High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension

The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves in Kerr media, and describes a range of important phenomena in nonlinear optics and in other areas. In our previous work, we developed a fourth order method for its numerical solution that involved an iterative solver based on freezing the nonlinearity. The method enabled a direct simulation of nonlinear self-focusing in the nonparaxial regime, and a quantitative prediction of backscattering. However, our simulations showed that there is a threshold value for the magnitude of the nonlinearity, above which the iterations diverge. In this study, we numerically solve the one-dimensional NLH using a Newton-type nonlinear solver. Because the Kerr nonlinearity contains absolute values of the field, the NLH has to be recast as a system of two real equations in order to apply Newton's method. Our numerical simulations show that Newton's method converges rapidly and, in contradistinction with the iterations based on freezing the nonlinearity, enables computations for very high levels of nonlinearity. In addition, we introduce a novel compact finite-volume fourth order discretization for the NLH with material discontinuities.The one-dimensional results of the current paper create a foundation for the analysis of multi-dimensional problems in the future.Comment: 47 pages, 8 figure

Local Luminous Infrared Galaxies: Spatially resolved mid-infrared observations with Spitzer/IRS

Luminous Infrared (IR) Galaxies (LIRGs) are an important cosmological class of galaxies as they are the main contributors to the co-moving star formation rate density of the universe at z=1. In this paper we present a GTO Spitzer IRS program aimed to obtain spectral mapping of a sample of 14 local (d<76Mpc) LIRGs. The data cubes map, at least, the central 20arcsec x 20arcsec to 30arcsec x 30arcsec regions of the galaxies, and use all four IRS modules covering the full 5-38micron spectral range. The final goal of this project is to characterize fully the mid-IR properties of local LIRGs as a first step to understanding their more distant counterparts. In this paper we present the first results of this GTO program. The IRS spectral mapping data allow us to build spectral maps of the bright mid-IR emission lines (e.g., [NeII], [NeIII], [SIII], H_2), continuum, the 6.2 and 11.3micron PAH features, and the 9.7micron silicate feature, as well as to extract 1D spectra for regions of interest in each galaxy. The IRS data are used to obtain spatially resolved measurements of the extinction using the 9.7micron silicate feature, and to trace star forming regions using the neon lines and the PAH features. We also investigate a number of AGN indicators, including the presence of high excitation emission lines and a strong dust continuum emission at around 6micron. We finally use the integrated Spitzer/IRS spectra as templates of local LIRGs. We discuss several possible uses for these templates, including the calibration of the star formation rate of IR-bright galaxies at high redshift. We also predict the intensities of the brightest mid-IR emission lines for LIRGs as a function of redshift, and compare them with the expected sensitivities of future space IR missions.Comment: Accepted for publication in Advances in Space Researc

Response GC-Biased Mutation Pressure and ORF Lengthening

Xia et al. (2003) discuss whether the lengths of exons in eukaryotes and of genes in prokaryotes vary and whether they do so in relation to base composition (G+C content). In the paper which generated this debate, Oliver and Marı ´ n (1996) suggested that, given the compositional AT bias of standard stop codons (TAA, TAG, and TGA), a differential density of these termination signals is expected in random DNA sequences of different base composition, and therefore the expected length of reading frames (sequence segments of sense codons flanked by inphase stop codons) is a function of GC content. In other words, in GC-poor random sequences, the stop-codon density is expected to be higher than in GC-rich ones, and therefore the higher the GC content, the longer the expected reading frames. Empirical support for the model was sought by analyzing a sample of prokaryotic genes and a sample of eukaryotic exon data (Oliver and Marı ´ n 1996). With the model, the expected distribution of open reading frame (ORF) lengths in any random sequence with a given base composition can be computed; by comparing true ORF lengths to such random expectations, evolutionary forces involved in ORF lengthening can then be identified. Such comparisons can also be used for accurately predicting the coding content in anonymous sequences (Carpena et al. 2002). Correspondence to: Jose ´ L. Oliver