Wavelength Dependent PSFs and their impact on Weak Lensing Measurements

We measure and model the wavelength dependence of the PSF in the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey. We find that PSF chromaticity is present in that redder stars appear smaller than bluer stars in the $g, r,$ and $i$-bands at the 1-2 per cent level and in the $z$ and $y$-bands at the 0.1-0.2 per cent level. From the color dependence of the PSF, we fit a model between the monochromatic PSF trace radius, $R$, and wavelength of the form $R(\lambda)\propto \lambda^{b}$. We find values of $b$ between -0.2 and -0.5, depending on the epoch and filter. This is consistent with the expectations of a turbulent atmosphere with an outer scale length of $\sim 10-100$ m, indicating that the atmosphere is dominating the chromaticity. We find evidence in the best seeing data that the optical system and detector also contribute some wavelength dependence. Meyers and Burchat (2015) showed that $b$ must be measured to an accuracy of $\sim 0.02$ not to dominate the systematic error budget of the Large Synoptic Survey Telescope (LSST) weak lensing (WL) survey. Using simple image simulations, we find that $b$ can be inferred with this accuracy in the $r$ and $i$-bands for all positions in the LSST field of view, assuming a stellar density of 1 star arcmin$^{-2}$ and that the optical PSF can be accurately modeled. Therefore, it is possible to correct for most, if not all, of the bias that the wavelength-dependent PSF will introduce into an LSST-like WL survey.Comment: 14 pages, 10 figures. Submitted to MNRAS. Comments welcom

Carpal Tunnel Syndrome: A Retrospective Analysis of Conservative Treatments

Objective: The purpose of this study was to identify which conservative occupational therapy (OT) treatment(s) were most effective in reducing pain in patients diagnosed with carpal tunnel syndrome (CTS). Design: A retrospective study of 222 de-identified treatment cases of patients seen from January 1st, 2004 to December 31st, 2013 were examined. Paired sample t-tests determined statistical significance between eight initial and final outcome measures. Binary logistic regressions determined statistical significance of clinically effective treatments that reduced pain at rest and pain with activity. Setting: The 222 cases were from 31 outpatient rehabilitation clinics offering occupational therapy services. Subjects: Participants were 18+ years of age and treated by an occupational therapist for conservative treatment of CTS. Methods: Twenty-two treatments were analyzed for statistical significance using the VAS at rest and VAS with activity. For cases with a clinical significance in the VAS at rest and VAS with activity, frequencies were used to identify predominant treatments utilized. Results: Massage was found to be statistically significant (p=0.027) in reducing pain at rest among those with a clinically significant reduction in pain at rest. Therapeutic exercises were found to be statistically significant (p=0.026) in reducing pain with activity among those with a clinically significant reduction in pain with activity. Therapeutic exercise, ultrasound, and manual therapy techniques were used in over 50% of treatments. Conclusion: This study found therapeutic exercise and massage to be statistically significant treatments in the conservative treatment of CTS. Further investigation is warranted to determine specific methods of treatment labeled as therapeutic exercises and massage

Correctors for some nonlinear monotone operators

In this paper we study homogenization of quasi-linear partial differential equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right) \right) =f_h on $\Omega$ with Dirichlet boundary conditions. Here the sequence $\left( \varepsilon _h\right)$ tends to $0$ as $h\rightarrow \infty$ and the map $a\left( x,y,\xi \right)$ is periodic in $y,$ monotone in $\xi$ and satisfies suitable continuity conditions. We prove that $u_h\rightarrow u$ weakly in $W_0^{1,p}\left( \Omega \right)$ as $h\rightarrow \infty ,$ where $u$ is the solution of a homogenized problem of the form -\mbox{div}\left( b\left( x,Du\right) \right) =f on $\Omega .$ We also derive an explicit expression for the homogenized operator $b$ and prove some corrector results, i.e. we find $\left( P_h\right)$ such that $Du_h-P_h\left( Du\right) \rightarrow 0$ in $L^p\left( \Omega, \mathbf{R}^n\right)$

Fragility and hysteretic creep in frictional granular jamming

The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bi-dispersed disks subject to quasi-static, uniaxial compression at zero granular temperature. Currently accepted results show the jamming transition occurs at a critical packing fraction $\phi_c$. In contrast, we observe the first compression cycle exhibits {\it fragility} - metastable configuration with simultaneous jammed and un-jammed clusters - over a small interval in packing fraction ($\phi_1 < \phi < \phi_2$). The fragile state separates the two conditions that define $\phi_c$ with an exponential rise in pressure starting at $\phi_1$ and an exponential fall in disk displacements ending at $\phi_2$. The results are explained through a percolation mechanism of stressed contacts where cluster growth exhibits strong spatial correlation with disk displacements. Measurements with several disk materials of varying elastic moduli $E$ and friction coefficients $\mu$, show friction directly controls the start of the fragile state, but indirectly controls the exponential slope. Additionally, we experimentally confirm recent predictions relating the dependence of $\phi_c$ on $\mu$. Under repetitive loading (compression), the system exhibits hysteresis in pressure, and the onset $\phi_c$ increases slowly with repetition number. This friction induced hysteretic creep is interpreted as the granular pack's evolution from a metastable to an eventual structurally stable configuration. It is shown to depend upon the quasi-static step size $\Delta \phi$ which provides the only perturbative mechanism in the experimental protocol, and the friction coefficient $\mu$ which acts to stabilize the pack.Comment: 12 pages, 10 figure

Some homogenization and corrector results for nonlinear monotone operators

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon _h},Du_h\right)\right)=f_h on $\Omega$ with Dirichlet boundary conditions. The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is periodic in $y$, monotone in $\xi$ and satisfies suitable continuity conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega )$, where $u$ is the solution of a homogenized problem \ -\limfunc{div}(b(x,Du))=f on $\Omega$. We also prove some corrector results, i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega ,R^n)$

Acoustic Energy and Momentum in a Moving Medium

By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum'' conservation laws are established in a systematic manner. In particular the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed co- and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and the mean flow mediated by the radiation stress tensor, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.Comment: 25 Pages, Late

An investigation of Prussian Blue analogues by Mossbauer spectroscopy and magnetic susceptibility

The Mossbauer spectra and magnetic susceptibilities have been obtained for a series of Prussian Blue analogues of general formula MjA[MB(CN)6]k[middle dot]mH2O where MA and MB are transition metal ions, j and k vary with the oxidation states of MA and MB and m typically has values from 8 to 14. The compounds were prepared from the hexacyano acids or with large quaternary ammonium counterions and are therefore not contaminated with alkali cations. In each analogue, A or B is iron and the second metal is Mn, Cu, Co, Cr or Ru. In each case it was possible to assign the site (A or B), oxidation state and spin state to each transition metal ion. This group of compounds are all class II mixed valence species from their colours, but do not show evidence of linkage isomerism or redox changes compared to the starting materials. The Mossbauer linewidths are consistent with the Ludi model of Prussian Blue.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24978/1/0000405.pd