Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion

We present an analytic method based on the Hadamard-WKB expansion to calculate the self-force for a particle with scalar charge that undergoes radial infall in a Schwarzschild spacetime after being held at rest until a time t = 0. Our result is valid in the case of short duration from the start. It is possible to use the Hadamard-WKB expansion in this case because the value of the integral of the retarded Green's function over the particle's entire past trajectory can be expressed in terms of two integrals over the time period that the particle has been falling. This analytic result is expected to be useful as a check for numerical prescriptions including those involving mode sum regularization and for any other analytical approximations to self-force calculations.Comment: 22 pages, 2 figures, Physical Review D version along with the corrections given in the erratu

Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. Darboux-Crum transformations are applied to connect the well-known shape invariant Hamiltonians of the radial oscillator and the Darboux-P\"oschl-Teller potential to the shape invariant potentials of Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional Laguerre polynomials by this method. The method is expanded to its full generality and many other ramifications, including the aspects of generalised Bochner problem and the bispectral property of the exceptional orthogonal polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure

Coarse-grained model of entropic allostery

Many signaling functions in molecular biology require proteins to bind to substrates such as DNA in response to environmental signals such as the simultaneous binding to a small molecule. Examples are repressor proteins which may transmit information via a conformational change in response to the ligand binding. An alternative entropic mechanism of "allostery" suggests that the inducer ligand changes the intramolecular vibrational entropy, not just the mean static structure. We present a quantitative, coarse-grained model of entropic allostery, which suggests design rules for internal cohesive potentials in proteins employing this effect. It also addresses the issue of how the signal information to bind or unbind is transmitted through the protein. The model may be applicable to a wide range of repressors and also to signaling in trans-membrane proteins

Astrophysical Fluid Dynamics via Direct Statistical Simulation

In this paper we introduce the concept of Direct Statistical Simulation (DSS) for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary importance to their statistical properties. We give examples of such problems including mixing and transport in planets, stars and disks. The method is described for a general set of evolution equations, before we consider the specific case of a spectral method optimised for problems on a spherical surface. The method is illustrated for the simplest non-trivial example of hydrodynamics and MHD on a rotating spherical surface. We then discuss possible extensions of the method both in terms of computational methods and the range of astrophysical problems that are of interest.Comment: 26 pages, 11 figures, added clarifying remarks and references, and corrected typos. This version is accepted for publication in The Astrophysical Journa

Instabilities in the Envelopes and Winds of Very Massive Stars

The high luminosity of Very Massive Stars (VMS) means that radiative forces play an important, dynamical role both in the structure and stability of their stellar envelope, and in driving strong stellar-wind mass loss. Focusing on the interplay of radiative flux and opacity, with emphasis on key distinctions between continuum vs. line opacity, this chapter reviews instabilities in the envelopes and winds of VMS. Specifically, we discuss how: 1) the iron opacity bump can induce an extensive inflation of the stellar envelope; 2) the density dependence of mean opacity leads to strange mode instabilities in the outer envelope; 3) desaturation of line-opacity by acceleration of near-surface layers initiates and sustains a line-driven stellar wind outflow; 4) an associated line-deshadowing instability leads to extensive small-scale structure in the outer regions of such line-driven winds; 5) a star with super-Eddington luminosity can develop extensive atmospheric structure from photon bubble instabilities, or from stagnation of flow that exceeds the "photon tiring" limit; 6) the associated porosity leads to a reduction in opacity that can regulate the extreme mass loss of such continuum-driven winds. Two overall themes are the potential links of such instabilities to Luminous Blue Variable (LBV) stars, and the potential role of radiation forces in establishing the upper mass limit of VMS.Comment: 44 pages, 13 figures. Chapter to appear in the book "Very Massive Stars in the Local Universe", Springer, J.S. Vink, e

Acute febrile illness and influenza disease burden in a rural cohort dedicated to malaria in Senegal, 2012-2013

Background African populations are considered to be particularly vulnerable to fever illnesses, including malaria, and acute respiratory disease, owing to limited resources and overcrowding. However, the overall burden of influenza in this context is poorly defined and incidence data for African countries are scarce. We therefore studied the fever syndrome incidence and more specifically influenza incidence in a cohort of inhabitants of Dielmo and Ndiop in Sokone district, Senegal. Methods Daily febrile-illness data were prospectively obtained from January 2012 to December 2013 from the cohort of the villages of Dielmo and Ndiop, initially dedicated to the study of malaria. Nasopharyngeal swabs were collected from, and malaria diagnosis tests (thick blood smears) carried out on, every febrile individual during clinical visits; reverse transcriptase- polymerase chain reaction was used to identify influenza viruses in the samples. Binomial negative regression analysis was used to study the relationship between the monthly incidence rate and various covariates. Results In Dielmo and Ndiop, the incidence ofmalaria has decreased, but fever syndromes remain frequent. Among the 1036 inhabitants included in the cohort, a total of 1,129 episodes of fever were reported. Influenza was present all year round with peaks in October-December 2012 and August 2013. The fever, ILI and influenza incidence density rates differed significantly between age groups. At both sites, the adjusted incidence relative risks for fever syndromes and ILI were significantly higher in the [6-24 months) than other age groups: 7.3 (95% CI: [5.7-9.3]) and 16.1 (95% CI: [11.1-23.3]) respectively. The adjusted incidence relative risk for influenza was significantly higher for the [0-6 months) than other age groups: 9.9 (95% CI: [2.9-33.6]). At both sites, incidence density rates were lowest among adults > = 50 years. Conclusions In this rural setting in Senegal, influenza was most frequent among the youngest children. Preventive strategies targeting this population should be implemented

Alfv\'en Reflection and Reverberation in the Solar Atmosphere

Magneto-atmospheres with Alfv\'en speed [a] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A common example involves uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfv\'en speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where a(x) is analytic and unbounded present no internal reflection of harmonic Alfv\'en waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as O(t-1) or O(t-1 ln t), depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfv\'en waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.Comment: Accepted by Solar Physic

Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects

In a companion paper [quant-ph/9904013] we have investigated several variations of Schwinger's proposed mechanism for sonoluminescence. We demonstrated that any realistic version of Schwinger's mechanism must depend on extremely rapid (femtosecond) changes in refractive index, and discussed ways in which this might be physically plausible. To keep that discussion tractable, the technical computations in that paper were limited to the case of a homogeneous dielectric medium. In this paper we investigate the additional complications introduced by finite-volume effects. The basic physical scenario remains the same, but we now deal with finite spherical bubbles, and so must decompose the electromagnetic field into Spherical Harmonics and Bessel functions. We demonstrate how to set up the formalism for calculating Bogolubov coefficients in the sudden approximation, and show that we qualitatively retain the results previously obtained using the homogeneous-dielectric (infinite volume) approximation.Comment: 23 pages, LaTeX 209, ReV-TeX 3.2, five figure

Direct Imaging of a Cold Jovian Exoplanet in Orbit around the Sun-like Star GJ 504

Several exoplanets have recently been imaged at wide separations of >10 AU from their parent stars. These span a limited range of ages (<50 Myr) and atmospheric properties, with temperatures of 800--1800 K and very red colors (J - H > 0.5 mag), implying thick cloud covers. Furthermore, substantial model uncertainties exist at these young ages due to the unknown initial conditions at formation, which can lead to an order of magnitude of uncertainty in the modeled planet mass. Here, we report the direct imaging discovery of a Jovian exoplanet around the Sun-like star GJ 504, detected as part of the SEEDS survey. The system is older than all other known directly-imaged planets; as a result, its estimated mass remains in the planetary regime independent of uncertainties related to choices of initial conditions in the exoplanet modeling. Using the most common exoplanet cooling model, and given the system age of 160 [+350, -60] Myr, GJ 504 b has an estimated mass of 4 [+4.5, -1.0] Jupiter masses, among the lowest of directly imaged planets. Its projected separation of 43.5 AU exceeds the typical outer boundary of ~30 AU predicted for the core accretion mechanism. GJ 504 b is also significantly cooler (510 [+30, -20] K) and has a bluer color (J-H = -0.23 mag) than previously imaged exoplanets, suggesting a largely cloud-free atmosphere accessible to spectroscopic characterization. Thus, it has the potential of providing novel insights into the origins of giant planets, as well as their atmospheric properties.Comment: 20 pages, 12 figures, Accepted for publication in ApJ. Minor updates from the version