Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.

A transmission problem for beams on nonlinear supports

A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Haemodynamic effects of aliskiren in decompensated severe heart failure

Aim: The renin-angiotensin-aldosterone system (RAAS) has dual pathways to angiotensin II production; therefore, multiple blockages may be useful in heart failure. In this study, we evaluated the short-term haemodynamic effects of aliskiren, a direct renin inhibitor, in patients with decompensated severe heart failure who were also taking angiotensin-converting enzyme ( ACE) inhibitors. Materials and methods: A total of 16 patients (14 men, two women, mean age: 60.3 years) were enrolled in the study. The inclusion criteria included hospitalisation due to decompensated heart failure, ACE inhibitor use, and an ejection fraction < 40% (mean: 21.9 +/- 6.7%). The exclusion criteria were: creatinine > 2.0 mg/dl, cardiac pacemaker, serum K+ > 5.5 mEq/l, and systolic blood pressure < 70 mmHg. Patients either received 150 mg/d aliskiren for 7 days (aliskiren group, n = 10) or did not receive aliskiren (control group, n = 6). Primary end points were systemic vascular resistance and cardiac index values. Repeated-measures analysis of variance (ANOVA) was used to assess variables before and after intervention. A two-sided p-value < 0.05 was considered statistically significant. Results: Compared to pre-intervention levels, systemic vascular resistance was reduced by 20.4% in aliskiren patients, but it increased by 2.9% in control patients (p = 0.038). The cardiac index was not significantly increased by 19.0% in aliskiren patients, but decreased by 8.4% in control patients (p = 0.127). No differences in the pulmonary capillary or systolic blood pressure values were observed between the groups. Conclusion: Aliskiren use reduced systemic vascular resistance in patients with decompensated heart failure taking ACE inhibitors.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Effectiveness of low-level laser therapy for patients with carpal tunnel syndrome: design of a randomized single-blinded controlled trial

Background: Carpal tunnel syndrome is the most common neuropathy in the upper extremity, resulting from the compression of the median nerve at wrist level. Clinical studies are essentials to present evidence on therapeutic resources use at early restoration on peripheral nerve functionality. Low-level laser therapy has been widely investigated in researches related to nerve regeneration. Therefore, it is suggested that the effect of low-level laser therapy associated with other conservative rehabilitation techniques may positively affect symptoms and overall hand function in compressive neuropathies such as carpal tunnel syndrome. The aim of this study is to evaluate the effectiveness of low-level laser therapy in addition to orthoses therapy and home orientations in patients with carpal tunnel syndrome. Methods/Design: Patients older than 18 years old will be included, with clinical diagnosis of carpal tunnel syndrome, excluding comorbidies. A physiotherapist will conduct intervention, with a blinding evaluator. Randomization will be applied to allocate the patients in each group: with association or not to low-level laser therapy. All of them will be submitted to orthoses therapy and home orientations. Outcome will be assessed through: pain visual analogic scale, Semmes Weinstein monofilaments (TM) threshold sensibility test, Pinch Gauge T, Boston Carpal Tunnel Questionnaire and two point discrimination test. Discussion: This paper describes the design of a randomized controlled trial, which aim to assess the effectiveness of conservative treatment added to low-level laser therapy for patients with carpal tunnel syndrome. Trial registration: Brazilian Clinical Trials Registry (ReBec) - 75ddtf / Universal Trial Number: U1111-1121-5184

Long-term cardiac changes in patients with systemic lupus erythematosus

Abstract Background The aim of this study was evaluate the late-onset repercussions of heart alterations of patients with systemic lupus erythematosus (SLE) after a 13-year follow up. Methods A historical prospective study was carried out involving the analysis of data from the charts of patients with a confirmed diagnosis of lupus in follow up since 1998. The 13-year evolution was systematically reviewed and tabulated to facilitate the interpretation of the data. Results Forty-eight patient charts were analyzed. Mean patient age was 34.5 ± 10.8 years at the time of diagnosis and 41.0 ± 10.3 years at the time of the study (45 women and 3 men). Eight deaths occurred in the follow-up period (two due to heart problems). Among the alterations found on the complementary exams, 46.2% of cases demonstrated worsening at reevaluation and four patients required a heart catheterization. In these cases, coronary angioplasty was performed due to the severity of the obstructions and one case required a further catheterization, culminating in the need for surgical myocardial revascularization. Conclusion The analysis demonstrated progressive heart impairment, with high rates of alterations on conventional complementary exams, including the need for angioplasty or revascularization surgery in four patients. These findings indicate the need for rigorous cardiac follow up in patients with systemic lupus erythematosus.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.