On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

Cross-entropy optimizer: a new tool to study precession in astrophysical jets

Evidence of jet precession in many galactic and extragalactic sources has been reported in the literature. Much of this evidence is based on studies of the kinematics of the jet knots, which depends on the correct identification of the components to determine their respective proper motions and position angles on the plane of the sky. Identification problems related to fitting procedures, as well as observations poorly sampled in time, may influence the follow-up of the components in time, which consequently might contribute to a misinterpretation of the data. In order to deal with these limitations, we introduce a very powerful statistical tool to analyse jet precession: the cross-entropy method for continuous multi-extremal optimization. Only based on the raw data of the jet components (right ascension and declination offsets from the core), the cross-entropy method searches for the precession model parameters that better represent the data. In this work we present a large number of tests to validate this technique, using synthetic precessing jets built from a given set of precession parameters. With the aim of recovering these parameters, we applied the cross-entropy method to our precession model, varying exhaustively the quantities associated with the method. Our results have shown that even in the most challenging tests, the cross-entropy method was able to find the correct parameters within a 1 per cent level. Even for a non-precessing jet, our optimization method could point out successfully the lack of precession.

MODELING VERY LONG BASELINE INTERFEROMETRIC IMAGES WITH THE CROSS-ENTROPY GLOBAL OPTIMIZATION TECHNIQUE

We present a new technique for obtaining model fittings to very long baseline interferometric images of astrophysical jets. The method minimizes a performance function proportional to the sum of the squared difference between the model and observed images. The model image is constructed by summing N(s) elliptical Gaussian sources characterized by six parameters: two-dimensional peak position, peak intensity, eccentricity, amplitude, and orientation angle of the major axis. We present results for the fitting of two main benchmark jets: the first constructed from three individual Gaussian sources, the second formed by five Gaussian sources. Both jets were analyzed by our cross-entropy technique in finite and infinite signal-to-noise regimes, the background noise chosen to mimic that found in interferometric radio maps. Those images were constructed to simulate most of the conditions encountered in interferometric images of active galactic nuclei. We show that the cross-entropy technique is capable of recovering the parameters of the sources with a similar accuracy to that obtained from the very traditional Astronomical Image Processing System Package task IMFIT when the image is relatively simple (e. g., few components). For more complex interferometric maps, our method displays superior performance in recovering the parameters of the jet components. Our methodology is also able to show quantitatively the number of individual components present in an image. An additional application of the cross-entropy technique to a real image of a BL Lac object is shown and discussed. Our results indicate that our cross-entropy model-fitting technique must be used in situations involving the analysis of complex emission regions having more than three sources, even though it is substantially slower than current model-fitting tasks (at least 10,000 times slower for a single processor, depending on the number of sources to be optimized). As in the case of any model fitting performed in the image plane, caution is required in analyzing images constructed from a poorly sampled (u, v) plane.

A geometric mass-preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)-based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE-based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well-suited for the highly stretched curvilinear grids used in CFD simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.

Iterative strong coupling of dimensionally heterogeneous models

In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Epidemics in networks of spatially correlated three-dimensional root-branching structures

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected- recovered (`SIR`) epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Esophageal Ulcer in Brazilian Patients with HIV: Prevalence and Comparative Analysis Among Diagnostic Methods

Esophageal ulcer (EU) represents an important comorbidity in AIDS. We evaluated the prevalence of EU, the accuracy of the endoscopic and histologic methods used to investigate viral EU in HIV-positive Brazilian patients and the numerical relevance of tissue sampling. A total of 399 HIV-positive patients underwent upper gastrointestinal (UGI) endoscopy. HIV-positive patients with EU determined by UGI endoscopy followed by biopsies were analyzed by the hematoxylin-eosin (HE) and immunohistochemical (IH) methods. EU was detected in 41 patients (mean age, 39.2 years; 23 males), with a prevalence of 10.27%. The median CD4 count was 49 cells/mm(3) (range, 1-361 cells/mm(3)) and the viral load was 58,869 copies per milliliter (range, 50-77,3290 copies per milliliter). UGI endoscopy detected 29 of 41 EU suggestive of cytomegalovirus (CMV) infection and 7 of 41 indicating herpes simplex virus (HSV) infection. HE histology confirmed 4 of 29 ulcers induced by CMV, 2 of 7 induced by HSV, and 1 of 7 induced by HSV plus CMV. IH for CMV and HSV confirmed the HE findings and detected one additional CMV-induced case. UGI endoscopy showed 100% sensitivity and 15% specificity for the diagnosis of EU due to CMV or HSV compared to HE and IH. HE proved to be an adequate method for etiologic evaluation, with 87% sensitivity and 100% specificity compared to IH. The number of samples did not influence the etiologic evaluation. The data support the importance of IH as a complementary method for HE in the diagnosis of EU of viral etiology.

PRECESSING JETS AND X-RAY BUBBLES FROM NGC 1275 (3C 84) IN THE PERSEUS GALAXY CLUSTER: A VIEW FROM THREE-DIMENSIONAL NUMERICAL SIMULATIONS

The Perseus galaxy cluster is known to present multiple and misaligned pairs of cavities seen in X-rays, as well as twisted kiloparsec-scale jets at radio wavelengths; both morphologies suggest that the active galactic nucleus (AGN) jet is subject to precession. In this work, we performed three-dimensional hydrodynamical simulations of the interaction between a precessing AGN jet and the warm intracluster medium plasma, whose dynamics are coupled to a Navarro-Frenk-White dark matter gravitational potential. The AGN jet inflates cavities that become buoyantly unstable and rise up out of the cluster core. We found that under certain circumstances precession can originate multiple pairs of bubbles. For the physical conditions in the Perseus cluster, multiple pairs of bubbles are obtained for a jet precession opening angle >40 degrees acting for at least three precession periods, reproducing both radio and X-ray maps well. Based on such conditions, assuming that the Bardeen-Peterson effect is dominant, we studied the evolution of the precession opening angle of this system. We were able to constrain the ratio between the accretion disk and the black hole angular momenta as 0.7-1.4. We were also able to constrain the present precession angle to 30 degrees-40 degrees, as well as the approximate age of the inflated bubbles to 100-150 Myr.

The merging cluster Abell 1758 revisited: multi-wavelength observations and numerical simulations

Context. Cluster properties can be more distinctly studied in pairs of clusters, where we expect the effects of interactions to be strong. Aims. We here discuss the properties of the double cluster Abell 1758 at a redshift z similar to 0.279. These clusters show strong evidence for merging. Methods. We analyse the optical properties of the North and South cluster of Abell 1758 based on deep imaging obtained with the Canada-France-Hawaii Telescope (CFHT) archive Megaprime/Megacam camera in the g' and r' bands, covering a total region of about 1.05 x 1.16 deg(2), or 16.1 x 17.6 Mpc(2). Our X-ray analysis is based on archive XMM-Newton images. Numerical simulations were performed using an N-body algorithm to treat the dark-matter component, a semi-analytical galaxy-formation model for the evolution of the galaxies and a grid-based hydrodynamic code with a parts per million (PPM) scheme for the dynamics of the intra-cluster medium. We computed galaxy luminosity functions (GLFs) and 2D temperature and metallicity maps of the X-ray gas, which we then compared to the results of our numerical simulations. Results. The GLFs of Abell 1758 North are well fit by Schechter functions in the g' and r' bands, but with a small excess of bright galaxies, particularly in the r' band; their faint-end slopes are similar in both bands. In contrast, the GLFs of Abell 1758 South are not well fit by Schechter functions: excesses of bright galaxies are seen in both bands; the faint-end of the GLF is not very well defined in g'. The GLF computed from our numerical simulations assuming a halo mass-luminosity relation agrees with those derived from the observations. From the X-ray analysis, the most striking features are structures in the metal distribution. We found two elongated regions of high metallicity in Abell 1758 North with two peaks towards the centre. In contrast, Abell 1758 South shows a deficit of metals in its central regions. Comparing observational results to those derived from numerical simulations, we could mimic the most prominent features present in the metallicity map and propose an explanation for the dynamical history of the cluster. We found in particular that in the metal-rich elongated regions of the North cluster, winds had been more efficient than ram-pressure stripping in transporting metal-enriched gas to the outskirts. Conclusions. We confirm the merging structure of the North and South clusters, both at optical and X-ray wavelengths.

Experimentally Witnessing the Quantumness of Correlations

The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

We assess the performance of three unconditionally stable finite-difference time-domain (FDTD) methods for the modeling of doubly dispersive metamaterials: 1) locally one-dimensional FDTD; 2) locally one-dimensional FDTD with Strang splitting; and (3) alternating direction implicit FDTD. We use both double-negative media and zero-index media as benchmarks.