Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

Diffusion processes with reaction generated by a nonlinear source are commonly encountered in practical applications related to ignition, pyrolysis and polymerization. In such processes, determining the intensity of reaction in time is of crucial importance for control and monitoring purposes. Therefore, this paper is devoted to such an identification problem of determining the time-dependent coefficient of a nonlinear heat source together with the unknown heat flux at an inaccessible boundary of a one-dimensional slab from temperature measurements at two sensor locations in the context of nonlinear transient heat conduction. Local existence and uniqueness results for the inverse coefficient problem are proved when the first three derivatives of the nonlinear source term are Lipschitz continuous functions. Furthermore, the conjugate gradient method (CGM) for separately reconstructing the reaction coefficient and the heat flux is developed. The ill-posedness is overcome by using the discrepancy principle to stop the iteration procedure of CGM when the input data is contaminated with noise. Numerical results show that the inverse solutions are accurate and stable

Hybrid Approach in Microscale Transport Phenomena: Application to Biodiesel Synthesis in Micro-reactors

A hybrid engineering approach to the study of transport phenomena, based on the synergy among computational, analytical, and experimental methodologies is reviewed. The focus of the chapter is on fundamental analysis and proof of concept developments in the use of nano- and micro-technologies for energy efficiency and heat and mass transfer enhancement applications. The hybrid approach described herein combines improved lumped-differential modeling, hybrid numericalanalytical solution methods, mixed symbolic-numerical computations, and advanced experimental techniques for micro-scale transport phenomena. An application dealing with micro-reactors for continuous synthesis of biodiesel is selected to demonstrate the instrumental role of the hybrid approach in achieving improved design and enhanced performance

Network-Guided Analysis of Genes with Altered Somatic Copy Number and Gene Expression Reveals Pathways Commonly Perturbed in Metastatic Melanoma

Cancer genomes frequently contain somatic copy number alterations (SCNA) that can significantly perturb the expression level of affected genes and thus disrupt pathways controlling normal growth. In melanoma, many studies have focussed on the copy number and gene expression levels of the BRAF, PTEN and MITF genes, but little has been done to identify new genes using these parameters at the genome-wide scale. Using karyotyping, SNP and CGH arrays, and RNA-seq, we have identified SCNA affecting gene expression (‘SCNA-genes’) in seven human metastatic melanoma cell lines. We showed that the combination of these techniques is useful to identify candidate genes potentially involved in tumorigenesis. Since few of these alterations were recurrent across our samples, we used a protein network-guided approach to determine whether any pathways were enriched in SCNA-genes in one or more samples. From this unbiased genome-wide analysis, we identified 28 significantly enriched pathway modules. Comparison with two large, independent melanoma SCNA datasets showed less than 10% overlap at the individual gene level, but network-guided analysis revealed 66% shared pathways, including all but three of the pathways identified in our data. Frequently altered pathways included WNT, cadherin signalling, angiogenesis and melanogenesis. Additionally, our results emphasize the potential of the EPHA3 and FRS2 gene products, involved in angiogenesis and migration, as possible therapeutic targets in melanoma. Our study demonstrates the utility of network-guided approaches, for both large and small datasets, to identify pathways recurrently perturbed in cancer

Extensive multiband study of the X-ray rich GRB 050408: A likely off-axis event with an intense energy injection

Aims. Understand the shape and implications of the multiband ligth curve of GRB 050408, an X-ray rich (XRR) burst. Methods. We present a multiband optical light curve, covering the time from the onset of the γ-ray event to several months after, when we only detect the host galaxy. Together with X-ray, millimetre and radio observations we compile what, to our knowledge, is the most complete multiband coverage of an XRR burst afterglow to date. Results. The optical and X-ray light curve is characterised by an early flattening and an intense bump peaking around 6 days after the burst onset. We explain the former by an off-axis viewed jet, in agreement with the predictions made for XRR by some models, and the latter with an energy injection equivalent in intensity to the initial shock. The analysis of the spectral flux distribution reveals an extinction compatible with a low chemical enrichment surrounding the burst. Together with the detection of an underlying starburst host galaxy we can strengthen the link between XRR and classical long-duration bursts. © ESO 2007

The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation

Haumea—one of the four known trans-Neptunian dwarf planets—is a very elongated and rapidly rotating body1, 2, 3. In contrast to other dwarf planets4, 5, 6, its size, shape, albedo and density are not well constrained. The Centaur Chariklo was the first body other than a giant planet known to have a ring system7, and the Centaur Chiron was later found to possess something similar to Chariklo’s rings8, 9. Here we report observations from multiple Earth-based observatories of Haumea passing in front of a distant star (a multi-chord stellar occultation). Secondary events observed around the main body of Haumea are consistent with the presence of a ring with an opacity of 0.5, width of 70 kilometres and radius of about 2,287 kilometres. The ring is coplanar with both Haumea’s equator and the orbit of its satellite Hi’iaka. The radius of the ring places it close to the 3:1 mean-motion resonance with Haumea’s spin period—that is, Haumea rotates three times on its axis in the time that a ring particle completes one revolution. The occultation by the main body provides an instantaneous elliptical projected shape with axes of about 1,704 kilometres and 1,138 kilometres. Combined with rotational light curves, the occultation constrains the three-dimensional orientation of Haumea and its triaxial shape, which is inconsistent with a homogeneous body in hydrostatic equilibrium. Haumea’s largest axis is at least 2,322 kilometres, larger than previously thought, implying an upper limit for its density of 1,885 kilograms per cubic metre and a geometric albedo of 0.51, both smaller than previous estimates1, 10, 11. In addition, this estimate of the density of Haumea is closer to that of Pluto than are previous estimates, in line with expectations. No global nitrogen- or methane-dominated atmosphere was detected.J.L.O. acknowledges funding from Spanish and Andalusian grants MINECO AYA-2014-56637-C2-1-P and J. A. 2012-FQM1776 as well as FEDER funds. Part of the research leading to these results received funding from the European Union’s Horizon 2020 Research and Innovation Programme, under grant agreement no. 687378. B.S. acknowledges support from the French grants ‘Beyond Neptune’ ANR-08-BLAN-0177 and ‘Beyond Neptune II’ ANR-11-IS56-0002. Part of the research leading to these results has received funding from the European Research Council under the European Community’s H2020 (2014-2020/ERC grant agreement no. 669416 ‘Lucky Star’). A.P. and R.S. have been supported by the grant LP2012-31 of the Hungarian Academy of Sciences. All of the Hungarian contributors acknowledge the partial support from K-125015 grant of the National Research, Development and Innovation Office (NKFIH). G.B.-R., F.B.-R., F.L.R., R.V.-M., J.I.B.C., M.A., A.R.G.-J. and B.E.M. acknowledge support from CAPES, CNPq and FAPERJ. J.C.G. acknowledges funding from AYA2015-63939-C2-2-P and from the Generalitat Valenciana PROMETEOII/2014/057. K.H. and P.P. were supported by the project RVO:67985815. The Astronomical Observatory of the Autonomous Region of the Aosta Valley acknowledges a Shoemaker NEO Grant 2013 from The Planetary Society. We acknowledge funds from a 2016 ‘Research and Education’ grant from Fondazione CRT. We also acknowledge the Slovakian project ITMS no. 26220120029