Dark matter halo's and self similarity

This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at the center of the system for initial conditions with power law index larger than $-(1/2)$. It is found that the first appearance of the $x^{-(1/2)}$ law corresponds to the formation of a singularity very close to the center. Finally the general properties of self similar multi dimensional solutions near equilibrium are investigated. Smooth and continuous self similar solutions have power law behavior at equilibrium. However cold initial conditions result in discontinuous phase space solutions, and the smoothed phase space density looses its auto similar properties. This problem is easily solved by observing that the probability distribution of the phase space density $P$ is identical except for scaling parameters to the probability distribution of the smoothed phase space density $P_S$. As a consequence $P_S$ inherit the self similar properties of $P$. This particular property is at the origin of the universal power law observed in numerical simulation for ${\rho}/{\sigma^3}$. The self similar properties of $P_S$ implies that other quantities should have also an universal power law behavior with predictable exponents. This hypothesis is tested using a numerical model of the phase space density of cold dark matter halo's, an excellent agreement is obtained.Comment: Final versio

Full regularity for a C*-algebra of the Canonical Commutation Relations. (Erratum added)

The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S,B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a generalised group algebra, explained below) for the \sigma-representation theory of the abelian group S where \sigma(.,.):=e^{iB(.,.)/2}. As an easy application, it then follows that for every regular representation of the Weyl algebra of (S,B) on a separable Hilbert space, there is a direct integral decomposition of it into irreducible regular representations (a known result). An Erratum for this paper is added at the end.Comment: An erratum was added to the original pape

Gravitational Lensing by Dark Matter Caustics

Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first three, the line of sight is tangent to a smooth caustic surface. The curvature of the surface at the tangent point is positive, negative or zero. In the fourth case the line of sight passes near a cusp. For each we derive the map between the image and source planes. In some cases, a point source has multiple images and experiences infinite magnification when the images merge. Unfortunately, for the dark matter caustics expected in realistic galactic halo models, the angular resolution required to resolve the multiple images is not presently achievable. A more promising approach aims to observe the distortions caused by dark matter caustics in the images of extended sources such as radio jets.Comment: 36 pages, 11 figure

A follow-up study of the class of 1944, Amherst High School.

Thesis (M.S.

Alien Registration- Fillmore, Perley C. (Baldwin, Cumberland County)

https://digitalmaine.com/alien_docs/32923/thumbnail.jp

Metaphor and intertextuality in media framings of the (1984-85) British Miners' Strike:a multimodal analysis

The British Miners’ Strike of 1984-1985 represents one of the most pivotal periods in British industrial relations. Media stance toward the miners remains a controversial issue today, as attested by recent publications looking back at the strike (Williams 2009a, 2014). Here, authors including miners, journalists and other commentators argue that media coverage of the strike followed a consistently anti trade union agenda in which the media sought to destabilise the strike. An internal BBC report only recently made public shows that the BBC themselves had concerns over possible imbalances in their coverage of the so-called ‘Battle of Orgreave’ (Harcup 2014). Despite the weight attached to media coverage in this context, however, surprisingly little research has been conducted from a discourse-analytical perspective to show systematically and empirically how such an agenda may have been manifested across media texts. In this paper, drawing on Critical Cognitive Linguistics, I show how one particular metaphorical framing of the strike, which construed the strike as a war between the State and the National Union of Miners, persisted through the year long period and consider the potential ideological functions of this framing in media strategies of (de)legitimation. I show how this metaphor featured in linguistic, visual and multimodal forms of media representatio

Lack of correlation of stem cell markers in breast cancer stem cells

BACKGROUND: Various markers are used to identify the unique sub-population of breast cancer cells with stem cell properties. Whether these markers are expressed in all breast cancers, identify the same population of cells, or equate to therapeutic response is controversial. METHODS: We investigated the expression of multiple cancer stem cell markers in human breast cancer samples and cell lines in vitro and in vivo, comparing across and within samples and relating expression with growth and therapeutic response to doxorubicin, docetaxol and radiotherapy. RESULTS: CD24, CD44, ALDH and SOX2 expression, the ability to form mammospheres and side-population cells are variably present in human cancers and cell lines. Each marker identifies a unique rather than common population of cancer cells. In vivo, cells expressing these markers are not specifically localized to the presumptive stem cell niche at the tumour/stroma interface. Repeated therapy does not consistently enrich cells expressing these markers, although ER-negative cells accumulate. CONCLUSIONS: Commonly employed methods identify different cancer cell sub-populations with no consistent therapeutic implications, rather than a single population of cells. The relationships of breast cancer stem cells to clinical parameters will require identification of specific markers or panels for the individual cancer

Supporting Transitions: Success Interventions for Transfer Students

The purpose of this project was to explore the barriers associated with transferring to a four year institution, and offer potential solutions to better support transfer student success. When students transfer to a new institution, they face a multitude of potential barriers in the pursuit of a degree. These challenges can range from difficulty adjusting to a new environment to issues with credit transfers and efficient degree completion. Through a review of literature addressing this transition I have suggested a Transfer Experience Course that can serve as a success intervention to better improve transfer student success at a new institution