Robust dangerous border-collision bifurcations in piecewise smooth systems

Physical and computer experiments involving systems describable by piecewise smooth continuous maps that are nondifferentiable on some surface in phase space exhibit novel types of bifurcations in which an attracting fixed point exists before and after the bifurcation. The striking feature of these bifurcations is that they typically lead to "unbounded behavior" of orbits as a system parameter is slowly varied through its bifurcation value. This new type of border-collision bifurcation is fundamental and robust. A method that prevents such "dangerous border-collision bifurcations" is given. These bifurcations may be found in a variety of experiments including circuits.     

Simultaneous Analysis of Fluoxetine, Norfluoxetine, Citalopram, and Haloperidol in Plasma by LC–ESI-IT-MS

A reliable and simple method has been developed for simultaneous analysis of fluoxetine, its metabolite norfluoxetine, citalopram, and haloperidol with lamotrigine as internal standard. The method is based on solid-phase extraction on mixed-mode cation-exchange cartridges followed by LC separation on a C₁₈ column at ambient temperature with a gradient prepared from acetonitrile and 5 mM ammonium acetate in 0.1% (v/v) aqueous formic acid. The flow rate was 0.5 mL min^?1. Eluted compounds were ionized by the electrospray ionization ion source of an ion-trap mass spectrometer and were detected by selected ion monitoring. Co-extracted endogenous compounds from plasma were eluted in the first 5 min and discarded by valve-switching. The target drugs were eluted in the period 5.5–11 min. Calibration plots were linear in the ranges 5 (or 10)–400 ng mL^?1 with correlation coefficients >0.999. Other statistical and validation results were within accepted ranges for clinical analysis.     

Cetyl‐alcohol‐reinforced hollow fiber solid/liquid‐phase microextraction and HPLC–DAD analysis of ezetimibe and simvastatin in human plasma and urine

A new cetyl‐alcohol‐reinforced hollow fiber solid/liquid‐phase microextraction (CA–HF–SLPME) followed by high‐performance liquid chromatography–diode array detection (HPLC–DAD) method was developed for simultaneous determination of ezetimibe and simvastatin in human plasma and urine samples. To prepare the CA–HF–SLPME device, the cetyl‐alcohol was immobilized into the pores of a 2.5 cm hollow fiber micro‐tube and the lumen of the micro‐tube was filled with 1‐octanol with the two ends sealed. Afterwards, the prepared device was introduced into 10 mL of the sample solution containing the analytes with agitation. Under optimized conditions, calibration curves plotted in spiked plasma and urine samples were linear in the ranges of 0.363–25/0.49–25 μg L^?1 for ezetimibe/simvastatin and 0.193–25/0.312–25 μg L^?1 for ezetimibe/simvastatin in plasma and urine samples, respectively. The limit of detection was 0.109/0.174 μg L^?1 for ezetimibe/simvastatin in plasma and 0.058/0.093 μg L^?1 for ezetimibe/simvastatin in urine. As a potential application, the proposed method was applied to determine the concentration of selected analytes in patient plasma and urine samples after medication and satisfactory results were achieved. In comparison with reference methods, the CA–HF–SLPME–HPLC–DAD method demonstrates considerable potential in the biopharmaceutical analysis of selected drugs.     

Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform

In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns with larger bandwidths. Also, the 2D-CWT technique reduces speckle noise significantly. Moreover, only a single fringe pattern is required in this technique. The 2D-CWT algorithm is capable of separating low frequency terms from the high frequency terms that contain phase-modulated fringe information, even when both interfere, greatly, in the frequency domain. The proposed algorithm is tested, both via computer simulation and using real fringe patterns. This revealed the robustness of this algorithm and also demonstrably enables the demodulation of a wider range of fringe patterns using the FTP technique.     

Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets

Fringe pattern analysis in coded structured light constitutes an active field of research. Techniques based on first projecting a sinusoidal pattern and then recovering the phase deviation permit the computation of the phase map and its corresponding depth map, leading to a dense acquisition of the measuring object. Among these techniques, the ones based on time-frequency analysis permit to extract the depth map from a single image, thus having potential applications measuring moving objects. The main techniques are Fourier Transform (FT), Windowed Fourier Transform (WFT) and Wavelet Transform (WT). This paper first analyzes the pros and cons of these three techniques, then a new algorithm for the automatic selection of the window size in WFT is proposed. This algorithm is compared to the traditional WT using adapted mother wavelet signals both with simulated and real objects, showing the performance results for quantitative and qualitative evaluations of the new method.     

Fringe-pattern demodulation using an iterative linear digital phase locked loop algorithm

A novel technique called an iterative linear digital phase locked loop (DPLL) for fringe-pattern demodulation is presented. The proposed technique has better noise immunity than the basic one-dimensional DPLL algorithms (e.g., conventional and linear DPLLs) because it processes a fringe pattern in two dimensions. In the first iteration of the proposed algorithm, it uses a flat reference to estimate the phase of the fringe pattern. The estimated phase map resulting from the first iteration is smoothed using a moving average window and then it is used as a reference to estimate the phase of the fringe pattern in the second iteration. In the third iteration, the phase map resulting from the second iteration is smoothed and used as a reference to estimate the phase of the fringe pattern in the fourth iteration and so on until the demodulated phase map has a good signal-to-noise ratio.     

Three-dimensional Fourier Fringe Analysis

Over the years two-dimensional Fourier Fringe Analysis (2D-FFA) has demonstrated both its capability and its relative robustness in analysing fringe patterns within a short time-frame from static objects. Nowadays, there is an increasing demand to measure dynamic objects. Today 2D-FFA is seen as a fast and flexible method of processing fringe patterns for dynamic objects. But it is still inherently a 2D approach, i.e. it deals with three-dimensional data (video sequences) on an individual 2D frame-by-frame basis. In this paper, a novel three-dimensional Fourier Fringe Analysis (3D-FFA) algorithm is proposed to demodulate fringe pattern sequences taken from dynamic objects. This technique processes the stack of fringe patterns as a single 3D volume, not as a set of individual 2D frames that are each processed in isolation. The proposed algorithm has been evaluated on both computer simulated and real dynamic objects. Results show that the proposed technique is able to demodulate fringe pattern volumes successfully.     

Isobaric vapor–liquid equilibria of binary system ethyl acetate + ethyl benzene + lithium bromide

The isobaric vapor–liquid equilibrium (VLE) behaviors for binary system, ethyl acetate + ethyl benzene, and ethyl acetate + ethyl benzene + LiBr (at saturation) were studied at the local ambient pressure (707 ± 1 mmHg). Equilibrium still was used where both liquid and vapor were continuously circulated. The experimental results showed that salt-free ethyl acetate + ethyl benzene system does not form an azeotrope point. The experimental results for ethyl acetate + ethyl benzene system were in a very good agreement with the predicted results using UNIFAC, UNIQUAC, NRTL, and Wilson models. Adding LiBr, as a salt, did show slight effects on the VLE behavior of ethyl acetate + ethyl benzene system.     

Lyapunov and LMI analysis and feedback control of border collision bifurcations

Feedback control of piecewise smooth discrete-time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasistatically varied. The class of systems studied is piecewise smooth maps that depend on a parameter, where the system dimension n can take any value. The goal of the control effort in this work is to replace the bifurcation so that in the closed-loop system, the steady state remains locally attracting and locally unique (“nonbifurcation with persistent stability”). To achieve this, Lyapunov and linear matrix inequality (LMI) techniques are used to derive a sufficient condition for nonbifurcation with persistent stability. The derived condition is stated in terms of LMIs. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce the desirable behavior noted earlier. Numerical examples that demonstrate the effectiveness of the proposed control techniques are given.