The interpretation of hard X-ray polarization measurements in solar flares

Observations of polarization of moderately hard X-rays in solar flares are reviewed and compared with the predictions of recent detailed modeling of hard X-ray bremsstrahlung production by non-thermal electrons. The recent advances in the complexity of the modeling lead to substantially lower predicted polarizations than in earlier models and more fully highlight how various parameters play a role in determining the polarization of the radiation field. The new predicted polarizations are comparable to those predicted by thermal modeling of solar flare hard X-ray production, and both are in agreement with the observations. In the light of these results, new polarization observations with current generation instruments are proposed which could be used to discriminate between non-thermal and thermal models of hard X-ray production in solar flares

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Ceramic identity contributes to mechanical properties and osteoblast behavior on macroporous composite scaffolds.

Implants formed of metals, bioceramics, or polymers may provide an alternative to autografts for treating large bone defects. However, limitations to each material motivate the examination of composites to capitalize on the beneficial aspects of individual components and to address the need for conferring bioactive behavior to the polymer matrix. We hypothesized that the inclusion of different bioceramics in a ceramic-polymer composite would alter the physical properties of the implant and the cellular osteogenic response. To test this, composite scaffolds formed from poly(lactide-co-glycolide) (PLG) and either hydroxyapatite (HA), β-tricalcium phosphate (TCP), or bioactive glass (Bioglass 45S®, BG) were fabricated, and the physical properties of each scaffold were examined. We quantified cell proliferation by DNA content, osteogenic response of human osteoblasts (NHOsts) to composite scaffolds by alkaline phosphatase (ALP) activity, and changes in gene expression by qPCR. Compared to BG-PLG scaffolds, HA-PLG and TCP-PLG composite scaffolds possessed greater compressive moduli. NHOsts on BG-PLG substrates exhibited higher ALP activity than those on control, HA-, or TCP-PLG scaffolds after 21 days, and cells on composites exhibited a 3-fold increase in ALP activity between 7 and 21 days versus a minimal increase on control scaffolds. Compared to cells on PLG controls, RUNX2 expression in NHOsts on composite scaffolds was lower at both 7 and 21 days, while expression of genes encoding for bone matrix proteins (COL1A1 and SPARC) was higher on BG-PLG scaffolds at both time points. These data demonstrate the importance of selecting a ceramic when fabricating composites applied for bone healing

Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces

We use spatial light modulators (SLMs) to measure correlations between arbitrary superpositions of orbital angular momentum (OAM) states generated by spontaneous parametric down-conversion. Our technique allows us to fully access a two-dimensional OAM subspace described by a Bloch sphere, within the higher-dimensional OAM Hilbert space. We quantify the entanglement through violations of a Bell-type inequality for pairs of modal superpositions that lie on equatorial, polar, and arbitrary great circles of the Bloch sphere. Our work shows that SLMs can be used to measure arbitrary spatial states with a fidelity sufficient for appropriate quantum information processing systems

Quantum correlations in position, momentum, and intermediate bases for a full optical field of view

We report an eight-element, linear-array, single-photon detector that uses multiple fibers of differing lengths coupled to a single detector, the timing information from which reveals the position in which the photon was measured. Using two such arrays and two detectors we measure the correlations of photons produced by parametric downconversion, without recourse to mechanical scanning. Spatial light modulators acting as variable focal length lenses positioned between the downconversion crystal and the arrays allow us to switch between measurement of position, transverse momentum, or intermediate bases. We observe the product of the variances of the conditional probabilities for position and momentum to be more than an order of magnitude below the classical limit, realizing a full-field demonstration of the Einstein-Podolsky-Rosen paradox. Such, multistate measurement technologies allow access to the higher information content of the photon based upon spatial modes

Quasi-Lie schemes and Emden--Fowler equations

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Finally some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered