Third-order nonlinear spectra and optical limiting of lead oxifluoroborate glasses

We have determined two-photon absorption and nonlinear refraction spectra of the 50BO(1.5) - (50-x)PbF(2) - xPbO glasses (with x = 25, 35, 50 cationic %) at the range of the 470 and 1550 nm. The replacement of fluor atoms by oxygen leads to an increase in the third-order susceptibility, due to the formation of non-bridging oxygens (NBO). The nonlinear index of refraction is one order of magnitude higher than the one for fused silica, and it increases almost twice for the sample with x = 50. This sample has also shown promising features for all-optical switching as well as for optical limiting. (C) 2011 Optical Society of America

Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal

Time-resolved Z-scan measurements were performed in a Nd(3+)-doped Sr(0.61)Ba(0.39)Nb(2)O(6) laser crystal through ferroelectric phase transition. Both the differences in electronic polarizability (Delta alpha(p)) and cross section (Delta sigma) of the neodymium ions have been found to be strongly modified in the surroundings of the transition temperature. This observed unusual behavior is concluded to be caused by the remarkable influence that the structural changes associated to the ferro-to-paraelectric phase transition has on the 4f -> 5d transition probabilities. The maximum polarizability change value Delta alpha(p)=1.2x10(-25) cm(3) obtained at room temperature is the largest ever measured for a Nd(3+)-doped transparent material.

LATENT RANK CHANGE DETECTION FOR ANALYSIS OF SPLICE-JUNCTION MICROARRAYS WITH NONLINEAR EFFECTS

Alternative splicing of gene transcripts greatly expands the functional capacity of the genome, and certain splice isoforms may indicate specific disease states such as cancer. Splice junction microarrays interrogate thousands of splice junctions, but data analysis is difficult and error prone because of the increased complexity compared to differential gene expression analysis. We present Rank Change Detection (RCD) as a method to identify differential splicing events based upon a straightforward probabilistic model comparing the over-or underrepresentation of two or more competing isoforms. RCD has advantages over commonly used methods because it is robust to false positive errors due to nonlinear trends in microarray measurements. Further, RCD does not depend on prior knowledge of splice isoforms, yet it takes advantage of the inherent structure of mutually exclusive junctions, and it is conceptually generalizable to other types of splicing arrays or RNA-Seq. RCD specifically identifies the biologically important cases when a splice junction becomes more or less prevalent compared to other mutually exclusive junctions. The example data is from different cell lines of glioblastoma tumors assayed with Agilent microarrays.

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

NONLINEAR PERIODIZATION MAXIMIZES STRENGTH GAINS IN SPLIT RESISTANCE TRAINING ROUTINES

Monteiro, AG, Aoki, MS, Evangelista, AL, Alveno, DA, Monteiro, GA, Picarro, IDC, and Ugrinowitsch, C. Nonlinear periodization maximizes strength gains in split resistance training routines. J Strength Cond Res 23(4): 1321-1326, 2009-The purpose of our study was to compare strength gains after 12 weeks of nonperiodized (NP), linear periodized (LP), and nonlinear periodized (NLP) resistance training models using split training routines. Twenty-seven strength-trained men were recruited and randomly assigned to one of 3 balanced groups: NP, LP, and NLP. Strength gains in the leg press and in the bench press exercises were assessed. There were no differences between the training groups in the exercise pre-tests (p > 0.05) (i.e., bench press and leg press). The NLP group was the only group to significantly increase maximum strength in the bench press throughout the 12-week training period. In this group, upper-body strength increased significantly from pre-training to 4 weeks (p < 0.0001), from 4 to 8 weeks (p = 0.004), and from 8 weeks to the post-training (p < 0.02). The NLP group also exhibited an increase in leg press 1 repetition maximum at each time point (pre-training to 4 weeks, 4-8 week, and 8 weeks to post-training, p < 0.0001). The LP group demonstrated strength increases only after the eight training week (p = 0.02). There were no further strength increases from the 8-week to the post-training test. The NP group showed no strength increments after the 12-week training period. No differences were observed in the anthropometric profiles among the training models. In summary, our data suggest that NLP was more effective in increasing both upper- and lower-body strength for trained subjects using split routines.

Stability region bifurcations of nonlinear autonomous dynamical systems: Type-zero saddle-node bifurcations

The behavior of stability regions of nonlinear autonomous dynamical systems subjected to parameter variation is studied in this paper. In particular, the behavior of stability regions and stability boundaries when the system undergoes a type-zero sadle-node bifurcation on the stability boundary is investigated in this paper. It is shown that the stability regions suffer drastic changes with parameter variation if type-zero saddle-node bifurcations occur on the stability boundary. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation value is presented in this paper. Copyright (C) 2010 John Wiley & Sons, Ltd.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures

This paper deals with the application of the lumped dissipation model in the analysis of reinforced concrete structures, emphasizing the nonlinear behaviour of the materials The presented model is based on the original models developed by Cipollina and Florez-Lopez (1995) [12]. Florez-Lopez (1995) [13] and Picon and Florez-Lopez (2000) [14] However, some modifications were introduced in the functions that control the damage evolution in order to improve the results obtained. The efficiency of the new approach is evaluated by means of a comparison with experimental results on reinforced concrete structures such as simply supported beams, plane frames and beam-to-column connections Finally, the adequacy of the numerical model representing the global behaviour of framed structures is investigated and the limits of the analysis are discussed (C) 2009 Elsevier Ltd All rights reserved

A numerical model for the description of the nonlinear behaviour of multi-leaf masonry walls

A nonlinear finite element model was developed to simulate the nonlinear response of three-leaf masonry specimens, which were subjected to laboratory tests with the aim of investigating the mechanical behaviour of multiple-leaf stone masonry walls up to failure. The specimens consisted of two external leaves made of stone bricks and mortar joints, and an internal leaf in mortar and stone aggregate. Different loading conditions, typologies of the collar joints, and stone types were taken into account. The constitutive law implemented in the model is characterized by a damage tensor, which allows the damage-induced anisotropy accompanying the cracking process to be described. To follow the post-peak behaviour of the specimens with sufficient accuracy it was necessary to make the damage model non-local, to avoid mesh-dependency effects related to the strain-softening behaviour of the material. Comparisons between the predicted and measured failure loads are quite satisfactory in most of the studied cases. (c) 2007 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

Analytical solutions for geometrically nonlinear trusses

This paper presents an analytical method for analyzing trusses with severe geometrically nonlinear behavior. The main objective is to find analytical solutions for trusses with different axial forces in the bars. The methodology is based on truss kinematics, elastic constitutive laws and equilibrium of nodal forces. The proposed formulation can be applied to hyper elastic materials, such as rubber and elastic foams. A Von Mises truss with two bars made by different materials is analyzed to show the accuracy of this methodology.

Darcy`s law and the differential equation of motion

This note addresses the relation between the differential equation of motion and Darcy`s law. It is shown that, in different flow conditions, three versions of Darcy`s law can be rigorously derived from the equation of motion.