A Geometrical Method of Decoupling

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as for instance the method of Teng and Edwards. In a preceeding paper it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all thinkable cases. Hence a systematic derivation of a more general treatment seemed advisable. In a second paper the author suggested the use of real Dirac matrices as basic tools to coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. It is shown that this algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec P$, that were introduced with the so-called "electromechanical equivalence". We present a structure-preserving block-diagonalization of symplectic or Hamiltonian matrices, respectively. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires ${\cal O}(n^2)$ iterations to converge to a given precision.Comment: 13 pages, 1 figur

Evidence for Proportionate Partition Between the Magnetic Field and Hot Gas in Turbulent Cassiopeia A

We present a deep X-ray observation of the young Galactic supernova remnant Cas A, acquired with the ROSAT High Resolution Imager. This high dynamic range (232 ks) image reveals low-surface-brightness X-ray structure, which appears qualitatively similar to corresponding radio features. We consider the correlation between the X-ray and radio morphologies and its physical implications. After correcting for the inhomogeneous absorption across the remnant, we performed a point by point (4" resolution) surface brightness comparison between the X-ray and radio images. We find a strong (r = 0.75) log-log correlation, implying an overall relationship of $\log(\Sigma_{_{\rm X-ray}}) \propto (2.21\pm0.05) \times \log(\Sigma_{_{\rm radio}})$. This is consistent with proportionate partition (and possibly equipartition) between the local magnetic field and the hot gas --- implying that Cas A's plasma is fully turbulent and continuously amplifying the magnetic field.Comment: 8 pages with embedded bitmapped figures, Accepted by ApJ Letters 5/1/9

Measurement of tensor analyzing powers in deuteron photodisintegration

New accurate measurement of tensor analyzing powers T20, T21 and T22 in deuteron photodisintegration has been performed. Wide-aperture non-magnetic detectors allowed to cover broad kinematic ranges in a single setup: photon energy = 25 to 600 MeV, proton emission angle in CM = 24 to 48 deg. and 70 to 102 deg. New data provide a significant improvement of a few existing measurements. The angular dependency of the tensor asymmetries in deuteron photodisintegration is extracted for the first time.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Calculation of energy levels and transition amplitudes for barium and radium

The radium atom is a promising system for studying parity and time invariance violating weak interactions. However, available experimental spectroscopic data for radium is insufficient for designing an optimal experimental setup. We calculate the energy levels and transition amplitudes for radium states of significant interest. Forty states corresponding to all possible configurations consisting of the $7s$, $7p$ and $6d$ single-electron states as well as the states of the $7s8s$, $7s8p$ and $7s7d$ configurations have been calculated. The energies of ten of these states corresponding to the $6d^2$, $7s8s$, $7p^2$, and $6d7p$ configurations are not known from experiment. Calculations for barium are used to control the accuracy.Comment: 12 pages, 4 table

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Lipopolysaccharide-induced interferon response networks at birth are predictive of severe viral lower respiratory infections in the first year of life

Appropriate innate immune function is essential to limit pathogenesis and severity of severe lower respiratory infections (sLRI) during infancy, a leading cause of hospitalization and risk factor for subsequent asthma in this age group. Employing a systems biology approach to analysis of multi-omic profiles generated from a high-risk cohort (n = 50), we found that the intensity of activation of an LPS-induced interferon gene network at birth was predictive of sLRI risk in infancy (AUC = 0.724). Connectivity patterns within this network were stronger among susceptible individuals, and a systems biology approach identified IRF1 as a putative master regulator of this response. These findings were specific to the LPS-induced interferon response and were not observed following activation of viral nucleic acid sensing pathways. Comparison of responses at birth versus age 5 demonstrated that LPS-induced interferon responses but not responses triggered by viral nucleic acid sensing pathways may be subject to strong developmental regulation. These data suggest that the risk of sLRI in early life is in part already determined at birth, and additionally that the developmental status of LPS-induced interferon responses may be a key determinant of susceptibility. Our findings provide a rationale for the identification of at-risk infants for early intervention aimed at sLRI prevention and identifies targets which may be relevant for drug development

Assessment for learning : a model for the development of a child’s self competence in the early years of education

In recent years policy documents, curricula and other educational initiatives have promoted a pedagogy founded on the concept of independent learning. This is broadly defined as ‘having the belief in yourself to think through learning activities, problems or challenges, make decisions about your learning and act upon those decisions (Blandford and Knowles, 2009:336). The central role of Assessment for Learning (AfL) in this process is often overlooked in practice. By considering the findings from a small scale research study this article addresses the central role of the teacher /practitioner in developing effective AfL in the early years classroom (3-5 years)