Context. It has been shown for the weak-field Hanle effect that the Stokes parameters I, Q, and U can be represented by a set of six cylindrically symmetrical functions. The proof relies on azimuthal ...Fourier expansions of the radiation field and of the Hanle phase matrix. It holds for a plane-parallel atmosphere and scattering processes that can be described by a redistribution matrix where redistribution in frequency is decoupled from angle redistribution and polarization. Aims. We give a simpler and more general proof of the Stokes parameter decomposition using powerful new tools introduced for polarimetry, in particular the Landi DeglInnocenti spherical tensors {\mathcal T} Kappa _Q(i,\mbox{\boldmath$\displaystyle\Omega$ }). Methods. The elements of the Hanle phase matrix are written as a sum of terms that depend separately on the magnetic field vector and the directions \mbox{\boldmath$\displaystyle\Omega$ } and \mbox{\boldmath$\displaystyle\Omega$ } of the incoming and scattered beams. The dependence on \mbox{\boldmath$\displaystyle\Omega$ } and \mbox{\boldmath$\displaystyle\Omega$ } is expressed in terms of the spherical tensors {\mathcal T} Kappa _Q(i,\mbox{\boldmath$\displaystyle\Omega$ }) where i refers to the Stokes parameters ( i=0,\ldots,3). A multipolar expansion in terms of the {\mathcal T} Kappa _Q(i,\mbox{\boldmath$\displaystyle\Omega$ }) is then established for the source term in the transfer equation for the Stokes parameters. Results. We show that the Stokes parameters have a multipolar expansion that can be written as I_i(\nu,\mbox{\boldmath$\displaystyle\Omega$ }) = \sum_{\mathcal T} Kappa _Q(i,\mbox{\boldmath$\displaystyle\Omega$ }) I_Q Kappa (\nu,\theta) ( K =0,1,2,-K\le Q\le +K) where the I sub( )Q super( )Kare nine cylindrically symmetrical, irreducible tensors, \theta being the inclination of \mbox{\boldmath$\displaystyle\Omega$ } with respect to the vertical in the atmosphere. The proof is generalized to frequency-dependent phase matrices. It is applied both to partial frequency redistribution with angle-averaged scalar frequency redistribution functions and to complete frequency redistribution with the Hanle effect in the line core and Rayleigh scattering in the wings. Non-LTE transfer equations for the I sub( )Q super( )Kand integral equations for the associated source functions S sub( )Q super( )Kare established. Formal vectors and matrices constructed with I sub( )Q super( )K S sub( )Q super( )K and {\mathcal T}_Q Kappa are introduced in order to present the results in a compact matrix notation. In particular, a simple factorized form is proposed for the Hanle phase matrix.
Context. The linear polarization of a strong resonance lines observed near the solar limb is created by a multiple-scattering process. Partial frequency redistribution (PRD) effects must be accounted ...for to explain the polarization profiles. The redistribution matrix describing the scattering process is a sum of terms, each containing a PRD function multiplied by a Rayleigh type phase matrix. A standard approximation made in calculating the polarization is to average the PRD functions over all the scattering angles, because the numerical work needed to take the angle-dependence of the PRD functions into account is large and not always needed for reasonable evaluations of the polarization. Aims. This paper describes a Stokes parameters decomposition method, that is applicable in plane-parallel cylindrically symmetrical media, which aims at simplifying the numerical work needed to overcome the angle-average approximation. Methods. The decomposition method relies on an azimuthal Fourier expansion of the PRD functions associated to a decomposition of the phase matrices in terms of the Landi Degl’Innocenti irreducible spherical tensors for polarimetry ${\mathcal T}^K_Q(i,\bm \Omega)$𝒯QK(i,Ω) (i Stokes parameter index, Ω ray direction). The terms that depend on the azimuth of the scattering angle are retained in the phase matrices. Results. It is shown that the Stokes parameters I and Q, which have the same cylindrical symmetry as the medium, can be expressed in terms of four cylindrically symmetrical components ${\mathcal I}_Q^K$ℐQK (K = Q = 0, K = 2, Q = 0,1,2). The components with Q = 1,2 are created by the angular dependence of the PRD functions. They go to zero at disk center, ensuring that Stokes Q also goes to zero. Each component ${\mathcal I}_Q^K$ℐQK is a solution to a standard radiative transfer equation. The source term ${\mathcal S}_Q^K$𝒮QK are significantly simpler than the source terms corresponding to I and Q. They satisfy a set of integral equations that can be solved by an accelerated lambda iteration (ALI) method.
The study was performed to examine the hypothesis that functional outcomes following major lower-extremity trauma sustained in the military would be similar between patients treated with amputation ...and those who underwent limb salvage.
This is a retrospective cohort study of 324 service members deployed to Afghanistan or Iraq who sustained a lower-limb injury requiring either amputation or limb salvage involving revascularization, bone graft/bone transport, local/free flap coverage, repair of a major nerve injury, or a complete compartment injury/compartment syndrome. The Short Musculoskeletal Function Assessment (SMFA) questionnaire was used to measure overall function. Standard instruments were used to measure depression (the Center for Epidemiologic Studies Depression Scale), posttraumatic stress disorder (PTSD Checklist-military version), chronic pain (Chronic Pain Grade Scale), and engagement in sports and leisure activities (Paffenbarger Physical Activity Questionnaire). The outcomes of amputation and salvage were compared by using regression analysis with adjustment for age, time until the interview, military rank, upper-limb and bilateral injuries, social support, and intensity of combat experiences.
Overall response rates were modest (59.2%) and significantly different between those who underwent amputation (64.5%) and those treated with limb salvage (55.4%) (p = 0.02). In all SMFA domains except arm/hand function, the patients scored significantly worse than population norms. Also, 38.3% screened positive for depressive symptoms and 17.9%, for posttraumatic stress disorder (PTSD). One-third (34.0%) were not working, on active duty, or in school. After adjustment for covariates, participants with an amputation had better scores in all SMFA domains compared with those whose limbs had been salvaged (p < 0.01). They also had a lower likelihood of PTSD and a higher likelihood of being engaged in vigorous sports. There were no significant differences between the groups with regard to the percentage of patients with depressive symptoms, pain interfering with daily activities (pain interference), or work/school status.
Major lower-limb trauma sustained in the military results in significant disability. Service members who undergo amputation appear to have better functional outcomes than those who undergo limb salvage. Caution is needed in interpreting these results as there was a potential for selection bias.
We propose PET scanners using low atomic number media that undergo a persistent local change of state along the paths of the Compton recoil electrons. Measurement of the individual scattering ...locations and angles, deposited energies, and recoil electron directions allows using the kinematical constraints of the 2-body Compton scattering process to perform a statistical time-ordering of the scatterings, with a high probability of precisely identifying where the gamma first interacted in the detector. In these cases the Line-of-Response is measured with high resolution, determined by the underlying physics processes and not the detector segmentation. There are multiple such media that act through different mechanisms. As an example in which the change of state is quantum-mechanical through a change in molecular configuration, rather than thermodynamic, as in a bubble chamber, we present simulations of a two-state photoswitchable organic dye, a ‘Switchillator’, that is activated to a fluorescent-capable state by the ionization of the recoil electrons. The activated state is persistent, and can be optically excited multiple times to image individual activated molecules. Energy resolution is provided by counting the activated molecules. Location along the LOR is implemented by large-area time-of-flight MCP-PMT photodetectors with single photon time resolution in the tens of ps and sub-mm spatial resolution. Simulations indicate a large reduction of dose.
Chain entanglements are one of many parameters that can significantly influence fiber formation during polymer electrospinning. While the importance of chain entanglements has been acknowledged, ...there is no clear understanding of how many entanglements are required to affect/stabilize fiber formation. In this paper, polymer solution rheology arguments have been extrapolated to formulate a semi-empirical analysis to explain the transition from electrospraying to electrospinning in the good solvent, non-specific polymer–polymer interaction limit. Utilizing entanglement and weight average molecular weights (
M
e,
M
w), the requisite polymer concentration for fiber formation may be determined a priori, eliminating the laborious trial-and-error methodology typically employed to produce electrospun fibers. Incipient, incomplete fiber formation is correctly predicted for a variety of polymer/solvent systems at one entanglement per chain. Complete, stable fiber formation occurs at ≥2.5 entanglements per chain.
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