Auswahl der wissenschaftlichen Literatur zum Thema „Poisson suspensions“

We establish a necessary and sufficient condition for a Poisson suspension to be prime. The proof is based on the Fock space structure of the $L^{2}$-space of the Poisson suspension. We give examples of explicit infinite measure-preserving systems, in particular of non-singular compact group rotations that give rise to prime Poisson suspensions. We also compare some properties of so far known prime transformations with those of our examples, showing that these examples are new.

A dilute suspension of uniform, non-Brownian spheres settles slowly in a viscous solvent. The initially well-mixed system showing Poisson or random occupancy statistics evolves to a system having reduced number fluctuations, but otherwise appearing random. The reduced number fluctuations are consistent with recent measurements of velocity fluctuations in settling suspensions. These experimental results test the assumptions leading to the theoretical predictions by Calflisch and Luke that the velocity fluctuations increase without limit with increasing sample dimension. The theoretical prediction assumes Poisson occupation statistics contrary to our observations.

AbstractWe investigate the ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure-preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite-measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaussian dynamical systems.

The purpose of the study was to mathematically model the dynamics of inhomogeneous electrically charged media, such as that of gas suspensions, i.e., solid particles suspended in a gas. The mathematical model implemented a continuum approach to modeling the dynamics of inhomogeneous media, which implies taking into account intercomponent heat transfer and momentum exchange. The carrier medium was described as a viscous, compressible, heat-conducting gas, the equations of the model were supplemented with initial and boundary conditions, and the system of the equations was integrated by an explicit finite-difference method. To obtain a monotonic grid function, a nonlinear scheme for correcting the numerical solution was used. The mathematical model was supplemented with the Poisson equation describing the electric field, which is formed by electrically charged disperse inclusions. The Poisson equation was integrated by finite-difference methods on a gas-dynamic grid. The flow of a gas suspension caused by the motion of dispersed particles under the action of the Coulomb force was studied numerically. Flows of gas suspensions with surface and mass densities of electric charge were modeled. For the surface charge density model, the Coulomb force acting on the unit mass of the gas suspension increases with a decrease in the dispersion of particles. For the mass charge density, the dispersion of particles does not affect the specific Coulomb force acting on the particles. The intensity of the gas suspension flow increases with decreasing particle size, both for the mass and surface models of charge density. For the surface charge density model, as the particle size decreases, the intensity of the gas pressure drop in the emerging gas suspension flow increases more than when modeling the gas suspension dynamics with a mass distribution of the electric charge density

Continuum many spectrally disjoint Sidon automorphisms with tensor square isomorphic to a planar translation are produced. Their spectra do not have the group property. To show that their spectra are singular the polynomial rigidity of operators is used, which is related to the concept of linear determinism in the sense of Kolmogorov. In the class of mixing Gaussian and Poisson suspensions over Sidon automorphisms new sets of spectral multiplicities are realized. Bibliography: 12 titles.

Dans cette thèse, nous explorons les structures possibles des systèmes dynamiques de la forme $\bfX :=(X, \A, \mu, T)$ et leurs tribus facteur $\B \subset \A$. Les deux premiers chapitres étudient les différentes façons dont une tribu facteur $\B$ peut s'inclure dans un système dynamique $\bfX :=(X, \A, \mu, T)$, c'est-à-dire que nous étudions certaines structures possibles de l'\emph{extension} $\A \arr \B$. Dans le premier chapitre, nous considérons les concepts de \emph{super-innovations} et de \emph{standardité} des extensions, inspirés de la théorie des filtrations. Un point important est l'introduction de la notion d'\emph{extensions confinées}, qui nous intéressent parce qu'elles n'ont pas de super-innovation. Nous donnons plusieurs exemples et étudions des propriétés supplémentaires de ces extensions, y compris des résultats de relèvement. Ensuite, nous montrons notre résultat principal : l'existence d'extensions non-standard. Enfin, ce résultat trouve une application dans l'étude des filtrations dynamiques, qui sont les filtrations de la forme $(\F_n)_{n \leq 0}$ telles que chaque $\F_n$ est une tribu facteur. Nous montrons qu'il existe des \emph{filtrations dynamiques I-confortables non standard}.Le deuxième chapitre approfondit l'étude des extensions confinées en trouvant un nouveau type de telles extensions, dans le cadre des suspensions de Poisson : nous prenons un système dynamique $(X, \mu, T)$ en mesure $\s$-finie infinie et une extension compacte $(X \times G, \mu \otimes m_G, T_\phi)$, puis nous considérons l'extension de Poisson correspondante $((X \times G)^*, (\mu \otimes m_G)^*, (T_\phi)_*) \to (X^*, \mu^*, T_*)$. Nous donnons des conditions sous lesquelles cette extension est confinée et construisons un exemple qui correspond à ces conditions.Enfin, le troisième chapitre se concentre sur une famille de filtrations dynamiques : les \emph{filtrations de Pinsker faible}. L'existence de ces filtrations sur tout système ergodique provient d'un résultat récent d'Austin \cite{austin}, et elles se présentent comme un outil potentiel pour décrire les systèmes à entropie positive. Nous explorons les liens entre la structure asymptotique des filtrations de Pinsker faible et les propriétés du système dynamique sous-jacent. Naturellement, nous demandons aussi si, sur un système donné, la structure des filtrations de Pinsker faible est unique à isomorphisme près. Nous donnons une réponse partielle, dans le cas où le système sous-jacent est un schéma de Bernoulli. Nous concluons notre travail en donnant deux exemples explicites de filtrations de Pinsker faible
In this thesis, we explore the possible structures of measure preserving dynamical systems of the form $\bfX :=(X, \A, \mu, T)$ and their factor $\s$-algebras $\B \subset \A$. The first two chapters investigate various ways in which a factor $\s$-algebra $\B$ can sit in a dynamical system $\bfX :=(X, \A, \mu, T)$, i.e. we study some possible structures of the \emph{extension} $\A \arr \B$. In the first chapter, we consider the concepts of \emph{super-innovations} and \emph{standardness} of extensions, which are inspired from the theory of filtrations. An important focus of our work is the introduction of the notion of \emph{confined extensions}, which first interested us because they have no super-innovation. We give several examples and study additional properties of confined extensions, including several lifting results. Then, we show our main result: the existence of non-standard extensions. Finally, this result finds an application to the study of dynamical filtrations, i.e. filtrations of the form $(\F_n)_{n \leq 0}$ such that each $\F_n$ is a factor $\s$-algebra. We show that there exist \emph{non-standard I-cosy dynamical filtrations}.The second chapter furthers the study of confined extensions by finding a new kind of such extensions, in the setup of Poisson suspensions: we take an infinite $\s$-finite measure-preserving dynamical system $(X, \mu, T)$ and a compact extension $(X \times G, \mu \otimes m_G, T_\phi)$, then we consider the corresponding Poisson extension $((X \times G)^*, (\mu \otimes m_G)^*, (T_\phi)_*) \to (X^*, \mu^*, T_*)$. We give conditions under which that extension is confined and build an example which fits those conditions.Lastly, the third chapter focuses on a family of dynamical filtrations: \emph{weak Pinsker filtrations}. The existence of those filtrations on any ergodic system comes from a recent result by Austin \cite{austin}, and they present themselves as a potential tool to describe positive entropy systems. We explore the links between the asymptotic structure of weak Pinsker filtrations and the properties of the underlying dynamical system. Naturally, we also ask whether, on a given system, the structure of weak Pinsker filtrations is unique up to isomorphism. We give a partial answer, in the case where the underlying system is Bernoulli. We conclude our work by giving two explicit examples of weak Pinsker filtrations

Cette thèse est consacrée aux écoulements homogènes de bulles, ainsi qu'à leur couplage avec le transport d'un scalaire et la turbulence. Elle s'intéresse plus spécifiquement aux effets de taille finie, des interactions hydrodynamiques et de la microstructure de la suspension qui sont étudiés à l'aide de simulations numériques directes à l'échelle d'une seule bulle. La dynamique d'une suspension laminaire de bulles induite par la seule gravité est d'abord revisitée. L'influence de la fraction volumique sur la vitesse de dérive des bulles est établie analytiquement et numériquement pour une suspension parfaitement ordonnée, puis des ressemblances entre suspensions ordonnées et suspensions désordonnées sont mises en évidence. Ces résultats sont ensuite mis à profit pour la modélisation du transport d'un scalaire passif au sein d'une suspension laminaire, tel que décrit par une diffusivité effective tensorielle, et des différences essentielles entre systèmes ordonnés et systèmes désordonnés concernant le transport de scalaire sont mises en exergue. Enfin, la turbulence est prise en compte dans les simulations et son interaction avec une bulle de taille finie est caractérisée. Il est montré que le comportement dynamique d'une bulle de taille comparable à la microéchelle de Taylor ressemble qualitativement à celui d'une microbulle, avec, notamment, une préférence pour certaines régions caractéristiques de l'écoulement. Une définition de l'écoulement vu par la bulle compatible avec les modèles standards de masse ajoutée et de portance est finalement proposée
This thesis is devoted to the study of homogeneous bubbly flows and their coupling with scalar transport and turbulence. It focuses on the effects of finite size, hydrodynamic interactions, and suspension microstructure, which are investigated using direct numerical simulations at the bubble scale. The dynamics of laminar buoyancy-driven bubbly suspensions is first revisited. More specifically, the effect of volume fraction on the bubble drift velocity is clarified by connecting numerical results to theory for dilute ordered systems, and similarities between perfectly ordered and free disordered suspensions are evidenced. These results are then used for the modeling of passive scalar transport in laminar suspensions as described by an effective diffusivity tensor, and crucial differences between ordered and disordered systems with respect to scalar transport are highlighted. Lastly, turbulence is included in the simulations, and its interaction with a finite-size bubble is characterized. The behavior of a bubble as large as Taylor microscale is shown to share a number of common features with that of a microbubble, most notably, the flow sampled by the bubble is biased. A definition of the liquid flow seen by the bubble, as it enters in usual models for the added mass and the lift forces, is finally proposed

L’exposition cutanée aux produits chimiques par des rejets criminels ou accidentels impose une méthode de décontamination rapide et efficace pour sauver des vies et limiter le transfert de la contamination. L’exploration bibliographique recense des produits toxiques (armes chimiques, toxiques industriels) ainsi que les décontaminants naturels ou synthétiques et leurs méthodes d’application dans un contexte d’intervention sur le terrain. Le sujet vise à la qualification d’un outil de décontamination, la terre de foulon dans des formulations simples, faciles à mettre en œuvre en urgence par les services de Sécurité civile (sapeurs-pompiers). Le travail réalisé comporte :La caractérisation chimique et structurale de la poudre de terre de foulon NBC-Sys qui a permis d’identifier le composant principal : la palygorskite, La formulation et la caractérisation galénique et physico-chimique (granulométrie, zêta potentiel) en milieu concentré et milieu dilué des systèmes dispersés,La capacité d’adsorption de la terre de foulon et ses formulations vis-à-vis d’un modèle contaminant, le 4-cyanophenol, d’intérêt pour l’évaluation de la décontamination, in vitro en milieu aqueux, ex vivo sur explant cutané. L’adsorption du 4-CP en solution aqueuse (10, 100 et 500 mg/L-1) est rapide (5-15min) au contact de la terre de foulon, varie avec le ratio terre de foulon/4-CP, atteint un plateau (saturation) entre 45 et 60 min, l’équilibre entre 60 min et 120 min. Les suspensions de terre de foulon sont plus efficaces (90%) pour la décontamination que les poudres (70%) et l’eau (60%) dans des conditions expérimentales identiques. L’évaluation de la terre de foulon et ses formulations sur les paramètres physiologiques de la peau (perte insensible en eau et conductance) in vivo chez l’homme ne montre pas d’altération de la fonction barrière cutanée.L’ensemble est un premier pas vers une référence (qui n’existe pas actuellement), incluant une méthodologie de décontamination chimique
Cutaneous exposure to contaminants chemicals after criminal or accidental release enforces a rapid and efficient decontamination to save lives and avoid cross contamination. A bibilographic exploration of this work identifies toxic chemical (chemical warfare agents, toxic industrial chemicals), raw and synthetic decontaminants and their application methods applied in emergency. The aim of this study focuses on a decontamination tool qualification, the fuller’s earth (FE), simple formulated, easy to apply in emergency by civil Security services (fire fighter brigades). The work performed includes :The chemical and structural characterization of the powder of fuller’earth NBC-Sys , that lead to identify the palygorskite as main component, The formulation of dispersed systems and their physico chemical characterization (granulometry, zêta potentiel) in concentrated or diluted medium. The adsorption capacity of the FE and formulations for a contaminant model, the 4-cyanophenol, to assess decontamination in vitro, in aqueous medium, ex vivo on cutaneous explant.4-CP adsorption in aqueous solutions (10, 100 et 500 mg/L-1) is rapid (5-15min), when contact with FE, vary with the ratio FE/ 4-CP, to reach a plateau phase (saturation) between 45 and 60 minutes, and an steady state between 60 and 120 min. FE suspensions are more efficient (90%) than powder (70%) and water (60%) in the same experimental conditions. L’évaluation de la terre de foulon et ses formulations sur les paramètres physiologiques de la peau (perte insensible en eau et conductance) in vivo chez l’homme ne montre pas d’altération de la fonction barrière cutanée. FE and its suspensions were assessed on physiological skin parameters (Transepidermal water loss and conductance) in vivo in a human study and exhibit no alteration on the skin barrier function. Results obtained is a first step towards a reference (that actually don’t exist) including a chemical decontamination method

Abstract Frictional impact analysis requires a friction model capable of correct detection of all possible impact modes such as sliding, sticking, and reverse sliding. Conventional methods for frictional impact analysis have either shown energy gain or not developed for jointed mechanical system, and especially not for closed-chain multibody systems. This paper presents a general formulation for the analysis of impact problems with friction in both open- and closed-loop multibody mechanical systems. The Poisson’s hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of the Newton’s hypothesis are avoided. A canonical form of the system equations of motion using Cartesian coordinates and Cartesian momenta is utilized. The canonical momentum-balance equations are formulated and solved for the change in the system Cartesian momenta using an extension of Routh’s graphical method for the normal and tangential impulses. The velocity jumps are calculated by balancing the accumulated system momenta during the contact period. The formulation is shown to recognize all modes of impact; i.e., sliding, sticking, and reverse sliding. The impact problems are classified into seven cases, and based on the pre-impact system configuration and velocities, expressions for the normal and tangential impulses are derived for each impact case. Examples including the impact of a falling rod on the ground, the tip of a double pendulum impacting the ground, and the impact of the rear wheel and suspension system of an automobile executing a very stiff bump are analyzed with the developed formulation.

Tractor drivers often exposed to high-amplitude and low frequency vibrations that could impact the ride comfort. Tractor-terrain interaction emits vibrations that transmitted to the driver’s body through the seat-pan, mainly. In present study, the vibration transmissibility response (i.e. from the seat base to seat pan location) has been evaluated using Finite Element Method (FEM). Three dimensional model of the tractor seat was designed by considering the various seat elements (i.e. frame, sub-frame, cushion, Swing-arm, spring, damper, and roller) and their material properties (i.e. Density, Young’s modulus, Poisson’s Ratio) in SoildWorks 2014. Three different types of seat suspension systems of varying spring stiffness (0.3 kg/mm; 0.55 kg/mm; and 0.7 kg/mm) with damping coefficient of 1465.9 Ns/m has been considered to analyze transmissibility response. Seat cushion of Polyurethane (PU) light foam material with thickness of 54 mm; density of 68 kg/m³, seat backrest inclination of 12º with cushion thickness of 45 mm has been set uniform throughout the investigation. Vibration transmissibility responses were analyzed within the frequency range of 0-20 Hz at 0.5 m/s2 along the vertical direction. Tractor seat found to exhibit maximum transmissibility between 2 to 6 Hz frequency ranges. In addition, the seat suspension with spring stiffness of 0.55 kg/mm showed approximately 16% minimum vibration transmissibility compared to other suspension systems. In conclusion, the dominant frequency ranges found in the vicinity of natural frequency of various human body parts that may impact the ride comfort; and the spring stiffness has considerable effect on the vibration transmissibility.

ABSTRACT: The unconventional Bone Spring and Wolfcamp Formations are the development focus in the Delaware Basin. However, the high heterogeneity of the reservoir rocks challenges the selection of landing zones and increases the uncertainty of well performance. Estimating faithful elastic properties and predicting stress profiles along the wellbores are key to improve production and stimulation design. We acquire over 3,000 feet of continuous cores from five wells in New Mexico, Delaware Basin. We combine a variety of high-resolution, whole core-based characterization techniques that include hyperspectral and dual energy computed tomography imaging, ultrasonic velocities, and scratch index profiling, to quantify intrinsic, fine-scale variability in vertical transversely isotropic elastic properties indicating Young's modulus and Poisson's ratio perpendicular and parallel to bedding. Geomechanical averaging of this thinly bedded medium is then upscaled to a petro-mechanical facies scale for geological modeling and stress prediction. Elastic anisotropy as an emergent property of the upscaling process is contrasted with the anisotropy determined from the traditional core-plug based approach. Implications for stress profile prediction are discussed. 1. INTRODUCTION The Permian Basin of west Texas and southeast New Mexico constitutes the largest oil reserve and the highest producing oil field in the United States. The component Delaware Basin to the west incorporates significant development in the Bone Spring and Wolfcamp Formations. The Bone Spring Formation represents a mixed siliciclastic-carbonate succession deposited as sediment gravity flows under cyclical sea level fluctuations (Montgomery, 1997; Blake, 2020). Due to the cyclic sedimentation associated with changing sea level, the Bone Spring Formation can be subdivided into 1st, 2nd, and 3rd Bone Spring carbonates followed by sand units. The underlying Wolfcamp Formation records deepwater deposition of organic-rich mudstones interbedded with calcareous mudstones, calcareous siltstones, carbonates, and argillaceous mudstones that were deposited within mixed carbonate-siliciclastic fan systems (Yeap, 2021). In general, the Wolfcamp Formation can further be separated into A, B, C, and D units (Gaswirth, 2017). Both formations consist of mixed sediment gravity flow and suspension sedimentation deposits which often exhibit thin beds and facies resulting in high heterogeneity (Bievenour and Sonnenberg, 2019). Thin bed analysis is critical for reservoir property characterization but can be challenging when heterogeneity regularly exists at length scales below wireline log resolution (2 – 3 feet). Therefore, acquiring high-resolution measurements can significantly assist in identifying and quantifying thin-bed heterogeneity and properties assignment.