Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

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.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Indirect hydrogen analysis by gas chromatography coupled to mass spectrometry (GC-MS).

Gas chromatography (GC) is an analytical tool very useful to investigate the composition of gaseous mixtures. The different gases are separated by specific columns but, if hydrogen (H2 ) is present in the sample, its detection can be performed by a thermal conductivity detector or a helium ionization detector. Indeed, coupled to GC, no other detector can perform this detection except the expensive atomic emission detector. Based on the detection and analysis of H2 isotopes by low-pressure chemical ionization mass spectrometry (MS), a new method for H2 detection by GC coupled to MS with an electron ionization ion source and a quadrupole analyser is presented. The presence of H2 in a gaseous mixture could easily be put in evidence by the monitoring of the molecular ion of the protonated carrier gas. Copyright © 2013 John Wiley & Sons, Ltd.

Validation of an analytical method for nitrous oxide (N2O) laughing gas by headspace gas chromatography coupled to mass spectrometry (HS-GC-MS): Forensic application to a lethal intoxication.

Drug abuse is a widespread problem affecting both teenagers and adults. Nitrous oxide is becoming increasingly popular as an inhalation drug, causing harmful neurological and hematological effects. Some gas chromatography-mass spectrometry (GC-MS) methods for nitrous oxide measurement have been previously described. The main drawbacks of these methods include a lack of sensitivity for forensic applications; including an inability to quantitatively determine the concentration of gas present. The following study provides a validated method using HS-GC-MS which incorporates hydrogen sulfide as a suitable internal standard allowing the quantification of nitrous oxide. Upon analysis, sample and internal standard have similar retention times and are eluted quickly from the molecular sieve 5Å PLOT capillary column and the Porabond Q column therefore providing rapid data collection whilst preserving well defined peaks. After validation, the method has been applied to a real case of N2O intoxication indicating concentrations in a mono-intoxication.

Dynamics of HIV latency and reactivation in a primary CD4+ T cell model.

HIV latency is a major obstacle to curing infection. Current strategies to eradicate HIV aim at increasing transcription of the latent provirus. In the present study we observed that latently infected CD4+ T cells from HIV-infected individuals failed to produce viral particles upon ex vivo exposure to SAHA (vorinostat), despite effective inhibition of histone deacetylases. To identify steps that were not susceptible to the action of SAHA or other latency reverting agents, we used a primary CD4+ T cell model, joint host and viral RNA sequencing, and a viral-encoded reporter. This model served to investigate the characteristics of latently infected cells, the dynamics of HIV latency, and the process of reactivation induced by various stimuli. During latency, we observed persistence of viral transcripts but only limited viral translation. Similarly, the reactivating agents SAHA and disulfiram successfully increased viral transcription, but failed to effectively enhance viral translation, mirroring the ex vivo data. This study highlights the importance of post-transcriptional blocks as one mechanism leading to HIV latency that needs to be relieved in order to purge the viral reservoir.

Population dynamics of aquatic snails in Pampulha reservoir

An attempt was made to determine more accurately the density of molluskan populations in the Pampulha reservoir, using the quadrate method, intending to detect the fluctuation of the populations density, the habitat conditions and the possible competitive interactions among Biomphalaria tenagophila, Melanoides tuberculata, Pomacea haustrum and Biomphalaria glabrata, through the analysis of populational parameters. Among the most significative facts observed in the reservoir it has to be mentioned: the almost disappearance of B. glabrata; the invasion, colonization, fixation and fast growing of M. tuberculata population until reaching about 11,000 individuals/[square metre]; the density fluctuations of B. tenagophila, P. haustrum and M. tuberculata alives and deads; differences on the habitat preference of these three molluskan species at the edge (at the limit earth-water, at 0.70m and 1.40m from the shore line); monthly mortality rates and reproduction seasons of the species.

Estudi de la reductibilitat de catalitzadors basats en cobalt i el seu comportament en la reacció de desplaçament de gas d'aigua de CO

Projecte de recerca elaborat a partir d’una estada a la universitat d'Udine, Itàlia, entre setembre i desembre del 2006.S'han caracteritzat mitjançant la reducció a temperatura programada i tests catalítics catalitzadors en pols basats en cobalt i supostats en òxid de zinc i monòlits ceràmics funcionaliltzats també amb cobalt i òxid de zinc. L'addició de promotors (manganès, crom i ferro ) als catalitzadors en pols, preparats per impregnació i precipitació, no afecta significativament ni la temperatura a la qual té lloc la reducció ni al percentatge global de reducció. En els cicles de reducció-oxidació sí que s'observen diferències entre el primer perfil de reducció i els següents, especialment en el cas de la mostra que té ferro com a promotor, on les diferències s'accentuen en cicles successius (fins al quart). S'ha evaluat l'activitat d'aquests catalitzadors en la reacció de desplaçament de gas d'aigua, obtenint uns resultats satisfactoris. Finalment s'han realitzat reduccions a temperatura programada i tests catalítics en la reacció de desplaçament de gas d'aigua amb monòlits funcionalitzats amb cobalt i òxid de zinc (en cap d'ells s'ha introduït promotors). El nivell de conversió assolit és menor que en el cas de catalitzadors en pols, fet que s'associa a la geometria d'aquests sistemes catalítics, però la relació CH4/CO2 és més favorable que en els catalitzadors en pols, el que els converteix en sistemes molt selectius.

Membrane potential dynamics of neocortical projection neurons driving target-specific signals.

Primary sensory cortex discriminates incoming sensory information and generates multiple processing streams toward other cortical areas. However, the underlying cellular mechanisms remain unknown. Here, by making whole-cell recordings in primary somatosensory barrel cortex (S1) of behaving mice, we show that S1 neurons projecting to primary motor cortex (M1) and those projecting to secondary somatosensory cortex (S2) have distinct intrinsic membrane properties and exhibit markedly different membrane potential dynamics during behavior. Passive tactile stimulation evoked faster and larger postsynaptic potentials (PSPs) in M1-projecting neurons, rapidly driving phasic action potential firing, well-suited for stimulus detection. Repetitive active touch evoked strongly depressing PSPs and only transient firing in M1-projecting neurons. In contrast, PSP summation allowed S2-projecting neurons to robustly signal sensory information accumulated during repetitive touch, useful for encoding object features. Thus, target-specific transformation of sensory-evoked synaptic potentials by S1 projection neurons generates functionally distinct output signals for sensorimotor coordination and sensory perception.

Optimized venous return with a self-expanding cannula: from computational fluid dynamics to clinical application.

The Smart canula concept allows for collapsed cannula insertion, and self-expansion within a vein of the body. (A) Computational fluid dynamics, and (B) bovine experiments (76+/-3.8 kg) were performed for comparative analyses, prior to (C) the first clinical application. For an 18F access, a given flow of 4 l/min (A) resulted in a pressure drop of 49 mmHg for smart cannula versus 140 mmHg for control. The corresponding Reynolds numbers are 680 versus 1170, respectively. (B) For an access of 28F, the maximal flow for smart cannula was 5.8+/-0.5 l/min versus 4.0+/-0.1 l/min for standard (P<0.0001), for 24F 5.5+/-0.6 l/min versus 3.2+/-0.4 l/min (P<0.0001), and for 20F 4.1+/-0.3 l/min versus 1.6+/-0.3 l/min (P<0.0001). The flow obtained with the smart cannula was 270+/-45% (20F), 172+/-26% (24F), and 134+/-13% (28F) of standard (one-way ANOVA, P=0.014). (C) First clinical application (1.42 m2) with a smart cannula showed 3.55 l/min (100% predicted) without additional fluids. All three assessment steps confirm the superior performance of the smart cannula design.

Rapid high-performance liquid chromatographic determination with fluorescence detection of furosemide in human body fluids and its confirmation by gas chromatography-mass spectrometry.

Furosemide (FD: Lasix) is a loop diuretic which strongly increases both urine flow and electrolyte urinary excretion. Healthy volunteers were administered 40 mg orally (dissolved in water) and concentrations of FD were determined in serum and urine for up to 6 h for eight subjects, who absorbed water at a rate of 400 ml/h. Quantification was performed by HPLC with fluorescence detection (excitation at 233 nm, emission at 389 nm) with a limit of detection of 5 ng/ml for a 300-microliters sample. The elution of FD was completed within 4 min using a gradient of acetonitrile concentration rising from 30 to 50% in 0.08 M phosphoric acid. The delay to the peak serum concentration ranged from 60 to 120 min. FD was still easily measurable in the sera from all subjects 6 h after administration. In urine, the excretion rates reached their maximum between 1 and 3 h. The total amount of FD excreted in the urine averaged 11.2 mg (range 7.6-14.0 mg), with a mean urine volume of 3024 ml (range 2620-3596 ml). Moreover, the urine density was lower than 1.010 (recommended as an upper limit in doping analysis to screen diuretics) only for 2 h. An additional volunteer was administered 40 mg of FD and his urine was collected over a longer period. FD was still detectable 48 h after intake. Gas chromatography-mass spectrometry with different types of ionization was used to confirm the occurrence of FD after permethylation of the extract. Negative-ion chemical ionization, with ammonia as reactant gas, was found to be the most sensitive method of detection.

Setting boundaries: brain dynamics of modal and amodal illusory shape completion in humans.

Normal visual perception requires differentiating foreground from background objects. Differences in physical attributes sometimes determine this relationship. Often such differences must instead be inferred, as when two objects or their parts have the same luminance. Modal completion refers to such perceptual "filling-in" of object borders that are accompanied by concurrent brightness enhancement, in turn termed illusory contours (ICs). Amodal completion is filling-in without concurrent brightness enhancement. Presently there are controversies regarding whether both completion processes use a common neural mechanism and whether perceptual filling-in is a bottom-up, feedforward process initiating at the lowest levels of the cortical visual pathway or commences at higher-tier regions. We previously examined modal completion (Murray et al., 2002) and provided evidence that the earliest modal IC sensitivity occurs within higher-tier object recognition areas of the lateral occipital complex (LOC). We further proposed that previous observations of IC sensitivity in lower-tier regions likely reflect feedback modulation from the LOC. The present study tested these proposals, examining the commonality between modal and amodal completion mechanisms with high-density electrical mapping, spatiotemporal topographic analyses, and the local autoregressive average distributed linear inverse source estimation. A common initial mechanism for both types of completion processes (140 msec) that manifested as a modulation in response strength within higher-tier visual areas, including the LOC and parietal structures, is demonstrated, whereas differential mechanisms were evident only at a subsequent time period (240 msec), with amodal completion relying on continued strong responses in these structures.

Modelling of bird distribution under complex mediterranean landscape dynamics: open habitat birds and fire (MEDFIRE)

Report for the scientific sojourn at the Simon Fraser University, Canada, from July to September 2007. General context: landscape change during the last years is having significant impacts on biodiversity in many Mediterranean areas. Land abandonment, urbanisation and specially fire are profoundly transforming large areas in the Western Mediterranean basin and we know little on how these changes influence species distribution and in particular how these species will respond to further change in a context of global change including climate. General objectives: integrate landscape and population dynamics models in a platform allowing capturing species distribution responses to landscape changes and assessing impact on species distribution of different scenarios of further change. Specific objective 1: develop a landscape dynamic model capturing fire and forest succession dynamics in Catalonia and linked to a stochastic landscape occupancy (SLOM) (or spatially explicit population, SEPM) model for the Ortolan bunting, a species strongly linked to fire related habitat in the region. Predictions from the occupancy or spatially explicit population Ortolan bunting model (SEPM) should be evaluated using data from the DINDIS database. This database tracks bird colonisation of recently burnt big areas (&50 ha). Through a number of different SEPM scenarios with different values for a number of parameter, we should be able to assess different hypothesis in factors driving bird colonisation in new burnt patches. These factors to be mainly, landscape context (i.e. difficulty to reach the patch, and potential presence of coloniser sources), dispersal constraints, type of regenerating vegetation after fire, and species characteristics (niche breadth, etc).