Integrable deformations of strings on symmetric spaces

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

Narradores e clandestinidade em contos de Os Cavalinhos de Platiplanto, de José J. Veiga: uma possibilidade de discussão sobre o espaço ficcional

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma abordagem geométrica para princípios de localização de integrais funcionais

Pós-graduação em Física - IFT

Effective transport barriers in nontwist systems

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.

Generalized correlation functions for conductance fluctuations and the mesoscopic spin Hall effect

We study the spin Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the latter are conveniently parametrized as deformed Lorentzian shape lines, functions of an external applied magnetic field and the Fermi energy. We find that the charge current fluctuations show quite unique statistical features at the symplectic-unitary crossover regime. Our findings are based on an evaluation of the generalized transmission coefficients correlation functions within the stub model and are amenable to experimental test. DOI: 10.1103/PhysRevB.86.235112

Bifurcation effects on the plasma edge of tokamaks with ergodic limiter.

In the present paper, we solve a twist symplectic map for the action of an ergodic magnetic limiter in a large aspect-ratio tokamak. In this model, we study the bifurcation scenarios that occur in the remnants regular islands that co-exist with chaotic magnetic surfaces. The onset of atypical local bifurcations created by secondary shearless tori are identified through numerical profiles of internal rotation number and we observe that their rupture can reduce the usual magnetic field line escape at the tokamak plasma edge.

Collective effects for the LHC injectors: non-ultrarelativistic approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the LHC performances in exploring new physics frontiers. One of the main limitations to the upgrade is represented by the collective instabilities. These are intensity dependent phenomena triggered by electromagnetic fields excited by the interaction of the beam with its surrounding. These fields are represented via wake fields in time domain or impedances in frequency domain. Impedances are usually studied assuming ultrarelativistic bunches while we mainly explored low and medium energy regimes in the LHC injector chain. In a non-ultrarelativistic framework we carried out a complete study of the impedance structure of the PSB which accelerates proton bunches up to 1.4 GeV. We measured the imaginary part of the impedance which creates betatron tune shift. We introduced a parabolic bunch model which together with dedicated measurements allowed us to point to the resistive wall impedance as the source of one of the main PSB instability. These results are particularly useful for the design of efficient transverse instability dampers. We developed a macroparticle code to study the effect of the space charge on intensity dependent instabilities. Carrying out the analysis of the bunch modes we proved that the damping effects caused by the space charge, which has been modelled with semi-analytical method and using symplectic high order schemes, can increase the bunch intensity threshold. Numerical libraries have been also developed in order to study, via numerical simulations of the bunches, the impedance of the whole CERN accelerator complex. On a different note, the experiment CNGS at CERN, requires high-intensity beams. We calculated the interpolating Hamiltonian of the beam for highly non-linear lattices. These calculations provide the ground for theoretical and numerical studies aiming to improve the CNGS beam extraction from the PS to the SPS.

Mechanismen der Caveolin-Genregulation in neuralen Zellsystemen

Caveolae sind vesikuläre Invaginationen der eukaryontischen Zellmembran, die bei einer Vielzahl zellbiologischer Prozesse eine bedeutende Rolle spielen. Die strukturellen und funktionellen Hauptbestandteile der Caveolae sind die Caveolin-Proteine, welche von drei homologen Genen (Caveolin-1,-2,-3) kodiert werden. Die Caveoline stellen die Struktur-Organisatoren der Caveolae dar, und regulieren direkt die Aktivität von zahlreichen Caveolae-assoziierten Rezeptorproteinen und Signalmolekülen. Oftmals werden die pleiotropen Effekte der Caveoline über eine Veränderung der Caveolin-Genexpressionsstärke moduliert. In der vorliegenden Arbeit wurden drei unterschiedliche biologische Steuerfaktoren identifiziert, unter deren Kontrolle die Caveolin-Genexpression in neuralen Zellsystemen steht. Bei diesen Faktoren handelt es sich um das Steroidhormon Oestrogen und seine Rezeptoren, den Wachstumsfaktor TGFa und den sekundären Botenstoff zyklisches AMP (cAMP). Oestrogen wirkt über die Aktivierung von Oestrogen-Rezeptoren (ERs) im zentralen Nervensystem in der Regel als neurotropher Faktor. In der vorliegenden Arbeit konnte erstmalig gezeigt werden, daß in humanen Neuroblastom-Zellen (SK-N-MC) die stabile, rekombinante Expression des ERa-Subtyps zu einer drastischen Reduktion der Caveolin-1/-2-Transkription führt, und daß in der Folge die zelluläre Caveolin-Biosynthese eingestellt wird. Eine Analyse des Caveolin-1-Gens ergab, daß einhergehend mit der Inaktivierung der Caveolin-1-Transkription eine Vielzahl der im Promoter enthaltenen CpG-Dinukleotide methyliert vorliegen. Durch pharmakologische Inhibition der nukleären DNA-Methyltransferasen sowie der Histon-Deacetylasen konnte die Caveolin-1-Transkription teilweise wiederhergestellt werden. Diese Befunde lassen auf die Existenz eines DNA-Methylierungs-abhängigen Stilllegungsmechanismus der Caveolin-Genexpression durch ERa schließen. Dagegen führte die Überexpression des ERb-Subtyps in SK-N-MC-Zellen zu keiner Veränderung der Caveolin-1/-2-Expression. Interessanterweise wurde die supprimierende Wirkung des ERa durch die gleichzeitige Überexpression des ERb vollständig aufgehoben. Der mitogene Wachstumsfaktor TGFa wurde als zweites extrazelluläres Signalmolekül identifiziert, welches eine Reduktion der Caveolin-1/-2-Genexpression bewirkt. In primären kortikalen Astrozyten konnte gezeigt werden, daß TGFa seine supprimierende Wirkung auf die Caveolin-1-Expression partiell über die Aktivierung des PI3-Kinase-abhängigen Signalweges vermittelt. Zudem wurde die supprimierende Wirkung von TGFa durch einen Inhibitior der Histon-Deacetylasen relativiert. Daher scheinen sowohl für den ERa als auch für TGFa epigenetische Prozesse bei der Suppression der Caveolin-1-Genexpression eine entscheidende Rolle zu spielen. Intrazellulär wirkte neben der PI3-Kinase auch der Botenstoff cAMP in kortikalen Astrozyten als Suppressor der Caveolin-Genexpression. Es wäre denkbar, daß die Caveolin-Suppression funktioneller Bestandteil des seit langem etablierten Effekts der cAMP-induzierten Astrozyten-Differenzierung ist. Desweiteren wiesen der cAMP- und TGFa-abhängige Signalweg ein überlappendes, Gehirnregion-spezifisches Regulationsprofil der Caveolin-Expression in Astrozyten auf: während in Kortex und Striatum eine Regulation durch cAMP und TGFa erfolgte, blieb diese in Klein- und Zwischenhirn aus. Somit bewirken drei zentrale regulatorische Faktoren der Proliferation und Differenzierung neuraler Zellen eine Reduktion in der Konzentration der pleiotrop funktionellen Caveoline. Zukünftige Studien müssen zeigen, inwieweit die reduzierte Caveolin-Expression für die morphologischen und biochemischen Primärwirkungen dieser Faktoren während der Entwicklung und im Zuge der Tumorgenese mitverantwortlich ist. Außerdem könnten über die Beobachtungen der zellbiologischen Auswirkungen reduzierter Caveolin-Spiegel neue Erkenntnisse über die Funktion dieser Proteine gewonnen werden.

The swelling behaviour of polyelectrolyte networks

Being basic ingredients of numerous daily-life products with significant industrial importance as well as basic building blocks for biomaterials, charged hydrogels continue to pose a series of unanswered challenges for scientists even after decades of practical applications and intensive research efforts. Despite a rather simple internal structure it is mainly the unique combination of short- and long-range forces which render scientific investigations of their characteristic properties to be quite difficult. Hence early on computer simulations were used to link analytical theory and empirical experiments, bridging the gap between the simplifying assumptions of the models and the complexity of real world measurements. Due to the immense numerical effort, even for high performance supercomputers, system sizes and time scales were rather restricted until recently, whereas it only now has become possible to also simulate a network of charged macromolecules. This is the topic of the presented thesis which investigates one of the fundamental and at the same time highly fascinating phenomenon of polymer research: The swelling behaviour of polyelectrolyte networks. For this an extensible simulation package for the research on soft matter systems, ESPResSo for short, was created which puts a particular emphasis on mesoscopic bead-spring-models of complex systems. Highly efficient algorithms and a consistent parallelization reduced the necessary computation time for solving equations of motion even in case of long-ranged electrostatics and large number of particles, allowing to tackle even expensive calculations and applications. Nevertheless, the program has a modular and simple structure, enabling a continuous process of adding new potentials, interactions, degrees of freedom, ensembles, and integrators, while staying easily accessible for newcomers due to a Tcl-script steering level controlling the C-implemented simulation core. Numerous analysis routines provide means to investigate system properties and observables on-the-fly. Even though analytical theories agreed on the modeling of networks in the past years, our numerical MD-simulations show that even in case of simple model systems fundamental theoretical assumptions no longer apply except for a small parameter regime, prohibiting correct predictions of observables. Applying a "microscopic" analysis of the isolated contributions of individual system components, one of the particular strengths of computer simulations, it was then possible to describe the behaviour of charged polymer networks at swelling equilibrium in good solvent and close to the Theta-point by introducing appropriate model modifications. This became possible by enhancing known simple scaling arguments with components deemed crucial in our detailed study, through which a generalized model could be constructed. Herewith an agreement of the final system volume of swollen polyelectrolyte gels with results of computer simulations could be shown successfully over the entire investigated range of parameters, for different network sizes, charge fractions, and interaction strengths. In addition, the "cell under tension" was presented as a self-regulating approach for predicting the amount of swelling based on the used system parameters only. Without the need for measured observables as input, minimizing the free energy alone already allows to determine the the equilibrium behaviour. In poor solvent the shape of the network chains changes considerably, as now their hydrophobicity counteracts the repulsion of like-wise charged monomers and pursues collapsing the polyelectrolytes. Depending on the chosen parameters a fragile balance emerges, giving rise to fascinating geometrical structures such as the so-called pear-necklaces. This behaviour, known from single chain polyelectrolytes under similar environmental conditions and also theoretically predicted, could be detected for the first time for networks as well. An analysis of the total structure factors confirmed first evidences for the existence of such structures found in experimental results.

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Moduli spaces of (G,h)-constellations

Given a reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G → N_0, we construct the moduli space M_Ө(X) of Ө-stable (G,h)-constellations on X, which is a common generalisation of the invariant Hilbert scheme after Alexeev and Brion and the moduli space of Ө-stable G-constellations for finite groups G introduced by Craw and Ishii. Our construction of a morphism M_Ө(X) → X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G. Furthermore, we determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl_2 on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure for the realisation of such calculations. We also consider questions of smoothness and connectedness and thereby show that our Hilbert scheme gives a resolution of singularities of the symplectic reduction of the action.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.