Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

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.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

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.

The CATH Hierarchy Revisited-Structural Divergence in Domain Superfamilies and the Continuity of Fold Space

This paper explores the structural continuum in CATH and the extent to which superfamilies adopt distinct folds. Although most superfamilies are structurally conserved, in some of the most highly populated superfamilies (4% of all superfamilies) there is considerable structural divergence. While relatives share a similar fold in the evolutionary conserved core, diverse elaborations to this core can result in significant differences in the global structures. Applying similar protocols to examine the extent to which structural overlaps occur between different fold groups, it appears this effect is confined to just a few architectures and is largely due to small, recurring super-secondary motifs (e.g., alpha beta-motifs, alpha-hairpins). Although 24% of superfamilies overlap with superfamilies having different folds, only 14% of nonredundant structures in CATH are involved in overlaps. Nevertheless, the existence of these overlaps suggests that, in some regions of structure space, the fold universe should be seen as more continuous.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

2D evaluation of crack openings using smeared and embedded crack models

This work deals with the determination of crack openings in 2D reinforced concrete structures using the Finite Element Method with a smeared rotating crack model or an embedded crack model In the smeared crack model, the strong discontinuity associated with the crack is spread throughout the finite element As is well known, the continuity of the displacement field assumed for these models is incompatible with the actual discontinuity However, this type of model has been used extensively due to the relative computational simplicity it provides by treating cracks in a continuum framework, as well as the reportedly good predictions of reinforced concrete members` structural behavior On the other hand, by enriching the displacement field within each finite element crossed by the crack path, the embedded crack model is able to describe the effects of actual discontinuities (cracks) This paper presents a comparative study of the abilities of these 2D models in predicting the mechanical behavior of reinforced concrete structures Structural responses are compared with experimental results from the literature, including crack patterns, crack openings and rebar stresses predicted by both models

Adoption of Strategic Alliances by Shoes Industries of the Vale do Rio dos Sinos-RS and Franca-SP clusters: an exploratory study

The new environment of the companies, result of the relative opening of the market caused by the globalization has set a new challenge to assure the continuity of the businesses. Competitive strategies have been implemented aiming to overcome such challenge and, amongst them, strategic alliances have shown to be a viable alternative. In this context, this article has as objective to investigate the degree of use of strategic alliances by the medium and large companies of the shoes industries located in clusters of Vale do Rio dos Sinos (RS) and Franca (SP). This exploratory and descriptive research had the participation of 54 companies, being 3 from Vale do Rio dos Sinos and 21 from Franca, which answered a questionnaire with closed questions. The analysis of the data was given through descriptive statistics. Main conclusions, follow as: (1) the majority of the companies have joint activities; (2) the companies are nearer to alliances that do business than to the strategic ones; (3) alliances with competitors are inexpressive - suppliers and customers predominate; (4) the control of alliances result is insufficient; (5) trust and adequate partner are determinative factors.

TRANSFER OF A FASCICLE FROM THE POSTERIOR CORD TO THE SUPRASCAPULAR NERVE AFTER INJURY OF THE UPPER ROOTS OF THE BRACHIAL PLEXUS: TECHNICAL CASE REPORT

OBJECTIVE: A new nerve transfer technique using a healthy fascicle of the posterior cord for suprascapular nerve reconstruction is presented. This technique was used in a patient with posttraumatic brachial plexopathy resulting in upper trunk injury with proximal root stumps that were unavailable for grafting associated with multiple nerve dysfunction. CLINICAL PRESENTATION: A 45-year-old man sustained a right brachial plexus injury after a bicycle accident. Clinical evaluation and electromyography indicated upper trunk involvement. Trapezius muscle function and triceps strength were normal on physical examination. INTERVENTION: The patient underwent a combined supra- and infraclavicular approach to the brachial plexus. A neuroma-in-continuity of the upper trunk and fibrotic C5 and C6 roots were identified. Electrical stimulation of the phrenic and spinal accessory nerves produced no response. The suprascapular nerve was dissected from the upper trunk, transected, and rerouted to the infraclavicular fossa. A healthy fascicle of the posterior cord to the triceps muscle was transferred to the suprascapular nerve. At the time of the 1-year follow-up evaluation, arm abduction against gravity and external rotation reached 40 and 34 degrees, respectively. CONCLUSION: The posterior cord can be used as a source of donor fascicle to the suprascapular nerve after its infraclavicular relocation. This new intraplexal nerve transfer could be applied in patients with isolated injury of the upper trunk and concomitant lesion of the extraplexal nerve donors usually used for reinnervation of the suprascapular nerve.

SEM observation of the bond integrity of fiber-reinforced composite posts cemented into root canals

Objectives. To test the null hypothesis that continuity of resin cement/dentin interfaces is not affected by location along the root canal walls or water storage for 3 months when bonding fiber posts into root canals. Methods. Fiber posts were luted to bovine incisors using four resinous luting systems: Multilink, Variolink II, Enforce Dual and Enforce PV. After cementation, roots were longitudinally sectioned and epoxy resin replicas were prepared for SEM analysis (baseline). The original halves were immersed in solvent, replicated and evaluated. After 3 months water storage and a second solvent immersion, a new set of replicas were made and analyzed. The ratio (%) between the length (mm) of available bonding interface and the actual extension of bonded cement/dentin interface was calculated. Results. Significant lower percent values of bond integrity were found for Multilink (8.25%) and Variolink 11 (10.08%) when compared to Enforce Dual (25.11%) and Enforce PV (27.0%) at baseline analysis. The same trend was observed after immersion in solvent, with no significant changes. However, bond integrity was significantly reduced after 3 months water storage and a second solvent immersion to values below 5% (Multilink = 3.31%, Variolink=1.87%, Enforce Dual=1.20%, and Enforce PV=0.75%). The majority of gaps were depicted at the apical and middle thirds at baseline and after immersion in solvent. After 3 months, gaps were also detected at the cervical third. Significance. Bond integrity at the cement/dentin interface was surprisingly low after cementation of fiber posts to root canals with all resin cements. That was not significantly altered after immersion in solvent, but was further compromised after 3 months water storage. Gaps were mainly seen at middle and apical thirds throughout the experiment and extended to the cervical third after water storage for 3 months. Bond integrity of fiber posts luted to root canals was affected both by location and water storage. (C) 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Histological evaluation of the effectiveness of increased apical enlargement for cleaning the apical third of curved canals

P>Objective To evaluate the influence of apical size on cleaning of the apical third of curved canals prepared with rotary instruments. Methodology Forty-four mesiobuccal canals of maxillary molars teeth were instrumented to different apical sizes (30, 0.02; 35, 0.02; 40, 0.02; 45, 0.02) using a crown-down technique. After canal preparation, the apical thirds of the roots were submitted to histological processing and examination. The specimens were analysed at 40x magnification and the images were submitted to morphometric analysis with an integration grid to evaluate the percentage of debris and uninstrumented root canal walls. The action of the instruments on the root canal walls was assessed based on the surface regularity, abrupt change on the continuity of root canal walls, and partial or total pre-dentine removal. The results were statistically compared using one-way anova with post hoc Tukey test. Pearson`s correlation was performed to identify potential correlations between values. Results The percentage of uninstrumented root canal dentine was higher when apical enlargement was performed with instruments 30, 0.02 taper (55.64 +/- 4.62%) and 35, 0.02 taper (49.03 +/- 5.70%) than with instruments 40, 0.02 taper (38.08 +/- 10.44%) and 45, 0.02 taper (32.65 +/- 8.51%) (P < 0.05). More debris were observed when apical enlargement was performed with instruments 30, 0.02 taper (34.62 +/- 9.49%) and 35, 0.02 taper (25.33 +/- 7.37%) (P < 0.05). There was a significant correlation between the amount of remaining debris and the perimeter of uninstrumented root canal dentine (r = 0.9130, P < 0.001). Conclusion No apical enlargement size allowed the root canal walls to be prepared completely. Apical third cleanliness could be predicted by instrument diameter.