Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Strong surjectivity of maps from 2-complexes into the 2-sphere

Given a model 2-complex K(P) of a group presentation P, we associate to it an integer matrix Delta(P) and we prove that a cellular map f : K(P) -> S(2) is root free (is not strongly surjective) if and only if the diophantine linear system Delta(P) Y = (deg) over right arrow (f) has an integer solution, here (deg) over right arrow (f) is the so-called vector-degree of f

Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features. Published by Elsevier Ltd.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given. (c) 2007 Elsevier Ltd. All rights reserved.

Genetic Algorithm for the Determination of Linear Viscoelastic Relaxation Spectrum from Experimental Data

Conventional procedures employed in the modeling of viscoelastic properties of polymer rely on the determination of the polymer`s discrete relaxation spectrum from experimentally obtained data. In the past decades, several analytical regression techniques have been proposed to determine an explicit equation which describes the measured spectra. With a diverse approach, the procedure herein introduced constitutes a simulation-based computational optimization technique based on non-deterministic search method arisen from the field of evolutionary computation. Instead of comparing numerical results, this purpose of this paper is to highlight some Subtle differences between both strategies and focus on what properties of the exploited technique emerge as new possibilities for the field, In oder to illustrate this, essayed cases show how the employed technique can outperform conventional approaches in terms of fitting quality. Moreover, in some instances, it produces equivalent results With much fewer fitting parameters, which is convenient for computational simulation applications. I-lie problem formulation and the rationale of the highlighted method are herein discussed and constitute the main intended contribution. (C) 2009 Wiley Periodicals, Inc. J Appl Polym Sci 113: 122-135, 2009

Surface modification and crystallization of the BaO-B2O3-SiO2 glassy system using CO2 laser irradiation

The surface modification and crystallization process of BaO-B2O3-SiO2 glass compositions when exposed to CO2 laser irradiation was evaluated as a function of the laser power, irradiation time and surface condition. The glass surface was modified by the application of laser power exceeding 0.40 W and an irradiation time of more than 300 s. Micro-Raman and X-ray diffraction measurements revealed at high laser power the formation of beta-BaB2O4 (beta-BBO) crystalline phase. The crystallization of the irradiated region was enhanced when beta-BBO micrometer sized particles were dispersed on the surface of the glass sample. The intensity of the second harmonic generation observed in the crystallized region was found to depend mainly on the condition of the glassy surface prior to glass irradiation. (C) 2007 Elsevier B.V. All rights reserved.

Fully electrochemical hyphenated flow system for preconcentration, cleanup, stripping, capillary electrophoresis with stacking and contactless conductivity detection of trace heavy metals

Successful coupling of electrochemical preconcentration (EPC) to capillary electrophoresis (CE) with contactless conductivity detection (C(4)D) is reported for the first time. The EPC-CE interface comprises a dual glassy carbon electrode (GCE) block, a spacer and an upper block with flow inlet and outlet, pseudo-reference electrode and a fitting for the CE silica column, consisting of an orifice perpendicular to the surface of a glassy carbon electrode with a bushing inside to ensure a tight press fit. The end of the capillary in contact with the GCE is slant polished, thus defining a reproducible distance from the electrode surface to the column bore. First results with EPC-CE-C(4)D are very promising, as revealed by enrichment factors of two orders of magnitude for Tl, Cu, Pb and Cd ion peak area signals. Detection limits for 10 min deposition time fall around 20 nmol L(-1) with linear calibration curves over a wide range. Besides preconcentration, easy matrix exchange between accumulation and stripping/injection favors procedures like sample cleanup and optimization of pH, ionic strength and complexing power. This was demonstrated for highly saline samples by using a low conductivity buffer for stripping/injection to improve separation and promote field-enhanced sample stacking during electromigration along the capillary. (C) 2010 Elsevier B.V. All rights reserved.

Peat as a natural solid-phase for copper preconcentration and determination in a multicommuted flow system coupled to flame atomic absorption spectrometry

The physical and chemical characteristics of peat were assessed through measurement of pH, percentage of organic matter, cationic exchange capacity (CEC), elemental analysis, infrared spectroscopy and quantitative analysis of metals by ICP OES. Despite the material showed to be very acid in view of the percentage of organic matter, its CEC was significant, showing potential for retention of metal ions. This characteristic was exploited by coupling a peat mini-column to a flow system based on the multicommutation approach for the in-line copper concentration prior to flame atomic absorption spectrometric determination. Cu(II) ions were adsorbed at pH 4.5 and eluted with 0.50 mol L(-1) HNO(3). The influence of chemical and hydrodynamic parameters, such as sample pH, buffer concentration, eluent type and concentration, sample flow-rate and preconcentration time were investigated. Under the optimized conditions, a linear response was observed between 16 and 100 mu g L(-1), with a detection limit estimated as 3 mu g L(-1) at the 99.7% confidence level and an enrichment factor of 16. The relative standard deviation was estimated as 3.3% (n = 20). The mini-column was used for at least 100 sampling cycles without significant variation in the analytical response. Recoveries from copper spiked to lake water or groundwater as well as concentrates used in hemodialysis were in the 97.3-111 % range. The results obtained for copper determination in these samples agreed with those achieved by graphite furnace atomic absorption spectrometry (GFAAS) at the 95% confidence level. (C) 2009 Elsevier B.V. All rights reserved.

A multicommuted flow-system for spectrophotometric determination of tannin exploiting the Cu(I)/BCA complex formation

A flow system exploiting the multicommutation approach is proposed for spectrophotometric determination of tannin in beverages. The procedure is based on the reduction of Cu(II) in the presence of 4,4`-dicarboxy-2,2`-biquinoline, yielding a complex with maximum absorption at 558 nm. Calibration graph was linear (r=0.999) for tannic acid concentrations up to 5.00 mu mol L-1. The detection limit and coefficient of variation were estimated as 10 nmol L-1 (99.7% confidence level) and 1% (1.78 mu mol L-1 tannic acid, n=10), respectively. The sampling rate was 50 determinations per hour. The proposed procedure is more sensitive and selective than the official Folin-Denis method, also minimizing drastically waste generation. Recoveries within 91.8 and 115% were estimated for total tannin determination in tea and wine samples. (C) 2007 Elsevier B.V. All rights reserved.

Simultaneous analysis of five antidepressant drugs using direct injection of biofluids in a capillary restricted-access media-liquid chromatography-tandem mass spectrometry system

Direct analysis, with minimal sample pretreatment, of antidepressant drugs, fluoxetine, imipramine, desipramine, amitriptyline, and nortriptyline in biofluids was developed with a total run time of 8 min. The setup consists of two HPLC pumps, injection valve, capillary RAM-ADS-C18 pre-column and a capillary analytical C 18 column connected by means of a six-port valve in backflush mode. Detection was performed with ESI-MS/MS and only 1 mu m of sample was injected. Validation was adequately carried out using FLU-d(5) as internal standard. Calibration curves were constructed under a linear range of 1-250 ng mL(-1) in plasma, being the limit of quantification (LOQ), determined as 1 ng mL(-1), for all the analytes. With the described approach it was possible to reach a quantified mass sensitivity of 0.3 pg for each analyte (equivalent to 1.1-1.3 fmol), translating to a lower sample consumption (in the order of 103 less sample than using conventional methods). (C) 2008 Elsevier B.V. All rights reserved.

Determination of Minoxidil by Bleaching the Permanganate Carrier Solution in a Flow-Based Spectrophotometric System

The determination of minoxidil (MX) with potassium permanganate as a carrier in a flow injection method is described. The detection at 550nm was linear from 1.0x10-5 to 5.0x10-4mol L-1. The limit of detection (3 sigma/slope) was 8.92x10-6mol L-1, with an analytical frequency of 32h-1. The proposed method was applied to commercial samples, with recoveries from 104.7 to 106.4%. Comparison with the HPLC procedure reveled relative errors from 0.48 to 1.4%, and the results agreed within a 95% confidence level.