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.

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.

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.

Pre- and Postoperative Quantitative Analysis of Contour Abnormalities in Graves Upper Eyelid Retraction

Purpose: One of the most common problems of the surgical management of Graves upper eyelid retraction is the occurrence of eyelid contour abnormalities. In the present study, the postoperative contour of a large sample of eyelids of patients with Graves orbitopathy was measured. Methods: The postoperative upper eyelid contour of 62 eyes of 43 patients with Graves orbitopathy was subjectively classified by 3 experienced surgeons in 3 categories: poor, fair, and good. The shape of the eyelid contours in each category was then measured with a recently developed custom-made software by measuring multiple midpupil eyelid distances each 15 degrees along the palpebral fissure. The upper eyelid contour of 60 normal subjects was also quantified as a control group. Results: The mean ratio between the sum of the lateral and medial midpupil eyelid distances (lateral/medial ratio) was 1.10 +/- 0.11 standard deviation in controls and 1.15 +/- 0.13 standard deviation in patients. Postoperatively, the mean midpupil eyelid distance at 90 degrees was 4.16 +/- 1.13 mm standard deviation. The distribution lateral/medial ratios of the eyelids judged as having good contours was similar to the distribution of the controls with a modal value centered on the interval between 1.0 and 1.10. The distribution of lateral/medial ratios of the eyelids judged as having poor contour was bimodal, with eyelids with low and high lateral/medial ratios. Low lateral/medial ratios occurred when there was a lateral overcorrection, giving the eyelid a flat or a medial ptosis appearance. High lateral/medial ratios were due to a central or medial overcorrection or a lateral peak maintenance. Conclusions: Postoperative upper eyelid contour abnormalities can be quantified by comparing the sum of multiple midpupil eyelid distances of the lateral and medial sectors of the eyelid. Low and high lateral/medial ratios are anomalous and judged as unpleasant. (Ophthal Plast Reconstr Surg 2012;28:429-433)

A Comparative Wet Collapse Buckling Study for the Carcass Layer of Flexible Pipes

When there is a failure on the external sheath of a flexible pipe, a high value of hydrostatic pressure is transferred to its internal plastic layer and consequently to its interlocked carcass, leading to the possibility of collapse. The design of a flexible pipe must predict the maximum value of external pressure the carcass layer can be subjected to without collapse. This value depends on the initial ovalization due to manufacturing tolerances. To study that problem, two numerical finite element models were developed to simulate the behavior of the carcass subjected to external pressure, including the plastic behavior of the materials. The first one is a full 3D model and the second one is a 3D ring model, both composed by solid elements. An interesting conclusion is that both the models provide the same results. An analytical model using an equivalent thickness approach for the carcass layer was also constructed. A good correlation between analytical and numerical models was achieved for pre-collapse behavior but the collapse pressure value and post-collapse behavior were not well predicted by the analytical model. [DOI: 10.1115/1.4005185]

Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

Analysis of energy dissipation in stirred suspension polymerisation reactors using computational fluid dynamics

This work evaluates the spatial distribution of normalised rates of droplet breakage and droplet coalescence in liquidliquid dispersions maintained in agitated tanks at operation conditions normally used to perform suspension polymerisation reactions. Particularly, simulations are performed with multiphase computational fluid dynamics (CFD) models to represent the flow field in liquidliquid styrene suspension polymerisation reactors for the first time. CFD tools are used first to compute the spatial distribution of the turbulent energy dissipation rates (e) inside the reaction vessel; afterwards, normalised rates of droplet breakage and particle coalescence are computed as functions of e. Surprisingly, multiphase simulations showed that the rates of energy dissipation can be very high near the free vortex surfaces, which has been completely neglected in previous works. The obtained results indicate the existence of extremely large energy dissipation gradients inside the vessel, so that particle breakage occurs primarily in very small regions that surround the impeller and the free vortex surface, while particle coalescence takes place in the liquid bulk. As a consequence, particle breakage should be regarded as an independent source term or a boundary phenomenon. Based on the obtained results, it can be very difficult to justify the use of isotropic assumptions to formulate particle population balances in similar systems, even when multiple compartment models are used to describe the fluid dynamic behaviour of the agitated vessel. (C) 2011 Canadian Society for Chemical Engineering

Drag force in a strongly coupled anisotropic plasma

We calculate the drag force experienced by an in finitely massive quark propagating at constant velocity through an anisotropic, strongly coupled N = 4 plasma by means of its gravity dual. We find that the gluon cloud trailing behind the quark is generally misaligned with the quark velocity, and that the latter is also misaligned with the force. The drag coefficient mu can be larger or smaller than the corresponding isotropic value depending on the velocity and the direction of motion. In the ultra-relativistic limit we find that generically mu proportional to p. We discuss the conditions under which this behaviour may extend to more general situations.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Reddenings of Cepheids

The aim of this work is to derive precise reddenings for 31 Cepheids using multiphase high-resolution spectroscopic observations and literature-derived colors. Each individual reddening value was determined as a difference between the observed (B - V) value and a calculated (B - V) value based on Castelli stellar model atmospheres and atmosphere parameters (effective temperature and gravity) previously determined through high-resolution spectroscopic analysis. This procedure was repeated for all pulsational phases at which spectra were obtained (typically 11 spectra for each star). After that, the mean reddening value for a given Cepheid was obtained. The reddening values derived were compared to values based on the use of distances and multiband photometry, reaching the general conclusion that reddening derived in this manner agrees with those from other methods.

New Optimization Algorithms for Structural Reliability Analysis

Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on the HLRF, but uses a new differentiable merit function with Wolfe conditions to select step length in linear search. It is shown in the article that, under certain assumptions, the proposed algorithm generates a sequence that converges to the local minimizer of the problem. Two new augmented Lagrangian methods are also presented, which use quadratic penalties to solve nonlinear problems with equality constraints. Performance and robustness of the new algorithms is compared to the classic augmented Lagrangian method, to HLRF and to the improved HLRF (iHLRF) algorithms, in the solution of 25 benchmark problems from the literature. The new proposed HLRF algorithm is shown to be more robust than HLRF or iHLRF, and as efficient as the iHLRF algorithm. The two augmented Lagrangian methods proposed herein are shown to be more robust and more efficient than the classical augmented Lagrangian method.

Use of Carr-Purcell pulse sequence with low refocusing flip angle to measure T-1 and T-2 in a single experiment

The Carr-Purcell pulse sequence, with low refocusing flip angle, produces echoes midway between refocusing pulses that decay to a minimum value dependent on T*(2). When the refocusing flip angle was pi/2 (CP90) and tau > T*(2), the signal after the minimum value, increased to reach a steady-state free precession regime (SSFP), composed of a free induction decay signal after each pulse and an echo, before the next pulse. When tau < T*(2), the signal increased from the minimum value to the steady-state regime with a time constant (T*) = 2T(1)T(2)/(T-1 + T-2). identical to the time constant observed in the SSFP sequence, known as the continuous wave free precession (CWFP). The steady-state amplitude obtained with M-cp90 = M0T2/(T-1+T-2) was identical to CWFP. Therefore, this sequence was named CP-CWFP because it is a Carr-Purcell sequence that produces results similar to the CWFP. However, CP-CWFP is a better sequence for measuring the longitudinal and transverse relaxation times in single scan, when the sample exhibits T-1 similar to T-2. Therefore, this sequence can be a useful method in time domain NMR and can be widely used in the agriculture, food and petrochemical industries because those samples tend to have similar relaxation times in low magnetic fields. (C) 2011 Elsevier Inc. All rights reserved.

The contrast-enhanced Doppler ultrasound with perfluorocarbon exposed sonicated albumin does not improve the diagnosis of renal artery stenosis compared with angiography

There are no studies investigating the effect of the contrast infusion on the sensitivity and specificity of the main Doppler criteria of renal artery stenosis (RAS). Our aim was to evaluate the accuracy of these Doppler criteria prior to and following the intravenous administration of perfluorocarbon exposed sonicated albumin (PESDA) in patients suspected of having RAS. Thirty consecutive hypertensive patients (13 males, mean age of 57 ± 10 years) suspected of having RAS by clinical clues, were submitted to ultrasonography (US) of renal arteries before and after enhancement using continuous infusion of PESDA. All patients underwent angiography, and haemodynamically significant RAS was considered when ≥50%. At angiography, it was detected RAS ≥50% in 18 patients, 5 with bilateral stenosis. After contrast, the examination time was slightly reduced by approximately 20%. In non-enhanced US the sensitivity was better when based on resistance index (82.9%) while the specificity was better when based on renal aortic ratio (89.2%). The predictive positive value was stable for all indexes (74.0%–88.0%) while negative predictive value was low (44%–51%). The specificity and positive predictive value based on renal aortic ratio increased after PESDA injection respectively, from 89 to 97.3% and from 88 to 95%. In hypertensives suspected to have RAS the sensitivity and specificity of Duplex US is dependent of the criterion evaluated. Enhancement with continuous infusion of PESDA improves only the specificity based on renal aortic ratio but do not modify the sensitivity of any index.