Information Filtering and Array Algorithms for Discrete-Time Markovian Jump Linear Systems

This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.

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.

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 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.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Ressonância não linear de uma bússola em campos magnéticos

Fenômenos oscilatórios e ressonantes são explorados em vários cursos experimentais de física. Em geral os experimentos são interpretados no limite de pequenas oscilações e campos uniformes. Neste artigo descrevemos um experimento de baixo custo para o estudo da ressonância em campo magnético da agulha de uma bússola fora dos limites acima. Nesse caso, termos não lineares na equação diferencial são responsáveis por fenômenos interessantes de serem explorados em laboratórios didáticos.

Development of a Multicommutated Flow System with Chemiluminometric Detection for Quantification of Gentamicin in Pharmaceuticals

A new flow procedure based on multicommutation with chemiluminometric detection was developed to quantify gentamicin sulphate in pharmaceutical formulations. This approach is based on gentamicin's ability to inhibit the chemiluminometric reaction between luminol and hypochlorite in alkaline medium, causing a decrease in the analytical signal. The inhibition of the analytical signal is proportional to the concentration of gentamicin sulphate, within a linear range of 1 to 4 mu g mL(-1) with a coefficient variation <3%. A sample throughput of 55 samples h(-1) was obtained. The developed method is sensitive, simple, with low reagent consumption, reproducible, and inexpensive, and when applied to the analysis of pharmaceutical formulations (eye drops and injections) it gave results with RSD between 1.10 and 4.40%.

Ionic mobility of the solvated proton and acid-base titration in a four-compartment capillary electrophoresis system

Although H(+) and OH(-) are the most common ions in aqueous media, they are not usually observable in capillary electrophoresis (CE) experiments, because of the extensive use of buffer solutions as the background electrolyte. In the present work, we introduce CE equipment designed to allow the determination of such ions in a similar fashion as any other ion. Basically, it consists of a four-compartment piece of equipment for electrolysis-separated experiments (D. P. de Jesus et at, Anal. Chem., 2005, 77, 607). In such a system, the ends of the capillary are placed in two reservoirs, which are connected to two other reservoirs through electrolyte-filled tubes. The electrodes of the high-voltage power source are positioned in these reservoirs. Thus, the electrolysis products are kept away from the inputs of the capillary. The detection was provided by two capacitively coupled contactless conductivity detectors (CD), each one positioned about 11 cm from the end of the capillary. Two applications were demonstrated: titration-like procedures for nanolitre samples and mobility measurements. Strong and weak acids (pK(a) < 5), pure or mixtures, could be titrated. The analytical curve is linear from 50 mu M up to 10 mM of total dissociable hydrogen (r = 0.99899 for n =10) in 10-nL samples. By including D(2)O in the running electrolyte, we could demonstrate how to measure the mixed proton/deuteron mobility. When H(2)O/D(2)O (9 : 1 v/v) was used as the solvent, the mobility was 289.6 +/- 0.5 x 10(-5) cm(2) V(-1) s(-1). Due to the fast conversion of the species, this value is related to the overall behaviour of all isotopologues and isotopomers of the Zundel and Eigen structures, as well as the Stokesian mobility of proton and deuteron. The effect of neutral (o-phenanthroline) and negatively charged (chloroacetate) bases and aprotic solvent (DMSO) over the H(+) mobility was also demonstrated.

An environmentally friendly flow system for high-sensitivity spectrophotometric determination of free chlorine in natural waters

A green and highly sensitive analytical procedure was developed for the determination of free chlorine in natural waters, based on the reaction with N,N-diethyl-p-phenylenediamine (DPD). The flow system was designed with solenoid micro-pumps in order to improve mixing conditions by pulsed flows and to minimize reagent consumption as well as waste generation. A 100-cm optical path flow cell based on a liquid core waveguide was employed to increase sensitivity. A linear response was observed within the range 10.0 to 100.0 mu g L(-1), with the detection limit, coefficient of variation and sampling rate estimated as 6.8 mu g (99.7% confidence level), 0.9% (n = 20) and 60 determinations per hour, respectively. The consumption of the most toxic reagent (DPD) was reduced 20,000-fold and 30-fold in comparison to the batch method and flow injection with continuous reagent addition, respectively. The results for natural and tap water samples agreed with those obtained by the reference batch spectrophotometric procedure at the 95% confidence level. (C) 2010 Elsevier By. All rights reserved.

Downscaling a multicommuted flow injection analysis system for the photometric determination of iodate in table salt

In this work a downscaled multicommuted flow injection analysis setup for photometric determination is described. The setup consists of a flow system module and a LED based photometer, with a total internal volume of about 170 mu L The system was tested by developing an analytical procedure for the photometric determination of iodate in table salt using N,N-diethyl-henylenediamine (DPD) as the chromogenic reagent. Accuracy was accessed by applying the paired r-test between results obtained using the proposed procedure and a reference method, and no significant difference at the 95% confidence level was observed. Other profitable features, such as a low reagent consumption of 7.3 mu g DPD per determination: a linear response ranging from 0.1 up to 3.0 m IO(3)(-), a relative standard deviation of 0.9% (n = 11) for samples containing 0.5 m IO(3)(-), a detection limit of 17 mu g L(-1) IO(3)(-), a sampling throughput of 117 determination per hour, and a waste generation 600 mu L per determination, were also achieved. (C) 2010 Elsevier B.V. All rights reserved.

Sequential spectrofluorimetric determination of free and total glycerol in biodiesel in a multicommuted flow system

A new procedure for spectrofluorimetric determination of free and total glycerol in biodiesel samples is presented. It is based on the oxidation of glycerol by periodate, forming formaldehyde, which reacts with acetylacetone, producing the luminescent 3,5-diacetyl-1,4-dihydrolutidine. A flow system with solenoid micro-pumps is proposed for solution handling. Free glycerol was extracted off-line from biodiesel samples with water, and total glycerol was converted to free glycerol by saponification with sodium ethylate under sonication. For free glycerol, a linear response was observed from 5 to 70 mg L(-1) with a detection limit of 0.5 mg L(-1), which corresponds to 2 mg kg(-1) in biodiesel. The coefficient of variation was 0.9% (20 mg L(-1), n = 10). For total glycerol, samples were diluted on-line, and the linear response range was 25 to 300 mg L(-1). The detection limit was 1.4 mg L(-1) (2.8 mg kg(-1) in biodiesel) with a coefficient of variation of 1.4% (200 mg L(-1), n = 10). The sampling rate was ca. 35 samples h(-1) and the procedure was applied to determination of free and total glycerol in biodiesel samples from soybean, cottonseed, and castor beans.