé constitue un élément essentiel pour l’amélioration de la qualité des soins. Les piliers d’une formation de qualité pour les professionnels de la santé ont été présentés dans des documents clés comme étant des soins centrés sur le client, une formation interprofessionnelle, un travail d’équipe et un apprentissage collaboratif , la mobilisation du savoir et la pratique fondée sur des résultats probants, la conscience des limites de son savoir comme fondement d’une pratique réflexive et d’un apprentissage continu, ainsi que la maîtrise d’un domaine de pratique. L’AMR intègre des éléments de l’apprentissage par problèmes, de la méthode d’ études de cas et de la pédagogie narrative. Le fait que l’AMR soit centré sur l’étudiant(e) cadre avec les principes philosophiques des soins infirmiers centrés sur le client : le respect de l’expérience vécue, le dialogue participatif et l’évaluation critique des contextes liés à la santé. Après avoir donné un aperçu de l’AMR, nous discutons du pouvoir des récits à engager les apprenants dans un apprentissage orienté vers la pratique. Nous présentons la manière dont l’AMR sensibilise les apprenants à identifier les besoins d’apprentissage, à développer une maîtrise de l’information et à reconnaître les questions éthiques, personnelles, interpersonnelles et liées à l’équipe de santé. Nous abordons la manière dont l’AMR favorise l’apprentissage collaboratif et participatif. À partir d’une perspective infirmière, les apprenants qui utilisent l’AMR déterminent une orientation pour l’intervention infirmière, un processus de négociation des soins infirmiers et les sources de soutien appropriées. Le processus d’AMR se termine en amenant les apprenants à réfléchir à ce qu’ils ont appris sur l’apprentissage et sur les sciences infirmières. L’AMR est conçu pour que les apprenants développent une habitude de la pensée pour le raisonnement clinique, la pratique réflexive et la prestation de soins infirmiers de qualité

Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.Comment: 9 pages, Latex, 6 PostScript figures in uuencoded compressed tar file are appende

Fast electron slowing-down and diffusion in a high temperature coronal X-ray source

Finite thermal velocity modifications to electron slowing-down rates may be important for the deduction of solar flare total electron energy. Here we treat both slowing-down and velocity diffusion of electrons in the corona at flare temperatures, for the case of a simple, spatially homogeneous source. Including velocity diffusion yields a consistent treatment of both "accelerated" and "thermal" electrons. It also emphasises that one may not invoke finite thermal velocity target effects on electron lifetimes without simultaneously treating the contribution to the observed X-ray spectrum from thermal electrons. We present model calculations of the X-ray spectra resulting from injection of a power-law energy distribution of electrons into a source with finite temperature. Reducing the power-law distribution low-energy cutoff to lower and lower energies only increases the relative magnitude of the thermal component of the spectrum, because the lowest energy electrons simply join the background thermal distribution. Acceptable fits to RHESSI flare data are obtained using this model. These also demonstrate, however, that observed spectra may in consequence be acceptably consistent with rather a wide range of injected electron parameters

Does a magnetic field modify the critical behaviour at the metal-insulator transition in 3-dimensional disordered systems?

The critical behaviour of 3-dimensional disordered systems with magnetic field is investigated by analyzing the spectral fluctuations of the energy spectrum. We show that in the thermodynamic limit we have two different regimes, one for the metallic side and one for the insulating side with different level statistics. The third statistics which occurs only exactly at the critical point is {\it independent} of the magnetic field. The critical behaviour which is determined by the symmetry of the system {\it at} the critical point should therefore be independent of the magnetic field.Comment: 10 pages, Revtex, 4 PostScript figures in uuencoded compressed tar file are appende