Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Coincidence theorems and its applications to equilibrium problems

Given two maps h : X x K -> R and g : X -> K such that, for all x is an element of X, h(x, g(x)) = 0, we consider the equilibrium problem of finding (x) over tilde is an element of X such that h((x) over tilde, g(x)) >= 0 for every x is an element of X. This question is related to a coincidence problem.

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod-Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark`s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm. [DOI: 10.1115/1.3142903]

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

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.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

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.

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.

Adding value to the meat of spent laying hens manufacturing sausages with a healthy appeal

The aim of this study was to evaluate the viability of the use of spent laying hens' meat in the manufacturing of mortadella-type sausages with healthy appeal by using vegetable oil instead of animal fat. 120 Hy-line® layer hens were distributed in a completely randomized design into two treatments of six replicates with ten birds each. The treatments were birds from light Hy-line® W36 and semi-heavy Hy-line® Brown lines. Cold carcass, wing, breast and leg fillets yields were determined. Dry matter, protein, and lipid contents were determined in breast and leg fillets. The breast and legg fillets of three replicates per treatment were used to manufacture mortadella. After processing, sausages were evaluated for proximal composition, objective color, microbiological parameters, fatty acid profile and sensory acceptance. The meat of light and semi-heavy spent hens presented good yield and composition, allowing it to be used as raw material for the manufacture of processed products. Mortadellas were safe from microbiological point of view, and those made with semi-heavy hens fillets were redder and better accepted by consumers. Values for all sensory attributes were evaluated over score 5 (neither liked nor disliked). Both products presented high polyunsaturated fatty acid contents and good polyunsaturated to saturated fatty acid ratio. The excellent potential for the use of meat from spent layer hens of both varieties in the manufacturing of healthier mortadella-type sausage was demonstrated.

Benign focal seizures of adolescence and neuropsychological findings in patients from community

RATIONALE: Benign focal seizures of adolescence (BFSA) described by Loiseau et al in 1972, is considered a rare entity, but maybe underdiagnosed. Although mild neuropsychological deficits have been reported in patients with benign epilepsies of childhood, these evaluations have not so far been described in BFSA. The aim of this study is to evaluate neuropsychological functions in BFSA with new onset seizures (<12 months). METHODS: Eight patients with BFSA (according to Loiseau et al, 1972, focal or secondarily tonic clonic generalized seizures between the ages of 10-18 yrs., normal neurologic examination, normal EEG or with mild focal abnormalities) initiated in the last 12 months were studied between July 2008 to May 2009. They were referred from the Pediatric Emergency Section of the Hospital Universitário of the University of Sao Paulo, a secondary care regionalized facility located in a district of middle-low income in Sao Paulo city, Brazil. The study was approved by the Ethics Committee of the Institution. All patients performed neurological, EEG, brain CT and neuropsychological evaluation which consisted of Raven's Special Progressive Matrices - General and Special Scale (according to different ages), Wechsler Children Intelligence Scale-WISC III with ACID Profile, Trail Making Test A/B, Stroop Test, Bender Visuo-Motor Test, Rey Complex Figure, Rey Auditory Verbal Learning Test-RAVLT, Boston Naming Test, Fluency Verbal for phonological and also conceptual patterns - FAS/Animals and Hooper Visual Organization Test. For academic achievement, we used a Brazilian test for named "Teste do Desempenho Escolar", which evaluates abilities to read, write and calculate according to school grade. RESULTS: There were 2 boys and 6 girls, with ages ranging from 10 yrs. 9 m to 14 yrs. 3 m. Most (7/8) of the patients presented one to two seizures and only three of them received antiepileptic drugs (AEDs). Six had mild EEG focal abnormalities and all had normal brain CT. All were literate, attended regular public schools and scored in a median range for IQ, and seven showed discrete higher scores for the verbal subtests. There were low scores for attention in different modalities in six patients, mainly in alternated attention as well as inhibitory subtests (Stroop test and Trail Making Test part B). Four of the latter cases who showed impairment both in alternated and inhibitory attention were not taking AEDs. Visual memory was impaired in five patients (Rey Complex Figure). Executive functions analysis showed deficits in working memory in five, mostly observed in Digits Indirect Order and Arithmetic tests (WISC III). Reading and writing skills were below the expected average for school grade in six patients according to the achievement scholar performance test utilized. One patient of this series who had the best scores in all tests was taking phenobarbital. CONCLUSIONS: Neuropsychological imbalance between normal IQ and mild dysfunctions such as in attention domain and in some executive abilities like working memory and planning, as well as difficulties in visual memory and in reading and writing, were described in this group of patients with BFSA from community. This may reflect mild higher level neurological dysfunctions in adolescence idiopathic focal seizures probably caused by an underlying dysmaturative epileptogenic process. Although academic problems often have multiple causes, a specific educational approach may be necessary in these adolescents, in order to improve their scholastic achievements, helping in this way, to decrease the stigma associated to epileptic seizures in the community.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.