Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Disturbance and Recovery of Salt Marsh Arthropod Communities following BP Deepwater Horizon Oil Spill

Oil spills represent a major environmental threat to coastal wetlands, which provide a variety of critical ecosystem services to humanity. The U.S. Gulf of Mexico is a hub of oil and gas exploration activities that historically have impacted intertidal habitats such as salt marsh. Following the BP Deepwater Horizon oil spill, we sampled the terrestrial arthropod community and marine invertebrates found in stands of Spartina alterniflora, the most abundant plant in coastal salt marshes. Sampling occurred in 2010 as oil was washing ashore and a year later in 2011. In 2010, intertidal crabs and terrestrial arthropods (insects and spiders) were suppressed by oil exposure even in seemingly unaffected stands of plants; however, Littoraria snails were unaffected. One year later, crab and arthropods had largely recovered. Our work is the first attempt that we know of assessing vulnerability of the salt marsh arthropod community to oil exposure, and it suggests that arthropods are both quite vulnerable to oil exposure and quite resilient, able to recover from exposure within a year if host plants remain healthy

Planck intermediate results: LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters

The six parameters of the standard ΛCDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We have investigated these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium, the baryon density ω b , the matter density ω m , the angular size of the sound horizon the spectral index of the primordial power spectrum, n s , and A s e -2τ (where A s is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment 800, or splitting at a different multipole, yields similar results. We examined the 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is, which, at fixed A s e -2τ , affects the > 800 temperature power spectrum solely through the associated change in A s and the impact of that on the lensing potential power spectrum. We also ask, "what is it about the power spectrum at < 800 that leads to somewhat different best-fit parameters than come from the full range?" We find that if we discard the data at < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full range, the < 800 best-fit parameters shift significantly towards the < 2500 best-fit parameters. In contrast, including < 30, this previously noted "low-deficit" drives n s up and impacts parameters correlated with n s , such as ω m and H 0 . As expected, the < 30 data have a much greater impact on the < 800 best fit than on the < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatory-like set of high-residuals and the deficit in low-power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model

Diminished Medial Prefrontal Activity behind Autistic Social Judgments of Incongruent Information

Individuals with autism spectrum disorders (ASD) tend to make inadequate social judgments, particularly when the nonverbal and verbal emotional expressions of other people are incongruent. Although previous behavioral studies have suggested that ASD individuals have difficulty in using nonverbal cues when presented with incongruent verbal-nonverbal information, the neural mechanisms underlying this symptom of ASD remain unclear. In the present functional magnetic resonance imaging study, we compared brain activity in 15 non-medicated adult males with high-functioning ASD to that of 17 age-, parental-background-, socioeconomic-, and intelligence-quotient-matched typically-developed (TD) male participants. Brain activity was measured while each participant made friend or foe judgments of realistic movies in which professional actors spoke with conflicting nonverbal facial expressions and voice prosody. We found that the ASD group made significantly less judgments primarily based on the nonverbal information than the TD group, and they exhibited significantly less brain activity in the right inferior frontal gyrus, bilateral anterior insula, anterior cingulate cortex/ventral medial prefrontal cortex (ACC/vmPFC), and dorsal medial prefrontal cortex (dmPFC) than the TD group. Among these five regions, the ACC/vmPFC and dmPFC were most involved in nonverbal-information-biased judgments in the TD group. Furthermore, the degree of decrease of the brain activity in these two brain regions predicted the severity of autistic communication deficits. The findings indicate that diminished activity in the ACC/vmPFC and dmPFC underlies the impaired abilities of individuals with ASD to use nonverbal content when making judgments regarding other people based on incongruent social information

The effects of stimulus complexity on the preattentive processing of self-generated and nonself voices: an ERP study

The ability to differentiate one's own voice from the voice of somebody else plays a critical role in successful verbal self-monitoring processes and in communication. However, most of the existing studies have only focused on the sensory correlates of self-generated voice processing, whereas the effects of attentional demands and stimulus complexity on self-generated voice processing remain largely unknown. In this study, we investigated the effects of stimulus complexity on the preattentive processing of self and nonself voice stimuli. Event-related potentials (ERPs) were recorded from 17 healthy males who watched a silent movie while ignoring prerecorded self-generated (SGV) and nonself (NSV) voice stimuli, consisting of a vocalization (vocalization category condition: VCC) or of a disyllabic word (word category condition: WCC). All voice stimuli were presented as standard and deviant events in four distinct oddball sequences. The mismatch negativity (MMN) ERP component peaked earlier for NSV than for SGV stimuli. Moreover, when compared with SGV stimuli, the P3a amplitude was increased for NSV stimuli in the VCC only, whereas in the WCC no significant differences were found between the two voice types. These findings suggest differences in the time course of automatic detection of a change in voice identity. In addition, they suggest that stimulus complexity modulates the magnitude of the orienting response to SGV and NSV stimuli, extending previous findings on self-voice processing.This work was supported by Grant Numbers IF/00334/2012, PTDC/PSI-PCL/116626/2010, and PTDC/MHN-PCN/3606/2012, funded by the Fundacao para a Ciencia e a Tecnologia (FCT, Portugal) and the Fundo Europeu de Desenvolvimento Regional through the European programs Quadro de Referencia Estrategico Nacional and Programa Operacional Factores de Competitividade, awarded to A.P.P., and by FCT Doctoral Grant Number SFRH/BD/77681/2011, awarded to T.C.info:eu-repo/semantics/publishedVersio

Loss of cholinergic innervation differentially affects eNOS-mediated blood flow, drainage of Aβ and cerebral amyloid angiopathy in the cortex and hippocampus of adult mice

Vascular dysregulation and cholinergic basal forebrain degeneration are both early pathological events in the development of Alzheimer’s disease (AD). Acetylcholine contributes to localised arterial dilatation and increased cerebral blood flow (CBF) during neurovascular coupling via activation of endothelial nitric oxide synthase (eNOS). Decreased vascular reactivity is suggested to contribute to impaired clearance of β-amyloid (Aβ) along intramural periarterial drainage (IPAD) pathways of the brain, leading to the development of cerebral amyloid angiopathy (CAA). However, the possible relationship between loss of cholinergic innervation, impaired vasoreactivity and reduced clearance of Aβ from the brain has not been previously investigated. In the present study, intracerebroventricular administration of mu-saporin resulted in significant death of cholinergic neurons and fibres in the medial septum, cortex and hippocampus of C57BL/6 mice. Arterial spin labelling MRI revealed a loss of CBF response to stimulation of eNOS by the Rho-kinase inhibitor fasudil hydrochloride in the cortex of denervated mice. By contrast, the hippocampus remained responsive to drug treatment, in association with altered eNOS expression. Fasudil hydrochloride significantly increased IPAD in the hippocampus of both control and saporin-treated mice, while increased clearance from the cortex was only observed in control animals. Administration of mu-saporin in the TetOAPPSweInd mouse model of AD was associated with a significant and selective increase in Aβ40-positive CAA. These findings support the importance of the interrelationship between cholinergic innervation and vascular function in the aetiology and/or progression of CAA and suggest that combined eNOS/cholinergic therapies may improve the efficiency of Aβ removal from the brain and reduce its deposition as CAA

Planck 2015 results I. Overview of products and scientific results

The European Space Agency's Planck satellite, which is dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds