Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Open Circuit Interaction of Formic Acid with Oxidized Pt Surfaces: Experiments, Modeling, and Simulations

We report in this work the study of the interaction between formic acid and an oxidized platinum surface under open circuit conditions. The investigation was carried out with the aid of in situ infrared spectroscopy, and results analyzed in terms of a mathematical model and numerical simulations. It has been found that during the first seconds of the interaction a small amount of CO(2) is produced and absolutely no adsorbed CO was observed. A sudden drop in potential then follows, which is accompanied by a steep increase first of CO(2) production and then by adsorbed CO. The steep transient was rationalized in terms of an autocatalytic production of free platinum sites which enhances the overall rate of reaction. Modeling and simulation showed nearly quantitative agreement with the experimental observations and provided further insight into some experimentally inaccessible variables such as surface free sites. Finally, based on the understanding provided from the combined experimental and theoretical approach, we discuss the general aspects influencing the open circuit transient.

Migração lateral da desembocadura do Rio Itapocú, SC, Brasil: evolução morfológica e condicionantes físicas

Desembocaduras são ambientes bastante dinâmicos e sujeitos à complexa interação entre fatores estabilizadores e desestabilizadores. Dependendo dessa interação, desembocaduras podem apresentar a tendência de migração ao longo de barreiras arenosas. Um dos mecanismos mais eficientes de transporte de sedimento paralelo à costa, e consequentemente migração de canais, são as correntes longitudinais geradas pelas ondas se aproximando obliquamente à costa. A motivação do presente trabalho é entender o comportamento morfodinâmico do sistema de desembocadura do rio Itapocú, localizado no centro-norte de Santa Catarina (SC), frente aos processos forçantes que atuam na sua migração ao longo da linha de costa. A morfologia dos pontais arenosos foi obtida a partir de levantamentos morfológicos com o uso de DGPS. Para analisar a refração de ondas foi utilizado o modelo numérico MIKE 21 SW, sendo considerados como condições de contorno os dados de ondas referentes ao ano de 2002 e os dados de ondas previstos referentes ao período de coleta. Os dados de saída do modelo foram utilizados para estimar a deriva litorânea potencial na região. Os resultados morfológicos obtidos demonstraram uma migração da desembocadura para o norte durante o período analisado, sendo mais intenso durante o inverno e o verão. Ondas incidentes do quadrante sul sofreram mais o fenômeno da refração e as ondas de leste apresentaram menor variação angular ao se aproximarem à costa. A deriva litorânea potencial anual para os dados de ondas de 2002 apresentou sentido norte-sul, com inversão de sentido durante o outono. Utilizando os dados de ondas previstas para o período dos levantamentos, a deriva litorânea potencial estimada apresentou sentido sul-norte, concordando com a migração observada. Na região próxima a desembocadura, nos pontais arenosos, a deriva potencial apresentou direção para o norte durante todas as estações. Os dados de descarga fluvial não apresentaram influência na migração do canal, porém apresentaram uma relação com a largura do mesmo sazonalmente.Os dados de morfologia juntamente com os dados de deriva litorânea referentes às ondas de 2004/2005 mostraram claramente a migração do canal para o norte sendo a deriva a principal contribuinte para a migração da desembocadura.

Brazilian offshore wave climate based on NWW3 reanalysis

This paper provides a description of the wave climate off the Brazilian coast based on an eleven-year time series (Jan/1997-Dec/2007) obtained from the NWW3 operational model hindcast reanalysis. Information about wave climate in Brazilian waters is very scarce and mainly based on occasional short-term observations, the present analysis being the first covering such temporal and spatial scales. To define the wave climate, six sectors were defined and analyzed along the Brazilian shelf-break: South (W1), Southeast (W2), Central (W3), East (W4), Northeast (W5) and North (W6). W1, W2 and W3 wave regimes are determined by the South Atlantic High (SAH) and the passage of synoptic cold fronts; W4, W5 and W6 are controlled by the Intertropical Convergence Zone (ITCZ) and its meridional oscillation. The most energetic waves are from the S, generated by the strong winds associated to the passage of cold fronts, which mainly affect the southern region. Wave power presents a decrease in energy levels from south to north, with its annual variation showing that the winter months are the most energetic in W1 to W4, while in W5 and W6 the most energetic conditions occur during the austral summer. The information presented here provides boundary conditions for studies related to coastal processes, fundamental for a better understanding of the Brazilian coastal zone.

PARTITIONED ANALYSIS FOR DIMENSIONALLY-HETEROGENEOUS HYDRAULIC NETWORKS

In this work an iterative strategy is developed to tackle the problem of coupling dimensionally-heterogeneous models in the context of fluid mechanics. The procedure proposed here makes use of a reinterpretation of the original problem as a nonlinear interface problem for which classical nonlinear solvers can be applied. Strong coupling of the partitions is achieved while dealing with different codes for each partition, each code in black-box mode. The main application for which this procedure is envisaged arises when modeling hydraulic networks in which complex and simple subsystems are treated using detailed and simplified models, correspondingly. The potentialities and the performance of the strategy are assessed through several examples involving transient flows and complex network configurations.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Transport properties of single vacancies in nanotubes

We present density of states and electronic transport calculations of single vacancies in carbon nanotubes. We confirm that the defect reconstructs into a pentagon and a nonagon, following the removal of a single carbon atom. This leads to the formation of a dangling bond. Finally, we demonstrate that care must be taken when calculating the density of states of impurities in one-dimensional systems in general. Traditional treatments of these systems using periodic boundary conditions leads to the formation of minigaps even in the limit of large unit cells.

Classical noncommutative electrodynamics with external source

In a U(1)(*)-noncommutative gauge field theory we extend the Seiberg-Witten map to include the (gauge-invariance-violating) external current and formulate-to the first order in the noncommutative parameter-gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size a, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, 1/r included, from the solutions. The static charge proves to be a magnetic dipole, with its magnetic moment being inversely proportional to its size a. The external magnetic field modifies the long-range Coulomb field and some electromagnetic form factors. We also analyze the ambiguity in the Seiberg-Witten map and show that at least to the order studied here it is equivalent to the ambiguity of adding a homogeneous solution to the current-conservation equation.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

Dynamical Casimir effect for a massless scalar field between two concentric spherical shells

In this work we consider the dynamical Casimir effect for a massless scalar field-under Dirichlet boundary conditions-between two concentric spherical shells. We obtain a general expression for the average number of particle creation, for an arbitrary law of radial motion of the spherical shells, using two distinct methods: by computing the density operator of the system and by calculating the Bogoliubov coefficients. We apply our general expression to breathing modes: when only one of the shells oscillates and when both shells oscillate in or out of phase. Since our results were obtained in the framework of the perturbation theory, under resonant breathing modes they are restricted to a short-time approximation. We also analyze the number of particle production and compare it with the results for the case of plane geometry.

Comparison of univariate and multivariate calibration for the determination of micronutrients in pellets of plant materials by laser induced breakdown spectrometry

The application of laser induced breakdown spectrometry (LIBS) aiming the direct analysis of plant materials is a great challenge that still needs efforts for its development and validation. In this way, a series of experimental approaches has been carried out in order to show that LIBS can be used as an alternative method to wet acid digestions based methods for analysis of agricultural and environmental samples. The large amount of information provided by LIBS spectra for these complex samples increases the difficulties for selecting the most appropriated wavelengths for each analyte. Some applications have suggested that improvements in both accuracy and precision can be achieved by the application of multivariate calibration in LIBS data when compared to the univariate regression developed with line emission intensities. In the present work, the performance of univariate and multivariate calibration, based on partial least squares regression (PLSR), was compared for analysis of pellets of plant materials made from an appropriate mixture of cryogenically ground samples with cellulose as the binding agent. The development of a specific PLSR model for each analyte and the selection of spectral regions containing only lines of the analyte of interest were the best conditions for the analysis. In this particular application, these models showed a similar performance. but PLSR seemed to be more robust due to a lower occurrence of outliers in comparison to the univariate method. Data suggests that efforts dealing with sample presentation and fitness of standards for LIBS analysis must be done in order to fulfill the boundary conditions for matrix independent development and validation. (C) 2009 Elsevier B.V. All rights reserved.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Proposal of a test specimen to evaluate the shear strength of vertical interfaces of running bond masonry walls

There is no normalized test to assess the shear strength of vertical interfaces of interconnected masonry walls. The approach used to evaluate this strength is normally indirect and often unreliable. The aim of this study is to propose a new test specimen to eliminate this deficiency. The main features of the proposed specimen are failure caused by shear stress on the vertical interface and a small number of units (blocks). The paper presents a numerical analysis based on the finite element method, with the purpose of showing the theoretical performance of the designed specimen, in terms of its geometry, boundary conditions, and loading scheme, and describes an experimental program using the specimen built with full- and third-scale clay blocks. The main conclusions are that the proposed specimen is easy to build and is appropriate to evaluate the sheaf strength of vertical interfaces of masonry walls.

Parametrical study of masonry walls subjected to in-plane loading through numerical modeling

This paper deals with the numerical assessment of the influence of parameters such as pre-compression level, aspect ratio, vertical and horizontal reinforcement ratios and boundary conditions on the lateral strength of masonry walls under in-plane loading. The numerical study is performed through the software DIANA (R) based on the Finite Element Method. The validation of the numerical model is carried out from a database of available experimental results on masonry walls tested under cyclic lateral loading. Numerical results revealed that boundary conditions play a central role on the lateral behavior of masonry walls under in-plane loading and determine the influence of level of pre-compression as well as the reinforcement ratio on the wall strength. The lateral capacity of walls decreases with the increase of aspect ratio and with the decrease of pre-compression. Vertical steel bars appear to have almost no influence in the shear strength of masonry walls and horizontal reinforcement only increases the lateral strength of masonry walls if the shear response of the walls is determinant for failure, which is directly related to the boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.