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.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

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.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

On paternalistic leadership fit: exploring cross-cultural endorsement, leader-follower fit, and the boundary role of organizational culture

Although cross-cultural leadership research has thrived in international business literature, little attention has been devoted to understanding the effectiveness of non-western theories beyond their original contexts. The purpose of this study is to examine the cross-cultural endorsement of paternalistic leadership, an emerging non-western leadership theory, using data from GLOBE project. Using multigroup confirmatory factor analyses we found measurement equivalence of a scale derived from GLOBE’s data, which enabled us to compare the endorsement of paternalistic leadership dimensions across 10 cultural clusters and 55 societies. Our study revealed that there are significant differences in the importance societies give to each dimension, suggesting that paternalism as leadership style is not universally nor homogeneously endorsed. Furthermore, results suggest that different patterns of endorsement of each of these dimensions give rise to idiosyncratic shades of paternalistic leadership across societies. Implications for theory and future research on international business are discussed.

Design of boundary-scan testing in CMOS image sensors for industrial applications: internship repor

Tests on printed circuit boards and integrated circuits are widely used in industry,resulting in reduced design time and cost of a project. The functional and connectivity tests in this type of circuits soon began to be a concern for the manufacturers, leading to research for solutions that would allow a reliable, quick, cheap and universal solution. Initially, using test schemes were based on a set of needles that was connected to inputs and outputs of the integrated circuit board (bed-of-nails), to which signals were applied, in order to verify whether the circuit was according to the specifications and could be assembled in the production line. With the development of projects, circuit miniaturization, improvement of the production processes, improvement of the materials used, as well as the increase in the number of circuits, it was necessary to search for another solution. Thus Boundary-Scan Testing was developed which operates on the border of integrated circuits and allows testing the connectivity of the input and the output ports of a circuit. The Boundary-Scan Testing method was converted into a standard, in 1990, by the IEEE organization, being known as the IEEE 1149.1 Standard. Since then a large number of manufacturers have adopted this standard in their products. This master thesis has, as main objective: the design of Boundary-Scan Testing in an image sensor in CMOS technology, analyzing the standard requirements, the process used in the prototype production, developing the design and layout of Boundary-Scan and analyzing obtained results after production. Chapter 1 presents briefly the evolution of testing procedures used in industry, developments and applications of image sensors and the motivation for the use of architecture Boundary-Scan Testing. Chapter 2 explores the fundamentals of Boundary-Scan Testing and image sensors, starting with the Boundary-Scan architecture defined in the Standard, where functional blocks are analyzed. This understanding is necessary to implement the design on an image sensor. It also explains the architecture of image sensors currently used, focusing on sensors with a large number of inputs and outputs.Chapter 3 describes the design of the Boundary-Scan implemented and starts to analyse the design and functions of the prototype, the used software, the designs and simulations of the functional blocks of the Boundary-Scan implemented. Chapter 4 presents the layout process used based on the design developed on chapter 3, describing the software used for this purpose, the planning of the layout location (floorplan) and its dimensions, the layout of individual blocks, checks in terms of layout rules, the comparison with the final design and finally the simulation. Chapter 5 describes how the functional tests were performed to verify the design compliancy with the specifications of Standard IEEE 1149.1. These tests were focused on the application of signals to input and output ports of the produced prototype. Chapter 6 presents the conclusions that were taken throughout the execution of the work.

Boundary decisions of the firm: make, buy, cooperate

Firms are not atomistic hierarchies only linked with one another at arm’s-length distance in markets. Instead, a myriad of long-lived, highly cooperative relationships between suppliers and customers are pervasively found in the B2B world. And it is within those enmeshed relationships and networks that the co-evolution of capabilities and business specialisms is brought about and developed. If that is the actual ‘topography’ of the business landscape, then the coordination of economic activities in general, and the boundary decisions of each and every firm in particular, are unlikely to be reduced to a (dual) choice between ‘making’ or ‘buying’. Inter-firm cooperation is in itself a third governance structure, in alternative to the hierarchical and the market modes of coordination. And, what is also equally important to note, it is through the make-or-buy-or-cooperate decisions that the (embedded) firm is able to change its nature and scope, redefine its (fuzzy) boundaries, and thus adapt to an ever-changing business setting.

Superconducting boundary conditions for mesoscopic circular samples

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

Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.