Event detection occurrence for planar piece-wise affine hybrid systems

Many switched circuits are made of linear components switched by a simple logic unit. In this paper, we use a generic planar Piece-wise Affine Hybrid System (PWAHS) to model this kind of circuit. Usually, simulations are run by analytical methods (adapted to a specific simple model) or by numerical simulations that can miss some events’ occurrences. We propose a generic planar method to simulate PWAHSs with periodic and state dependent events. Using analytical expressions, our approach can reach arbitrary accuracy in event detections without any loss. As a result, we have implemented our method in Scilab and Matlab toolboxes.     

A new L-curve for ill-posed problems

The truncated singular value decomposition is a popular method for the solution of linear ill-posed problems. The method requires the choice of a truncation index, which affects the quality of the computed approximate solution. This paper proposes that an L-curve, which is determined by how well the given data (right-hand side) can be approximated by a linear combination of the first (few) left singular vectors (or functions), be used as an aid for determining the truncation index.     

Experimental determination of the helicoidal electric field inside a twisted mesophase, in the selective reflection band

We consider the interface between a twisted birefringent mesophase and an isotropic medium. In the selective reflection band, when illuminated at normal incidence, the interface creates a coupling between the located dielectric reflection and the spread selective reflection. This coupling enables experimental measurement of the standing electric field orientation inside the liquid crystal.     

Fast solvers for discretized Navier-Stokes problems using vector extrapolation

We discuss the design and implementation of a vector extrapolation method for computing numerical solutions of the steady-state Navier-Stokes equation system. We describe a “proof of concept” implementation of vector extrapolation, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package ( http://www.manchester.ac.uk/ifiss).     

Evaluation of the Effect of Citronellol Group on Functionalized Mesogenic Materials by Capillary GC

In this paper, the effects of functionalization with terpenes on two new liquid-crystalline stationary phases for gas chromatography (GC) are described. Citronellol was used as the terminal group in the first material, and tetrahydrogeraniol was used with a second material. Inverse GC showed that the new materials have wide liquid-crystalline ranges (mesophases), 371–500 and 395–501 K, respectively. Moreover, they show good thermal stability up to 523 K and good potential as stationary phases for capillary GC. To clarify the effects of the liquid crystal structures and functional groups on retention and separation, the chromatographic behaviors of the two stationary phases were compared by eluting alkylbenzenes, polycyclic aromatic hydrocarbons, aromatic compounds, and terpenoids. The selectivities for a wide range of analytes achieved using the citronellol column were significantly better than those obtained using the tetrahydrogeraniol column. The columns showed different retention behaviors and fine resolutions for some of the main constituents of essential oils. Introduction of the double bond of citronellol greatly improved the polarization interactions involved in the shape recognition of the liquid-crystalline state for isomers. The new citronellol liquid-crystalline stationary phase, therefore, has a high affinity for natural compounds.

     

Recursive polynomial interpolation algorithm (RPIA)

Two difference schemes are derived for numerically solving the one-dimensional time distributed-order fractional wave equations. It is proved that the schemes are unconditionally stable and convergent in the \(L^{\infty }\) norm with the convergence orders O(τ ² + h ²+Δγ ²) and O(τ ² + h ⁴+Δγ ⁴), respectively, where τ,h, and Δγ are the step sizes in time, space, and distributed order. A numerical example is implemented to confirm the theoretical results.     

Rheology and gelation kinetics of PVC plastisols

Oscillatory rheological experiments at different temperatures and over a wide range of frequencies have been used to investigate the gelation process and, more particularly, the sol–gel transition of various poly(vinyl chloride) (PVC) plastisols. The sol–gel transition process was found to be universal with respect to the temperature and solid volume fraction according to the similarity of the fractal structure in PVC plastisols. The variation of the gel time (t _gel) with temperature for any composition of PVC plastisols was predicted from the Dickinson’s model (E. Dickinson, J Chem Soc Faraday Trans, 93:111–114, 1997). Dynamic viscoelastic properties of PVC plastisols have also been studied as a function of temperature that allowed us to follow the gelation process of various plastisols. Thus, the influence of the type and concentration of PVC resins in gelation process was investigated. The variation of the complex shear modulus at a constant frequency was depicted by a master curve regarding the dependence of the moduli on PVC concentrations.     

Nanopore formation on low-doped p-type silicon under illumination

Porous silicon layers were elaborated by anodization of highly resistive p-type silicon in HF/ethylene glycol solution under front side illumination, as a function of etching time, HF concentration and illumination intensity. The porous layer morphology was investigated by scanning electron microscopy (SEM). The illumination during anodization was provided by a tungsten lamp or lasers of different wavelengths. Under anodization, a microporous layer is formed up to a critical thickness above which macropores appear. Under illumination, the instability limiting the growth of the microporous layer occurs at a critical thickness much larger than in the dark. This critical thickness depends on HF concentration, illumination wavelength and intensity. These non-trivial dependencies are rationalized in a model in which photochemical etching in the electrochemically formed porous layer plays the central role.     

A Monomial-by-Monomial Method for Computing Regular Solutions of Systems of Pseudo-Linear Equations

This paper deals with the local analysis of systems of pseudo-linear equations. We define regular solutions and use this as a unifying theoretical framework for discussing the structure and existence of regular solutions of various systems of linear functional equations. We then give a generic and flexible algorithm for the computation of a basis of regular solutions. We have implemented this algorithm in the computer algebra system Maple in order to provide novel functionality for solving systems of linear differential, difference and q-difference equations given in various input formats.     

A Note on Drazin Invertibility for Upper Triangular Block Operators

A bounded linear operator A acting on a Banach space X is said to be an upper triangular block operators of order n, and we write ${A \in \mathcal{UT}_{n}(X)}$ , if there exists a decomposition of ${X = X_{1} \oplus . . . \oplus X_{n}}$ and an n × n matrix operator ${(A_{i,j})_{\rm 1 \leq i, j \leq n}}$ such that ${A = (A_{i, j})_{1 \leq i, j \leq n}, A_{i, j} = 0}$ for i > j. In this note we characterize a large set of entries A _{i, j} with j > i such that ${\sigma_{\rm D} (A) = {\bigcup\limits_{i = 1}^{n}} \sigma_{\rm D} (A_{i, i})}$ ; where σ_D(.) is the Drazin spectrum. Some applications concerning the Fredholm theory and meromorphic operators are given.