Numerical investigations on global error estimation for ordinary differential equations

AbstractFour techniques of global error estimation, which are Richardson extrapolation (RS), Zadunaisky's technique (ZD), Solving for the Correction (SC) and Integration of Principal Error Equation (IPEE) have been compared in different integration codes (DOPRI5, DVODE, DSTEP). Theoretical aspects concerning their implementations and their orders are first given. Second, a comparison of them based on a large number of tests is presented. In terms of cost and precision, SC is a method of choice for one-step methods. It is much more precise and less costly than RS, and leads to the same precision as ZD for half its cost. IPEE can provide the order of the error for a cheap cost in codes based on one-step methods. In multistep codes, only RS and IPEE have been implemented since they are the only ones whose theoretical justification has been extended to this case. There, RS still provides a more reliable estimation than IPEE. However, as these techniques are based on variations of the global error, irrespective of the numerical method used, they fail to provide any more usefull information once the numerical method has reached its limit of accuracy due to the finite arithmetic

Statistics of Core Lifetimes in Numerical Simulations of Turbulent, Magnetically Supercritical Molecular Clouds

We present measurements of the mean dense core lifetimes in numerical simulations of magnetically supercritical, turbulent, isothermal molecular clouds, in order to compare with observational determinations. "Prestellar" lifetimes (given as a function of the mean density within the cores, which in turn is determined by the density threshold n_thr used to define them) are consistent with observationally reported values, ranging from a few to several free-fall times. We also present estimates of the fraction of cores in the "prestellar", "stellar'', and "failed" (those cores that redisperse back into the environment) stages as a function of n_thr. The number ratios are measured indirectly in the simulations due to their resolution limitations. Our approach contains one free parameter, the lifetime of a protostellar object t_yso (Class 0 + Class I stages), which is outside the realm of the simulations. Assuming a value t_yso = 0.46 Myr, we obtain number ratios of starless to stellar cores ranging from 4-5 at n_thr = 1.5 x 10^4 cm^-3 to 1 at n_thr = 1.2 x 10^5 cm^-3, again in good agreement with observational determinations. We also find that the mass in the failed cores is comparable to that in stellar cores at n_thr = 1.5 x 10^4 cm^-3, but becomes negligible at n_thr = 1.2 x 10^5 cm^-3, in agreement with recent observational suggestions that at the latter densities the cores are in general gravitationally dominated. We conclude by noting that the timescale for core contraction and collapse is virtually the same in the subcritical, ambipolar diffusion-mediated model of star formation, in the model of star formation in turbulent supercritical clouds, and in a model intermediate between the previous two, for currently accepted values of the clouds' magnetic criticality.Comment: 25 pages, 8 figures, ApJ accepted. Fig.1 animation is at http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies/Galvan_etal07/Galvan_etal07.htm

Evolutionary processes and its environmental correlates in the cranial morphology of western chipmunks (Tamias).

The importance of the environment in shaping phenotypic evolution lies at the core of evolutionary biology. Chipmunks of the genus Tamias (subgenus Neotamias) are part of a very recent radiation, occupying a wide range of environments with marked niche partitioning among species. One open question is if and how those differences in environments affected phenotypic evolution in this lineage. Herein we examine the relative importance of genetic drift versus natural selection in the origin of cranial diversity exhibited by clade members. We also explore the degree to which variation in potential selective agents (environmental variables) are correlated with the patterns of morphological variation presented. We found that genetic drift cannot explain morphological diversification in the group, thus supporting the potential role of natural selection as the predominant evolutionary force during Neotamias cranial diversification, although the strength of selection varied greatly among species. This morphological diversification, in turn, was correlated with environmental conditions, suggesting a possible causal relationship. These results underscore that extant Neotamias represent a radiation in which aspects of the environment might have acted as the selective force driving species' divergence

Linear mixing model applied to coarse resolution satellite data

A linear mixing model typically applied to high resolution data such as Airborne Visible/Infrared Imaging Spectrometer, Thematic Mapper, and Multispectral Scanner System is applied to the NOAA Advanced Very High Resolution Radiometer coarse resolution satellite data. The reflective portion extracted from the middle IR channel 3 (3.55 - 3.93 microns) is used with channels 1 (0.58 - 0.68 microns) and 2 (0.725 - 1.1 microns) to run the Constrained Least Squares model to generate fraction images for an area in the west central region of Brazil. The derived fraction images are compared with an unsupervised classification and the fraction images derived from Landsat TM data acquired in the same day. In addition, the relationship betweeen these fraction images and the well known NDVI images are presented. The results show the great potential of the unmixing techniques for applying to coarse resolution data for global studies

Evidence of a discontinuous disk structure around the Herbig Ae star HD 139 614

A new class of pre-main sequence objects has been recently identified as pre-transitional disks. They present near-infrared excess coupled to a flux deficit at about 10 microns and a rising mid-infrared and far-infrared spectrum. These features suggest a disk structure with inner and outer dust components, separated by a dust-depleted region (or gap). We here report on the first interferometric observations of the disk around the Herbig Ae star HD 139614. Its infrared spectrum suggests a flared disk, and presents pre-transitional features,namely a substantial near-infrared excess accompanied by a dip around 6 microns and a rising mid-infrared part. In this framework, we performed a study of the spectral energy distribution (SED) and the mid-infrared VLTI/MIDI interferometric data to constrain thespatial structure of the inner dust disk region and assess its possibly multi-component structure. We based our work on a temperature-gradient disk model that includes dust opacity. While we could not reproduce the SED and interferometric visibilities with a one-component disk, a better agreement was obtained with a two-component disk model composed of an optically thin inner disk extending from 0.22 to 2.3 au, a gap, and an outer temperature-gradient disk starting at 5.6 au. Therefore, our modeling favors an extended and optically thin inner dust component and in principle rules out the possibility that the near-infrared excess originates only from a spatially confined region. Moreover, the outer disk is characterized by a very steep temperature profile and a temperature higher than 300 K at its inner edge. This suggests the existence of a warm component corresponding to a scenario where the inner edge of the outer disk is directly illuminated by the central star. This is an expected consequence of the presence of a gap, thus indicative of a pre-transitional structure.Comment: 14 pages, 6 figure

Robustness of proxy-based climate field reconstruction methods

We present results from continued investigations into the fidelity of covariance-based climate field reconstruction (CFR) approaches used in proxy-based climate reconstruction. Our experiments employ synthetic “pseudoproxy” data derived from simulations of forced climate changes over the past millennium. Using networks of these pseudoproxy data, we investigate the sensitivity of CFR performance to signal-to-noise ratios, the noise spectrum, the spatial sampling of pseudoproxy locations, the statistical representation of predictors used, and the diagnostic used to quantify reconstruction skill. Our results reinforce previous conclusions that CFR methods, correctly implemented and applied to suitable networks of proxy data, should yield reliable reconstructions of past climate histories within estimated uncertainties. Our results also demonstrate the deleterious impact of a linear detrending procedure performed recently in certain CFR studies and illustrate flaws in some previously proposed metrics of reconstruction skill

Dwarf Galaxy Dark Matter Density Profiles Inferred from Stellar and Gas Kinematics

We present new constraints on the density profiles of dark matter (DM) halos in seven nearby dwarf galaxies from measurements of their integrated stellar light and gas kinematics. The gas kinematics of low mass galaxies frequently suggest that they contain constant density DM cores, while N-body simulations instead predict a cuspy profile. We present a data set of high resolution integral field spectroscopy on seven galaxies and measure the stellar and gas kinematics simultaneously. Using Jeans modeling on our full sample, we examine whether gas kinematics in general produce shallower density profiles than are derived from the stars. Although 2/7 galaxies show some localized differences in their rotation curves between the two tracers, estimates of the central logarithmic slope of the DM density profile, gamma, are generally robust. The mean and standard deviation of the logarithmic slope for the population are gamma=0.67+/-0.10 when measured in the stars and gamma=0.58+/-0.24 when measured in the gas. We also find that the halos are not under concentrated at the radii of half their maximum velocities. Finally, we search for correlations of the DM density profile with stellar velocity anisotropy and other baryonic properties. Two popular mechanisms to explain cored DM halos are an exotic DM component or feedback models that strongly couple the energy of supernovae into repeatedly driving out gas and dynamically heating the DM halos. We investigate correlations that may eventually be used to test models. We do not find a secondary parameter that strongly correlates with the central DM density slope, but we do find some weak correlations. Determining the importance of these correlations will require further model developments and larger observational samples. (Abridged)Comment: 29 pages, 18 figures, 10 tables, accepted for publication in Ap