Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain 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 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests. (C) 2009 Elsevier B.V. All rights reserved.

The role of an insulating surface layer on the relaxation time of the ionic redistribution in an electrolytic cell

We analyze the influence of a surface dielectric layer on the transient phenomena related to the ionic redistribution in an electrolytic cell submitted to a step-like external voltage. The adsorption-desorption phenomenon is taken into account in the famework of the Gouy-Chapman approximation, where the ions are assumed dimensionless. In the limit of small amplitude of the applied voltage, where the equations of the problem can be linearized, we obtain an analytical solution for the surface densities of ions, for the electrical potential and for the relaxation time for the transient phenomena. In the general case, when the linearized analysis is no longer valid, the solution of the problem is obtained numerically. The role of the thickness of the dielectric layer on the relaxation time is also discussed.

Determination of Very Slow Diffusion of Paramagnetic Ions by NMR Spectroscopy

In this paper, we propose a new method of measuring the very slow paramagnetic ion diffusion coefficient using a commercial high-resolution spectrometer. If there are distinct paramagnetic ions influencing the hydrogen nuclear magnetic relaxation time differently, their diffusion coefficients can be measured separately. A cylindrical phantom filled with Fricke xylenol gel solution and irradiated with gamma rays was used to validate the method. The Fricke xylenol gel solution was prepared with 270 Bloom porcine gelatin, the phantom was irradiated with gamma rays originated from a (60)Co source and a high-resolution 200 MHz nuclear magnetic resonance (NMR) spectrometer was used to obtain the phantom (1)H profile in the presence of a linear magnetic field gradient. By observing the temporal evolution of the phantom NMR profile, an apparent ferric ion diffusion coefficient of 0.50 mu m(2)/ms due to ferric ions diffusion was obtained. In any medical process where the ionizing radiation is used, the dose planning and the dose delivery are the key elements for the patient safety and success of treatment. These points become even more important in modern conformal radio therapy techniques, such as stereotactic radiosurgery, where the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Several methods have been proposed to obtain the three-dimensional (3-D) dose distribution. Recently, we proposed an alternative method for the 3-D radiation dose mapping, where the ionizing radiation modifies the local relative concentration of Fe(2+)/Fe(3+) in a phantom containing Fricke gel and this variation is associated to the MR image intensity. The smearing of the intensity gradient is proportional to the diffusion coefficient of the Fe(3+) and Fe(2+) in the phantom. There are several methods for measurement of the ionic diffusion using NMR, however, they are applicable when the diffusion is not very slow.

On ""Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field""

Recently the paper ""Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field"" by G. C. Nayak was published [Eur. Phys. J. C 59: 715, 2009; arXiv:0708.2430]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the socalled ""shift theorem""[arXiv:hep-th/0609192] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

Magnetic resonance study of a vanadium pentoxide gel

In this work we report results from continuous-wave (CW) and pulsed electron paramagnetic resonance (EPR) and proton nuclear magnetic resonance (NMR) studies of the vanadium pentoxide xerogel V2O5:nH(2)O (n approximate to 1.6). The low temperature CW-EPR spectrum shows hyperfine structure due to coupling of unpaired V4+ electron with the vanadium nucleus. The analysis of the spin Hamiltonian parameters suggests that the V4+ ions are located in tetragonally distorted octahedral sites. The transition temperature from the rigid-lattice low-temperature regime to the high temperature liquid-like regime was determined from the analysis of the temperature dependence of the hyperfine splitting and the V4+ motional correlation time. The Electron Spin Echo Envelope Modulation (ESEEM) data shows the signals resulting from the interaction of H-1 nuclei with V4+ ions. The modulation effect was observed only for field values in the center of the EPR absorption spectrum corresponding to the single crystals orientated perpendicular to the magnetic field direction. At least three protons are identified in the xerogel by our magnetic resonance experiments: (I) the OH groups in the equatorial plane, (ii) the bound water molecules in the axial V=O bond and (iii) the free mobile water molecules between the oxide layers. Proton NMR lineshapes and spin-lattice relaxation times were measured in the temperature range between 150 K and 323 K. Our analysis indicates that only a fraction of the xerogel protons contribute to the measured conductivity.

On exact time averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterized by a rate of events, lambda(t), and a magnitude, Phi, following an exponential distribution. We tackle the problem by performing exact time averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

Abnormal Corpus Callosum Integrity in Bipolar Disorder: A Diffusion Tensor Imaging Study

Objective: Abnormalities in the anterior interhemispheric connections provided by the corpus callosum (CC) have long been implicated in bipolar disorder (BID). In this study, we used complementary diffusion tensor imaging methods to study the structural integrity of the CC and localization of potential abnormalities in BD. Methods: Subjects included 33 participants with BID and 40 healthy comparison participants. Fractional anisotropy (FA) measures were compared between groups with region of interest (ROD methods to investigate the anterior, middle, and posterior CC and voxel-based methods to further localize abnormalities. Results: In ROI-based analyses, FA was significantly decreased in the anterior and middle CC in the BID group (p <.05). Voxel-based analyses similarly localized group differences to the genu, rostral body, and anterior midbody of CC (p <.05, corrected). Conclusion: The findings demonstrate abnormalities in the structural integrity of the anterior CC in BID that might contribute to altered interhemispheric connectivity in this disorder.

Abnormal anterior cingulum integrity in bipolar disorder determined through diffusion tensor imaging

Background Convergent evidence implicates white matter abnormalities in bipolar disorder. The cingulum is an important candidate structure for study in bipolar disorder as it provides substantial white matter connections within the corticolimbic neural system that subserves emotional regulation involved in the disorder. Aims To test the hypothesis that bipolar disorder is associated with abnormal white matter integrity in the cingulum. Method Fractional anisotropy in the anterior and posterior cingulum was compared between 42 participants with bipolar disorder and 42 healthy participants using diffusion tensor imaging. Results Fractional anisotropy was significantly decreased in the anterior cingulum in the bipolar disorder group compared with the healthy group (P=0.003); however, fractional anisotropy in the posterior cingulum did not differ significantly between groups. Conclusions Our findings demonstrate abnormalities in the structural integrity of the anterior cingulum in bipolar disorder. They extend evidence that supports involvement of the neural system comprising the anterior cingulate cortex and its corticolimbic gray matter connection sites in bipolar disorder to implicate abnormalities in the white matter connections within the system provided by the cingulum.

Corpus callosum in maltreated children with posttraumatic stress disorder: A diffusion tensor imaging study

Contrary to expectations derived from preclinical studies of the effects of stress, and imaging studies of adults with posttraumatic stress disorder (PTSD), there is no evidence of hippocampus atrophy in children with PTSD. Multiple pediatric studies have reported reductions in the corpus callosum - the primary white matter tract in the brain. Consequently, in the present study, diffusion tensor imaging was used to assess white matter integrity in the corpus callosum in 17 maltreated children with PTSD and 15 demographically matched normal controls. Children with PTSD had reduced fractional anisotropy in the medial and posterior corpus, a region which contains interhemispheric projections from brain structures involved in circuits that mediate the processing of emotional stimuli and various memory functions - core disturbances associated with a history of trauma. Further exploration of the effects of stress on the corpus callosum and white matter development appears a promising strategy to better understand the pathophysiology of PTSD in children. (C) 2007 Elsevier Ireland Ltd. All rights reserved.

Bond Strength and Etching Pattern of Adhesive Systems to Enamel: Effects of Conditioning Time and Enamel Preparation

Statement of the problem: The performance of self-etch systems on enamel is controversial and seems to be dependent on the application technique and the enamel preparation. Purpose of the Study: To examine the effects of conditioning time and enamel surface preparation on bond strength and etching pattern of adhesive systems to enamel. Materials and Methods: Ninety-six teeth were divided into 16 conditions (N = 6) in function of enamel preparation and conditioning time for bond strength test. The adhesive systems OptiBond FL (Kerr, Orange, CA, USA), OptiBond SOLO Plus (Kerr), Clearfil SE Bond (Kuraray, Osaka, Japan), and Adper Prompt L-Pop (3M ESPE, St. Paul, MN, USA) were applied on unground or ground enamel following the manufacturers` directions or doubling the conditioning time. Cylinders of Filtek Flow (0.5-mm height) were applied to each bonded enamel surface using a Tygon tube (0.7 mm in diameter; Saint-Gobain Corp., Aurora, OH, USA). After storage (24 h/37 degrees C), the specimens were subjected to shear force (0.5 mm/min). The data were treated by a three-way analysis of variance and Tukey`s test (alpha = 0.05). The failure modes of the debonded interfaces and the etching pattern of adhesives were observed using scanning electron microscopy. Results: Only the main factor ""adhesive"" was statistically significant (p < 0.001). The lowest bond strength value was observed for OptiBond FL. The most defined etching pattern was observed for 35% phosphoric acid and for Adper Prompt L-Pop. Mixed failures were observed for all adhesives, but OptiBond FL showed cohesive failures in resin predominantly. Conclusions: The increase in the conditioning time as well as the enamel pretreatment did not provide an increase in the resin-enamel bond strength values for the studied adhesives. CLINICAL SIGNIFICANCE The surface enamel preparation and the conditioning time do not affect the performance of self-etch systems to enamel. (J Esthet Restor Dent 20:322-336, 2008)

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.