Search

info:eu-repo/semantics/published, 1

info:eu-repo/semantics/published

In this paper, we analyze some properties of quasi-polynomial dynamical systems. This general class can be related to the class of quadratic Lotka-Volterra systems through a suitable mapping and change of variables. We analyze a criterion for convergence of solutions and the structure of ω-limit sets., SCOPUS: ar.j, info:eu-repo/semantics/published

In this paper we consider analytical properties of a class of general nonlinear systems known as Quasi-Polynomial systems. We analyze sufficient conditions for permanence and boundedness of solutions, and illustrate our approach with an application to Lamb equations describing the evolution of electromagnetic modes in an optical maser., SCOPUS: ar.j, info:eu-repo/semantics/published

In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games., SCOPUS: ar.j, info:eu-repo/semantics/published

In this work, we study the time evolution of systems containing a large number of particles interacting via a $1/r$ binary interaction potential, such as Coulombian and self-gravitating systems. In particular, we study the effect on the dynamics of the Holtsmark-Chandrasekhar theory, which describes the static fluctuations of the total force field around the Vlasov mean-field. We derive these effects by developing a new perturbative theory using the fundamental representation of Statistical Mechanics :The BBGKY hierarchy. This leads to a modification of the Vlasov equation by an additional term involving a fractional Laplacian to the power $3/4$ in velocity space, and a fractional iterated time integral of order $1/2$. We show that one of the consequences of this new term for spatially homogeneous systems is the appearance in the velocity distribution of long tails in $v^{-5/2}$. By extension, similar behaviors can be expected for weakly inhomogeneous systems. These long tails correspond to a universal mechanism related to the divergence of the interaction potential in $1/r$. More specifically, they are induced by the long tails of the total force field distribution as described by the Holtsmark-Chandrasekhar theory. Such a result cannot be obtained from theories based on the weak-coupling between particles, which lead to the Vlasov term, and, the Landau collision operator at the next order. We verify numerically these results by means of molecular dynamics simulations. We study the evolution of the velocity distributions for times very short compared to the violent relaxation time. In this particular time regime, we find, as expected, power laws in $v^{alpha}$ for the velocity distribution tail. In particular, when the regularization parameter of the interaction potential tends to $0$, the exponent in the power law indeed tends from below toward the theoretically predicted value $alpha=-5/2$., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Cambridge University, info:eu-repo/semantics/published

Turbulent phenomena are found in both natural (e.g. the Earth's oceans, the Sun's corona) and artificial (e.g. flows through pipes, the plasma in a tokamak device) settings; evidence suggests that turbulence is usually the normal behaviour in most cases. Turbulence has been studied extensively for more than a century, but a complete and consistent theoretical description of it has not yet been proposed. It is in this context that the motion of particles under the influence of turbulent fields is studied in this work, with direct numerical simulations. The thesis is structured in three main parts. The first part describes the tools that are used. Methods of integrating particle trajectories are presented, together with a discussion of the properties that these methods should have. The simulation of magnetohydrodynamic (MHD) turbulence is discussed, while also introducing fundamental concepts of fluid turbulence. Particle trajectory integration requires information that is not readily available from simulations of turbulent flows, so the interpolation methods needed to adapt the fluid simulation results are constructed as well. The second part is dedicated to the study of two MHD problems. Simulations of Kolmogorov flow in incompressible MHD are presented and discussed, and also simulations of the dynamo effect in compressible MHD. These two scenarios are chosen because large scale structures are formed spontaneously by the turbulent flow, and there is an interest in studying particle transport in the presence of structures. Studies of particle transport are discussed in the third part. The properties of the overall approach are first analyzed in detail, for stationary predefined fields. Focus is placed on the qualitative properties of the different methods presented. Charged article transport in frozen turbulent fields is then studied. Results concerning transport of particles in fully developed, time-evolving, turbulent fields are presented in the final chapter., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Dans cette dissertation, nous considérons l’écoulement des liquides conducteurs d’électricité dans un champ magnétique externe. De tels écoulements sont décrits par les équations de la magnétohydrodynamique (MHD) quasi-statique, et sont fréquemment rencontrés dans des applications pratiques. Il suit qu’il y a un intérêt fort pour des outils numérques qui peuvent simuler ces écoulements dans des géometries complexes.La première partie de cette thèse (chapitres 2 et 3) est dédiée à la présentation de la machinerie numérique qui a été utilisée et implémentée afin de résoudre les équations de la MHD quasi-statistique (incompressible). Plus précisément, nous avons contribué au développement d’un solveur volumes finis non-structuré parallèle. La discussion sur ces méthodes est accompagnée d’une analyse numérique qui est aussi valable pour des mailles non-structurées. Dans le chapitre 3, nous vérifions notre implémentation par la simulation d’un certain nombre de cas tests avec un accent sur des écoulements dans un champ magnétique intense.Dans la deuxième partie de cette thèse (chapitres 4-6), nous avons utilsé ce solveur pour étudier des écoulements MHD de proche paroi .La première géometrie considérée (chapitre 4) est celle d’une conduite circulaire infini d’axe à haut nombre de Hartmann. Nous avons investitgué la sensitivité des résultats numériques au schéma de discrétisation et à la topologie de la maille. Nos résultats permettent de caractériser in extenso l’écoulement MHD dans une conduite avec des bords bien conducteurs par moyen des lois d’échelle.Le sujet du cinquième chapitre est l’écoulement dans une conduite toroïdale à section carée. Une étude du régime laminaire confirme une analyse asymptotique pour ce qui concerne les couches de cisaillement. Nous avons aussi effectué des simulations des écoulements turbulents afin d’évaluer l’effet d’un champ magnétique externe sur l’état des couches limites limites.Finalement, dans le chapitre 6, nous invest, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Egyptian National Environmental Division Chapter 14, SCOPUS: ch.b, info:eu-repo/semantics/published

La digitation visqueuse est une instabilité hydrodynamique apparaissant lorsque, dans un milieu poreux, un fluide moins visqueux déplace un fluide plus visqueux. L'objectif de notre thèse est l'étude expérimentale des propriétés des motifs de digitation lorsque l'échantillon de fluide visqueux est de taille finie et lorsqu'une réaction chimique modifie la viscosité dans un milieu poreux modèle, en l'occurrence une cellule de Hele-Shaw. En particulier, notre étude a permis de quantifier la contribution de dispersion et de la digitation visqueuse, l'étalement dans l'espace d'échantillons de taille finie en fonction des paramètres expérimentaux (contraste de viscosité, vitesse de déplacement et taille de l'échantillon). Pour les fluides réactifs, nous analysons la digitation induite par une réaction A + B C dont le produit C est plus visqueux que les réactifs A et B, ceux-ci ayant la même viscosité. Nous mettons en évidence l'effet des concentrations en réactifs, du choix du fluide vecteur et du débit d'injection sur le motif de digitation., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

In this thesis we mainly focus on the study of the turbulent transport of impurity particles in the plasma due to the electrostatic drift wave microinstabilities. In a fusion reactor, the helium produced as a result of the fusion process is an internal source of impurity. Moreover, impurities are released from the material surfaces surrounding the plasma by a variety of processes: by radiation from plasma, or as a result of sputtering, arcing and evaporation. Impurities in tokamak plasmas introduce a variety of problems. The most immediate effect is the radiated power loss (radiative cooling). Another effect is that the impurity ions produce many electrons and in view of the operating limits on density and pressure, this has the effect of replacing fuel ions. For example, at a given electron density, $n_{e}$, each fully ionized carbon ion (used in the wall materials in the form of graphite) replaces six fuel ions, so that a 7\\% concentration of fully ionized carbon in the plasma core, would reduce the fusion power to one half of the value in a pure plasma. Therefore, for all tokamaks it become an immediate and continuing task to reduce impurities to acceptably low concentrations. However, the presence of impurities, with control, can be beneficial for the plasma performance and reduction of strong plasma heat loads on the plasma facing walls. The radiative cooling effect which was mentioned above can be used at the edge of the plasma in order to distribute the plasma heat more evenly on the whole surface of the vessel walls and therefore, reduce significantly plasma heat bursts on the small regions on the divertor or limiter tiles. The experiments at TEXTOR show that the presence of the impurities at the plasma edge can also improve the performance and reduce the turbulent transport across the magnetic field lines. The observed behavior was explained trough the proposed mechanism of suppression of the most important plasma drift wave microinstability in this region, Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

Le couplage important entre les différentes échelles d’un écoulement est une des caractéristiques prin-cipales des turbulences. Cela est exprimé mathématiquement par les termes non linéaires présents dans les équations d’équilibre de l’écoulement, dominants en dynamique turbulente. En magnétohy-drodynamique (MHD), la force de Lorentz influe sur l’équation de conservation de l’impulsion et le nombre de termes non linéaires passe à quatre au lieu d’un seul pour un fluide non conducteur.L’objectif principal de cette thèse est d’analyser le transport d’énergie inter-échelles en utilisant une simulation numérique directe d’un écoulement turbulent MHD. Les propriétés de localité du transport de l’énergie entre les échelles pour un écoulement anisotropique ou isotropique, généré par la présence d’un champ magnétique constant, sont renforcées. Un objectif secondaire est d’établir un cadre de travail pour l’étude du transport de particules test chargées dans un champ électromagnétique turbu-lent, i.e. généré par le mouvement d’un fluide conducteur, qui possède des structures à plusieurs ordres de grandeur. La structure de la thèse est présentée ci-dessous.Dans la première partie, composée des deux premiers chapitres, l’auteur présente les notions de turbu-lences, aussi bien hydrodynamiques que MHD. Ces deux chapitres sont des synthèses.La deuxième partie est la principale source de nouveaux résultats. Le chapitre 3 présente les méthodes numériques pour la résolution des équations, les méthodes pseudo-spectrales. Un nouveau type de force est introduit, imposant un niveau de dissipation pour tous les invariants. Dans le chapitre 4, il est effectué une analyse du transfert d'énergie entre ordres de grandeur pour les turbulences MHD. Pour explorer ces transferts d'énergie, le domaine spectral est décomposé en une série de coques de même nombre d'onde. Le transfert moyen d'énergie entre ces coques est analysé. Les transferts d'énergie s'avèrent être surtout locaux en ord, Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

La magnétohydrodynamique (MHD) est la science et le formalisme qui décrivent les mouvements d'un fluide conducteur d'électricité. Il est possible que de tels mouvements donnent lieu à l'effet dynamo qui consiste en la génération d'un champ magnétique stable et de grande échelle. Ce phénomène est vraisemblablement à l'origine des champs magnétiques des planètes, des étoiles et des galaxies. Il est surprenant qu'alors que les mouvements fluides à l'intérieur de ces objets célestes sont turbulents, les champs magnétiques généré soient de grande échelle spatiale et stables sur de longues périodes de temps. De plus, ils peuvent présenter une dynamique temporelle régulière comme c'est le cas pour le champ magnétique solaire dont la polarité s'inverse tous les onze ans. Décrire et prédire les mouvements d'un fluide turbulent reste l'un des problèmes les plus difficiles de la mécanique classique. %La description aussi bien analytique que numérique d'un fluide hautement turbulent est d'une effroyable complexité, si pas tout simplement impraticable. Dans cette situation, Il est donc utile de construire des modèles aussi proches que possible du système de départ mais de moindre complexité de sorte que des études théoriques et numériques deviennent envisageables.Deux approches ont été considérées ici. D'une part, nous avons développé des modèles présentant un très petit nombre de degrés de liberté (de l'ordre de la dizaine). Une étude analytique est alors possible. Ces modèles ont une dépendance en les paramètres physiques - nombres de Reynolds cinétique et magnétique et injection d'hélicité - qualitativement similaire aux dynamos célestes et expérimentales.D'autre part, les modèles en couches permettent de caractériser les transferts d'énergie entre les structures de différentes tailles présentes au sein du champ de vitesse. Nous avons développé un nouveau formalisme qui permet d'étudier aussi les échanges avec le champ magnétique. De plus, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

This thesis is devoted to the study of a deformable material interface between two immiscible movingmedia, both of them being magnetizable. The first part concerns the establishment of a complete set of dynamical equations allowing a complete description of the non equilibrium phenomena including a coupling between the internal angular momentum and the electromagnetic field. The effects of the relaxation processes are also discussed. We show that the deformation of the interface introduces a nonlinear term, proportional to the mean curvature, inthe surface dynamical equations of mass momentum and angular momentum. That termintervenes also in the singular magnetic and electric fields inside the interface which lead tothe influence of currents and charge densities at the interface. In a second part, we give the expressionfor the entropy production inside the interface as well as in the bulk phase. Using the general principles of non equilibrium thermodynamics, we compute the different thermodynamical fluxes., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Les interactions gravitationnelles et électrostatiques sont deux exemples fondamentaux de systèmes en interaction de longue portée. Les propriétés d'équilibre de modèles simples en interaction de longue portée sont bien comprises et révèlent des comportemens exotiques: capacité spécifique négative et inéquivalence des ensembles statistiques par exemple.La compréhension de l'évolution dynamique dans le cas de systèmes en interaction de longue portée représente encore actuellement un défi théorique. Des modèles simples présentent des propriétés telles que des transitions de phase hors d'équilibre ou des états quasi-stationnaires.Le but de la présente thèse est d'étudier les propriétés dynamiques de systèmes en interaction de longue portée pour des modèles à une dimension. La description cinétique adéquate est donnée par l'équation de Vlasov. Une théorie statistique proposée par D. Lynden-Bell est appropriée pour prédire dans certaines situations l'aboutissement de la dynamique. Un outil de simulation pour l'équation de Vlasov complète cette approche.Une étude détaillée de la transition de phase dans le Laser à Electrons Libres est présentée et la transition est analysée à l'aide de la théorie de Lynden-Bell.Ensuite, la présence d'étirement et de repliement est étudiée dans le modèle Hamiltonian Mean-Field en analogie avec la dynamique des fluides.Enfin, un système de pendules découplés dont les états asymptotiques sont similaires à ceux du modèle Hamiltonian Mean-Field est introduit. Son évolution asymptotique est prédite par la théorie de Lynden-Bell et par une approche exacte. Ce système présente une évolution initiale rapide similaire à la relaxation violente présente dans des modèles plus compliqués. De plus, une transition de phase hors d'équilibre est trouvée si une condition d'auto-consistence est imposée.En résumé, la présente thèse comporte des résultats originaux liés à la présence d'états quasi-stationnaires et de transitions d, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

The results of the Car-Free Sundays in Brussels demonstrate the close relationship between the traffic and the presence of the gaseous pollutants such as NO, NO2, CO, CO2 and O3 in a traffic environment. The relationship with PM10 and PM2.5 seems to be much more complex. In fact, the PM10 andPM2.5 concentrations on the Car-Free Sunday 2006 were amongst the highest that year and they were three times higher than on an average Sunday or working day. Analysis of the data indicate that direct particle emissions from traffic only have a limited contribution to the overall PM concentration. © 2010 Inderscience Enterprises Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published

The purpose of this study was to measure the impact of urban activities on airborne particle dynamics during weekend periods in Brussels urban area. Differences in the granulometry and micromorphology between particles sampled on working days and weekends were studied.We quantified the area, size, number, and the chemistry parameters of the airborne particles and compared between Saturday, Sunday, and Monday. We report and analyze data on airborne particles up to PM10, measured in the Brussels region from October 2002 to September 2003. Our investigation reveals detailed information regarding chemical composition of the airborne particles over the weekend period in the Brussels urban area. Furthermore, the majority of the airborne particles in the Brussels region may belong to sources geographically outside the (in situ) Brussels area. © Springer Science + Business Media B.V. 2009., SCOPUS: ar.j, info:eu-repo/semantics/published

Magnetohydrodynamics describes the motions of an electrically conducting fluid under the influence of magnetic fields. Such flows are encountered in a large variety of applications, from steel industry to heat exchangers of nuclear fusion reactors. Here we are concerned with situations where the magnetic field is relatively strong and the flow manifests turbulent motions. The interaction of the fluid with the electromagnetic field is still insufficiently understood and efficient predicting methods are lacking. Our goal is to provide more insight on this problem by making heavy use of numerical methods. In this work, two different classes of problem are investigated. First we consider that the turbulent character of the fluid is well developed and that solid boundaries are sufficiently far away to be completely neglected. The main effects of a strong magnetic field in that case are to damp the motion and to homogenize the flow along its direction, leading to a quasi two dimensional state. Using numerical simulations we have studied the dynamics of the flow in Fourier space and in particular the non linear energy transfers between turbulent eddies. Further we investigated the scale-by-scale anisotropy and compared various methods to address this quantity. Finally, the evolution of a passive scalar embedded in the flow was analyzed and it turned out that the characteristic anisotropy of the velocity field is reflected in the distribution of the scalar quantity. In the second problem, the flow in a duct of square cross section subject to a transverse magnetic field has been considered. Here, unlike in the previous situation, the magnetic field has globally a destabilizing effect on the flow, because of the strong inhomogeneities it produces. For instance, high velocity regions develop along the walls that are parallel to the magnetic field. There, we are mostly interested in the possible development of persistent time-dependent fluctuations. It is obse, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

A theoretical framework is presented for the description of active transport of solid particles in turbulent fluids. Active transport exists when large enough particle concentration is present in the fluid and when the mass of particles is large enough for inertia effects to be non negligible. In such situations, particles trajectories differ from fluid flow lines, the reaction forces of particles on the fluid are important and modify the Navier-Stokes equation, collisions between solid particles are non negligible and are affected by the turbulent fluctuations of the fluid velocity field. As a consequence the Navier-Stokes turbulent hierarchy is coupled to an inelastic Boltzmann-like kinetic equation for the phase-space one particle distribution of the solid particles. Effects of fluid velocity field fluctuations on binary collisions of particles are discussed and shown to modify the collision term of the kinetic equation. Moreover, we show that the Lagrangian equations of motion for the particles in the fluid are fractional differential equations. This is due to the non-Markovian character of the hydrodynamical forces acting on particles dispersed in unsteady flows., SCOPUS: ar.j, info:eu-repo/semantics/published

Le travail présenté ici porte sur l’étude de la production et du transport du monoxyde d’azote (NO) dans le poumon humain. Le NO est une molécule dont l’implication dans des processus physiologiques n’a été mis en évidence qu’en 1987. Depuis, il a été démontré que le NO joue de nombreux rôles dans le corps humain. Le NO est un gaz labile (instable) dans les conditions physiologiques, il diffuse très facilement au travers des parois et il a une grande affinité pour l’hémoglobine. La production du NO est liée à 3 isoformes différentes de la protéine appelées synthases du NO ou NO synthases., Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

The first and main part of this thesis concerns the quantization of the transverse transport in diverse periodic quantum systems. From a theoretical point of view, the Hall conductivity's quantization may be understood at the single-particle level in terms of topological invariants. In periodic media such as crystals, the single-particle energy spectrum depicts a specific band structure. A modern approach, based on topology and differential geometry, consists in assigning an abstract mathematical object, a fibre bundle, to each energy band. The fibre bundle's topology is measured by a topological invariant, called the Chern number, which only takes integral values. Surprisingly, the transverse conductivity can be expressed as a sum of Chern numbers. In this work, one provides a rigorous derivation of this fact and one presents several methods which allow the numerical and analytical computation of the Chern numbers for diverse systems. The first original study concerns the physics of ultracold atoms trapped in optical lattices. These very popular experimental setups, which are currently designed in several laboratories worldwide, allow for the exploration of fundamental problems encountered in modern physics. In particular atoms trapped in optical lattices reproduce with a very high accuracy the physics of the Hubbard-type models which describe a huge variety of condensed matter phenomena, such as high-Tc superconductivity and the Mott quantum phase transition. Particularly interesting is the possibility to create artificial magnetic fields in optical lattices. Generated by complex laser configurations or by rotation of the trap, these artificial fields allow the simulation of electronic systems subjected to intense magnetic fields. In this thesis, one explores the possibility of a quantum Hall-like effect for neutral particles in such arrangements. In particular one focuses on the exotic situation in which non-Abelian gauge potentials are generated in the, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Motivés par les développements récents dans le domaine des nanosciences, nous étudions les propriétés statistiques et thermodynamiques des systèmes mésoscopiques. En particulier, nous nous concentrons sur les résultats connus sous le nom de théorèmes de fluctuation. Ces relations donnent des prédictions sur le comportement de différents quantités dynamiques dans des situations loin de l'équilibre, tout en tenant compte des fluctuations de l'évolution temporelle., Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

Erosion, transport and deposition of atmospheric dust are largely determined by the nature and state of the earth's surface (the dust source) and the physical characteristics of the atmosphere. The state of the atmosphere is subject to important temporal variations related to diurnal and seasonal cycles and to synoptic conditions. The dynamic evolution of particulate concentrations measured at Brussels showed a significant peak in PM10 during 24-25 March 2007. The 4-day backward trajectories calculated for this peak attributed its cause to a dust storm that had occurred 2 days earlier in the Sahara. Chemical analysis showed a significant similarity to Saharan dust composition, primarily oxides of Si, Fe, and Al. On 29 March, another peak with a very high PM concentration and an elevated PM2.5-to-PM10 ratio was recorded in Brussels. Analysis of its PM profile showed that it was mainly caused by formation of secondary aerosols. © 2008 Elsevier Ltd. All rights reserved., SCOPUS: ar.j, info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

The main objective of our research was to compare the airborne particle micromorphology and chemistry in the Brussels environment during agriculture working periods in the surrounding farming region. We used specific methods and instrumentation that are adapted to the climate peculiarities of the Brussels region, the period of investigations (12 months) and the proposed objectives. For the agricultural works we defined the following six periods: before sowing, sowing, after sowing, before harvest, harvest and after harvest. The results indicate a possible temporal correlation between agricultural work periods and airborne particle concentration, micromorphology and chemistry in the Brabant-Brussels region. For wheat and corn plant-growth periods, the average particle size, defined as the area obtained by a planar projection of the particulate, showed important variations in time. For sugar beet and endive, the average area size variations are less important. The roughness and sphericity parameters for the growth periods of the four different plants also showed significant differences. Many of the larger particulates (> 10 microm) are aggregates of even finer particles coated with many still finer ones. The airborne particle chemistry averages (atomic percentage At%), showed that three constituents (Si, S and Fe) dominate all the samples (except for particles 3-10 microm in size, which contain a relatively large percentage of Al). Applying similar investigation methods to study the correlations between airborne particle dynamics in urban zones and the agriculture working periods in their surrounding regions could be of interest to better understand the complexity of the PM problematic., Journal Article, info:eu-repo/semantics/published

info:eu-repo/semantics/published

We report and analyze data on the PM10 fraction of airborne particles measured at five recording stations in the Brussels region from October 2002 till September 2003. These stations are representative of the various activity sectors of the Brussels urban area. The objective was the determination of the origin of the PM10 particles (particles up to 10 mum) that are recorded in that region in order to follow the EU directives concerning tolerance level of airborne particles concentration. In order to evaluate the impacts of local and external factors that inject solid particles in the atmosphere of Brussels we compared concentration data from working and not working (holidays) periods. Moreover, we also compared concentrations from periods of agricultural activity and rest in the Brabant provinces surrounding the Brussels region for various crop types. The results lead to the conclusion that the impact or urban traffic is rather limited while that of the agricultural activities is important. Moreover, there appears a clear-cut distinction between different types of crops., info:eu-repo/semantics/published

This recent article constitutes a new orientation of the author's research activity. It is shown that the requirement of invariance of the laws of mechanics under a group of transformations acting on the precision of measurement leads to the emergence of the non-relativistic quantum mechanical Schrödinger equation. Furthermore, the invariance under these transformations requires the existence of a dual type of physical evolution that happens to be equivalent to the so-called Brownian Bridge stochastic process. This process has already been studied by E. Schrödinger in 1932 in order to find a classical origin to the quantum prescription for the calculation of averages. The author's hope is that this duality could have some relation with the existence of two types of processes in quantum mechanics :unitary processes between two successive measurements and non-unitary measurement processes., info:eu-repo/semantics/published

info:eu-repo/semantics/published