Piecewise Affine Dynamical Models of Petri Nets – Application to Emergency Call Centers*

We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We establish an equivalence theorem between priority-free fluid timed Petri nets and semi-Markov decision processes, from which we derive the convergence to a periodic regime and the polynomial-time computability of the throughput. More generally, we develop an approach inspired by tropical geometry, characterizing the congestion phases as the cells of a polyhedral complex. We illustrate these results by a current application to the performance evaluation of emergency call centers in the Paris area. We show that priorities can lead to a paradoxical behavior: in certain regimes, the throughput of the most prioritary task may not be an increasing function of the resources.

In Situ Analyses of Surface-Layer Composition of CxNy Thin Films Using Methods Based on Penning Ionization Processes—Introductory Investigations

Carbon nitride materials have received much attention due to their excellent tribological, mechanical and optical properties. It was found that these qualities depend on the N/C ratio; therefore, the possibility to control it in situ in the sputtered film is of high importance. The plasma-electron spectroscopy method based on the Penning ionization process analysis is developed here to control this ratio in CNx films produced by plasma-sputtering in a pulsed-periodic regime of glow discharge. The electron energy distribution function is determined by the means of a single Langmuir probe placed in the center of the discharge tube. The mixture N2:CH4:He was used in the process of sputtering. The applied concentrations of CH4 varied in the range of 2–8%, and He concentration was 80–90%. The gas pressure in the discharge tube used for sputtering varied between 1 and 10 Torr, and the current was between 10 and 50 mA. It was shown that the proposed method enables the extraction of information on the composition of the surface layer of the investigated film and the development of an on-line inspection, without extracting the film from the sputtering chamber.

Emerging Adaptive Strategies Under Temperature Fluctuations in a Laboratory Evolution Experiment of Escherichia Coli

Generalists and specialists are types of strategies individuals can employ that can evolve in fluctuating environments depending on the extremity and periodicity of the fluctuation. To evaluate whether the evolution of specialists or generalists occurs under environmental fluctuation regimes with different levels of periodicity, 24 populations of Escherichia coli underwent laboratory evolution with temperatures alternating between 15 and 43°C in three fluctuation regimes: two periodic regimes dependent on culture's cell density and one random (non-periodic) regime with no such dependency, serving as a control. To investigate contingencies on the genetic background, we seeded our experiment with two different strains. After the experiment, growth rate measurements at the two temperatures showed that the evolution of specialists was favored in the random regime, while generalists were favored in the periodic regimes. Whole genome sequencing demonstrated that several gene mutations were selected in parallel in the evolving populations with some dependency on the starting genetic background. Given the genes mutated, we hypothesized that the driving force behind the observed adaptations is the restoration of the internal physiology of the starting strains' unstressed states at 37°C, which may be a means of improving fitness in the new environments. Phenotypic array measurements supported our hypothesis by demonstrating a tendency of the phenotypic response of the evolved strains to move closer to the starting strains' response at the optimum of 37°C, especially for strains classified as generalists.

Photonic Crystal Surface Emitting Laser Operating in Pulse-Periodic Regime with Ultralow Divergence Angle

The nanosecond-level pulse-operation characteristics of photonic-crystal surface-emitting lasers (PCSELs) with ultralow divergence were investigated in detail. We demonstrate a maximum peak output power of 14 W for a current pulse width of 9 ns, which is about 28 times the saturated power under continuous wave (CW) operation. The full width at half maximum (FWHM) of the optical response pulse is about 3 ns wider than the current pulse. The maximum repetition frequency reaches 400 kHz at 10 A without significant degradation of output power while the value is 100 kHz at 40 A. Moreover, the multimode behavior of the PCSEL at a high peak current was analyzed.

On the Control of the 2D Navier–Stokes Equations with Kolmogorov Forcing

This paper is devoted to the control problem of a nonlinear dynamical system obtained by a truncation of the two-dimensional (2D) Navier–Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction. This special case of the 2D N-S equations is known as the 2D Kolmogorov flow. Firstly, the dynamics of the 2D Kolmogorov flow which is represented by a nonlinear dynamical system of seven ordinary differential equations (ODEs) of a laminar steady state flow regime and a periodic flow regime are analyzed; numerical simulations are given to illustrate the analysis. Secondly, an adaptive controller is designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime; the value of the Reynolds number is determined using an update law. Then, a static sliding mode controller and a dynamic sliding mode controller are designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime. Numerical simulations are presented to show the effectiveness of the proposed three control schemes. The simulation results clearly show that the proposed controllers work well.

Influence of Heat Generation/Absorption on Mixed Convection Flow Behaviour in the Presence of Lorentz Forces in a Vertical Micro Circular Duct Having Time Periodic Boundary Conditions: Steady Periodic Regime

The problem of mixed convection flow of a heat generating/absorbing fluid in the presence existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface has been studied taking the first-order slip and jump effects into consideration. The research analysis is carried out by considering a fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations which arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. A parametric study of some of the physical parameters involved in the problem is conducted. The results of this research revealed that the magnetic field has a damping impact on the flow and results in decreases in fluid velocity for both air and water. Furthermore, the presence of the heat generation parameter is seen to enhance the temperature distribution and this is reflected as an increase in the magnitude of the oscillation dimensionless velocity, whereas in the presence of heat absorption a reversed trend occurs.

Stabilization of the response of cyclically loaded lattice spring models with plasticity

This paper develops an analytic framework to design both stress-controlled and displacement-controlled T -periodic loadings which make the quasistatic evolution of a one-dimensional network of elastoplastic springs converging to a unique periodic regime. The solution of such an evolution problem is a function t->(e(t),p(t)), where ei(t) and pi(t) are the elastic and plastic deformations of spring i, that satisfies the initial condition (e(t0),p(t0)). After we rigorously convert the problem into a Moreau sweeping process with a moving polyhedron C(t) in a vector space E of dimension d, it becomes natural to expect (based on a result by Krejci) that the elastic component t->e(t) always converges to a T-periodic function. The achievement of the present paper is in spotting a class of loadings where the Krejci's limit doesn't depend on the initial condition (e(t0),p(t0)) and so all the trajectories approach the same T-periodic regime. The proposed class of sweeping processes is the one for which the normal vectors of any d different facets of the moving polyhedron C(t) are linearly independent. We further link this geometric condition to mechanical properties of the given network of springs. In this way we obtain an analogue of the Frederick-Armstrong theorem from continuum mechanics.

Numerical simulation of a wind excited quasi-periodic regime of a stochastic van der Pol-type equation

The contribution regards a mathematical single-degree-of-freedom model of a slender structure vibrating in an air flow. Based on an experimental investigation, movement of such structures can be expressed by van der PolDuffing-type equations. Several particular configuration parameter settings for a white and non-white Gaussian random excitation together with deterministic harmonic forcing are considered and numerically analysed. The results support recently published analytic formulas.