A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Formulação fisicamente não - linear da teoria generalizada de vigas

Dissertação para obtenção do grau de Mestre em Engenharia Civil

Statistical learning theory for geospatial data. Case study: Aral sea

In recent years there has been an explosive growth in the development of adaptive and data driven methods. One of the efficient and data-driven approaches is based on statistical learning theory (Vapnik 1998). The theory is based on Structural Risk Minimisation (SRM) principle and has a solid statistical background. When applying SRM we are trying not only to reduce training error ? to fit the available data with a model, but also to reduce the complexity of the model and to reduce generalisation error. Many nonlinear learning procedures recently developed in neural networks and statistics can be understood and interpreted in terms of the structural risk minimisation inductive principle. A recent methodology based on SRM is called Support Vector Machines (SVM). At present SLT is still under intensive development and SVM find new areas of application (www.kernel-machines.org). SVM develop robust and non linear data models with excellent generalisation abilities that is very important both for monitoring and forecasting. SVM are extremely good when input space is high dimensional and training data set i not big enough to develop corresponding nonlinear model. Moreover, SVM use only support vectors to derive decision boundaries. It opens a way to sampling optimization, estimation of noise in data, quantification of data redundancy etc. Presentation of SVM for spatially distributed data is given in (Kanevski and Maignan 2004).

Les modèles vectoriels et multiplicatifs avec erreurs non-négatives de séries chronologiques.

L'objectif du présent mémoire vise à présenter des modèles de séries chronologiques multivariés impliquant des vecteurs aléatoires dont chaque composante est non-négative. Nous considérons les modèles vMEM (modèles vectoriels et multiplicatifs avec erreurs non-négatives) présentés par Cipollini, Engle et Gallo (2006) et Cipollini et Gallo (2010). Ces modèles représentent une généralisation au cas multivarié des modèles MEM introduits par Engle (2002). Ces modèles trouvent notamment des applications avec les séries chronologiques financières. Les modèles vMEM permettent de modéliser des séries chronologiques impliquant des volumes d'actif, des durées, des variances conditionnelles, pour ne citer que ces applications. Il est également possible de faire une modélisation conjointe et d'étudier les dynamiques présentes entre les séries chronologiques formant le système étudié. Afin de modéliser des séries chronologiques multivariées à composantes non-négatives, plusieurs spécifications du terme d'erreur vectoriel ont été proposées dans la littérature. Une première approche consiste à considérer l'utilisation de vecteurs aléatoires dont la distribution du terme d'erreur est telle que chaque composante est non-négative. Cependant, trouver une distribution multivariée suffisamment souple définie sur le support positif est plutôt difficile, au moins avec les applications citées précédemment. Comme indiqué par Cipollini, Engle et Gallo (2006), un candidat possible est une distribution gamma multivariée, qui impose cependant des restrictions sévères sur les corrélations contemporaines entre les variables. Compte tenu que les possibilités sont limitées, une approche possible est d'utiliser la théorie des copules. Ainsi, selon cette approche, des distributions marginales (ou marges) peuvent être spécifiées, dont les distributions en cause ont des supports non-négatifs, et une fonction de copule permet de tenir compte de la dépendance entre les composantes. Une technique d'estimation possible est la méthode du maximum de vraisemblance. Une approche alternative est la méthode des moments généralisés (GMM). Cette dernière méthode présente l'avantage d'être semi-paramétrique dans le sens que contrairement à l'approche imposant une loi multivariée, il n'est pas nécessaire de spécifier une distribution multivariée pour le terme d'erreur. De manière générale, l'estimation des modèles vMEM est compliquée. Les algorithmes existants doivent tenir compte du grand nombre de paramètres et de la nature élaborée de la fonction de vraisemblance. Dans le cas de l'estimation par la méthode GMM, le système à résoudre nécessite également l'utilisation de solveurs pour systèmes non-linéaires. Dans ce mémoire, beaucoup d'énergies ont été consacrées à l'élaboration de code informatique (dans le langage R) pour estimer les différents paramètres du modèle. Dans le premier chapitre, nous définissons les processus stationnaires, les processus autorégressifs, les processus autorégressifs conditionnellement hétéroscédastiques (ARCH) et les processus ARCH généralisés (GARCH). Nous présentons aussi les modèles de durées ACD et les modèles MEM. Dans le deuxième chapitre, nous présentons la théorie des copules nécessaire pour notre travail, dans le cadre des modèles vectoriels et multiplicatifs avec erreurs non-négatives vMEM. Nous discutons également des méthodes possibles d'estimation. Dans le troisième chapitre, nous discutons les résultats des simulations pour plusieurs méthodes d'estimation. Dans le dernier chapitre, des applications sur des séries financières sont présentées. Le code R est fourni dans une annexe. Une conclusion complète ce mémoire.

STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories

Torque in mooring chain. Part 1: Background and theory

Chain in both its forms - common (or stud-less) and stud-link - has many engineering applications. It is widely used as a component in the moorings of offshore floating systems, where its ruggedness and corrosion resistance make it an attractive choice. Chain exhibits some interesting behaviour in that when straight and subject to an axial load it does not twist or generate any torque, but if twisted or loaded when in a twisted condition it behaves in a highly non-linear manner, with the torque dependent upon the level of twist and axial load. Clearly an understanding of the way in which chains may behave and interact with other mooring components (such as wire rope, which also exhibits coupling between axial load and generated torque) when they are in service is essential. However, the sizes of chain that are in use in offshore moorings (typical bar diameters are 75 mm and greater) are too large to allow easy testing. This paper, which is in two parts, aims to address the issues and considerations relevant to torque in mooring chain. The first part introduces a frictionless theory that predicts the resultant torques and 'lift' in the links as non-dimensionalized functions of the angle of twist. Fortran code is presented in an Appendix, which allows the reader to make use of the analysis. The second part of the paper presents results from experimental work on both stud-less (41 mm) and stud-link (20.5 and 56 mm) chains. Torsional data are presented in both 'constant twist' and 'constant load' forms, as well as considering the lift between the links.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

An Anisotropic Model of Damage and Unilateral Effect for Brittle Materials

This work deals with the initial applications and formulation of an aniscitropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

A mixture theory based method for three-dimensional modeling of reinforce concrete members with embedded crack finite elements

The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 31) composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

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

Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

On non-ideal simple portal frame structural model: Experimental results under a non-ideal excitation

We present measurements of the non-linear oscillations of a portal frame foundation for a non-ideal motor. We consider a three-time redundant structure with two columns, clamped in their bases and a horizontal beam. An electrical unbalanced motor is mounted at mid span of the beam. Two non-linear phenomena are studied: a) mode saturation and energy transfer between modes; b) interaction between high amplitude motions of the structure and the rotation regime of a real limited power motor. The dynamic characteristics of the structure were chosen to have one-to-two internal resonance between the anti-symmetrical mode (sway motions) and the first symmetrical mode natural frequencies. As the excitation frequency reaches near resonance conditions with the 2nd natural frequency, the amplitude of this mode grows up to a certain level and then it saturates. The surplus energy pumped into the system is transferred to the sway mode, which experiences a sudden increase in its amplitude. Energy is transformed from low amplitude high frequency motion into high amplitude low frequency motion. Such a transformation is potentially dangerous.We consider the fact that real motors, such as the one used in this study, have limited power output. In this case, this energy source is said to be non-ideal, in contrast to the ideal source whose amplitude and frequency are independent of the motion of the structure. Our experimental research detected the Sommerfeld Effect: as the motor accelerates to reach near resonant conditions, a considerable part of its output energy is consumed to generate large amplitude motions of the structure and not to increase its own angular speed. For certain parameters of the system, the motor can get stuck at resonance not having enough power to reach higher rotation regimes. If some more power is available, jump phenomena may occur from near resonance to considerably higher motor speed regimes, no stable motions being possible between these two.

Conservative power theory discussion and evaluation by means of virtual instrumentation

Considering different single and multiphase circuits feeding linear and non-linear loads, this paper presents theoretical discussions and experimental evaluation of the recent Conservative Power Theory (CPT), by means of Virtual Instrumentation concepts. The main goal is to analyze the results of such power theory definitions under nonsinusoidal and unbalanced conditions, pointing out its major advantages, possible drawbacks or relevant aspects for discussion. © 2009 IEEE.