Modeling and analysis using hybrid Petri nets

This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. Keywords: Hybrid dynamic systems; D-elementary hybrid Petri nets; Hybrid automata; Controller synthesi

Continuous flow Systems and Control Methodology Using Hybrid Petri nets

International audienceIn this paper, we consider the controller synthesis for continuous flow systems. These lasts are a sub-class of hybrid dynamic systems. Their main characteristics are positiveness and linearity. Transport, manufacturing, communication and biological systems are examples of continuous flow systems. Numerous tools and techniques exist in the literature for modelling and analyzing such systems. As positiveness is a hard constraint, an appropriate tool integrating naturally this constraint is strongly needed. Hybrid Petri Nets are an elegant modeling tool of positive systems, while Hybrid Automata are a powerful tool giving formally the reachable dynamic space. Combining these two tools aim to a sound approach for control synthesis of continuous flow systems. We start by considering the process to control and compute its reachable state space using specialized software like PHAVer. Algebraic inequalities define this reachable state space. The constrained behaviour is obtained by restricting this state space into a smaller desired space. This reduction is expressed in term of linear constraints only over the continuous variables; while the control is given by the discrete transitions (occurrence dates of controllable events). The controller synthesis methodology is based on the control of a hybrid system modelled by a D-elementary hybrid Petri Net. The control consists in modifying the guard of the controllable transitions so as the reachable controlled state space is maximally permissive

Th substituted SmFeAsO: structural details and superconductivity with Tc above 50 K

Superconducting poly- and single-crystalline samples of Sm1-xThxFeAsO with partial substitution of Sm3+ by Th4+ were synthesized and grown under high pressure and their structural, magnetic and transport properties are studied. The superconducting Tc reaches values higher than 50 K. Bulk superconducting samples (x = 0.08, 0.15, 0.3) do not show any signs of a phase transition from tetragonal to orthorhombic crystal structure at low temperatures. With Th substitution the unit cell parameters a and c shrink and the fractional atomic coordinate of the As site zAs remains almost unchanged, while that of Sm/Th zSm/Th increases. Upon warming from 5 K to 295 K the expansion of the FeAs layer thickness is dominant, while the changes in the other structural building blocks are smaller by a factor of 1/5, and they compensate each other, since the As-Sm/Th distance appears to contract by about the same amount as the O-Sm/Th expands. The poly- and single-crystalline samples are characterized by a full diamagnetic response in low magnetic field, by a high intergrain critical-current density for polycrystalline samples, and by a critical current density of the order of 8 x 105 A/cm2 for single crystals at 2 K in fields up to 7 T. The magnetic penetration depth anisotropy {\gamma}{\lambda} increases with decreasing temperature, a similar behavior to that of SmFeAsO1-xFy single crystals. The upper critical field estimated from resistance measurements is anisotropic with slopes of 5.4 T/K (H//ab plane) and 2.7 T/K (H//c axis), at temperatures sufficiently far below Tc. The upper critical field anisotropy {\gamma}H is in the range of 2, consistent with the tendency of a decreasing {\gamma}H with decreasing temperature, already reported for SmFeAsO1-xFy single crystals.Comment: 30 pages, 2 tables, 15 figure

Hierarchical regulation of the NikR-mediated nickel response in Helicobacter pylori

Nickel is an essential metal for Helicobacter pylori, as it is the co-factor of two enzymes crucial for colonization, urease and hydrogenase. Nickel is taken up by specific transporters and its intracellular homeostasis depends on nickel-binding proteins to avoid toxicity. Nickel trafficking is controlled by the Ni(II)-dependent transcriptional regulator NikR. In contrast to other NikR proteins, NikR from H. pylori is a pleiotropic regulator that depending on the target gene acts as an activator or a repressor. We systematically quantified the in vivo Ni2+-NikR response of 11 direct NikR targets that encode functions related to nickel metabolism, four activated and seven repressed genes. Among these, four targets were characterized for the first time (hpn, hpn-like, hydA and hspA) and NikR binding to their promoter regions was demonstrated by electrophoretic mobility shift assays. We found that NikR-dependent repression was generally set up at higher nickel concentrations than activation. Kinetics of the regulation revealed a gradual and temporal NikR-mediated response to nickel where activation of nickel-protection mechanisms takes place before repression of nickel uptake. Our in vivo study demonstrates, for the first time, a chronological hierarchy in the NikR-dependent transcriptional response to nickel that is coherent with the control of nickel homeostasis in H. pylori

A Second Order Penalized Direct Forcing for Hybrid Cartesian/Immersed Boundary Flow Simulations

International audienceFlows around complex stationary/moving solids take an important place in life-science context or in many engineering applications. Usually, these problems are solved by body-fitted approaches on unstructured meshes with boundary conditions directly imposed on the domain boundary. Another way is using immersed boundary (IB) techniques: the physical domain is immersed in a fixed fictitious one of simpler geometry on Cartesian grids. It allows to use efficient, fast and accurate numerical methods avoiding the tedious task of re-meshing in case of time varying geometry. In contrast, one needs specific methods to take into account the IB conditions (IBC). Here, we propose a second order penalized direct forcing method for unsteady incompressible flows with Dirichlet's IBC. It consists in adding a penalized forcing term to the initial problem, applied only on Cartesian nodes near the IB, in order to bring back the variable to the imposed one. Regarding Navier-Stokes solvers using a projection scheme, the forcing term is distributed both in the velocity prediction and in the correction equations. It leads to a natural way to prescribe the pressure boundary conditions around obstacles. Numerical experiments, performed for laminar flows around static/moving solids, assess the validity and illustrate the ability of our method, showing in particular a quadratic convergence rate

Riemannian Holonomy Groups of Statistical Manifolds

Normal distribution manifolds play essential roles in the theory of information geometry, so do holonomy groups in classification of Riemannian manifolds. After some necessary preliminaries on information geometry and holonomy groups, it is presented that the corresponding Riemannian holonomy group of the $d$-dimensional normal distribution is $SO\left(\frac{d\left(d+3\right)}{2}\right)$, for all $d\in\mathbb{N}$. As a generalization on exponential family, a list of holonomy groups follows.Comment: 11 page

Modeling and Analysis of Hybrid Dynamic Systems Using Hybrid Petri Nets

International audienceWe consider in this paper the extensions of the PN formalism in the direction of hybrid modeling. We briefly presents hybrid dynamic systems. Then the hybrid automata model. Is introduced and we discuss continuous Petri nets. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Two hybrid PN models, which differ in the class of HDS they can deal with, are studied. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. The general control structure based on hybrid PNs is briefly described