Note on the thermal history of decoupled massive particles

This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in Ref.\cite{Weinberg}, the strategies employed here are simpler, and the results obtained here are more general.Comment: JHEP style, 4 pages, to appear in CQ

The Picard group of the loop space of the Riemann sphere

The loop space of the Riemann sphere consisting of all C^k or Sobolev W^{k,p} maps from the circle S^1 to the sphere is an infinite dimensional complex manifold. We compute the Picard group of holomorphic line bundles on this loop space as an infinite dimensional complex Lie group with Lie algebra the first Dolbeault group. The group of Mobius transformations G and its loop group LG act on this loop space. We prove that an element of the Picard group is LG-fixed if it is G-fixed; thus completely answer the question by Millson and Zombro about G-equivariant projective embedding of the loop space of the Riemann sphere.Comment: International Journal of Mathematic

Oscillation-free method for semilinear diffusion equations under noisy initial conditions

Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.Comment: 19 pages, 9 figure

Analytic continuation of single-particle resonance energy and wave function in relativistic mean field theory

Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant state $\nu 1g_{9/2}$ in $^{60}$Ca as an example, we examine the analyticity of the eigenvalue and eigenfunction for the Dirac equation with respect to the coupling constant by means of a \pade approximant of the second kind. The RMF-ACCC approach is then applied to $^{122}$Zr and, for the first time, this approach is employed to investigate both the energies, widths and wave functions for $l\ne 0$ resonant states close to the continuum threshold. Predictions are also compared with corresponding results obtained from the scattering phase shift method.Comment: 19 pages, 9 figure

The Height Structure of the Solar Atmosphere from the EUV Perspective

We investigate the structure of the solar chromosphere and transition region using full Sun images obtained with the Extreme Ultraviolet Imaging Telescope (EIT) aboard the Solar and Heliospheric Observatory (SOHO) spacecraft. The limb seen in the EIT coronal images (taken in lines of Fe IX/X at 171 \AA, Fe XII at 195 \AA and Fe XV at 284 \AA) is an absorption limb predicted by models to occur at the top of the chromosphere where the density of neutral hydrogen becomes significant ($\sim10^{10}$ cm$^{-3}$). The transition-region limb seen in He II 304 \AA images is an emission limb. We find: (1) the limb is higher at the poles than at the equator both in the coronal images (by 1300 $\pm$ 650 km) and the 304 \AA images (by 3500 $\pm$ 120 0 km); and (2) the 304 \AA limb is significantly higher than the limb in the coronal images. The height difference is 3100 $\pm$ 1200 km at the equator, and 6600 $\pm$ 1200 km at the poles. We suggest that the elevation of the 304 \AA limb above the limb in the coronal images may be due to the upper surface of the chromosphere being bumpy, possibly because of the presence of spicules. The polar extension is consistent with a reduced heat input to the chromosphere in the polar coronal holes compared with the quiet--Sun atmosphere at the equator.Comment: 6 pages, 2 figure

Comparative Analysis Of Zebrafish And Planarian Model Systems For Developmental Neurotoxicity Screens Using An 87-Compound Library

There is a clear need to establish and validate new methodologies to more quickly and efficiently screen chemicals for potential toxic effects, particularly on development. The emergence of alternative animal systems for rapid toxicology screens presents valuable opportunities to evaluate how systems complement each other. In this article, we compare a chemical library of 87-compounds in two such systems, developing zebrafish and freshwater planarians, by screening for developmental neurotoxic effects. We show that the systems’ toxicological profiles are complementary to each other, with zebrafish yielding more detailed morphological endpoints and planarians more behavioral endpoints. Overall, zebrafish was more sensitive to this chemical library, yielding 86/87 hits, compared to 50/87 hits in planarians. The difference in sensitivity could not be attributed to molecular weight, Log Kow or the bioconcentration factor. Of the 87 chemicals, 28 had previously been evaluated in mammalian developmental neuro- (DNT), neuro- or developmental toxicity studies. Of the 28, 20 were hits in the planarian, and 27 were hits in zebrafish. Eighteen of the 28 had previously been identified as DNT hits in mammals and were highly associated with activity in zebrafish and planarian behavioral assays in this study. Only 1 chemical (out of 28) was a false negative in both zebrafish and planarian systems. Differences in endpoint coverage and system sensitivity illustrate the value of a dual systems approach to rapidly query a large chemical-bioactivity space and provide weight-of-evidence for prioritization of chemicals for further testing