Scattering of string-waves on black hole background

We consider the propagation of perturbations along an infinitely long stationary open string in the background of a Schwarzschild black hole. The equations of motion for the perturbations in the 2 transverse physical directions are solved to second order in a weak field expansion. We then set up a scattering formalism where an ingoing wave is partly transmitted and partly reflected due to the interaction with the gravitational field of the black hole. We finally calculate the reflection coefficient to third order in our weak field expansion.Comment: 18 pages + 2 figures, Latex, Nordita-93/52

Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions

The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $\tau$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(\dot{S}>0)$: $E\neq 0$ even at $S=0$, $E$ decreases for small $S$ and increases $\propto\hspace*{-1mm}S$ for large $S$. For an oscillating string $(0\leq S\leq S_{max})$, the average energy $$ over one oscillation period is expressed as a function of $S_{max}$ as a complete elliptic integral of the third kind.Comment: 32 pages, Latex file, figures available from the authors under request. LPTHE-PAR 93-5

Propagation of perturbations along strings

A covariant formalism for physical perturbations propagating along a string in an arbitrary curved spacetime is developed. In the case of a stationary string in a static background the propagation of the perturbations is described by a wave-equation with a potential consisting of 2 terms: The first term describing the time-dilation and the second is connected with the curvature of space. As applications of the developed approach the propagation of perturbations along a stationary string in Rindler, de Sitter, Schwarzschild and Reissner-Nordstrom spacetimes are investigated.Comment: 18 pages, LaTeX, Nordita-93/17

Evaluation of the CABLEv2.3.4 land surface model coupled to NU‐WRFv3.9.1.1 in simulating temperature and precipitation means and extremes over CORDEX AustralAsia within a WRF physics ensemble

The Community Atmosphere Biosphere Land Exchange (CABLE) model is a third‐generation land surface model (LSM). CABLE is commonly used as a stand‐alone LSM, coupled to the Australian Community Climate and Earth Systems Simulator global climate model and coupled to the Weather Research and Forecasting (WRF) model for regional applications. Here, we evaluate an updated version of CABLE within a WRF physics ensemble over the COordinated Regional Downscaling EXperiment (CORDEX) AustralAsia domain. The ensemble consists of different cumulus, radiation and planetary boundary layer (PBL) schemes. Simulations are carried out within the NASA Unified WRF modeling framework, NU‐WRF. Our analysis did not identify one configuration that consistently performed the best for all diagnostics and regions. Of the cumulus parameterizations the Grell‐Freitas cumulus scheme consistently overpredicted precipitation, while the new Tiedtke scheme was the best in simulating the timing of precipitation events. For the radiation schemes, the RRTMG radiation scheme had a general warm bias. For the PBL schemes, the YSU scheme had a warm bias, and the MYJ PBL scheme a cool bias. Results are strongly dependent on the region of interest, with the northern tropics and southwest Western Australia being more sensitive to the choice of physics options compared to southeastern Australia which showed less overall variation and overall better performance across the ensemble. Comparisons with simulations using the Unified Noah LSM showed that CABLE in NU‐WRF has a more realistic simulation of evapotranspiration when compared to GLEAM estimates

Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP

We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy_1 process. This result holds more generally for the observation points located along any space-like path in the space-time plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.Comment: 39 pages,6 figure

Mesoscopic superconductors in the London limit: equilibrium properties and metastability

We present a study of the behaviour of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be observable. We propose also a local description of both thermodynamic and metastable states based on elementary topological considerations; we find structural phase transitions of vortex patterns between these metastable states and we calculate the corresponding critical fields.Comment: 24 pages, 20 figure

Parton Densities in a Nucleon

In this paper we re-analyse the situation with the shadowing corrections (SC) in QCD for the proton deep inelastic structure functions. We reconsider the Glauber - Mueller approach for the SC in deep inelastic scattering (DIS) and suggest a new nonlinear evolution equation. We argue that this equation solves the problem of the SC in the wide kinematic region where \as \kappa = \as \frac{3 \pi \as}{2 Q^2R^2} x G(x,Q^2) \leq 1. Using the new equation we estimate the value of the SC which turn out to be essential in the gluon deep inelastic structure function but rather small in $F_2(x,Q^2)$. We claim that the SC in $xG(x,Q^2)$ is so large that the BFKL Pomeron is hidden under the SC and cannot be seen even in such "hard" processes that have been proposed to test it. We found that the gluon density is proportional to $\ln(1/x)$ in the region of very small $x$. This result means that the gluon density does not reach saturation in the region of applicability of the new evolution equation. It should be confronted with the solution of the GLR equation which leads to saturation.Comment: latex file 53 pages, 27 figures in eps file

Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime

We extensively study the exact solutions of the massless Dirac equation in 3D de Sitter spacetime that we published recently. Using the Newman-Penrose formalism, we find exact solutions of the equations of motion for the massless classical fields of spin s=1/2,1,2 and to the massive Dirac equation in 4D de Sitter metric. Employing these solutions, we analyze the absorption by the cosmological horizon and de Sitter quasinormal modes. We also comment on the results given by other authors.Comment: 31 page

Statistical properties of the Burgers equation with Brownian initial velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its $n$-point correlations. In the same limit, we derive the $n-$point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.Comment: 42 pages, published in J. Stat. Phy

Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection

We investigate the merit of deriving an estimate of the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{R}_0$$ \end{document} early in an outbreak of an (emerging) infection from estimates of the incidence and generation interval only. We compare such estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{R}_0$$ \end{document} with estimates incorporating additional model assumptions, and determine the circumstances under which the different estimates are consistent. We show that one has to be careful when using observed exponential growth rates to derive an estimate of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{R}_0$$ \end{document} , and we quantify the discrepancies that arise