8,075 research outputs found

    Saturn’s axisymmetric field: A low Rm nonlinear analysis

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    Transforming a 4th year Modern Optics Course Using a Deliberate Practice Framework

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    We present a study of active learning pedagogies in an upper division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15 % improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier Transforms, partial differential equations, vector calculus), we expect the transformation process could be applied to most upper division physics courses having a similar mathematical base.Comment: 31 page

    On the preservation of Lipschitz classes under the Faber transformation

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    Let [omega] be a nonempty open, simply connected subset of the complex plane and let [delta] = \z ǁ ǁ z ǁ \u3c 1. Then there is a bijective analytic mapping g: \doubc - [macron][omega] → \doubc - [macron][delta]. We note that g has a continuous extension to the boundary [gamma] of [omega]. Let A([delta]) be the Banach algebra of functions continuous on [macron][delta] and analytic on [delta];We consider the tranformation T mapping f in A([delta]) to (Tf)(w) = 1 [over] 2[pi] i Ï”t[limits][subscript][gamma] f(g(t)) [over] t-w dtin the Banach algebra of functions continuous on [macron][omega] and analytic on [omega]. The mapping T is called the Faber transformation and is an injective continuous linear transformation;It is of interest to determine the properties of f which are preserved under the Faber transformation T. In particular, we assume that f satisifies a Lipschitz condition on [macron] [delta] and consider the Lipschitz class of Tf on [macron][omega]. We show that the Lipschitz class of Tf is affected by the Lipschitz class of f and the smoothness of [gamma], and, under suitable conditions on [gamma], we obtain qualitative results when g satisfies a Lipschitz condition

    Everything is at stake; yet nothing is at stake : exploring meaning-making in game-centred approaches

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    While not wishing to cover old ground in articulating the promise or continued promise of phenomenology within the physical education and sports domains, this paper aims to explore the ‘human’ nature of the game-centred approach (GCA) from an existential-phenomenological perspective. In a recent review of literature on the current state of research on GCAs, Harvey and Jarrett made the call for phenomenological-oriented empirical studies. Urging the academic fraternity to embrace such ‘participatory epistemologies’ is an extremely positive and important step by the authors. This is because, although they do not explicitly make the point, to call for the embrace of phenomenological-oriented research into GCAs, the authors are accepting the fundamental importance of individual experience and meaning in games teaching. If we focus on the individual it then becomes a distinct possibility of structuring increasingly meaningful game-centred practice. In this respect we analyze Martin Heidegger's notion of ‘being-in-the-world’ and illustrate how Arnold's three categories of meaningful movement—primordial, contextual and existential—can help facilitate ideas for pedagogical practice and provide an appropriate interpretive lens for future research into GCAs

    Nonlinear Particle Acceleration in Relativistic Shocks

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    Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to increase above test-particle values. Modified shocks with Lorentz factors less than about 3 can have compression ratios considerably greater than 3 and the momentum distribution of energetic particles no longer follows a power law relation. These results may be important for the interpretation of gamma-ray bursts if mildly relativistic internal and/or afterglow shocks play an important role accelerating particles that produce the observed radiation. For shock Lorentz factors greater than about 10, r approaches 3 and the so-called `universal' test-particle result of N(E) proportional to E^{-2.3} is obtained for sufficiently energetic particles. In all cases, the absolute normalization of the particle distribution follows directly from our model assumptions and is explicitly determined.Comment: Updated version, Astroparticle Physics, in press, 29 pages, 13 figure

    Particle acceleration at ultrarelativistic shocks: an eigenfunction method

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    We extend the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock fronts to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte-Carlo simulations, we find the index of the power-law distribution of accelerated particles which undergo isotropic diffusion in angle at an ultrarelativistic, unmagnetized shock is s=4.23 (where s=-d(ln f)/dp with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of a=0.62 (taking cooling into account a=1.12), where a=-d(ln F)/dn, F is the radiation flux and n the frequency. We also present an approximate analytic expression for the angular distribution of accelerated particles, which displays the effect of particle trapping by the shock: compared with the non-relativistic case the angular distribution is weighted more towards the plane of the shock and away from its normal. We investigate the sensitivity of our results to the transport properties of the particles and the presence of a magnetic field. Shocks in which the ratio of Poynting to kinetic energy flux upstream is not small are less compressive and lead to larger values of ss.Comment: Minor additions on publicatio

    Amino-terminal cysteine residues of RGS16 are required for palmitoylation and modulation of G(i)- and G(q)-mediated signaling

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    RGS proteins (Regulators of G protein Signaling) are a recently discovered family of proteins that accelerate the GTPase activity of heterotrimeric G protein α subunits of the i, q, and 12 classes. The proteins share a homologous core domain but have divergent amino-terminal sequences that are the site of palmitoylation for RGS-GAIP and RGS4. We investigated the function of palmitoylation for RGS16, which shares conserved amino-terminal cysteines with RGS4 and RGS5. Mutation of cysteine residues at residues 2 and 12 blocked the incorporation of [3H]palmitate into RGS16 in metabolic labeling studies of transfected cells or into purified RGS proteins in a cell-free palmitoylation assay. The purified RGS16 proteins with the cysteine mutations were still able to act as GTPase-activating protein for Giα. Inhibition or a decrease in palmitoylation did not significantly change the amount of protein that was membrane-associated. However, palmitoylation-defective RGS16 mutants demonstrated impaired ability to inhibit both Gi- and Gq-linked signaling pathways when expressed in HEK293T cells. These findings suggest that the amino-terminal region of RGS16 may affect the affinity of these proteins for Gα subunits in vivo or that palmitoylation localizes the RGS protein in close proximity to Gα subunits on cellular membranes

    Diffusive Shock Acceleration of High Energy Cosmic Rays

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    The process of diffusive acceleration of charged particles in shocked plasmas is widely invoked in astrophysics to account for the ubiquitous presence of signatures of non-thermal relativistic electrons and ions in the universe. A key characteristic of this statistical energization mechanism is the absence of a momentum scale; astrophysical systems generally only impose scales at the injection (low energy) and loss (high energy) ends of the particle spectrum. The existence of structure in the cosmic ray spectrum (the "knee") at around 3000 TeV has promoted contentions that there are at least two origins for cosmic rays, a galactic one supplying those up to the knee, and even beyond, and perhaps an extragalactic one that can explain even the ultra-high energy cosmic rays (UHECRs) seen at 1-300 EeV. Accounting for the UHECRs with familiar astrophysical sites of acceleration has historically proven difficult due to the need to assume high magnetic fields in order to reduce the shortest diffusive acceleration timescale, the ion gyroperiod, to meaningful values. Yet active galaxies and gamma-ray bursts remain strong and interesting candidate sources for UHECRs, turning the theoretical focus to relativistic shocks. This review summarizes properties of diffusive shock acceleration that are salient to the issue of UHECR generation. These include spectral indices, acceleration efficencies and timescales, as functions of the shock speed and mean field orientation, and also the nature of the field turbulence. The interpretation of these characteristics in the context of gamma-ray burst models for the production of UHECRs is also examined.Comment: 10 pages, 2 embedded figures, To appear in Nuclear Physics B, Proceedings Supplements, as part of the volume for the CRIS 2004, Cosmic Ray International Seminar: "GZK and Surroundings.
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