Spectral and linear stability of peakons in the Novikov equation

The Novikov equation is a peakon equation with cubic nonlinearity which, like the Camassa-Holm and the Degasperis-Procesi, is completely integrable. In this article, we study the spectral and linear stability of peakon solutions of the Novikov equation. We prove spectral instability of the peakons in $L^2(\mathbb{R})$. To do so, we start with a linearized operator defined on $H^1(\mathbb{R})$ and extend it to a linearized operator defined on weaker functions in $L^2(\mathbb{R})$. The spectrum of the linearized operator in $L^2(\mathbb{R})$ is proven to cover a closed vertical strip of the complex plane. Furthermore, we prove that the peakons are spectrally unstable on $W^{1,\infty}(\mathbb{R})$ and linearly and spectrally stable on $H^1(\mathbb{R})$. The result on $W^{1,\infty}(\mathbb{R})$ are in agreement with previous work about linear stability, while our results on $H^1(\mathbb{R})$ are in agreement with the orbital stability obtained previously.Comment: 19 pages, no figur

When is negativity not a problem for the ultra-discrete limit?

The `ultra-discrete limit' has provided a link between integrable difference equations and cellular automata displaying soliton like solutions. In particular, this procedure generally turns strictly positive solutions of algebraic difference equations with positive coefficients into corresponding solutions to equations involving the "Max" operator. Although it certainly is the case that dropping these positivity conditions creates potential difficulties, it is still possible for solutions to persist under the ultra-discrete limit even in their absence. To recognize when this will occur, one must consider whether a certain expression, involving a measure of the rates of convergence of different terms in the difference equation and their coefficients, is equal to zero. Applications discussed include the solution of elementary ordinary difference equations, a discretization of the Hirota Bilinear Difference Equation and the identification of integrals of motion for ultra-discrete equations

Symétries et intégrabilité des équations aux différences finies

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal

Surface and near surface geochemical surveying of a CO2 injection pilot: application study to the French Pyrenean foreland (Rousse CCS pilot)

The geochemical monitoring of the Rousse injection pilot, operated by TOTAL Exploration Pproduction France, is presented over a 5- years long time period. The monitoring consisted in the acquisition at regular frequency of soil gas concentrations and fluxes at selected sampling points, coupled with the study of the geochemical parameters evolution of a perched aquifer overlying the storage reservoir through a dedicated 85 m depth borehole. Baseline data were acquired between September 2008 and December 2009 then the monitoring shifted to the surveying of the pilot during the operating phase. This second phase ended in March 2013. Data acquired during these two phases are presented and discussed

Impact of mine closure and access facilities on gas emissions from old mine workings to surface : examples of French iron and coal Lorraine basins

International audienceClosure methods and techniques of mine shafts located in the iron Lorraine basin, in the Lorraine and in North-East coal basins are quite different. For the first, they are associated with adits. Some are closed by a simple grid to avoid entrance in mine workings but gas entrance and exit are allowed. Coal shafts are secured and can be equipped with a vent to enable mine gas outflow in specific conditions. Measurements stations were installed on mine accesses to monitor mine gas parameters (oxygen, carbon dioxide and methane volumetric content, radon volumetric activity, flow velocity, gas temperature and differential pressure) and external parameters (temperature and barometric pressure). The results show that gas flow can be regulated mainly by temperature gradient between external atmosphere and mine workings (in iron mines) or by barometric pressure (in coal mines). Gas emissions from iron mines may require extra securing protocol that prevents population exposal to noxious gas

Bisimulation, the Supervisory Control Problem and Strong Model Matching for Finite State Machines

A fundamental relationship between the controllability of a language with respect to another language and a set of uncontrollable events in the Supervisory Control Theory initiated by (Ramadge and Wonham, 1989) and bisimulation of automata models is derived. The theoretical results relating bisimulation to controllability support an efficient solution to the Basic Supervisory Control Problem. Using (Fernandez, 1990) generalization of the partition refinement algorithm of (Paige and Tarjan, 1987), it is possible to find a partition which represents the supremal controllable sublanguage of an automaton with respect to the language of another automaton and a set of events in a worst-case running time of O( m log( n )), where m is the number of transitions and n is the number of states. Utilizing the bisimulation property of language controllability and derived relationships between automata languages and input/output finite-state machine behaviors, a precise relationship is formally derived between Supervisory Control Theory and the system-theoretic problem posed by (DiBenedetto et al., 1994) called Strong Input/Output FSM Model Matching. Specifically, it is proven that in deterministic settings instances of each problem can be mapped to the other framework and solved.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45127/1/10626_2004_Article_184721.pd

On nonconflicting languages that arise in supervisory control of discrete event systems

We study four classes of nonconflicting sublanguages of a given language that arise in supervisory control of discrete event systems. We first present closed-form expressions for the supremal nonconflicting sublanguage and for the supremal closed nonconflicting sublanguage of a given language. The nonconflicting condition is with respect to a second given language. We then present algorithms to compute the supremal nonconflicting controllable sublanguage and the supremal closed nonconflicting controllable sublanguage of a given language. The regularity properties of these languages are also investigated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29184/1/0000237.pd

First steps in coupling continuous carbon isotopic measurements with already proven subsurface gas monitoring methods above underground carbon dioxide storage sites

International audienceThe main role of INERIS (French National Institute for Industrial Environment and Risks) is to assess and avert accidental and chronic risks to both people and the environment linked to industrial installations, chemical substances and underground operations. INERIS is thus involved in research consortiums for underground storages of wastes, hydrocarbons or carbon dioxide. Concerning carbon dioxide storage, INERIS works for many years on defining and testing monitoring methods. As a French expert, the institute also performs integrated risk assessment studies. This paper focuses on the last improvements concerning the monitoring methods developed or patented by INERIS. Because the institute was created from the research centre of the former French national coal mining company, it has a well-established know-how in monitoring gas atmospheres. Having developed monitoring methods for mining contexts, INERIS has tools to constrain gas migrations in subsurface: 1. to determine gas flux between soil and atmosphere with dynamic accumulation chambers; 2. to determine gas concentrations in unsaturated zones through integrated gas sensor systems linked to subsurface boreholes (from 0 to about 300 meters depth). Initially designed for mining context, these two methods have been tested and proven for the monitoring of CO2 geological storage contexts. For example between 2005 and 2007, INERIS was one of the five partners involved in the 'GeoCarbone MONITORING' research project. This project was funded by the French Research Agency and aims at defining methods to monitor CO2 storage sites. Today the institute is involved in other projects studying pilot sites. In this paper we present results collected in analog contexts to CO2 storage sites. We will discuss in which conditions the carbon isotopic signature can help to determine the possible origins of the gas analyzed in our devices and to better understand the physical and chemical processes which can have led to the studied gas compositions. We will also highlight the fact that in some cases, there is a real need of using isotopic tracing methods otherwise the identification of these different processes cannot be done easily