Conjunctions of Among Constraints

Many existing global constraints can be encoded as a conjunction of among constraints. An among constraint holds if the number of the variables in its scope whose value belongs to a prespecified set, which we call its range, is within some given bounds. It is known that domain filtering algorithms can benefit from reasoning about the interaction of among constraints so that values can be filtered out taking into consideration several among constraints simultaneously. The present pa- per embarks into a systematic investigation on the circumstances under which it is possible to obtain efficient and complete domain filtering algorithms for conjunctions of among constraints. We start by observing that restrictions on both the scope and the range of the among constraints are necessary to obtain meaningful results. Then, we derive a domain flow-based filtering algorithm and present several applications. In particular, it is shown that the algorithm unifies and generalizes several previous existing results.Comment: 15 pages plus appendi

Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity

Striations in electronegative capacitively coupled radio-frequency plasmas: effects of the pressure, voltage, and electrode gap

Capacitively coupled radio-frequency (CCRF) CF_4 plasmas have been found to exhibit a self-organized striated structure at operating conditions, where the plasma is strongly electronegative and the ion-ion plasma in the bulk region (largely composed of CF_3^+ and F^- ions) resonates with the excitation frequency. In this work we explore the effects of the gas pressure, the RF voltage, and the electrode gap on this striated structure by Phase Resolved Optical Emission Spectroscopy and Particle-In-Cell/Monte Carlo Collisions simulations. The measured electronic excitation patterns at different external parameters show a good general agreement with the spatio-temporal plots of the ionization rate obtained from the simulations. For a fixed driving frequency the minima of the CF_3^+ and F^- ion densities (between the density peaks in the bulk) are comparable and independent of other external parameters. However, the ion density maxima generally increase as a function of the pressure or RF voltage, leading to the enhanced spatial modulation of plasma parameters. The striation gap (defined as the distance between two ion density peaks) is approximately inversely proportional to the pressure, while it exhibits a weak dependence on the RF voltage and the electrode gap. A transition between the striated and non-striated modes can be observed by changing either the pressure or the RF voltage; for 13.56 MHz and 18 MHz driving frequencies we present a phase diagram as a function of the pressure and voltage amplitude parameters.Comment: 32 pages, 18 figures. arXiv admin note: text overlap with arXiv:1703.0588

Well dispersed fractal aggregates as filler in polymer-silica nanocomposites: long range effects in rheology

We are presenting a new method of processing polystyrene-silica nanocomposites, which results in a very well-defined dispersion of small primary aggregates (assembly of 15 nanoparticles of 10 nm diameter) in the matrix. The process is based on a high boiling point solvent, in which the nanoparticles are well dispersed, and controlled evaporation. The filler's fine network structure is determined over a wide range of sizes, using a combination of Small Angle Neutron Scattering (SANS) and Transmission Electronic Microscopy (TEM). The mechanical response of the nanocomposite material is investigated both for small (ARES oscillatory shear and Dynamical Mechanical Analysis) and large deformations (uniaxial traction), as a function of the concentration of the particles. We can investigate the structure-property correlations for the two main reinforcement effects: the filler network contribution, and a filler-polymer matrix effect. Above a silica volume fraction threshold, we see a divergence of the modulus correlated to the build up of a connected network. Below the threshold, we obtain a new additional elastic contribution of much longer terminal time than the matrix. Since aggregates are separated by at least 60 nm, this new filler-matrix contribution cannot be described solely with the concept of glassy layer (2nm)

Bridging the gap between global models and full fluid models : a fast 1D semi-analytical fluid model for electronegative plasmas

Analytical and numerical models allow investigation of complicated discharge phenomena and the interplay that makes plasmas such a complex environment. Global models are quick to implement and can have almost negligible computation cost, but provide only bulk or spatially averaged values. Full fluid models take longer to develop, and can take days to solve, but provide accurate spatio-temporal profiles of the whole plasma. The work presented here details a different type of model, analytically similar to fluid models, but computationally closer to a global model, and able to give spatially resolved solutions for the challenging environment of electronegative plasmas. Included are non-isothermal electrons, gas heating, and coupled neutral dynamics. Solutions are reached in seconds to minutes, and spatial profiles are given for densities, fluxes, and temperatures. This allows the semi-analytical model to fill the gap that exists between global and full fluid models, extending the tools available to researchers. The semi-analytical model can perform broad parameter sweeps that are not practical with more computationally expensive models, as well as exposing non-trivial trends that global models cannot capture. Examples are given for a low pressure oxygen CCP. Excellent agreement is shown with a full fluid model, and comparisons are drawn with the corresponding global model

Determination of set-membership identifiability sets

International audienceThis paper concerns the concept of set-membership identifiability introduced in \cite{jauberthie}. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely {\it mincing}, {\it evaluating} and {\it regularization} (\cite{jaulin2}). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples