Auswahl der wissenschaftlichen Literatur zum Thema „Dynamical filtrations“

La première partie de ce manuscrit entre dans le cadre de la théorie des probabilités, et est consacrée à l’étude de filtrations engendrées par des automates cellulaires. On étudie deux versions d’un automate algébrique agissant sur des configurations dont les états sont à valeurs dans un groupe abélien fini : l’une est déterministe, et consiste à additionner les états de deux cellules consécutives, et la seconde est une perturbation aléatoire de la première. À partir de ces automates, on construit des processus aléatoires markoviens et on étudie les filtrations engendrées par ces processus. On montre en utilisant le critère de I-confort que les deux filtrations sont standards au sens développé par Vershik. Cependant, les automates cellulaires ont comme particularité de commuter avec l’opérateur de décalages des coordonnées, appelé « shift ». Dans cette thèse, on introduit une nouvelle classification des filtrations dite « dynamique » qui tient compte de l’action de cette transformation. Les filtrations sont définies non plus sur des espaces de probabilité mais sur des systèmes dynamiques, ce sont dans ce cas des filtrations « facteurs » : chaque tribu est invariante par la dynamique du système. Le pendant de la standardité du point de vue dynamique est étudié. On crée ainsi un critère nécessaire pour la standardité dynamique appelé « I-confort dynamique ». La question de savoir si le I-confort dynamique est suffisant reste ouverte mais un premier résultat dans cette direction est donné, en montrant qu’une version renforcée du I-confort dynamique entraîne la standardité dynamique. En établissant qu’elle ne satisfait pas le critère de I-confort dynamique, on prouve que la filtration facteur engendrée par l’automate déterministe n’est pas dynamiquement standard, et donc que la classification dynamique des filtrations diffère de la classification développée par Vershik. L’automate probabiliste dépend d’un paramètre d’erreur, et on montre par un argument de percolation que la filtration facteur engendrée par cet automate est dynamiquement standard pour des valeurs assez grandes de ce paramètre. 0n conjecture qu’elle ne sera pas dynamiquement standard pour les valeurs très petites de ce paramètre. La deuxième partie de ce manuscrit, plus algébrique, tire son origine d’une problématique musicale, liée au calcul d’intervalles dans une ligne mélodique périodique. Les travaux présentés ici poursuivent les recherches du compositeur roumain Anatol Vieru et de Moreno Andreatta et Dan Vuza mais d’une manière originale en se plaçant du point des vue des automates cellulaires. On étudie l’action sur des suites périodiques de deux automates cellulaires algébriques, dont l’un est identique à celui de la première partie. Les questions sur la caractérisation des suites réductibles et reproductibles ainsi que les temps associés ont été approfondies et améliorées pour ces deux automates. Le calcul des antécédents et des images via les deux automates a été explicité. La question de l’évolution des périodes a été traitée avec la création d’un outil appelé « caractéristique » qui permet de décrire et de contrôler l’évolution de la période dans les temps négatifs. Des simulations permettent de voir que l’évolution des périodes lorsque l’on tire au hasard des antécédents suit un motif presque régulier, et l’explication de ce phénomène reste une question ouverte. Les résultats mathématiques de cette deuxième partie ont été utilisés dans le module « automaton » d’un logiciel de composition gratuit, nommé « UPISketch. Ce module permet à un compositeur de créer des lignes mélodiques en itérant les images ou en prenant des antécédents successifs d’une ligne mélodique de départ<br>The first part of this manuscript falls within the framework of probability theory, and is devoted to the study of filtrations generated by some cellular automata. We study two versions of an algebraic automaton acting on configurations whose states take values in a finite Abelian group: one is deterministic, and consists in adding the states of two consecutive cells, and the second is a random perturbation of the first one. From these automata, random Markovian processes are constructed and the filtrations generated by these processes are studied. Using the I-cosiness criterion, we show that the two filtrations are standard in the sense developed by Vershik. However, cellular automata have the particularity of commuting with the coordinate shift operator. In this thesis, we introduce a new classification of the filtrations called "dynamic" which takes into account the action of this transformation. Filtrations are no longer defined on probability spaces but on dynamical systems, and are in this case "factor" filtrations: each sigma-algebra is invariant by the dynamics of the system. The counterpart of standardity from the dynamic point of view is studied. This creates a necessary criterion for dynamic standardity called "dynamic I-cosiness". The question of whether the dynamic I-cosiness is sufficient remains open, but a first result in this direction is given, showing that a strengthened version of the dynamic I-cosiness leads to dynamic standardity. By establishing that it does not satisfy the criterion of dynamic I-cosiness, it is proved that the factor filtration generated by the deterministic automaton is not dynamically standard, and therefore that the dynamic classification of the filtrations differs from the classification developed by Vershik. The probabilistic automaton depends on an error parameter, and it is shown by a percolation argument that the factor filtration generated by this automaton is dynamically standard for large enough values of this parameter. It is conjectured that it will not be dynamically standard for very small values of this parameter. The second part of this manuscript, more algebraic, has its origin in a musical problem, linked to the calculation of intervals in a periodic melodic line. The work presented here continues the research of the Romanian composer Anatol Vieru and of Moreno Andreatta and Dan Vuza, but in an original way from the point of view of cellular automata. We study the action on periodic sequences of two algebraic cellular automata, one of which is identical to that of the first part. The questions on the characterization of reducible and reproducible sequences as well as the associated times have been deepened and improved for these two automata. The calculation of preimages and images via the two automata was explained. The question of the evolution of the periods was treated with the creation of a tool called "characteristic" which allows to describe and control the evolution of the period in negative times. Simulations show that the evolution of the periods when the preimages are drawn at random follows an almost regular pattern, and the explanation of this phenomenon remains an open question. The mathematical results of this second part have been used in the "Automaton" module of a free composing software called "UPISketch ». This module allows a composer to create melodic lines by iterating images or taking successive preimages of a starting melodic line

The soil-geotextile filtration mechanism is a complex process which depends on physical compatibility between the geotextile and the soil to be retained. Geotextiles often perform well under steady state conditions like those found in dams. However, when the soil-geotextile interface is subjected to dynamic loading, the requirements for successful filtering are uncertain and/ or conservative as the controlling factors are not well understood in these circumstances. There are few filter design criteria available for dynamic flow conditions. These criteria do not properly address the internal instability of soils for which the rearrangement of particles adjacent to the filter interface is complex. Unstable soils may exist in roadway bases adjacent to pavement edge drain. Therefore, this research work was carried out to better understand the filtration behaviour of non-woven geotextiles with internally stable and unstable soils beneath roads. To carry out the filtration tests, a flexible wall gradient ratio (GR) apparatus was developed. The GR tests were performed to investigate the effect of different factors on the filtration performance of the soil-geotextile interface under dynamic conditions. The factors included hydraulic gradient, vertical stress and frequency of loading, soil gradation and geotextile properties. Test results were interpreted in terms of head loss within the soil and across the geotextile, GR values, permeability ratio, mass and gradation of particles passed through geotextiles, microscopic images of geotextiles after test, partial geotextile clogging levels and hydrometer sieve analyses of soil samples to compare the gradation of samples after test with the original gradation. All the tests were performed under a hydraulic gradient of five. The internal stability of soil samples were evaluated by three geometric criteria. The test results showed that a high hydraulic gradient has the ability to lead to the internal instability of soils which resulted in migration of fines towards the geotextiles. The dynamic loading resulted in increase of soil migration within the base soil as well as washing out of soil particles through geotextiles. No significant effect of increase in frequency and vertical stress was observed on filtration behaviour of soil-geotextile combinations. The geotextile pore size was found to be the main factor controlling the filtration behaviour as compared to other geotextile properties. The Kenney and Lau (1985) and the Kezdi (1979) criteria predicted well the internal instability of soils under dynamic conditions. In this research study, a new method was suggested which is able to measure the pore sizes along the entire thickness of geotextiles. The filtration tests showed that geotextiles having the same large openings but different pore size distributions may result in different filtration performances. Based on the test results, filter design criteria were suggested for piping and blinding limits which were compared with the existing design criteria. These new filter criteria were found to be more appropriate in terms of piping and blinding limit states.

In axial electrofiltration, a DC electric field is imposed between a rotating inner cylinder and a stationary outer cylinder giving rise to four mechanisms which act to minimize solute accumulation at the filter surface: turbulence, centrifugal force, electrophoresis and shear stress which removes solute aggregates.<br>Four dynamic membranes, Zr(IV) oxide, calcium oleate, poly-2-vinylpyridine and cadmium sulfide, were used to filter bovine serum albumin (BSA) in a disodium phosphate solution at pH = 8 and Prussian blue in distilled water. Prussian blue is a particle of 0.01(mu)m diameter with a zeta potential of -41mV while BSA is a macromolecule of 69,000 molecular weight, a Stokes-Einstein radius of 0.0038(mu)m and a zeta potential of -23.3mV at pH = 8. For BSA, the flux declined with time while the rejection increased. Filtrate fluxes increased with rotation rate and electric field and declined with concentration for both feeds. The flux declined beyond N = 2000rpm and was constant above C(,0) = 5.0wt%. For Prussian blue, the rejection was greater than 90% at all levels of E, N and C(,0). For BSA, the rejection increased with rotation rate and declined with concentration. The BSA rejection declined above N = 2000rpm and was constant beyond C(,0) = 0.5wt%.<br>A mathematical model was derived to predict the time variation of filtrate flux and a rejection model was used to predict the effect of surface concentration on BSA rejection.

Asset protection in the form of fluid filtration makes up an ever-increasing part of the civilized and industrialized world. Fluid filtration applications in the conditioned environment and life sciences are affording the world’s population a chance to better realize their potential, while industrial applications help ensure that high demand processes can be carried out safely, reliably, and effectively. In the present work, a tool has been developed, using the computational fluid dynamics package FLUENT, to allow the designer to better predict the magnitude of geometric imperfections within a given pleat configuration. Pleated rectangular filters, intended to improve the quality of air for human occupants, with a U-shaped pleat form have been chosen as the focus of this study. A simulation study is developed to investigate the maximum local velocity normal to the filtration surface and to characterize the magnitude of the pleatwise velocity distribution across a range of pleated geometries and flow conditions. The geometry of the U-shaped pleat form can be characterized by, amongst other parameters, the width of the pleat channel, the overall height of the individual pleat, as well as the thickness of the filtration medium. The various geometries of the current study were developed by changing the width of the pleat channel, as well as the channel height, while keeping the medium thickness constant throughout. Changing the width of the pleat channel allows the designer to achieve varying pleat densities, expressed as a number of pleats along a one inch section of the overall pleated pack. Pleat densities of 6.5, 7, 7.5, 8, and 8.5 pleats per inch are considered in the current study. Pleat heights of 1.0, 0.75, and 0.50 inches are also investigated in the current study. Furthermore, the filter velocity can be characterized by the free stream velocity at the face of the filter pack, termed the face velocity, and by the velocity of the fluid at the interface with the filtration medium, referred to as media velocity. In the present work, the face velocity was adjusted in each case to achieve the desired media velocities across the study, which are 10.5, 9.0, 7.5, and 6.0 feet per minute. In an effort to more clearly communicate the results of the study, the results are presented in the form of a non-dimensionalized plots which present the designer with a way to quickly gauge the effect of pleat geometry on maximum velocity. Additionally, two tools are presented to aid the designer in more accurately predicting the maximum filtration velocity. These tools are then evaluated for effectiveness using the method of absolute relative percent error. The assumption of uniform flow through the filtration media leads to an average absolute relative percent error of 27%. The first tool the reader is presented with is a simple correction factor which predicts the maximum filtration velocity with an average absolute relative percent error of 10% over the study domain. The second tool, which takes a slightly more complicated y-intercept form, characterizes the maximum filtration velocity as a function of average velocity and aspect ratio. This approach further reduces the average absolute relative percent error to 4%. The results of the simulation herein are successfully employed to develop a set of simple yet effective tools that allow the filter designer to more accurately predict maximum velocities through a pleated air filter.

A mathematical model has been developed which describes the fluid exchange from a capillary network of realistic topology, and calculates the spatial distribution of extravascular pressure. In this model, the capillaries are represented by a superposition of sources and sinks, resulting from a D'Arcy's Law description of flow in tissue of uniform fluid conductivity. The combination of this representation and Starling's Hypothesis, which relates the forces influencing transmural fluid exchange, yields an integral equation of the second kind which is solved numerically for the source strength distribution. Two important features of this approach are that: (i) it allows for interaction between the local tissue pressure field and fluid exchange (the model is called, therefore, the tissue pressure interaction model); and (ii) complex network morphologies are easily modeled. In single capillaries, this interaction, which decreases the predicted fluid exchange, increases with the magnitude of the ratio of capillary wall to extravascular fluid conductivities. For multiple capillaries, in addition to the "self" interaction of a capillary with the local extravascular pressure field, there is the possibility of interaction between capillaries ("capillary-capillary" interaction). The ratio of conductivities, and the additional factors of intercapillary distance and the number of capillaries, also affect interaction in capillary networks. Although interaction is only a weak function of intercapillary distance, it depends strongly on the number of capillaries. The major result from this work is that for the entire physiological range of conductivity ratios, interaction cannot be neglected in predicting fluid exchange. Although tissue pressure interaction affects the magnitude of fluid exchange, it does not greatly alter the pattern of extravascular flow. Therefore, previous models which neglected interaction are not invalidated by the present findings. The effect of interaction on planar capillary networks within a semi-infinite tissue space was also investigated. Flow boundary conditions were imposed at opposed planar boundaries, parallel with the capillary network. Interaction was found to decrease with decreasing distance between the boundary and plane of the capillaries. It still exerted a large effect, however, for distances greater than one-fourth the reference capillary length.

As the economy has been growing fast in China, Chinese people have more incomes and then higher standard of living. In the case of household water treatment, more and more urban residents in China use bottled water or water filtration system instead of tap water because people start to worry about polluted tap water. According to a survey from China Water Supply Services Promotion Alliance in 2014, 59% of urban residents drinking water is from tap water (after being boiled), 41% from bottled water and water filtration system. The 41% participants prefer bottled water as the first choice over a water filtration system. The comparative advantages and disadvantages of home water filtration system and bottled water are analyzed using comparative analysis. The reasons why home water filtration industry has grown slowly in urban China even though it is less expensive and has environmental benefits are analyzed using a system dynamics model. The model focuses on the physical system of home water filtration industry. The study shows that order delivery delay and service time are key factors to the adoption rate of home water filtration system. However, initial cost becomes a limiting factor to the growth of the market of home water filtration system. The study proposes the according market policy, demand policy, and supply policy to improve the current scenario.