Spin-Gap Proximity Effect Mechanism of High Temperature Superconductivity

When holes are doped into an antiferromagnetic insulator they form a slowly fluctuating array of ``topological defects'' (metallic stripes) in which the motion of the holes exhibits a self-organized quasi one-dimensional electronic character. The accompanying lateral confinement of the intervening Mott-insulating regions induces a spin gap or pseudogap in the environment of the stripes. We present a theory of underdoped high temperature superconductors and show that there is a {\it local} separation of spin and charge, and that the mobile holes on an individual stripe acquire a spin gap via pair hopping between the stripe and its environment; i.e. via a magnetic analog of the usual superconducting proximity effect. In this way a high pairing scale without a large mass renormalization is established despite the strong Coulomb repulsion between the holes. Thus the {\it mechanism} of pairing is the generation of a spin gap in spatially-confined {\it Mott-insulating} regions of the material in the proximity of the metallic stripes. At non-vanishing stripe densities, Josephson coupling between stripes produces a dimensional crossover to a state with long-range superconducting phase coherence. This picture is established by obtaining exact and well-controlled approximate solutions of a model of a one-dimensional electron gas in an active environment. An extended discussion of the experimental evidence supporting the relevance of these results to the cuprate superconductors is given.Comment: 30 pages, 2 figure

Computing Limit Points of Quasi-components of Regular Chains and its Applications

Computing limit is a fundamental task in mathematics and different mathematical concepts are defined in terms of limit computations. Among these mathematical concepts, we are interested in three different types of limit computations: first, computing the limit points of solutions of polynomial systems represented by regular chains, second, computing tangent cones of space curves at their singular points which can be viewed as computing limit of secant lines, and third, computing the limit of real multivariate rational functions. For computing the limit of solutions of polynomial systems represented by regular chains, we present two different methods based on Puiseux series expansions and linear changes of coordinates. The first method, which is based on Puiseux series expansions, addresses the problem of computing real and complex limit points corresponding to regular chains of dimension one. The second method studies regular chains under changes of coordinates. It especially computes the limit points corresponding to regular chains of dimension higher than one for some cases. we consider strategies where these changes of coordinates can be either generic or guided by the input. For computing the Puiseux parametrizations corresponding to regular chains of dimension one, we rely on extended Hensel construction (EHC). The Extended Hensel Construction is a procedure which, for an input bivariate polynomial with complex coefficients, can serve the same purpose as the Newton-Puiseux algorithm, and, for the multivariate case, can be seen as an effective variant of Jung-Abhyankar Theorem. We show that the EHC requires only linear algebra and univariate polynomial arithmetic. We deduce complexity estimates and report on a software implementation together with experimental results. We also outline a method for computing the tangent cone of a space curve at any of its points. We rely on the theory of regular chains and Puiseux series expansions. Our approach is novel in that it explicitly constructs the tangent cone at arbitrary and possibly irrational points without using a Standard basis. We also present an algorithm for determining the existence of the limit of a real multivariate rational function q at a given point which is an isolated zero of the denominator of q. When the limit exists, the algorithm computes it, without making any assumption on the number of variables. A process, which extends the work of Cadavid, Molina and V´elez, reduces the multivariate setting to computing limits of bivariate rational functions. By using regular chain theory and triangular decomposition of semi-algebraic systems, we avoid the computation of singular loci and the decomposition of algebraic sets into irreducible components

Actions and Invariants of Residually Finite Groups: Asymptotic Methods

The workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle

Experimentation of Entangled photon-pairs generation using an ultrafast source at gigahertz

In this dissertation we will present the experimental study of polarization entangled photon pairs generation, through spontaneous parametric down conversion (SPDC) using an ultrafast source at gigahertz. The laser source that we used is the TACCOR 8. The optical process of second harmonic generation (SHG) is generated by a periodically poled KTP (PPKTP) crystal. Finally, we measured the photon-pairs generation rate in the best case of conversion efficiency of SHG with PPKTP

Simulating a Flexible Robotic System based on Musculoskeletal Modeling

Humanoid robotics offers a unique research tool for understanding the human brain and body. The synthesis of human motion is a complex procedure that involves accurate reconstruction of movement sequences, modeling of musculoskeletal kinematics, dynamics and actuation, and characterization of reliable performance criteria. Many of these processes have much in common with the problems found in robotics research, with the recent advent of complex humanoid systems. This work presents the design and development of a new-generation bipedal robot. Its modeling and simulation has been realized by using an open-source software to create and analyze dynamic simulation of movement: OpenSim. Starting from a study by Fuben He, our model aims to be used as an innovative approach to the study of a such type of robot in which there are series elastic actuators represented by active and passive spring components in series with motors. It has provided of monoarticular and biarticular joint in a very similar manner to human musculoskeletal model. This thesis is only the starting point of a wide range of other possible future works: from the control structure completion and whole-body control application, to imitation learning and reinforcement learning for human locomotion, from motion test on at ground to motion test on rough ground, and obviously the transition from simulation to practice with a real elastic bipedal robot biologically-inspired that can move like a human bein

Interfaces and Quantum Algebras, I: Stable Envelopes

The stable envelopes of Okounkov et al. realize some representations of quantum algebras associated to quivers, using geometry. We relate these geometric considerations to quantum field theory. The main ingredients are the supersymmetric interfaces in gauge theories with four supercharges, relation of supersymmetric vacua to generalized cohomology theories, and Berry connections. We mainly consider softly broken compactified three dimensional $\mathcal{N} =4$ theories. The companion papers will discuss applications of this construction to symplectic duality, Bethe/gauge correspondence, generalizations to higher dimensional theories, and other topics.Comment: 152 pages; v2: references added, various explanations improve

Dynamics of emerging actin networks

Life is an ensemble of countless emerging properties arising through self-assembly and self-organization phenomena, manifesting at the cellular, the tissue and the organismal level. The mechanical integrity of a cell is orchestrated by the cytoskeleton, a dynamic system comprised of three biopolymers, actin, microtubules and intermediate filaments, acting in symphony, facilitated by a plethora of accessory proteins. Understanding the cytoskeletal functionality and its relation to other cellular components and properties is a prominent question in biophysics. Actin, a dynamic and polymorphic component, forms a variety of structures such as filaments, bundles, and their networks. The unique viscoelastic properties shown by actin-based structures have been extensively probed via rheological means. On the contrary, the underlying microstructural dynamics remain mostly uncovered. Actin bundles are crucial for eukaryotic cells; they are involved in the intracellular transport, contractive forces, mechanical stability, cell motility and environment exploration. This thesis takes a step forward to fathom the rich dynamics and emergent properties exhibited by actin bundles within flow-free confinements, a prerequisite for the study. To study a reversible reaction sequence in a step-by-step manner, one needs an open system. As a result, there have been relatively few studies in this direction, as most of the experimental systems are closed, for instance, sealed coverslips or liposomes. We created a straightforward microfluidic system, consisting of quasi two-dimensional, cell-sized compartments, enclosing sub-picolitre volumes. These `microchambers' are connected to the controlling channel (the reservoir) via narrow connecting channels, allowing exclusive diffusive transport into and out of the microchambers. The system represents an ideal environment to form an entangled network of actin filaments in a steady-state and is manipulable in a step-by-step fashion. We induce bundling of actin filaments in three ways: counterion condensation aided by magnesium ions, depletion interactions mimicked by polyethylene glycol, acting as a crowding agent, and specific interactions with actin exhibited by filamin, an actin binding protein. Above the critical concentration of bundling agents, actin filaments transform into an emerging network of actin bundles, a process associated with percolation, leading to a single connected entity. Sharing of filaments is an important parameter for the observed behaviour, as reducing the actin filament length exclusively forms bundles without percolation. We encounter a hierarchical process of bundling: filaments coalesce into small bundles that further fuse to form bigger bundles. Disassembly involves a similar hierarchy, additionally involving peeling-off of single filaments. We explore the reactions using time-lapse image analyses and apply kinetic models. Counterion condensation forms a network comprising of straight, rigid bundles facilitated by a zipping process (v ~ 12 µm/s), generating tension within the network. Disassembly leads to the release of the stored energy, utilized in the buckling of bundles, enabling us to estimate ~ 100 - 200 kT of stored energy. Crowding agents force the actin filaments to form an intriguing spindle-like structure, consisting of poles with sets of aligned filaments shared and stretched between them, which further transforms into a network of bundles. The disassembly constitutes the reversal of the process. Filamin forms ring-like networks, containing intrinsically curved bundles. Owing to the highly specific interactions, the network does not disassemble, even after 12 hours. In essence, using a bottom-up approach, we explore the emerging properties of actin bundles, with an emphasis on their dynamics

Electronic structure, morphology and chemical reactivity of nanoclusters and low-dimensional systems: fast photoemission spectroscopy studies

2008/2009L'obiettivo di questa tesi è l'applicazione della spettroscopia di fotoemissione allo studio di nanoparticelle supportate e di sistemi a bassa dimensionalità. Ad una primo periodo dedicato allo sviluppo del rivelatore e del software per un nuovo analizzatore d'energia per elettroni installato presso la linea di luce SuperESCA ad Elettra, è seguita una fase durante la quale ho eseguito una serie di esperimenti mirati ad esplorare le potenzialità del nuovo apparato sperimentale. Il primo risultato ottenuto riguarda la comprensione della relazione che intercorre tra le variazioni della reattività chimica del sistema Pd/Ru(0001) e il numero degli strati di Pd cresciuti in modo pseudomorfico sul substrato di rutenio. La risoluzione temporale raggiunta con la nuova strumentazione ci ha permesso di studiare processi dinamici su una scala temporale fino ad ora inaccessibile per la spettroscopia di fotoemissione dai livelli di core: in particolare abbiamo studiato la crescita del grafene ad alta temperatura sulla superficie (111) dell'iridio e la reattività chimica di nanocluster di Pt supportati su MgO. Nel primo caso abbiamo messo in evidenza come la formazione del grafene proceda attraverso la nucleazione di nano-isole di carbonio che assumono una peculiare forma di cupola. Nel secondo caso siamo riusciti a seguire sia la dinamica del processo di adsorbimento di CO, sia la reazione CO + 1/2 O2 -> CO2 sulle nanoparticelle di Pt depositate su un film ultra-sottile di ossido di magnesio. Infine, abbiamo caratterizzato la morfologia di nanoparticelle di Pd, Pt, Rh e Au cresciute su diversi substrati a base di carbonio, in particolare grafite, nanotubi a parete singola e grafene. Tra i vari risultati abbiamo compreso come l'interazione metallo-substrato dipenda dalla dimensione delle nano-particelle e abbiamo evidenziato il ruolo centrale dei difetti del substrato nei processi di nucleazione e intercalazione.The objective of this thesis is the application of photoelectron spectroscopy for the investigation of supported nanoclusters and low-dimensional systems. After a first stage devoted to the development of the detector and the software for the electron energy analyser installed on the SuperESCA beamline at Elettra, during the PhD project I've performed a series of experiments aimed to explore the capabilities of the new experimental apparatus. One of the first results concerns the understanding of the relation between the modifications in the chemical reactivity of the Pd/Ru(0001) system and the thickness of the pseudomorphically grown Pd overlayer. The temporal resolution achieved with the new experimental set-up allowed us to study dynamical processes on a new time scale, in particular the graphene growth process at high temperature on the Ir(111) surface and the chemical reactivity of Pt nanoclusters supported on MgO. In the former case, we discovered that graphene formation proceeds via preliminary nucleation of dome-shaped C nano-islands. In the second case, we succeded in following both the dynamics of CO adsorption process and the CO + 1/2 O2 -> CO2 reaction on Pt nanoclusters grown on a ultra-thin film of magnesium oxide. Finally, the morphology of Pd, Pt, Rh and Au nanoclusers grown on different carbon-based substrates (namely graphite, single-walled carbon nanotubes and graphene) has been characterized. Among the results we report the understanding of the dependence of the metal-substrate interaction on the cluster size and the role of defects in the nucleation and intercalation processes.XXII Ciclo197

Numerical modeling of dielectrophoretic effect for manipulation of bio-particles

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This text describes different aspects of the design of a Doctor-on-a-Chip device. Doctor-on-a-Chip is a DNA analysis system integrated on a single chip, which should provide all of the advantages that stem from the system integration, such as small sample volume, fast and accurate analysis, and low cost. The text describes all of the steps of the on-chip sample analysis, including DNA extraction from the sample, purification, PCR amplification, novel dielectrophoretic sorting of the DNA molecules, and finally detection. The overview is given of the technologies which are available to make the integration on a single chip possible. The microfluidic technologies that are used to manipulate the sample and other chemical reagents are already known and in this text they are analyzed in terms of their feasibility in the on-chip system integration. These microfluidic technologies include, but are not limited to, microvalves, micromixers, micropumps, and chambers for PCR amplification. The novelty in the DNA analysis brought by Doctor-on-a-Chip is the way in which the different DNA molecules in the sample (for example, human and virus DNA) are sorted into different populations. This is done by means of dielectrophoresis – the force experienced by dielectric particles (such as DNA molecules) when subject to a non-uniform electric field. Different DNA molecules within a sample experience different dielectrophoretic forces within the same electric field, which makes their separation, and therefore detection, possible. In this text, the emphasis is put on numerical modelling of the dielectrophoretic effect on biological particles. The importance of numerical modelling lies in the fact that with the accurate model it is easier to design systems of microelectrodes for dielectrophoretic separation, and tune their sub-micrometre features to achieve the maximum separation efficacy. The numerical model described in this text is also experimentally verified with the novel microelectrodes design for dielectrophoretic separation, which is successfully used to separate the mixture of different particles in the micron and sub-micron range