Quasi-stationary distributions and Yaglom limits of self-similar Markov processes

We discuss the existence and characterization of quasi-stationary distributions and Yaglom limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean the existence of a deterministic function $g$ and a non-trivial probability measure $\nu$ such that the process rescaled by $g$ and conditioned on non-extinction converges in distribution towards $\nu$. If the study of quasi-stationary distributions is easy and follows mainly from a previous result by Bertoin and Yor \cite{BYFacExp} and Berg \cite{bergI}, that of Yaglom limits is more challenging. We will see that a Yaglom limit exits if and only if the extinction time at 0 of the process is in the domain of attraction of an extreme law and we will then treat separately three cases, according whether the extinction time is in the domain of attraction of a Gumbel law, a Weibull law or a Fr\'echet law. In each of these cases, necessary and sufficient conditions on the parameters of the underlying L\'evy process are given for the extinction time to be in the required domain of attraction. The limit of the process conditioned to be positive is then characterized by a multiplicative equation which is connected to a factorization of the exponential distribution in the Gumbel case, a factorization of a Beta distribution in the Weibull case and a factorization of a Pareto distribution in the Fr\'echet case. This approach relies partly on results on the tail distribution of the extinction time, which is known to be distributed as the exponential integral of a L\'evy process. In that aim, new results on such tail distributions are given, which may be of independent interest. Last, we present applications of the Fr\'echet case to a family of Ornstein-Uhlenbeck processes

Entrained Flow Gasification: Impact of Fuel Spray Distribution on Reaction Zone Structure

Entrained flow gasification (EFG) is an important process for generating syngas from biogenic and anthropogenic waste based feedstocks for a future circular economy. The EFG process is characterized by complex interactions between different physical and thermo-chemical sub processes which determine syngas quality and process efficiency. The understanding of these sub processes is essential for the development of validated models, and therefore for design and scale up of EFG reactors. EFG processes using a central jet burner configuration feature flames that can be described as inverse diffusion flames superimposed by a fuel spray. The flames are characterised by (i) the conversion of liquid and slurry droplets and (ii) the oxidation of recirculating synthesis gas with the gasification medium. This work studies the interactions between fuel and oxidizer in the near-flame region of an atmospheric EFG process. The model fuel ethylene glycol was gasified using oxygen-enriched air for two different burner nozzle configurations. Spray imaging, OH-LIF and Fuel Tracer-LIF measurements were carried out in addition to gas temperature measurements to characterize the fuel distribution and the flame structure. The experimental results show that narrower fuel spray distributions result in shorter flames and changes in flame shape from a compact to a hollow cone shape in the downstream flame region. The experiments were accompanied by 2-phase free-jet modelling and RANS based CFD modeling. The models were improved to reflect the experimental findings including the fuel spray distributions. The simulation results predict the observed flame structures well using both models and for both burner nozzle configurations. The changes in flame structure for different spray distributions can be explained by local stoichiometry using the results of the 2-phase free-jet model

Entrained flow gasification: Impact of fuel spray distribution on reaction zone structure

Entrained flow gasification (EFG) is an important process for generating syngas from biogenic and anthropogenic waste based feedstocks for a future circular economy. The EFG process is characterized by complex interactions between different physical and thermo-chemical sub processes which determine syngas quality and process efficiency. The understanding of these sub processes is essential for the development of validated models, and therefore for design and scale up of EFG reactors. EFG processes using a central jet burner configuration feature flames that can be described as inverse diffusion flames superimposed by a fuel spray. The flames are characterised by (i) the conversion of liquid and slurry droplets and (ii) the oxidation of recirculating synthesis gas with the gasification medium. This work studies the interactions between fuel and oxidizer in the near-flame region of an atmospheric EFG process. The model fuel ethylene glycol was gasified using oxygen-enriched air for two different burner nozzle configurations. Spray imaging, OH-LIF and Fuel Tracer-LIF measurements were carried out in addition to gas temperature measurements to characterize the fuel distribution and the flame structure. The experimental results show that narrower fuel spray distributions result in shorter flames and changes in flame shape from a compact to a hollow cone shape in the downstream flame region. The experiments were accompanied by 2-phase free-jet modelling and RANS based CFD modeling. The models were improved to reflect the experimental findings including the fuel spray distributions. The simulation results predict the observed flame structures well using both models and for both burner nozzle configurations. The changes in flame structure for different spray distributions can be explained by local stoichiometry using the results of the 2-phase free-jet model

Mode Switching Control Using Lane Keeping Assist and Waypoints Tracking for Autonomous Driving in a City Environment

This paper proposes a mode switching supervisory controller for autonomous vehicles. The supervisory controller selects the most appropriate controller based on safety constraints and on the vehicle location with respect to junctions. Autonomous steering, throttle and deceleration control inputs are used to perform variable speed lane keeping assist, standard or emergency braking and to manage junctions, including roundabouts. Adaptive model predictive control with lane keeping assist is performed on the main roads and a linear pure pursuit inspired controller is applied using waypoints at road junctions where lane keeping assist sensors present a safety risk. A multi-stage rule based autonomous braking algorithm performs stop, restart and emergency braking maneuvers. The controllers are implemented in MATLAB® and Simulink™ and are demonstrated using the Automatic Driving Toolbox™ environment. Numerical simulations of autonomous driving scenarios demonstrate the efficiency of the lane keeping assist mode on roads with curvature and the ability to accurately track waypoints at cross intersections and roundabouts using a simpler pure pursuit inspired mode. The ego vehicle also autonomously stops in time at signaled intersections or to avoid collision with other road users

A TEMPORAL AND SPATIAL ANALYSIS OF EROSION PROCESSES IN CALANCHI BADLANDS. A CASE STUDY FROM THE UPPER ORCIA VALLEY WITH STATE-OF-THE-ART METHODOLOGIES

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Metal Transport in the Rhizobium-Legume Symbiosis

Metal Transport in the Rhizobium-legume Symbiosi