Propagation constant | EPFL Graph Search

The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the change per unit length, but it is otherwise dimensionless. In the context of two-port networks and their cascades, propagation constant measures the change undergone by the source quantity as it propagates from one port to the next. The propagation constant's value is expressed logarithmically, almost universally to the base e, rather than the more usual base 10 that is used in telecommunications in other situations. The quantity measured, such as voltage, is expressed as a sinusoidal phasor. The phase of the sinusoid varies with distance which results in the propagation constant being a complex number, the imaginary part bein

Dark curing kinetics of UV printing inks by real-time ATR-FTIR spectroscopy

Eric Jacques Nouzille

In UV-curable printing technology, an ink or a varnish is exposed to the UV-light source within a fraction of a second. Subsequent polymerization therefore proceeds in the dark, referred to as dark curing. Because dark curing can be critical and contributes to a large part of the overall conversion and to the final properties of the printed ink, the aim of this work was to get a better understanding of the dark curing process. Because an ink is a complex mixture of components, simpler systems representative of free radical and cationic chemistry were studied. Special attention was given to free radical polymerization with a detailed kinetic modeling. For cationic systems, the study was more application oriented. Attenuated-Total-Reflection Fourier-Transform Infrared (ATR-FTIR) spectroscopy was found to be the method of choice to follow in real-time the progress of the reaction under UV irradiation and in the dark. This technique allowed the study of curing conditions close to those encountered in industry. Dark curing of free radical was examined in systems consisting of a monomer (multifunctional acrylate) and a photoinitiator. The reactivities of different monomers were investigated and it was found that the chemistry of the spacer between the acrylate functional groups had an influence on the extent of dark curing. For example, TPGDA (tripropylene glycol diacrylate) led to higher overall conversion than HDDA (hexanediol diacrylate) although both are diacrylate monomers. Several explanations were put forward, such as the effect of dissolved oxygen, primary cyclization and initiation efficiency. The efficiency of photoinitiators (PIs) was examined and different behaviours were highlighted. For example, it was observed that DMPA (dimethoxyphenyl acetophenone) has a better quantum yield for α-cleavage compared to HCPK (1-hydroxycyclohexylphenyl ketone), whereas HCPK is more efficient in initiating the reaction, resulting in a better overall conversion in the dark. It is suggested that the two primary radicals resulting from the cleavage of the PI behave differently for DMPA and HCPK. One radical effectively initiates the reaction and the second is mainly involved in the termination process. These two different behaviours were observed under specific experimental conditions: (i) by covering the sample with a quartz plate and taking into account dissolved molecular oxygen and (ii) by curing under inert conditions with nitrogen. Photo-crosslinking polymerization reactions are strongly influenced by diffusion effects due to the formation of an infinite network. Therefore, it was proposed that a redistribution of reactivity within the system occurs, such as the diffusion of unreacted photoinitiators towards concentrations of unreacted monomers. This diffusion process has two positive effects: (i) for the same UV dose, but different intensities, a higher extent of conversion was reached with longer irradiation times under the condition investigated; (ii) multiple exposures led to a higher overall conversion than for a single exposure, for a fixed overall UV dose. Other parameters were explored, such as temperature and diffusing oxygen from air. With temperature, different trends were observed depending on the photoinitiator and the start of dark curing, either starting before the maximum rate of polymerization (Rp,max), or after Rp,max. The development of a kinetic model to describe dark curing of free radical polymerization was proposed. Existing models based on physical parameters, such as those incorporating diffusion-controlled phenomena and free-volume are relatively complex and require extensive information on the system studied. Therefore, a semi empirical approach was chosen in order to study the variation of fitting parameters when changing curing parameters, such as the photoinitiator concentration and type, the irradiation time, the UV light intensity and the temperature. The model was derived from kinetic data and it was assumed that rate coefficients are time-dependent and that termination, which was considered to be a first-order process, is propagation dependent. The kinetic equation has the form of a stretched exponential function and incorporates four fitting parameters. The model was evaluated for a large number of experimental data and very good fits were obtained with a random distribution of residuals. The exponent β was found to be sensitive to the termination process and reflected different reactivities in the dark as in the case of DMPA and HCPK. Dark curing of cationic systems continues until complete monomer conversion but at a slower rate. Thus systems with high reaction rates, both during UV irradiation and during the first seconds of the dark period, are of most importance for UV-curable printing technology. The most widely used diepoxide monomer in cationic ink formulation is 3,4-epoxycyclohexylmethyl-3,4-epoxycyclohexane carboxylate (DECC). In order to improve its reactivity during the first seconds of dark curing, the influence of several parameters was examined, such as the addition of an oxetane co-monomer (TMPO), the influence of relative humidity, UV dose, light intensity, temperature, and film thickness. The enhanced reactivity of DECC with TMPO was confirmed. During the cationic curing process, two reaction mechanisms compete; an activated chain end (ACE) mechanism and an activated monomer (AM) mechanism. It was observed that these two processes depend on the presence of hydroxyl containing compounds such as TMPO monomer, polyol compounds, and, most important, water. When the concentration of these components is increased the AM mechanism is enhanced, leading to higher conversion but at a slower curing rate, and a degradation of the mechanical properties. The presence of water is unavoidable and its concentration in the ink varies in presence of hydrophilic compounds, such as polyol. Furthermore, the water content increases with increasing relative humidity in air. It was shown that the reactivity of the system decreased as the percent of relative humidity increased. Moreover, although a higher overall conversion is achieved, the crosslink density of the film was severely reduced. This lower crosslink density was the result of the predominance of chain transfer reactions, leading to more pendant and short chains which were hydroxyl terminated. Moreover, the extent of conversion was thickness dependent since less water diffuses into the deeper layers occurred in thicker films.

EPFL2007

Wave propagation in periodic buckled beams

Florian Paul Robert Maurin

Folding of the earth's crust, wrinkling of the skin, rippling of fruits, vegetables and leaves are all examples of natural structures that can have periodic buckling. Periodic buckling is also present in engineering structures such as compressed lattices, cylinders, thin films, stretchable electronics, tissues, etc., and the question is to understand how wave propagation is affected by such media. These structures possess geometrical nonlinearities and intrinsic dispersive sources, two conditions which are necessary to the formation of stable, nonlinear waves called solitary waves. These waves are particular since dispersive effects are balanced by nonlinear ones, such that the wave characteristics remain constant during the propagation, without any decay or modification in the shape. It is the goal of this thesis to demonstrate that solitary waves can propagate in periodic buckled structures. This manuscript focuses specifically on periodically buckled beams that require either guided or pinned supports for stability purposes. Buckling is initially considered statically and investigations are made on stability, role played by imperfections, shape of the deflection, etc. Linear dispersion is analyzed employing the semi-analytical dispersion equation, a new method that relates the frequency explicitly to the propagation constant of the acoustic branch. This allows the quantification of the different dispersive sources and it is found that in addition to periodicity, transverse inertial and coupling effects are playing a dominant role. Modeling the system by a mass-spring chain that accounts for additional dispersive sources, homogenization and asymptotic procedures lead to the double-dispersion Boussinesq equation. Varying the pre-compression level and the support type, the main result of this thesis is to show that four different waves are possible, namely compressive supersonic, rarefaction (tension) supersonic, compressive subsonic and rarefaction subsonic solitary waves. For high-amplitude waves, models based on strongly-nonlinear PDEs as the one modeling wave propagation in granular media (Hertz power law) are more appropriate and adaptation of existing work is done. Analytical model results are then compared to finite-element simulations of the structure and experiments, and are found in excellent agreement. In this thesis, in addition to the semi-analytical dispersion equation, two other new methods are proposed. For periodic structures by translation with additional glide symmetries (e.g. buckled beams), Bloch theorem is revisited and allows the use of a smaller unit cell. Advantages are dispersion curves easier to interpret and computational cost reduced. Finally, the last contribution of this thesis is the use of NURBS-based isogeometric analysis (IGA) to solve the extensible-elastica problem requiring at least C1-continuous basis functions, which was not possible before with classical finite-element methods. The formulation is found efficient to solve dynamic problems involving slender beams as buckling.

EPFL2015

Reduction and Abstraction Techniques for BIP

Simon Bliudze, Mohammad Noureddine

Reduction and abstraction techniques have been proposed to address the state space explosion problem in verification. In this paper, we present reduction and abstraction techniques for component-based systems modeled in BIP (Behavior, Interaction and Priority). Given a BIP system consisting of several atomic components, we compute the product of two selected atomic components. The product operation often exposes opportunities for constant propagation in the product component that were hidden originally. Moreover, the product operation introduces states that are branching bisimilar. Our method detects and merges those states resulting in a behavior that may overapproximate the original one. The presented method is fully implemented. Our results show a drastic improvement in verifying BIP systems.

Springer2014