Estimation of coefficients and boundary parameters in hyperbolic systems

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given

Criteria for Core-Collapse Supernova Explosions by the Neutrino Mechanism

We investigate the criteria for successful core-collapse supernova explosions by the neutrino mechanism. We find that a critical-luminosity/mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic one-dimensional (1D) and two-dimensional (2D) simulations. We present 95 such simulations that parametrically explore the dependence on neutrino luminosity, mass accretion rate, resolution, and dimensionality. While radial oscillations mediate the transition between 1D accretion (non-exploding) and exploding simulations, the non-radial standing accretion shock instability characterizes 2D simulations. We find that it is useful to compare the average dwell time of matter in the gain region with the corresponding heating timescale, but that tracking the residence time distribution function of tracer particles better describes the complex flows in multi-dimensional simulations. Integral quantities such as the net heating rate, heating efficiency, and mass in the gain region decrease with time in non-exploding models, but for 2D exploding models, increase before, during, and after explosion. At the onset of explosion in 2D, the heating efficiency is $\sim$2% to $\sim$5% and the mass in the gain region is $\sim$0.005 M_{\sun} to $\sim$0.01 M_{\sun}. Importantly, we find that the critical luminosity for explosions in 2D is $\sim$70% of the critical luminosity required in 1D. This result is not sensitive to resolution or whether the 2D computational domain is a quadrant or the full 180$^{\circ}$. We suggest that the relaxation of the explosion condition in going from 1D to 2D (and to, perhaps, 3D) is of a general character and is not limited by the parametric nature of this study.Comment: 32 pages in emulateapj, including 17 figures, accepted for publication in ApJ, included changes suggested by the refere

Computational methods for estimation of parameters in hyperbolic systems

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized

Finding binaries among Kepler pulsating stars from phase modulation of their pulsations

We present a method for finding binaries among pulsating stars that were observed by the Kepler Mission. We use entire 4 yr light curves to accurately measure the frequencies of the strongest pulsation modes, and then track the pulsation phases at those frequencies in 10-d segments. This produces a series of time-delay measurements in which binarity is apparent as a periodic modulation whose amplitude gives the projected light travel time across the orbit. Fourier analysis of this time-delay curve provides the parameters of the orbit, including the period, eccentricity, angle of ascending node, and time of periastron passage. Differentiating the time-delay curve yields the full radial-velocity curve directly from the Kepler photometry, without the need for spectroscopy.We showexamples with δ scuti stars having large numbers of pulsation modes, including one system in which both components of the binary are pulsating. The method is straightforward to automate, thus radial velocity curves can be derived for hundreds of non-eclipsing binary stars from Kepler photometry alone

Modelling the response of vascular tumours to chemotherapy: A multiscale approach

An existing multiscale model is extended to study the response of a vascularised tumour to treatment with chemotherapeutic drugs which target proliferating cells. The underlying hybrid cellular automaton model couples tissue-level processes (e.g. blood flow, vascular adaptation, oxygen and drug transport) with cellular and subcellular phenomena (e.g. competition for space, progress through the cell cycle, natural cell death and drug-induced cell kill and the expression of angiogenic factors). New simulations suggest that, in the absence of therapy, vascular adaptation induced by angiogenic factors can stimulate spatio-temporal oscillations in the tumour's composition.\ud \ud Numerical simulations are presented and show that, depending on the choice of model parameters, when a drug which kills proliferating cells is continuously infused through the vasculature, three cases may arise: the tumour is eliminated by the drug; the tumour continues to expand into the normal tissue; or, the tumour undergoes spatio-temporal oscillations, with regions of high vascular and tumour cell density alternating with regions of low vascular and tumour cell density. The implications of these results and possible directions for future research are also discussed

Dynamical trapping and relaxation of scalar gravitational fields

We present a framework for nonlinearly coupled scalar-tensor theory of gravity to address both inflation and core-collapse supernova problems. The unified approach is based on a novel dynamical trapping and relaxation of scalar gravity in highly energetic regimes. The new model provides a viable alternative mechanism of inflation free from various issues known to affect previous proposals. Furthermore, it could be related to observable violent astronomical events, specifically by releasing a significant amount of additional gravitational energy during core-collapse supernovae. A recent experiment at CERN relevant for testing this new model is briefly outlined.Comment: 4 pages; version to appear in PL

Reduced neural sensitivity to social stimuli in infants at risk for autism

In the hope of discovering early markers of autism, attention has recently turned to the study of infants at risk owing to being the younger siblings of children with autism. Because the condition is highly heritable, later-born siblings of diagnosed children are at substantially higher risk for developing autism or the broader autism phenotype than the general population. Currently, there are no strong predictors of autism in early infancy and diagnosis is not reliable until around 3 years of age. Because indicators of brain functioning may be sensitive predictors, and atypical social interactions are characteristic of the syndrome, we examined whether temporal lobe specialization for processing visual and auditory social stimuli during infancy differs in infants at risk. In a functional near-infrared spectroscopy study, infants aged 4–6 months at risk for autism showed less selective neural responses to social stimuli (auditory and visual) than low-risk controls. These group differences could not be attributed to overall levels of attention, developmental stage or chronological age. Our results provide the first demonstration of specific differences in localizable brain function within the first 6 months of life in a group of infants at risk for autism. Further, these differences closely resemble known patterns of neural atypicality in children and adults with autism. Future work will determine whether these differences in infant neural responses to social stimuli predict either later autism or the broader autism phenotype frequently seen in unaffected family members