974 resultados para Volume of fluid (VOF)


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With the constant need to improve and make the production of asphalt mixtures more sustainable, new production techniques have been developed, the implementation of which implies the correct knowledge of their performance. One of the most promising asphalt production techniques is the use of foamed bitumen. However, it is essential to understand how this binder will behave when subject to the expansion process. The loss of volume of the foamed bitumen could be translated by a decay curve, which allows to determine the ideal temperature and water content added to the bitumen in order to assure adequate conditions to the mix the bitumen with the aggregates. On the present study, a conventional 160/220 pen grade bitumen was tested by using different temperatures and water contents, and it was concluded that the optimum temperature for the production of foamed bitumen (with the studied bitumen) is 150 ºC, which corresponds to a viscosity of 0.1 Pa.s. The water content mostly influence the half-life of the bitumen foam, resulting in quicker volume reductions for higher water contents.

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In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

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Observers can adjust the spectrum of illumination on paintings for optimal viewing experience. But can they adjust the colors of paintings for the best visual impression? In an experiment carried out on a calibrated color moni- tor images of four abstract paintings obtained from hyperspectral data were shown to observers that were unfamiliar with the paintings. The color volume of the images could be manipulated by rotating the volume around the axis through the average (a*, b*) point for each painting in CIELAB color space. The task of the observers was to adjust the angle of rotation to produce the best subjective impression from the paintings. It was found that the distribution of angles selected for data pooled across paintings and observers could be de- scribed by a Gaussian function centered at 10o, i.e. very close to the original colors of the paintings. This result suggest that painters are able to predict well what compositions of colors observers prefer.

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Among the various possible embodiements of Advanced Therapies and in particular of Tissue Engineering the use of temporary scaffolds to regenerate tissue defects is one of the key issues. The scaffolds should be specifically designed to create environments that promote tissue development and not merely to support the maintenance of communities of cells. To achieve that goal, highly functional scaffolds may combine specific morphologies and surface chemistry with the local release of bioactive agents. Many biomaterials have been proposed to produce scaffolds aiming the regeneration of a wealth of human tissues. We have a particular interest in developing systems based in nanofibrous biodegradable polymers1,2. Those demanding applications require a combination of mechanical properties, processability, cell-friendly surfaces and tunable biodegradability that need to be tailored for the specific application envisioned. Those biomaterials are usually processed by different routes into devices with wide range of morphologies such as biodegradable fibers and meshes, films or particles and adaptable to different biomedical applications. In our approach, we combine the temporary scaffolds populated with therapeutically relevant communities of cells to generate a hybrid implant. For that we have explored different sources of adult and also embryonic stem cells. We are exploring the use of adult MSCs3, namely obtained from the bone marrow for the development autologous-based therapies. We also develop strategies based in extra-embryonic tissues, such as amniotic fluid (AF) and the perivascular region of the umbilical cord4 (Whartonâ s Jelly, WJ). Those tissues offer many advantages over both embryonic and other adult stem cell sourcess. These tissues are frequently discarded at parturition and its extracorporeal nature facilitates tissue donation by the patients. The comparatively large volume of tissue and ease of physical manipulation facilitates the isolation of larger numbers of stem cells. The fetal stem cells appear to have more pronounced immunomodulatory properties than adult MSCs. This allogeneic escape mechanism may be of therapeutic value, because the transplantation of readily available allogeneic human MSCs would be preferable as opposed to the required expansion stage (involving both time and logistic effort) of autologous cells. Topics to be covered: This talk will review our latest developments of nanostructured-based biomaterials and scaffolds in combination with stem cells for bone and cartilage tissue engineering.

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Lactic acid bacteria (LAB) play a key role in the biopreservation of a wide range of fermented food products, such as yogurt, cheese, fermented milks, meat, fish, vegetables (sauerkraut, olives and pickles), certain beer brands, wines and silage, allowing their safe consumption, which gave to these bacteria a GRAS (Generally Recognised as Safe) status. Besides that, the use of LAB in food and feed is a promising strategy to reduce the exposure to dietary mycotoxins, improving their shelf life and reducing health risks, given the unique mycotoxin decontaminating characteristic of some LAB. Mycotoxins present carcinogenic, mutagenic, teratogenic, neurotoxic and immunosuppressive effects over animals and Humans, being the most important ochratoxin A (OTA), aflatoxins (AFB1), trichothecenes, zearalenone (ZEA), fumonisin (FUM) and patulin. In a previous work of our group it was observed OTA biodegradation by some strains of Pediococcus parvulus isolated from Douro wines. So, the aim of this study was to enlarge the screening of the biodetoxification over more mycotoxins besides OTA, including AFB1, and ZEA. This ability was checked in a collection of LAB isolated from vegetable (wine, olives, fruits and silage) and animal (milk and dairy products, sausages) sources. All LAB strains were characterized phenotypically (Gram, catalase) and genotypically. Molecular characterisation of all LAB strains was performed using genomic fingerprinting by MSP- PCR with (GTG)5 and csM13 primers. The identification of the isolates was confirmed by 16S rDNA sequencing. To study the ability of LAB strains to degrade OTA, AFB1 and ZEA, a MRS broth medium was supplemented with 2.0 g/mL of each mycotoxin. For each strain, 2 mL of MRS supplemented with the mycotoxins was inoculated in triplicate with 109 CFU/mL. The culture media and bacterial cells were extracted by the addition of an equal volume of acetonitrile/methanol/acetic acid (78:20:2 v/v/v) to the culture tubes. A 2 mL sample was then collected and filtered into a clean 2 mL vial using PP filters with 0.45 m pores. The samples were preserved at 4 °C until HPLC analysis. Among LAB tested, 10 strains isolated from milk were able to eliminate AFB1, belonging to Lactobacillus casei (7), Lb. paracasei (1), Lb. plantarum (1) and 1 to Leuconostoc mesenteroides. Two strains of Enterococcus faecium and one of Ec. faecalis from sausage eliminated ZEA. Concerning to strains of vegetal origin, one Lb. plantarum isolated from elderberry fruit, one Lb. buchnerii and one Lb. parafarraginis both isolated from silage eliminated ZEA. Other 2 strains of Lb. plantarum from silage were able to degrade both ZEA and OTA, and 1 Lb. buchnerii showed activity over AFB1. These enzymatic activities were also verified genotypically through specific gene PCR and posteriorly confirmed by sequencing analysis. In conclusion, due the ability of some strains of LAB isolated from different sources to eliminate OTA, AFB1 and ZEA one can recognize their potential biotechnological application to reduce the health hazards associated with these mycotoxins. They may be suitable as silage inoculants or as feed additives or even in food industry.

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The presence of mycotoxins in foodstuff is a matter of concern for food safety. Mycotoxins are toxic secondary metabolites produced by certain molds, being ochratoxin A (OTA) one of the most relevant. Wines can also be contaminated with these toxicants. Several authors have demonstrated the presence of mycotoxins in wine, especially ochratoxin A (OTA) [1]. Its chemical structure is a dihydro-isocoumarin connected at the 7-carboxy group to a molecule of L--phenylalanine via an amide bond. As these toxicants can never be completely removed from the food chain, many countries have defined levels in food in order to attend health concerns. OTA contamination of wines might be a risk to consumer health, thus requiring treatments to achieve acceptable standards for human consumption [2]. The maximum acceptable level of OTA in wines is 2.0 g/kg according to the Commission regulation No. 1881/2006 [3]. Therefore, the aim of this work was to reduce OTA to safer levels using different fining agents, as well as their impact on white wine physicochemical characteristics. To evaluate their efficiency, 11 commercial fining agents (mineral, synthetic, animal and vegetable proteins) were used to get new approaches on OTA removal from white wine. Trials (including a control without addition of a fining agent) were performed in white wine artificially supplemented with OTA (10 µg/L). OTA analysis were performed after wine fining. Wine was centrifuged at 4000 rpm for 10 min and 1 mL of the supernatant was collected and added of an equal volume of acetonitrile/methanol/acetic acid (78:20:2 v/v/v). Also, the solid fractions obtained after fining, were centrifuged (4000 rpm, 15 min), the resulting supernatant discarded, and the pellet extracted with 1 mL of the above solution and 1 mL of H2O. OTA analysis was performed by HPLC with fluorescence detection according to Abrunhosa and Venâncio [4]. The most effective fining agent in removing OTA (80%) from white wine was a commercial formulation that contains gelatine, bentonite and activated carbon. Removals between 10-30% were obtained with potassium caseinate, yeast cell walls and pea protein. With bentonites, carboxymethylcellulose, polyvinylpolypyrrolidone and chitosan no considerable OTA removal was verified. Following, the effectiveness of seven commercial activated carbons was also evaluated and compared with the commercial formulation that contains gelatine, bentonite and activated carbon. The different activated carbons were applied at the concentration recommended by the manufacturer in order to evaluate their efficiency in reducing OTA levels. Trial and OTA analysis were performed as explained previously. The results showed that in white wine all activated carbons except one reduced 100% of OTA. The commercial formulation that contains gelatine, bentonite and activated carbon (C8) reduced only 73% of OTA concentration. These results may provide useful information for winemakers, namely for the selection of the most appropriate oenological product for OTA removal, reducing wine toxicity and simultaneously enhancing food safety and wine quality.

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AbstractIntroduction:Cardiac allograft vasculopathy (CAV) is a major limitation for long-term survival of patients undergoing heart transplantation (HT). Some immunosuppressants can reduce the risk of CAV.Objectives:The primary objective was to evaluate the variation in the volumetric growth of the intimal layer measured by intracoronary ultrasound (IVUS) after 1 year in patients who received basiliximab compared with that in a control group.Methods:Thirteen patients treated at a single center between 2007 and 2009 were analyzed retrospectively. Evaluations were performed with IVUS, measuring the volume of a coronary segment within the first 30 days and 1 year after HT. Vasculopathy was characterized by the volume of the intima of the vessel.Results:Thirteen patients included (7 in the basiliximab group and 6 in the control group). On IVUS assessment, the control group was found to have greater vessel volume (120–185.43 mm3 vs. 127.77–131.32 mm3; p = 0.051). Intimal layer growth (i.e., CAV) was also higher in the control group (27.30–49.15 mm3 [∆80%] vs. 20.23–26.69 mm3[∆33%]; p = 0.015). Univariate regression analysis revealed that plaque volume and prior atherosclerosis of the donor were not related to intima growth (r = 0.15, p = 0.96), whereas positive remodeling was directly proportional to the volumetric growth of the intima (r = 0.85, p < 0.001).Conclusion:Routine induction therapy with basiliximab was associated with reduced growth of the intima of the vessel during the first year after HT.

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The article provides a method for long-term forecast of frame alignment losses based on the bit-error rate monitoring for structure-agnostic circuit emulation service over Ethernet in a mobile backhaul network. The developed method with corresponding algorithm allows to detect instants of probable frame alignment losses in a long term perspective in order to give engineering personnel extra time to take some measures aimed at losses prevention. Moreover, long-term forecast of frame alignment losses allows to make a decision about the volume of TDM data encapsulated into a circuit emulation frame in order to increase utilization of the emulated circuit. The developed long-term forecast method formalized with the corresponding algorithm is recognized as cognitive and can act as a part of network predictive monitoring system.

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We analyzed stomach contents of 58 specimens of Teius oculatus (D'Orbigny & Bibron, 1837) (20 adult males, 17 adult females and 21 juveniles) captured in Dom Feliciano, RS, Brazil, to evaluate diet composition and sexual and ontogenetic variations in prey consumption. Diet was composed of 15 prey categories, all arthropods. Orthoptera was the most frequent prey type. Quantitatively, termites were the most important prey item (59.5%). There were no significant differences between the diets of adult males and females. Ontogenetic differences were found, mainly concerning volume of prey consumed. Adult lizards ingested significantly larger prey than juveniles (U = 170.00; p < 0.001). Juveniles, although having a comparatively less diverse diet (10 prey types) consumed a larger number of items (45.7% of total). Diet similarity was higher between juveniles and adult males (Ojk = 0.97) and prey diversity was higher in the diet of adult females (H' = 2.65). Based on importance value index the most important item in the diet of T. oculatus was Orthoptera. We conclude that T. oculatus in Dom Feliciano has a relatively generalized diet and it is an opportunist lizard, feeding on arthropods, mainly insects.

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Shipworms are important decomposers of wood, especially in mangrove forests where productivity is high. However, little emphasis has been given to the activity of shipworms in relation to the export of nutrients from mangroves to adjacent coastal areas. As a first step to obtaining such information, the frequency of colonized mangrove driftwood as well as shipworm density and length were studied by collecting washed up logs during a year at Ajuruteua beach, state of Pará, northern Brazil. A single species, Neoteredo reynei (Bartsch, 1920), was found colonizing driftwood. Although large colonized logs were most common on the beach, shipworm density was higher in small logs, especially during the dry season. In general, however, density was higher during the wet season (January to April) and lowest in July. Overall shipworm mean length was 9.66cm. In large logs, mean length increased between the wet and dry seasons. However, there was no difference in length among log size categories. Mean shipworm length was similar throughout most of the year but tended to be greater in July. Although salinity varied between 10.9 and 40 during the year, no relationship was found between salinity and density or length. The results suggest that shipworm activity in driftwood logs is relatively constant throughout the year. Increased air humidity and rainfall may promote survival during the wet season. Large logs may take longer to colonize and thus have lower densities than small ones which are scarce probably because they are destroyed rapidly by shipworm activity. However, data on the disintegration of logs would be necessary to test this hypothesis. Larger size of shipworms in the dry season may be related to growth after an earlier recruitment period. Shipworms in large logs during the dry season may be better protected from dessication and high temperatures by the insulating properties of the larger volume of wood.

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The diet of the benthic-feeding fish Iheringichthys labrosus (Lütken, 1874) was analyzed. Samples were taken bimonthly from December 1999 to January 2002, in three sites of the Ibicuí River, a tributary of Uruguay River basin (Rio Grande do Sul, Brazil). In each sampling point the specimens were collected in lentic and lotic environments. Gillnets and trammel nets were examined every 6 hours (6h, 12h, 18h and 24h). Diet description was based on the frequency of occurrence and the volume of each food item to obtain the Alimentary Index (IAi). The average stomach fullness was adopted to detect variations in the feeding activity according to the season, the circadian rhythm and the environment. Chironomids were the most important food item, followed by mollusks, and feeding activity was highest in summer, during daylight (6h and 12h), and in the lotic environment of the second sampling point.

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Accurate size measurements are fundamental in characterizing the population structure and secondary production of a species. The purpose of this study was to determine the best morphometric parameter to estimate the size of individuals of Capitella capitata (Fabricius, 1780). The morphometric analysis was applied to individuals collected in the intertidal zones of two beaches on the northern coast of the state of São Paulo, Brazil: São Francisco and Araçá. The following measurements were taken: the width and length (height) of the 4th, 5th and 7th setigers, and the length of the thoracic region (first nine setigers). The area and volume of these setigers were calculated and a linear regression analysis was applied to the data. The data were log-transformed to fit the allometric equation y = ax b into a straight line (log y = log a + b * log x). The measurements which best correlated with the thoracic length in individuals from both beaches were the length of setiger 5 (r² = 0.722; p<0.05 in São Francisco and r² = 0.795; p<0.05 in Araçá) and the area of setiger 7 (r² = 0.705; p<0.05 in São Francisco and r² = 0.634; p<0.05 in Araçá). According to these analyses, the length of setiger 5 and/or the area of setiger 7 are the best parameters to evaluate the growth of individuals of C. capitata.

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The Ajjanahalli gold mine is spatially associated with a Late Archean craton-scale shear zone in the eastern Chitradurga greenstone belt of the Dharwar craton, India. Gold mineralization is hosted by an similar to100-m-wide antiform in a banded iron formation. Original magnetite and siderite are replaced by a peak metamorphic alteration assemblage of chlorite, stilpnomelane, minnesotaite, sericite, ankerite, arsenopyrite, pyrite, pyrrhotite, and gold at ca. 300degrees to 350degreesC. Elements enriched in the banded iron formation include Ca, Mg, C, S, An, As, Bi. Cu, Sb, Zn, Pb, Se, Ag, and Te, whereas in the wall rocks As, Cu, Zn, Bi, Ag, and An are only slightly enriched. Strontium correlates with CaO, MgO, CO2, and As, which indicates cogenetic formation of arsenopyrite and Mg-Ca carbonates. The greater extent of alteration in the Fe-rich banded iron formation layers than in the wall rock reflects the greater reactivity of the banded iron formation layers. The ore fluids, as interpreted from their isotopic composition (delta(18)O = 6.5-8.5parts per thousand; initial Sr-87/Sr-86 = 0.7068-0.7078), formed by metamorphic devolatilization of deeper levels of the Chitradurga greenstone belt. Arsenopyrite, chalcopyrite, and pyrrhotite have delta(34)S values within a narrow range between 2.1 and 2.7 per mil, consistent with a sulfur source in Chitradurga greenstone belt lithologies. Based on spatial and temporal relationships between mineralization, local structure development, and sinistral strike-slip deformation in the shear zone at the eastern contact of the Chitradurga greenstone belt, we suggest that the Ajjanahalli gold mineralization formed by fluid infiltration into a low strain area within the first-order structure. The ore fluids were transported along this shear zone into relatively shallow crustal levels during lateral terrane accretion and a change from thrust to transcurrent tectonics. Based on this model of fluid flow, exploration should focus on similar low strain areas or potentially connected higher order splays of the first-order shear zone.

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Summary : The hypothalamus represents less than 1 % of the total volume of the brain tissue, yet it plays a crucial role in endocrine regulations. Puberty is defined as a process leading to physical, sexual and psychosocial maturation. The hypothalamus is central to this process, via the activation of GnRH neurons. Pulsatile GnRH secretion, minimal during childhood, increases with the onset of puberty. The primary function of GnRH is to regulate the growth, development and function of testes in boys and ovaries in girls, by stimulating the pituitary gland secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH). Several factors contribute to the timing of puberty, including sex and ethnicity, genetics, dietary intake and energy expenditure. Kisspeptins constitute a family of small peptides arising from the proteolytic cleavage of metastin, a peptide with 54 amino acids initially purified from human placenta. These kisspeptins were the subject of much attention following their discovery because of their antimetastatic properties, but it was more recently that their determining role in the reproductive function was demonstrated. It was shown that kisspeptins are ligands of a receptor, GPR54, whose natural inactivating mutation in humans, or knockout in the mouse, lead to infertility. GnRH neurons play a pivotal role in the central regulation of fertility. Kisspeptin greatly increases GnRH release and GnRH neuron firing activity, but the neurobiological mechanisms for these actions are unknown. Gprotein-coupled receptor 54, the receptor for kisspeptin, is expressed by GnRH neurons as well as other hypothalamic neurons, suggesting that both direct and indirect effects are possible. In the first part of my thesis, we investigated a possible connection between the acceleration of sexual development induced by leptin and hypothalamic metastin neurons. However, the data generated by our preliminary experiments confirmed that the commercially available antibodies are non-specific. This finding constituted a major drawback for our studies, which relied heavily upon the neuroanatomical study of the hypothalamic metastinergic pathways to elucidate their sensitivity to exogenous leptin. Therefore, we decided to postpone any further in vivo experiment until a better antibody becomes available, and focused on in vitro studies to better understand the mechanisms of action of kisspeptins in the modulation of the activity of GnRH neurons. We used two GnRH-expressing neuronal cell lines to investigate the cellular and molecular mechanisms of action of metastin in GnRH neurons. We demonstrated that kisspeptin induces an early activation of the MAP kinase intracellular signaling pathway in both cell lines, whereas the SAP/JNK or the Akt pathways were unaffected. Moreover, we found an increase in GnRH mRNA levels after 6h of metastin stimulation. Thus, we can conclude that kisspeptin regulates GnRH neurons both at the secretion and the gene expression levels. The MAPK pathway is the major pathway activated by metastin in GnRH expressing neurons. Taken together, these data provide the first mechanism of action of kisspeptin on GnRH neurons. Résumé : L'hypothalamus est une zone située au centre du cerveau, dont il représente moins de 1 du volume total. La puberté est la période de transition entre l'enfance et l'age adulte, qui s'accompagne de transformations somatiques, psychologiques, métaboliques et hormonales conduisant à la possibilité de procréer. La fonction principale de la GnRH est la régulation de la croissance, du développement et de la fonction des testicules chez les hommes, et des ovaires chez les femmes en stimulant la sécrétion de l'hormone lutéinisante (LH) et de l'hormone folliculostimulante (FSH) par la glande hypophysaire. Plusieurs facteurs contribuent au déclanchement de la puberté, y compris le sexe et l'appartenance ethnique, la génétique, l'apport alimentaire et la dépense énergétique. Les Kisspeptines constituent une famille de peptides résultant de la dissociation proteolytique de la métastine, un peptide de 54 acides aminés initialement purifié à partir de placenta humain. Ces kisspeptines ont fait l'objet de beaucoup d'attention à la suite de leur découverte en raison de leurs propriétés anti-metastatiques, et c'est plus récemment que leur rôle déterminant dans la fonction reproductive a été démontré. Les kisspeptines sont des ligands du récepteur GPR54, dont la mutation inactivatrice chez l'homme, ou le knockout chez la souris, conduisent à l'infertilité par hypogonadisme hypogonadotrope. Les neurones à GnRH jouent un rôle central dans le règlement des fonctions reproductrices et la kisspeptine stimule l'activité des neurones à GnRH et la libération de GnRH par ces neurones. Toutefois, les mécanismes neurobiologiques de ces actions ne sont pas connus. Dans la première partie de ma thèse, nous avons étudié le lien potentiel entre l'accélération du développement sexuel induite par la leptine et les neurones hypothalamiques à metastine. Les données générées dans cette première série d'expériences ont malheureusement confirmé que les anticorps anti-metastine disponibles dans le commerce sont aspécifiques. Ceci a constitué un inconvénient majeur pour nos études, qui devaient fortement s'appuyer sur l' étude neuroanatomique des neurones hypothalamiques à metastine pour évaluer leur sensibilité à la leptine exogène. Nous avons donc décidé de focaliser nos travaux sur une étude in vitro des mécanismes d'action de la kisspeptine pour moduler l'activité des neurones à GnRH. Nous avons utilisé deux lignées de cellules neuronales exprimant la GnRH pour étudier les mécanismes d'action cellulaires et moléculaires de la metastine dans des neurones. Nous avons ainsi pu démontrer que la kisspeptine induit une activation précoce de la voie f de signalisation de la MAP kinase dans les deux lignées cellulaires, alors que nous n'avons observé aucune activation de la voie de signalisation de la P13 Kinase et de la SAP/JNK. Nous avons en outre démontré une augmentation de l'expression de la GnRH par la stimulation avec la Kisspeptine. L'ensemble de ces données contribue à élucider le mécanisme d'action avec lequel la kisspeptine agit dans les neurones à GnRH, en démontrant un effet sur l'expression génique de la GnRH. Nous pouvons également conclure que la voie de la MAPK est la voie principale activée par la metastine dans les neurones exprimant la GnRH.

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Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.