Negative even grade mKdV hierarchy and its soliton solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra (s) over capl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method based on non zero vacua. The sub-hierarchies admiting such class of solutions are classified.

BERRY PHASE, AHARONOV-BOHM EFFECT AND TOPOLOGY

The Berry phase for an electron in a one-dimensional box rotated around a magnetic flux line has contributions from the geometry and the magnetic flux, which gives an Aharonov-Bohm effect. For a circular box enclosing the magnetic flux, the Berry phase depends on the boundary conditions.

The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the mKdV-Liouville hierarchy and its self-similarity reduction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones

Memory hierarchy and data communication in heterogeneous reconfigurable SoCs

The miniaturization race in the hardware industry aiming at continuous increasing of transistor density on a die does not bring respective application performance improvements any more. One of the most promising alternatives is to exploit a heterogeneous nature of common applications in hardware. Supported by reconfigurable computation, which has already proved its efficiency in accelerating data intensive applications, this concept promises a breakthrough in contemporary technology development. Memory organization in such heterogeneous reconfigurable architectures becomes very critical. Two primary aspects introduce a sophisticated trade-off. On the one hand, a memory subsystem should provide well organized distributed data structure and guarantee the required data bandwidth. On the other hand, it should hide the heterogeneous hardware structure from the end-user, in order to support feasible high-level programmability of the system. This thesis work explores the heterogeneous reconfigurable hardware architectures and presents possible solutions to cope the problem of memory organization and data structure. By the example of the MORPHEUS heterogeneous platform, the discussion follows the complete design cycle, starting from decision making and justification, until hardware realization. Particular emphasis is made on the methods to support high system performance, meet application requirements, and provide a user-friendly programmer interface. As a result, the research introduces a complete heterogeneous platform enhanced with a hierarchical memory organization, which copes with its task by means of separating computation from communication, providing reconfigurable engines with computation and configuration data, and unification of heterogeneous computational devices using local storage buffers. It is distinguished from the related solutions by distributed data-flow organization, specifically engineered mechanisms to operate with data on local domains, particular communication infrastructure based on Network-on-Chip, and thorough methods to prevent computation and communication stalls. In addition, a novel advanced technique to accelerate memory access was developed and implemented.

The C-4-Dicarboxylate carriers DcuB and DctA of Escherichia coli: function as cosensors and topology

Das fakultativ anaerobe Enterobakterium Escherichia coli nutzt C4-Dicarboxylate sowohl unter aeroben als auch anaeroben Bedingungen als Kohlenstoff- und Energiequelle. Die Aufnahme der C4-Dicarboxylaten und die Energiekonservierung mittels Fumaratatmung wird durch das Zweikomponentensystem DcuSR reguliert. Die Sensorhistidinkinase DcuS und der nachgeschaltete Responseregulator DcuR aktivieren bei Verfügbarkeit von C4-Dicarboxylaten die Expression der Gene für den Succinat Transporter DctA, den anaeroben Fumarat/Succinat Antiporter DcuB, die Fumarase B sowie die Fumaratreduktase FrdABCD. Die Transportproteine DctA und DcuB wiederum regulieren die Expression der DcuSR-abhängigen Gene negativ. Fehlen von DctA oder DcuB resultiert bereits ohne Effektor in einer maximalen Expression von dctA bzw. dcuB. Durch gerichtete und ungerichtete Mutagenese wurde gezeigt, dass die Transportfunktion des Carriers DcuB unabhängig von seiner regulatorischen Funktion ist. DcuB kann daher als Cosensor des DcuSR Systems angesehen werden.rnUnter Verwendung von Reportergenfusionen von C-terminal verkürzten Konstrukten von DcuB mit der Alkalischen Phosphatase und der β-Galactosidase wurde die Topologie des Multitransmembranproteins DcuB bestimmt. Zusätzlich wurde die Zugänglichkeit bestimmter Aminosäurereste durch chemische Modifikation mit membran-durchlässigen und membran-undurchlässigen Thiolreagenzien untersucht. Die erhaltenen Ergebnisse deuten auf die Existenz eines tief in die Membran reichenden, hydrophilen Kanal hin, welcher zum Periplasma hin geöffnet ist. Mit Hilfe der Topologie-Studien, des Hydropathie-Blots und der Sekundärstruktur-Vorhersage wurde ein Modell des Carriers erstellt. DcuB besitzt kurze, periplasmatisch liegende Proteinenden, die durch 12 Transmembranhelices und zwei große hydrophile Schleifen jeweils zwischen TM VII/VIII und TM XI/XII verbunden sind. Die regulatorisch relevanten Reste K353, T396 und D398 befinden sich innerhalb von TM XI sowie auf der angrenzenden cytoplasmatischen Schleife XI-XII. Unter Berücksichtigung der strukturellen und funktionellen Aspekte wurde ein Regulationsmodell erstellt, welches die gemeinsam durch DcuB und DcuS kontrollierte C4-Dicarboxylat-abhängige Genexpression darstellt. rnDer Effekt von DctA und DcuSR auf die Expression einer dctA´-´lacZ Reportergenfusion und auf die aerobe C4-Dicarboxylat-Aufnahme wurde untersucht. In-vivo FRET-Messungen weisen auf eine direkte Wechselwirkung zwischen dem Carrier DctA und dem Sensor DcuS hin. Dieses Ergebnis stützt die Theorie der Regulation von DcuS durch C4-Dicarboxylate und durch die Cosensoren DctA bzw. DcuB mittels direkter Protein-Protein Interaktion.rn

The mass-hierarchy and CP-violation discovery reach of the LBNO long-baseline neutrino experiment

The next generation neutrino observatory proposed by the LBNO collaboration will address fundamental questions in particle and astroparticle physics. The experiment consists of a far detector, in its first stage a 20 kt LAr double phase TPC and a magnetised iron calorimeter, situated at 2300 km from CERN and a near detector based on a highpressure argon gas TPC. The long baseline provides a unique opportunity to study neutrino flavour oscillations over their 1st and 2nd oscillation maxima exploring the L/E behaviour, and distinguishing effects arising from δCP and matter. In this paper we have reevaluated the physics potential of this setup for determining the mass hierarchy (MH) and discovering CP-violation (CPV), using a conventional neutrino beam from the CERN SPS with a power of 750 kW. We use conservative assumptions on the knowledge of oscillation parameter priors and systematic uncertainties. The impact of each systematic error and the precision of oscillation prior is shown. We demonstrate that the first stage of LBNO can determine unambiguously the MH to > 5δ C.L. over the whole phase space. We show that the statistical treatment of the experiment is of very high importance, resulting in the conclusion that LBNO has ~ 100% probability to determine the MH in at most 4-5 years of running. Since the knowledge of MH is indispensable to extract δCP from the data, the first LBNO phase can convincingly give evidence for CPV on the 3δ C.L. using today’s knowledge on oscillation parameters and realistic assumptions on the systematic uncertainties.

Instability and topology bifurcations on a hemisphere-cylinder at high angle of attack

La configuración de un cilindro acoplado a una semi-esfera, conocida como ’hemispherecylinder’, se considera como un modelo simplificado para numerosas aplicaciones industriales tales como fuselaje de aviones o submarinos. Por tanto, el estudio y entendimiento de los fenómenos fluidos que ocurren alrededor de dicha geometría presenta gran interés. En esta tesis se muestra la investigación del origen y evolución de los, ya conocidos, patrones de flujo (burbuja de separación, vórtices ’horn’ y vórtices ’leeward’) que se dan en esta geometría bajo condiciones de flujo separado. Para ello se han llevado a cabo simulaciones numéricas (DNS) y ensayos experimentales usando la técnica de Particle Image Velocimetry (PIV), para una variedad de números de Reynolds (Re) y ángulos de ataque (AoA). Se ha aplicado sobre los resultados numéricos la teoría de puntos críticos obteniendo, por primera vez para esta geometría, un diagrama de bifurcaciones que clasifica los diferentes regímenes topológicos en función del número de Reynolds y del ángulo de ataque. Se ha llevado a cabo una caracterización completa sobre el origen y la evolución de los patrones estructurales característicos del cuerpo estudiado. Puntos críticos de superficie y líneas de corriente tridimensionales han ayudado a describir el origen y la evolución de las principales estructuras presentes en el flujo hasta alcanzar un estado de estabilidad desde el punto de vista topológico. Este estado se asocia con el patrón de los vórtices ’horn’, definido por una topología característica que se encuentra en un rango de números de Reynolds muy amplio y en regímenes compresibles e incompresibles. Por otro lado, con el objeto de determinar las estructuras presentes en el flujo y sus frecuencias asociadas, se han usado distintas técnicas de análisis: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) y análisis de Fourier. Dichas técnicas se han aplicado sobre los datos experimentales y numéricos, demostrándose la buena concordancia entre ambos resultados. Finalmente, se ha encontrado en ambos casos, una frecuencia dominante asociada con una inestabilidad de los vórtices ’leeward’. ABSTRACT The hemisphere-cylinder may be considered as a simplified model for several geometries found in industrial applications such as aircrafts’ fuselages or submarines. Understanding the complex flow phenomena that surrounds this particular geometry is therefore of major industrial interest. This thesis presents an investigation of the origin and evolution of the complex flow pattern; i.e. separation bubbles, horn vortices and leeward vortices, around the hemisphere-cylinder under separated flow conditions. To this aim, threedimensional Direct Numerical Simulations (DNS) and experimental tests, using Particle Image Velocimetry (PIV) techniques, have been performed for a variety of Reynolds numbers (Re) and angles of attack (AoA). Critical point theory has been applied to the numerical simulations to provide, for the first time for this geometry, a bifurcation diagram that classifies the different flow topology regimes as a function of the Reynolds number and the angle of attack. A complete characterization about the origin and evolution of the complex structural patterns of this geometry has been put in evidence. Surface critical points and surface and volume streamlines were able to describe the main flow structures and their strong dependence with the flow conditions up to reach the structurally stable state. This state was associated with the pattern of the horn vortices, found on ranges from low to high Reynolds numbers and from incompressible to compressible regimes. In addition, different structural analysis techniques have been employed: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) and Fourier analysis. These techniques have been applied to the experimental and numerical data to extract flow structure information (i.e. modes and frequencies). Experimental and numerical modes are shown to be in good agreement. A dominant frequency associated with an instability of the leeward vortices has been identified in both, experimental and numerical results.