Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Anatomy and histology of Embolyntha batesi MacLahlan, 1877 (Embiidina)

The Embioptera are rather generalized insects whose internal anatomy is simple and not subject to great modifications. For this reason these insects form an ideal group for elementary anatomical and histological studies (fig. 2). The digestive tract is a long, simple tube without convolutions or diverticulae from the buccal cavity to the rectum. The buccal structures are of the chewing type. The oesophagus and ingluvia are differentiated only by slight dilation of their walls. In nymphs and females the proventriculus is very distinct due to folds which flatten as the structure becomes packed with food. The enteron is the largest in such forms and in both sexes limited caudally by the Malpighian tubules. The proctodeus has six large rectal papillae. The nervous system is complete with only the fifth abdominal segment lacking a ganglion in the metathorax includes the ganglion of the first abdominal segment. The brain exhibits very clear structure in histological sections. The tracheal system includes two pairs of thoracic spiracles and eight abdominal pairs. Only th metathoracic spiracle has an air expiration function; all others serve for inspiration. Various structures in the spiracles protect the atrium. The circulatory system includes a long, simple dorsal vessel which extends forward from the ninth abdominal segment into the cranium. It opens anteriorly near the circumoesophageal connectives. The dorsal vessel has a pair of ostia and valves corresponding to each abdominal and thoracic segment. It lacks the diverticulae or folds commonly found in more highly evolved insects. The excretory system is represented by Malphighian tubules, pericardial cells, and fat-body. The number and disposition of Malpighian tubules is variable within the order. The pericardial cells are localized around the entire dorsal vessel up to the opening of the aorta in the head. The fat-bodies form compact layers in the dorsal and ventral regions of the body. In males they are more developed in the abdominal region. The mandibles, maxillae, and salivary glands are of a simple type with very few cytological modifications. Only the salivary glands which extend into the mesothoracic region show appreciable specialization. The reproductive system is bi-sixual and shows considerable sexual dimorphism. Males have five pair of testes with a metameric disposition, two distinct ducts, two epidymis, and the ejaculatory organs. The accessory glands vary in number and size and open in the anterior portion of the ejaculatory duct. The female reproductive organs are of the panoistic type. The system includes five pairs of ovarioles, two long paired oviducts a small, unpaired oviduct and the spermatheca which opens in the vagina. Reproduction usually involves a union of male and female gametes, and eggs are usually laid in clusters attached to a substrate.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

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.

Demyelination in brain cell aggregate cultures, induced by a monoclonal antibody against the myelin/oligodendrocyte glycoprotein (MOG).

Previous work has shown that aggregate cultures prepared from fetal rat telencephalon and grown in a chemically defined medium offer a useful model to study developmental processes such as myelin synthesis. Since compact myelin is formed in these cultures, we investigated the possibility to use this culture system to study demyelinating mechanisms. In particular, we examined the effect of a monoclonal antibody (8-18C5) directed against the myelin/oligodendrocyte glycoprotein (MOG). We found that addition of anti-MOG antibodies and complement to aggregate cultures led to a highly significant decrease in myelin basic protein (MBP) content and 2',3'-cyclic nucleotide 3'-phosphohydrolase (CNP) specific activity. These results indicate that, in our culture system, anti-MOG antibodies have a strong demyelinating effect.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Diseño de inversores de impedancias de microondas compactos basados en metamateriales: aplicación a divisores de potencia

Recientemente ha surgido un nuevo campo de investigación en el área del electromagnetismo aplicado y de la ingeniería de microondas, basado en el control de las propiedades electromagnéticas de estructuras artificiales, conocidas como metamateriales. El objetivo principal de este proyecto es el estudio y control del comportamiento de estas estructuras artificiales, y su posterior aplicación para la síntesis de dispositivos compactos de microondas. En el primer capítulo se hace una introducción a los metamateriales en la que se exponen sus principales propiedades electromagnéticas, para finalmente presentar las líneas de transmisión zurdas que se suelen utilizar en el diseño de metamateriales. En el segundo capítulo se realiza un estudio de las propiedades y del funcionamiento de una celda metamaterial. Finalmente en el tercer capítulo se exponen diferentes dispositivos diseñados mediante la utilización de este tipo de celdas.

Simulations of parasitic and intrinsic capacitances related to Multiple-Gate-Field-Effect Transistor architectures

Report for the scientific sojourn carried out at the Université Catholique de Louvain, Belgium, from March until June 2007. In the first part, the impact of important geometrical parameters such as source and drain thickness, fin spacing, spacer width, etc. on the parasitic fringing capacitance component of multiple-gate field-effect transistors (MuGFET) is deeply analyzed using finite element simulations. Several architectures such as single gate, FinFETs (double gate), triple-gate represented by Pi-gate MOSFETs are simulated and compared in terms of channel and fringing capacitances for the same occupied die area. Simulations highlight the great impact of diminishing the spacing between fins for MuGFETs and the trade-off between the reduction of parasitic source and drain resistances and the increase of fringing capacitances when Selective Epitaxial Growth (SEG) technology is introduced. The impact of these technological solutions on the transistor cut-off frequencies is also discussed. The second part deals with the study of the effect of the volume inversion (VI) on the capacitances of undoped Double-Gate (DG) MOSFETs. For that purpose, we present simulation results for the capacitances of undoped DG MOSFETs using an explicit and analytical compact model. It monstrates that the transition from volume inversion regime to dual gate behaviour is well simulated. The model shows an accurate dependence on the silicon layer thickness,consistent withtwo dimensional numerical simulations, for both thin and thick silicon films. Whereas the current drive and transconductance are enhanced in volume inversion regime, our results show thatintrinsic capacitances present higher values as well, which may limit the high speed (delay time) behaviour of DG MOSFETs under volume inversion regime.

Eimeria vitellini n. sp. (Apicomplexa: eimeriidae) from the brazilian toucan Rhamphastos vitellinus vitellinus Lichtenstein (Aves: Picicformes: Rhamplastidae)

Eimeria vitellini n. sp. is described from the faeces of the Rhamphastos v. vitellinus. Oocysts broadly ellipsoidal to oval (egg-shaped), 22,6 x 18.3 (20.0-25.0 x 16.3-22.5) micronm, shapeindex (length/width) 1.2 (1.1-1.1). Oocyst wall a single colourless layer about 0.5 micronm thick, becoming thinner at one ectremity, at which point the oocyst usually ruptures. No oocyst residuum, but 1 or 2 small polr bodies of about 1.0-1.5 x 0.5-1.0 micronm. Sporocysts ellongated ellipsoid (pearshaped), 14.3 x 7.5 (13.8-15.0 x 6.9-7.5) micronm, shape-index (1.9 (1.8-2.0), with a thin colourless wall bearing a very delicate Stieda body: a conspicuous sub-Stieda body is present. Sporozoites with anterior and posterior regractile bodies and strongly recurved around a bulky, compact sporocyst residuum composed of relatively fine granules and spherules.

Eimeria species (Apicomplexa: Eimeriidae) of podocnemis expansa (Schweigger) and geochelone denticulata (LINN.) from Amazonian Brazil (Reptilia: Chelonia)

Eimeria lagunculata, Eimeria mammiformis and Eimeria podocnemis n. spp., are described from the faeces of the fresh-water turtle Podocnemis expansa, in Pará State, north Brasil. Oocysts of E. lagunculata are ellipsoidal, 19.2 x 12.8 (17.0-20.7 x 11.8-14.1) mum, shape-index (= length/ width) 1.5 (1.4-1.7). Oocyst wall about 0.5-0.7 mum thick, with a prominent stopper-like micropyle at one pole. No oocyst residuum and no polar body. Sporocysts elongate ellipsoidal, 11.0 x 5.4 (10.4-11.8 x 5.2-6.0) mum, shape-index 2.0 (1.8-2.1): no Stieda body. A compact, ellipsoidal sporocyst residuum lies between the two sporozoites, which possess a posterior and an anterior refractile body. Oocysts of E. mammiformis broadly ellipsoidal, 30.0 x 19.4 (23.0-37.0 x 16.3-21.5) mum, shape-index 1.5 (1.1-1.9). Oocyst wall about 0.7 mum thick, with a prominent micropyle: no oocyst residuum and rarely a single polar body. Sporocysts ellipsoidal, 15.3 x 7.9 (14.8-17.0 x 7.4-9.6) mum, shape-index 2.0 (1.8-2.2), with a tiny Stieda body. Sporocyst residuum bulky, ellipsoidal: sporozoites with two conspicuous refractile bodies. E. podocnemis has broadly ellipsoidal oocysts, 17.0 x 12.8 (14.8-19.2 x 11.8-14.1) mum, shape-index 1.3 (1.1-1.4). Oocyst wall about 0.5-0.7 mum thick, with no micropyle. No oocyst residuum, but always a single polar body. Sporocysts ellipsoidal, 9.7 x 5.2 (8.9-10.4 x 4.4-6.0) mum, shape-index 1.9 (1.6-2.0), with no Stieda body. Sporocyst residuum bulky, ellipsoidal: sporocysts with 2 refractile bodies. Eimeria carinii n. sp., is recorded from the tortoise Geochelone denticulata, also from Pará. Oocyst wall about 1.2 mum thicl. No micropyle. Oocyst residuum limited to a number (about 10-20) of scattered granules: no polar body. Sporocysts broadly ellipsoidal, and with no Stieda body: they measure 8,8 x 7.3 (8.0-9.0 x 7.0-7.5) mum, shape-index 1.2 (1.1-1.3). Sporocyst residuum bulky, spherical to ellipsoidal: sporozoites possess both posterior and anterior refractile bodies.

IRM opératoire et chirurgie de l'épilepsie [Intraoperative MRI and epilepsy surgery].

Intraoperative imaging, in particular intraoperative MRI, is a developing area in neurosurgery and its role is currently being evaluated. Its role in epilepsy surgery has not been defined yet and its use has been limited. In our experience with a compact and mobile low-field intraoperative MRI system, a few epilepsy surgeries have been performed using this technique. As the integration of imaging and functional data plays an important role in the planning of epilepsy surgery, intraoperative verification of the surgical result may be highly valuable. Therefore, teams that have access to intraoperative MRI should be encouraged to use this technique prospectively to evaluate its current relevance in epilepsy surgery.

La reconversion du quartier Gare/Crêt-Taconnet à Neuchâtel: réflexions sur la densification qualifiée

La reconversion des friches industrielles des secteurs de gare est prometteuse dans l'optique d'un développement urbain dense alternatif à l'étalement. Elles constituent en effet une réserve foncière centrale et bien desservie par les transports publics. La densification de ces terrains stratégiques ne pourra cependant freiner l'étalement urbain qu'à condition d'offrir un cadre de vie attractif pour l'habitat. Notre hypothèse est que l'engagement des pouvoirs publics est déterminant pour assurer cette densification qualifiée. Brown fields regeneration in railway station areas is particularly promising in the perspective of a compact urban development alternative to sprawl. They indeed constitute a central land stock which is well connected to public transportation networks. However, the densification of these strategic lands will make it possible to moderate urban sprawl only by providing an attractive environment for residential activities. Our hypothesis is that public authorities involvement is decisive to ensure such a qualified densification. Die Umnutzung von Industriebrachen in Bahnhofsarealen scheint viel versprechend im Hinblick auf eine Stadtentwicklung nach innen als Alternative zur Ausbreitung. Zentralgelegen, stellen diese ungenutzten Flächen eine strategische Bodenreserve dar, welche gut an das öffentliche Verkehrsmittelnetz angeschlossen ist. Ihre Verdichtung kann jedoch die Stadtausbreitung nur eindämmen unter der Bedingung, einen attraktiven Lebens- und Wohnraum zu bieten. Unsere Hypothese lautet, dass das Ausmass des Engagements der öffentlichen Hand bestimmend ist um diese qualitative Verdichtung sicherzustellen.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Some personal views on the control of schistosomiasis mansoni

Our views are based, on a recent study of a district of Uniao dos Palmares (Alagoas). Although being a very compact community (32 city blocks holding two thousand families), transmission is very uneven, the geometric mean egg counts in the various blocks ranging between extremes of 96 and 1920. (Results do not correlate with the availability of domestic water supply). We thus are led to conclude that: (a) transmission is primarily peridomestic, resulting from pollution of open ditches and other collections of water; (b) control of transmission can be done on a selective basis, requiring quite medest investments. Given the inefficacy of population-based chemotherapy, when used alone, the author insists that this alternative cannot any longer be overlooked. He also regrets the emphasis placed upon vaccine development; allegations that this would, at any rate, prevent severe morbidity can be dismissed, since-whatever the cause-morbidity due to schistosomiasis has been rapidly declining in Northeast Brazil.