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1
Fraysse, Jérôme. "Composites polyaniline/polyméthacrylate de méthyle : percolation, transport électronique et propriétés mécaniques." Université Joseph Fourier (Grenoble), 2000. http://www.theses.fr/2000GRE10201.
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Dans ce travail nous nous interessons aux composites constitues par la dispersion d'un polymere conducteur electronique intrinseque : la polyaniline (pani) dans une matrice polymere isolante : le polymethacrylate de methyle (pmma). Ces materiaux sont une realisation exemplaire de systemes a tres faible seuil de percolation electrique. La comprehension des proprietes de transport electronique au voisinage de ce seuil renvoie d'une part aux proprietes intrinseques de la phase percolante, et d'autre part au phenomene de percolation. Nous exposons donc tout d'abord differents modeles decrivant le transport dans les milieux desordonnes et nous examinons leur pertinence dans le cadre des systemes de pani pure. Il apparait qu'un modele de sauts entre grains conducteurs faisant intervenir effet tunnel et activation thermique est bien adapte. Nous caracterisons ensuite la variation thermique de la conductivite de des composites et nous verifions que la loi d'echelle de la theorie de la percolation est suivie sur toute la gamme de temperature exploree (10-320 k). Alors que le seuil de percolation demeure constant, on obtient le resultat original d'un exposant critique augmentant continument lorsque la temperature diminue. Nous interpretons cette observation en invoquant la modification de la forme de la distribution de conductances locales et montrons qu'elle est coherente avec le modele de grains conducteurs precedemment cite. Enfin, un eclairage complementaire sur la structure et la morphologie de la phase de pani est apporte par des techniques d'imagerie directe et indirecte (notamment par analyse thermo-mecanique).
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Severo, Franco. "Interpolation schemes in percolation theory." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM004.
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Cette thèse fournit de nouveaux résultats concernant la transition de phase des modèles de percolation, en particulier la percolation de Bernoulli et les lignes de niveau du champ libre gaussien. La technique commune utilisée dans ces résultats consiste à comparer deux modèles de percolation différents en construisant une famille de modèles interpolant entre les deux. L’objectif principal de cette thèse est d’illustrer comment cette technique peut être appliquée dans un large contexteThis thesis provides new results concerning the phase transition of percolation models, specially Bernoulli percolation and level-sets of the Gaussian free field. The common technique used in theses results consists in comparing two different percolation models by continuously interpolating between them. The main purpose of this thesis is to illustrate how this technique can be applied to a wider variety of contexts than those previously studied
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Chen, Ying Ph D. Massachusetts Institute of Technology. "Percolation and homogenization theories for heterogeneous materials." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44389.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008.Includes bibliographical references (p. 139-145).
Most materials produced by Nature and by human beings are heterogeneous. They contain domains of different states, structures, compositions, or material phases. How these different domains are distributed in space, or in other words, how they connect to one another, determines their macroscopic properties to a large degree, making the simple rule-of-mixtures ineffective in most cases. This thesis studies the macroscopic effective diffusion, diffusional creep, and elastic properties of heterogeneous grain boundary networks and composite solids, both theoretically and numerically, and explores the microstructure-property correlations focusing on the effects of microstructural connectivity (topology). We have found that the effects of connectivity can be effectively captured by a percolation threshold, a case-specific volume fraction at which the macroscopic effective property undergoes a critical transition, and a set of critical scaling exponents, which also reflect the universality class that the property belongs to. Using these percolation quantities together with the generalized effective medium theory, we are able to directly predict the effective diffusivity and effective diffusional creep viscosity of heterogeneous grain boundary networks to a fairly accurate degree. Diffusion in composite solids exhibits different percolation threshold and scaling behaviors due to interconnectivity at both edges and corners. Continuum elasticity suffers from this complexity as well, in addition to the complicating factor that each phase is always characterized by several independent elastic constants. These issues are each addressed in detail. In addition to studying all the above properties for a random distribution of grain boundaries or phases, we have also studied the effects of correlations in spatial distributions.
(cont.) This topic is especially important in materials science, because virtually no materials exhibit random phase distributions. We have examined the percolation of effective properties for correlated microstructures spanning between the random distribution and the perfectly periodic distribution. An important result of this work is new understanding about what correlations may be considered small, or inconsequential, to the percolation scaling behavior, and which are large or long-range, and lead to a loss of universality. Finally, a rigorous, and easy-to-use, analytical homogenization method is developed for periodic composite materials.
by Ying Chen.
Ph.D.
4
Lee, Michael James. "Methods in Percolation." Thesis, University of Canterbury. Physics and Astronomy, 2008. http://hdl.handle.net/10092/2365.
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Algorithms are presented for the computationally efficient manipulation of graphs. These are subsequently used as the basis of a Monte Carlo method for sampling from the microcanonical ensemble of lattice configurations of a percolation model within a neighbourhood of the critical point. This new method arbitrarily increments and decrements the number of occupied lattice sites, and is shown to be a generalisation of several earlier, purely incremental, methods. As demonstrations of capability, the method was used to construct a phase diagram for exciton transport on a disordered surface, and to study finite size effects upon the incipient spanning cluster. Application of the method to the classical site percolation model on the two-dimensional square lattice resulted in an exceptionally precise estimate of the critical threshold. Although this estimate is not in agreement with earlier results, its accuracy was established through an application specific test of randomness, which is also introduced here. The same test suggests that many earlier results have been systematically biased due to the use of deficient pseudorandom number generators. The estimate made here has since been independently confirmed.
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Frary, Megan. "Crystallographically consistent percolation theory for grain boundary networks." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33402.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2005.Includes bibliographical references (p. 127-134).
Grain boundaries are known to play a role in many important material properties including creep resistance, ductility and cracking resistance. Although the structure and properties of individual boundaries are important, the overall behavior of the material is determined largely by the connectivity of grain boundaries in the microstructure. Grain boundary networks may be studied in the framework of percolation theory by classifying boundaries as special or general to the property of interest. In standard percolation theory, boundaries are randomly assigned as special or general; however, this approach is invalid in realistic grain boundary networks due to the requirement for crystallographic consistency around any closed circuit in the microstructure. The goal of this work is to understand the effects of these local constraints on the connectivity and percolation behavior of crystallographically consistent grain boundary networks. Using computer simulations and analytical models, the behavior of crystallographically consistent networks is compared to that of randomly-assembled networks at several different length scales. At the most local level, triple junctions and quadruple nodes are found to be preferentially coordinated by special and general boundaries, leading to nonrandom network topologies that are quantified using topological parameters.
(cont.) Although the properties of the simulated microstructures, including connectivity length and average cluster radius of gyration, are described by the same scaling exponents as in standard percolation theory, the amplitude prefactors in the scaling relationships are changed as a result of the crystallographic constraint. The percolation threshold, an important parameter in microstructural design, is also found to differ from that of standard percolation theory by as much as ±0.05. Although all of the simulated grain boundary networks studied here are distinctly nonrandom, no two cases have the same behavior, the details of which depend strongly on the specific microstructural model. Therefore, a unified approach for locally correlated percolation problems is developed that allows the effects of the requirement for crystallographic consistency to be compared directly from system to system. This new approach can be extended beyond the study of grain boundary networks to include other locally-correlated percolation problems.
by Megan E. Frary.
Ph.D.
6
Stacey, Alan Martin. "Bounds on the critical probability in oriented percolation models." Thesis, University of Cambridge, 1994. https://www.repository.cam.ac.uk/handle/1810/251746.
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Simmons, Jacob Joseph Harris. "Applications of Conformal Field Theory to Problems in 2D Percolation." Fogler Library, University of Maine, 2007. http://www.library.umaine.edu/theses/pdf/SimmonsJJH2007.pdf.
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Fortunato, Santo [Verfasser]. "Percolation and Deconfinement in SU(2) Gauge Theory / Santo Fortunato." Bielefeld : Universitätsbibliothek Bielefeld, 2000. http://d-nb.info/1034401173/34.
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Bocharova, Vera. "Electrically Conductive Low Dimensional Nanostructures: Synthesis, Characterisation and Application." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1231161926227-23379.
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Miniaturization has become a driving force in different areas of technology including microelectronics, sensoric- and bio-technologies and in fundamental science. Because of the well-known limitations of conventional lithographic methods, newly emerging bottom-up approach, utilizing self-assembly of various nanoobjects including single polymer molecules and carbon nanotubes constitutes a very promising alternative for fabrication of ultimately small devices. Carbon nanotubes are attractive materials for nanotechnology and hold much promise to revolutionize fundamental science in a investigation of phenomena, associated with the nanometer–sized objects.It was found in this work that grafted chains of poly(2-vinylpyridine) form a shell covering the carbon nanotubes that makes them dispersible in organic solvents and in acidic water (CNTs-g-P2VP).The positively charged poly(2-vinylpyridine) shell is responsible for the selective deposition of carbon nanotubes onto oppositely charged surfaces. It was established that the deposition CNTs-g-P2VP from aqueous dispersions at low pH is an effective method to prepare ultra-thin films with a tunable density of carbon nanotubes.It was shown that poly(2-vinylpyridine) grafted to carbon nanotubes is a universal support for the immobilization of various nanoclusters at the carbon nanotube's surface. Prussian Blue nanoparticles were selectively attached to the surface of CNTs-g-P2VP.Conducting polymer nanowires are another very promising kind of nanomaterials that could be also suitable for applications in nanodevices and nanosensors. In this work was developed a simple method to control the conformation and orientation of single adsorbed polyelectrolyte molecules by co-deposition with octylamine. A simple chemical route to conductive polypyrrole nanowires by the grafting of polypyrrole from molecules of polystyrensulfonic acid was developed. The dc conductivity of individual polypyrrole nanowires approaches the conductivity of polypyrole in bulk.The conductivity can be described using variable-range hopping model.
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Bocharova, Vera. "Electrically Conductive Low Dimensional Nanostructures: Synthesis, Characterisation and Application." Doctoral thesis, Technische Universität Dresden, 2008. https://tud.qucosa.de/id/qucosa%3A23607.
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Miniaturization has become a driving force in different areas of technology including microelectronics, sensoric- and bio-technologies and in fundamental science. Because of the well-known limitations of conventional lithographic methods, newly emerging bottom-up approach, utilizing self-assembly of various nanoobjects including single polymer molecules and carbon nanotubes constitutes a very promising alternative for fabrication of ultimately small devices. Carbon nanotubes are attractive materials for nanotechnology and hold much promise to revolutionize fundamental science in a investigation of phenomena, associated with the nanometer–sized objects.It was found in this work that grafted chains of poly(2-vinylpyridine) form a shell covering the carbon nanotubes that makes them dispersible in organic solvents and in acidic water (CNTs-g-P2VP).The positively charged poly(2-vinylpyridine) shell is responsible for the selective deposition of carbon nanotubes onto oppositely charged surfaces. It was established that the deposition CNTs-g-P2VP from aqueous dispersions at low pH is an effective method to prepare ultra-thin films with a tunable density of carbon nanotubes.It was shown that poly(2-vinylpyridine) grafted to carbon nanotubes is a universal support for the immobilization of various nanoclusters at the carbon nanotube's surface. Prussian Blue nanoparticles were selectively attached to the surface of CNTs-g-P2VP.Conducting polymer nanowires are another very promising kind of nanomaterials that could be also suitable for applications in nanodevices and nanosensors. In this work was developed a simple method to control the conformation and orientation of single adsorbed polyelectrolyte molecules by co-deposition with octylamine. A simple chemical route to conductive polypyrrole nanowires by the grafting of polypyrrole from molecules of polystyrensulfonic acid was developed. The dc conductivity of individual polypyrrole nanowires approaches the conductivity of polypyrole in bulk.The conductivity can be described using variable-range hopping model.
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Gillis, Gregory Nelson 1965. "Design considerations in manufacturing composite conductors: An exposition of Percolation Theory." Diss., The University of Arizona, 1998. http://hdl.handle.net/10150/282664.
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This dissertation is an exposition of Percolation Theory, directed to the audience of beginning undergraduate mathematics students, though this can include gifted high school students. The vehicle by which the theory is taught is that of problem solving. The reader of the dissertation is invited into a web of mathematical exploration and inquiry by attempting to solve the real real-world problem of designing composite conductors. By making real composite conductors, carrying out various experiments, using computers to do data collecting, and using calculators for subsequent data analysis the reader can participate in the creation of mathematics, the development of mathematical techniques, and in the discovery of new and unexpected connections. The mathematics of Percolation Theory are in this way constructed with the reader. The necessity and importance of this work are many-fold. It is the first such treatise on Percolation Theory that makes the theory accessible to a larger audience than mathematics graduate or senior college students. It will be of interest to high school and beginning college students who desire to know in what real-world contexts some of the mathematics they know can be put. This work will be of interest to educators for the hands-on way in which it reinforces the student's current mathematical ability, while enriching the student's understanding of problem solving, mathematical modeling, use of technology, and probability.
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Lundblad, Jacob. "Majority bootstrap percolation and paths in G(n, p)." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-453023.
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Zhang, Lin. "The application of percolation theory to diffusion and reaction in porous solids." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308196.
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Karahan, Murat. "Prioritized Exploration Strategy Based On Invasion Percolation Guidance." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611450/index.pdf.
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The major aim in search and rescue using mobile robots is to reach trapped survivors and
to support rescue operations through the disaster environments. Our motivation is based
on the fact that a search and rescue (SAR) robot can navigate within and penetrate a
disaster area only if the area in question possesses connected voids Traversability or
penetrability of a disaster area is a primary factor that guides the navigation of a search
and rescue (SAR) robot, since it is highly desirable that the robot, without hitting a dead
end or getting stuck, keeps its mobility for its primary task of reconnaissance and
mapping when searching the highly unstructured environment We propose two novel
guided prioritized exploration system: 1) percolation guided methodology where a
percolator estimates the existence of connected voids in the upcoming yet unexplored
region ahead of the robot so as to increase the efficiency of reconnaissance operation by
the superior ability of the percolation guidance in speedy coverage of the area2) the hybrid exploration methodology that makes the percolation guided exploration collaborate with entropy based SLAM under a switching control dependent on either priority given to position accuracy or to map accuracy This second methodology has proven to combine the superiority of both methods so that the active SLAM becomes speedy, with high coverage rate of the area as well as accurate in localization.
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Porter, Lee Brenson II. "The Kozeny-Carman Equation Considered With a Percolation Threshold." Wright State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1309878625.
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Yu, Fang. "Modeling of Soil Formation on The Basis of Chemical Weathering: Applications FromPercolation Theory." Wright State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=wright1526563165403061.
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Renlund, Henrik. "Recursive Methods in Urn Models and First-Passage Percolation." Doctoral thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-145430.
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This PhD thesis consists of a summary and four papers which deal with stochastic approximation algorithms and first-passage percolation. Paper I deals with the a.s. limiting properties of bounded stochastic approximation algorithms in relation to the equilibrium points of the drift function. Applications are given to some generalized Pólya urn processes. Paper II continues the work of Paper I and investigates under what circumstances one gets asymptotic normality from a properly scaled algorithm. The algorithms are shown to converge in some other circumstances, although the limiting distribution is not identified. Paper III deals with the asymptotic speed of first-passage percolation on a graph called the ladder when the times associated to the edges are independent, exponentially distributed with the same intensity. Paper IV generalizes the work of Paper III in allowing more edges in the graph as well as not having all intensities equal.
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Chabane, Amar. "Multifragmentation explosive dans la réaction 32S+27Al à 37. 5 MeV/nucléon." Université Joseph Fourier (Grenoble), 1995. http://www.theses.fr/1995GRE10057.
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L'etude des evenements complets dans la reaction #3#2s + #2#7al a permis de mettre en evidence un phenomene de multifragmentation du noyau compose residuel forme lors de la fusion du systeme cible-projectile pour des collisions centrales. La theorie de la percolation, idee novatrice en physique nucleaire, permet de montrer que nous sommes surcritique au sens de la percolation mais ne permet pas de conclure quand a un eventuel changement de phase dans la matiere nucleaire. Cette etude montre aussi, que les donnees experimentales sont incompatibles avec un code de simulation binaire sequentiel reconnu (gemini). Par contre, la comparaison avec un code de multifragmentation statistique (code de berlin) montre que les donnees sont bien representative d'une multifragmentation du noyau bien qu'au niveau energetique l'accord ne soit plus satisfaisant ; notamment les vitesses relatives entre fragments de masses intermediaires sont plus grandes dans le cas de l'experience ainsi que l'impulsion du fragment le plus lourd qui ne peut etre reproduite. L'etude des partitions en charges dans le cadre de l'ensemble boltzmann canonique met en evidence une thermalisation du noyau compose, avec emission de particules de preequilibre. La temperature deduite est d'environ 5 mev et le volume de freeze-out de l'ordre de 2. 3 fois le volume normal. Les variables dynamiques sont bien reproduites par un code simulant une desintegration explosive du noyau suite a la decompression de celui-ci. Cette energie radiale resulte du phenomene d'onde de choc qui apparait lorsque la vitesse de propagation de l'onde est superieure a celle du son dans la matiere nucleaire. La mesure de ce seuil permettrait de remonter au coefficient d'incompressibilite de la matiere k
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Fullwood, David T. "Percolation in Two-Dimensional Grain Boundary Structures and Polycrystal Property Closures." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1045.pdf.
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Idriss, Bilal. "Percolation-Based Techniques for Upscaling the Hydraulic Conductivity of Semi-Realistic Geological Media." Wright State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=wright1222101268.
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Ghanbarian-Alavijeh, Behzad. "Modeling Physical and Hydraulic Properties of Disordered Porous Media: Applications from Percolation Theory and Fractal Geometry." Wright State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=wright1401380554.
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Thomas, Kuryan. "A statistical theory of the epilepsies." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/87673.
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A new physical and mathematical model for the epilepsies is proposed, based on the theory of bond percolation on finite lattices. Within this model, the onset of seizures in the brain is identified with the appearance of spanning clusters of neurons engaged in the spurious and uncontrollable electrical activity characteristic of seizures. It is proposed that the fraction of excitatory to inhibitory synapses can be identified with a bond probability, and that the bond probability is a randomly varying quantity displaying Gaussian statistics. The consequences of the proposed model to the treatment of the epilepsies is explored.
The nature of the data on the epilepsies which can be acquired in a clinical setting is described. It is shown that such data can be analyzed to provide preliminary support for the bond percolation hypothesis, and to quantify the efficacy of anti-epileptic drugs in a treatment program. The results of a battery of statistical tests on seizure distributions are discussed.
The physical theory of the electroencephalogram (EEG) is described, and extant models of the electrical activity measured by the EEG are discussed, with an emphasis on their physical behavior. A proposal is made to explain the difference between the power spectra of electrical activity measured with cranial probes and with the EEG. Statistical tests on the characteristic EEG manifestations of epileptic activity are conducted, and their results described.
Computer simulations of a correlated bond percolating system are constructed. It is shown that the statistical properties of the results of such a simulation are strongly suggestive of the statistical properties of clinical data.
The study finds no contradictions between the predictions of the bond percolation model and the observed properties of the available data. Suggestions are made for further research and for techniques based on the proposed model which may be used for tuning the effects of anti-epileptic drugs.Ph. D.
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Franosch, Thomas, and Felix Höfling. "Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190406.
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For a continuum percolation model, it has been shown recentlythat the crossover from pure subdiffusion to normal diffusion extends over five decades in time [1, 2]; in addition, the asymptotic behavior is slowly approached and the large corrections cannot simply be ignored. Thus, it is of general interest to develop a systematic description of universal corrections to scaling in percolating systems.
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behavior at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker.
We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents [3].
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Franosch, Thomas, and Felix Höfling. "Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems." Diffusion fundamentals 11 (2009) 59, S. 1, 2009. https://ul.qucosa.de/id/qucosa%3A14024.
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For a continuum percolation model, it has been shown recentlythat the crossover from pure subdiffusion to normal diffusion extends over five decades in time [1, 2]; in addition, the asymptotic behavior is slowly approached and the large corrections cannot simply be ignored. Thus, it is of general interest to develop a systematic description of universal corrections to scaling in percolating systems.
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behavior at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker.
We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents [3].
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Clayton, Marianne E. "Modeling Piezoresistive Effects in Flexible Sensors." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7396.
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This work describes a model of the piezoresistive behavior in nanocomposite sensors. These sensors are also called flexible sensors because the polymer matrix allows for large deformations without failure. The sensors have conductive nanoparticles dispersed through an insulative polymer matrix. The insulative polymer gaps between nanoparticles are assumed to be possible locations for electron tunneling. When the distance between two nanoparticles is small enough, electrons can tunnel from one nanoparticle to the next and ultimately through the entire sensor. The evolution of this gap distance with strain is important to understand the overall conductivity of the strain sensor. The gap evolution was modeled in two ways: (1) applying Poisson's contraction to the sensor as a homogenous material, referred to as Simple Poisson's Contraction (SPC) and (2) modeling the nanoparticle-polymer system with Finite Element Analysis (FEA). These two gap evolution models were tested in a random resistor network model where each polymer gap was treated as a single resistor in the network. The overall resistance was calculated by solving the resistor network system. The SPC approach, although much simpler, was sufficient for cases where various orientations of nanoparticles were used in the same sensor. The SPC model differed significantly from the FEA, however, in cases where nanoparticles had specific alignment, e.g. all nanoparticles parallel to the tensile axis. It was also found that the distribution used to determine initial gap sizes for the polymer gaps as well as the mean of that distribution significantly impacted the overall resistivity of the sensor.Another key part of this work was to determine if the piezoresistivity in the sensors follows a percolation type behavior under strain. The conductance versus strain curve showed the characteristic s-curve behavior of a percolative system. The conductance-strain curve was also compared to the effective medium and generalized effective medium equations and the latter (which includes percolation theory) fit the random resistor network much more closely. Percolation theory is, therefore, an accurate way to describe this polymer-nanoparticle piezoresistive system.Finally, the FEA and SPC models were compared against experimental data to verify their accuracy. There are also two design problems addressed: one to find the sensor with the largest gauge factor and another to determine how to remove the characteristic initial spike in resistivity seen in nanocomposite sensors.
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Mukherjee, Sayak. "Applications of Field Theory to Reaction Diffusion Models and Driven Diffusive Systems." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/39293.
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In this thesis, we focus on the steady state properties of two systems which are genuinely out of equilibrium. The first project is an application of dynamic field theory to a specific non equilibrium critical phenomenon, while the second project involves both simulations and analytical calculations. The methods of field theory are used on both these projects. In the first part of this thesis, we investigate a generalization of the well-known field theory for directed percolation (DP). The DP theory is known to describe an evolving population, near extinction. We have coupled this evolving population to an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (model A) dynamics. We find two marginal couplings with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point. Some open questions and future work remain.
In the second project, we focus on a simple particle transport model far from equilibrium, namely, the totally asymmetric simple exclusion process (TASEP). While its stationary properties are well studied, many of its dynamic features remain unexplored. Here, we focus on the power spectrum of the total particle occupancy in the system. This quantity exhibits unexpected oscillations in the low density phase. Using standard Monte Carlo simulations and analytic calculations, we probe the dependence of these oscillations on boundary effects, the system size, and the overall particle density. Our simulations are fitted to the predictions of a linearized theory for the fluctuation of the particle density. Two of the fit parameters, namely the diffusion constant and the noise strength, deviate from their naive bare values [6]. In particular, the former increases significantly with the system size. Since this behavior can only be caused by nonlinear effects, we calculate the lowest order corrections in perturbation theory. Several open questions and future work are discussed.Ph. D.
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Huang, Zhen. "Interdependent Cyber Physical Systems: Robustness and Cascading Failures." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31517.
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The cyber-physical systems (CPS), such as smart grid and intelligent transportation system, permeate into our modern societies recently. The infrastructures in such systems are closely interconnected and related, e.g., the intelligent transportation system is based on the reliable communication system, which requires the stable electricity provided by power grid for the proper function. We call such mutually related systems interdependent networks.
This thesis addresses the cascading failure issue in interdependent cyber physical system. We consider CPS as a system that consists of physical-resource and computational-resource networks. The failure in physical-resource network might cause the failures in computational-resource network, and vice versa. This failure may recursively occur and cause a sequence of failures in both networks.
In this thesis, we propose two novel interdependence models that better capture the interdependent networks. Then, we study the effect of cascading failures using percolation theory and present the detailed mathematical analysis on failure propagation in the system. By calculating the size of functioning parts in both networks, we analyze the robustness of our models against the random attacks and failures.
The cascading failures in smart grid is also investigated, where two types of cascading failures are mixed. We estimate how the node tolerance parameter T (ratio of capacity to initial workload) affect the system performance. This thesis also explores the small clusters. We give insightful views on small cluster in interdependent networks, under different interdependence models and network topologies.
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Grijalva, Sebastian. "Boundary effects in quantum spin chains and Finite Size Effects in the Toroidal Correlated Percolation model." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP093.
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Cette thèse est divisée en deux parties : la première présente un modèle statistique en deux dimensions de percolation corrélée sur un réseau toroïdal. Nous présentons un protocole pour construire des surfaces corrélées à longue portée sur la base de surfaces gaussiennes fractionnaires, puis nous relions les ensembles de niveaux à une famille de modèles de percolation corrélés. Les clusters émergents sont ensuite étudiés numériquement, et nous testons leur symétrie conforme en vérifiant que les corrections de taille finie de connectivité à deux points suivent les prédictions de la théorie des champs conformes. Nous commentons également le comportement des fonctions à trois points et fournissons un code numérique pour reproduire les résultats. La deuxième partie de la thèse étudie la chaîne quantique XXZ intégrable de spin-1/2 avec des conditions aux bords ouvertes, pour un nombre pair et impair de sites. Dans régime antiferromagnétique, nous utilisons l'Ansatz de Bethe Algébrique pour déterminer les configurations possibles en termes des champs aux bords. On retrouve les conditions d'existence d'états fondamentaux quasi dégénérés séparés par un gap au reste du spectre. Nous calculons l'aimantation au bord à température nulle et constatons qu'elle dépend du champ sur le bord opposé même dans la limite de chaîne semi-infinie. Nous calculons enfin la fonction d'autocorrélation temporelle au bord et montrons que dans le cas de taille paire, elle est finie à la limite de temps long à cause de la quasi-dégénérescenceThis thesis is divided in two parts: The first one presents a 2D statistical model of correlated percolation on a toroidal lattice. We present a protocol to construct long-range correlated surfaces based on fractional Gaussian surfaces and then we relate the level sets to a family of correlated percolation models. The emerging clusters are then numerically studied, and we test their conformal symmetry by verifying that their planar-limit finite-size corrections follow the predictions of Conformal Field Theory. We comment also the behavior of three-point functions and provide a numerical code to reproduce the results.The second part of the thesis studies the quantum integrable XXZ spin-1/2 chain with open boundary conditions for even and odd number of sites. We concentrate in the anti-ferromagnetic regime and use the Algebraic Bethe Ansatz to determine the configurations that arise in terms of the boundary fields. We find the conditions of existence of quasi-degenerate ground states separated by a gap to the rest of the spectrum. We calculate the boundary magnetization at zero temperature and find that it depends on the field at the opposite edge even in the semi-infinite chain limit. We finally calculate the time autocorrelation function at the boundary and show that in the even-size case it is finite for the long-time limit as a result of the quasi-degeneracy
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Parviainen, Robert. "Connectivity Properties of Archimedean and Laves Lattices." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4251.
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Iusan, Diana Mihaela. "Density Functional Theory Applied to Materials for Spintronics." Doctoral thesis, Uppsala universitet, Materialteori, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119887.
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The properties of dilute magnetic semiconductors have been studied by combined ab initio, Monte Carlo, and experimental techniques. This class of materials could be very important for future spintronic devices, that offer enriched functionality by making use of both the spin and the charge of the electrons. The main part of the thesis concerns the transition metal doped ZnO. The role of defects on the magnetic interactions in Mn-doped ZnO was investigated. In the presence of acceptor defects such as zinc vacancies and oxygen substitution by nitrogen, the magnetic interactions are ferromagnetic. For dilute concentrations of Mn (~ 5%) the ordering temperature of the system is low, due to the short ranged character of the exchange interactions and disorder effects. The clustering tendency of the Co atoms in a ZnO matrix was also studied. The electronic structure, and in turn the magnetic interactions among the Co atoms, is strongly dependent on the exchange-correlation functional used. It is found that Co impurities tend to form nanoclusters and that the interactions among these atoms are antiferromagnetic within the local spin density approximation + Hubbard U approach. The electronic structure, as well as the chemical and magnetic interactions in Co and (Co,Al)-doped ZnO, was investigated by joined experimental and theoretical techniques. For a good agreement between the two, approximations beyond the local density approximation must be used. It is found that the Co atoms prefer to cluster within the semiconducting matrix, a tendency which is increased with Al co-doping. We envision that it is best to describe the system as superparamagnetic due to the formation of Co nanoclusters within which the interactions are antiferromagnetic. The magnetic anisotropy and evolution of magnetic domains in Fe81Ni19/Co(001) superlattices were investigated both experimentally, as well as using model spin dynamics. A magnetic reorientation transition was found.
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Blank, L. Aaron Jr. "Models of Disordered Media and Predictions of Associated Hydraulic Conductivity." Wright State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=wright1164985765.
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Lu, Chen. "Local K-Core Algorithm in Complex Networks." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377868996.
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Broadfoot, Stuart Graham. "Long distance entanglement distribution." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e7039911-f16b-4f49-8aab-8bb30ae97daa.
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Developments in the interdisciplinary field of quantum information open up previously impossible abilities in the realms of information processing and communication. Quantum entanglement has emerged as one property of quantum systems that acts as a resource for quantum information processing and, in particular, enables teleportation and secure cryptography. Therefore, the creation of entangled resources is of key importance for the application of these technologies. Despite a great deal of research the efficient creation of entanglement over long distances is limited by inevitable noise. This problem can be overcome by creating entanglement between nodes in a network and then performing operations to distribute the entanglement over a long distance. This thesis contributes to the field of entanglement distribution within such quantum networks. Entanglement distribution has been extensively studied for one-dimensional networks resulting in "quantum repeater" protocols. However, little work has been done on higher dimensional networks. In these networks a fundamentally different scaling, called "long distance entanglement distribution", can appear between the resources and the distance separating the systems to be entangled. I reveal protocols that enable long distance entanglement distribution for quantum networks composed of mixed state and give a few limitations to the capabilities of entanglement distribution. To aid in the implementation of all entanglement distribution protocols I finish by introducing a new system, composed of an optical nanofibre coupled to a carbon nanotube, that may enable new forms of photo-detectors and quantum memories.
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Flöser, Martina. "Transport local et non-local : Percolation dans les systèmes à effet Hallquantique corrélations croisées dans les structures hybrides supraconductrices." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00866133.
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Cette thèse est constituée de deux parties indépendantes. La première partie traite du transport dans des gaz d'électrons bidimensionnels dans le régime de l'effet Hall quantique. Dans la deuxième partie, le courant et les corrélations croisées en courant sont étudiées pour des structures hybrides conducteur normal- supraconducteur- conducteur normal (NSN). Dans le régime de haute température de l'effet Hall quantique, la conductance longitudinale est calculée par un formalisme diagrammatique basé sur une approche de conductivité locale. Ce calcul prend en compte l'effet de dérive des électrons sur les lignes équipotentielles du potentiel de désordre et permet la dérivation microscopique de l'exposant critique de transport qui était auparavant seulement conjecturé à partir d'arguments géométriques qualitatifs. Des expressions microscopiques pour la dépendance en température et en champ magnétique de la conductance longitudinale sont dérivées et comparées avec des expériences récentes. Dans le régime de basse température de l'effet Hall quantique, le passage du courant par effet tunnel sur des points selles est étudié à partir de la diffusion de paquets d'onde d'états semi-cohérents. Nous dérivons analytiquement le coefficient de transmission d'un point selle pour le potentiel scalaire dans le graphène et trouvons que les points selles asymétriques brisent la symétrie particule-trou de la conductance. Dans des structures hybrides NSN, nous étudions l'influence de barrières additionnelles sur la conductance (non-locale) et sur les corrélations croisées en courant avec la théorie de diffusion. Dans les systèmes métalliques, où la phase est moyennée, des barrières additionnelles augmentent les processus locaux par réflexion Andreev résonante (reflectionless tunneling), mais ont peu d'influence sur les processus non-locaux et sur les corrélations croisées en courant. Dans les systèmes balistiques, des barrières additionnelles causent des oscillations Fabry-Pérot et permettent de distinguer les différents processus contribuant à la conductance et aux corrélations croisées en courant.
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Warnke, Lutz. "Random graph processes with dependencies." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:71b48e5f-a192-4684-a864-ea9059a25d74.
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Random graph processes are basic mathematical models for large-scale networks evolving over time. Their systematic study was pioneered by Erdös and Rényi around 1960, and one key feature of many 'classical' models is that the edges appear independently. While this makes them amenable to a rigorous analysis, it is desirable, both mathematically and in terms of applications, to understand more complicated situations. In this thesis the main goal is to improve our rigorous understanding of evolving random graphs with significant dependencies. The first model we consider is known as an Achlioptas process: in each step two random edges are chosen, and using a given rule only one of them is selected and added to the evolving graph. Since 2000 a large class of 'complex' rules has eluded a rigorous analysis, and it was widely believed that these could give rise to a striking and unusual phenomenon. Making this explicit, Achlioptas, D'Souza and Spencer conjectured in Science that one such rule yields a very abrupt (discontinuous) percolation phase transition. We disprove this, showing that the transition is in fact continuous for all Achlioptas process. In addition, we give the first rigorous analysis of the more 'complex' rules, proving that certain key statistics are tightly concentrated (i) in the subcritical evolution, and (ii) also later on if an associated system of differential equations has a unique solution. The second model we study is the H-free process, where random edges are added subject to the constraint that they do not complete a copy of some fixed graph H. The most important open question for such 'constrained' processes is due to Erdös, Suen and Winkler: in 1995 they asked what the typical final number of edges is. While Osthus and Taraz answered this in 2000 up to logarithmic factors for a large class of graphs H, more precise bounds are only known for a few special graphs. We close this gap for the cases where a cycle of fixed length is forbidden, determining the final number of edges up to constants. Our result not only establishes several conjectures, it is also the first which answers the more than 15-year old question of Erdös et. al. for a class of forbidden graphs H.
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David, Stefan. "Extremal combinatorics and universal algorithms." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/278254.
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In this dissertation we solve several combinatorial problems in different areas of mathematics: automata theory, combinatorics of partially ordered sets and extremal combinatorics. Firstly, we focus on some new automata that do not seem to have occurred much in the literature, that of solvability of mazes. For our model, a maze is a countable strongly connected digraph together with a proper colouring of its edges (without two edges leaving a vertex getting the same colour) and two special vertices: the origin and the destination. A pointer or robot starts in the origin of a maze and moves naturally between its vertices, according to a sequence of specific instructions from the set of all colours; if the robot is at a vertex for which there is no out-edge of the colour indicated by the instruction, it remains at that vertex and proceeds to execute the next instruction in the sequence. We call such a finite or infinite sequence of instructions an algorithm. In particular, one of the most interesting and very natural sets of mazes occurs when our maze is the square lattice Z2 as a graph with some of its edges removed. Obviously, we need to require that the origin and the destination vertices are in the same connected component and it is very natural to take the four instructions to be the cardinal directions. In this set-up, we make progress towards a beautiful problem posed by Leader and Spink in 2011 which asks whether there is an algorithm which solves the set of all such mazes. Next, we address a problem regarding symmetric chain decompositions of posets. We ask if there exists a symmetric chain decomposition of a 2 × 2 × ... × 2 × n cuboid (k 2’s) such that no chain has a subchain of the form (a1,...,ak,0) ≺ ... ≺ (a1,...,ak,n−1)? We show this is true precisely when k≥5 and n≥3. Thisquestion arises naturally when considering products of symmetric chain decompositions which induce orthogonal chain decompositions — the existence of the decompositions provided in this chapter unexpectedly resolves the most difficult case of previous work by Spink on almost orthogonal symmetric chain decompositions (2017) which makes progress on a conjecture of Shearer and Kleitman. Moreover, we generalize our methods to other finite graded posets. Finally, we address two different problems in extremal combinatorics related to mathematical physics. Firstly, we study metastable states in the Ising model. We propose a general model for 1-flip spin systems, and initiate the study of extremal properties of their stable states. By translating local stability conditions into Sperner- type conditions, we provide non-trivial upper bounds which are often tight for large classes of such systems. The last topic we consider is a deterministic bootstrap percolation type problem. More specifically, we prove several extremal results about fast 2-neighbour percolation on the two dimensional grid.
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Guin, Arijit. "The Continuity of High-Permeability Zones in Sedimentary Deposits." Wright State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=wright1237579784.
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Lucas, Cyrille. "Étude du modèle de l'agrégation limitée par diffusion interne." Thesis, Paris 10, 2011. http://www.theses.fr/2011PA100173/document.
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Cette thèse contient quatre travaux sur le modèle d'Agrégation Limitée par Diffusion Interne (iDLA), qui est un modèle de croissance pour la construction récursive d'ensembles aléatoires. Le premier travail concerne la dimension 1 et étudie le cas où les marches aléatoires formant l'agrégat évoluent dans un milieu aléatoire. L'agrégat normalisé converge alors non pas vers une forme limite déterministe comme dans le cas de marches aléatoires simples mais converge en loi vers un segment contenant l'origine dont les extrémités suivent la loi de l'Arcsinus. Dans le deuxième travail, on considère le cas où l'agrégat est formé par des marches aléatoires simples en dimension d > 1. On donne alors des résultats de convergence et de fluctuations sur la fonction odomètre introduite par Levine et Peres, qui compte en chaque point le nombre de passages des marches ayant formé l'agrégat. Dans le troisième travail, on s'intéresse au cas où l'agrégat est formé par des marches aléatoires multidimensionnelles qui ne sont pas centrées. On montre que sous une normalisation appropriée, l'agrégat converge vers une forme limite qui s'identifie à une vraie boule de chaleur. Nous répondons ainsi à une question ouverte en analyse concernant l'existence d'une telle boule bornée. Le quatrième travail concerne le cas particulier où une borne intérieure est connue pour l'agrégat. On donne alors des conditions suffisantes sur le graphe ainsi que sur la nature de cette borne pour qu'elle implique une borne extérieure. Ce résultat est appliqué au cas de marches évoluant sur un amas de percolation par arêtes surcritique, complétant ainsi un résultat de ShellefThis thesis contains four works on the Internal Diffusion Limited Aggregation model (iDLA), which is a growth model that recursively builds random sets. The first work is set in dimension 1 and studies the case where the random walks that build the aggregate evolve in a random environment. The normalised aggregate then does not converges towards a deterministic limiting shape as it is the case for simple random walks, but converges in law towards a segment that contains the origin and which extremal points follow the Arcsine law. In the second work, we consider the case where the aggregate is built by simple random walks in dimension d > 1. We give convergence and fluctuation results on the odometer function introduced by Levine and Peres, which counts at each point the number of visits of walkers throughout the construction of the aggregate. In the third work, we examine the case where the aggregate is built using multidimensional drifted random walks. We show that under a suitable normalisation, the aggregate converges towards a limiting shape which is identified as a true heat ball. We thus give an answer to an open question in analysis concerning the existence of such a bounded shape. The last work deals with the special case where an interior bound is known for the aggregate. We give a set of conditions on the graph and on the nature of this interior bound that are sufficient to imply an outer bound. This result is applied to the case of random walks on the supercritical bond percolation cluster, thus completing a result by Shellef
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Kanjilal, Suranita [Verfasser], Harro [Akademischer Betreuer] [Gutachter] Schmeling, and Doris [Gutachter] Breuer. "Theory and numerical modelling of two phase flow : melt percolation process through porosity dependent viscous matrix inside the Earth / Suranita Kanjilal ; Gutachter: Harro Schmeling, Doris Breuer ; Betreuer: Harro Schmeling." Frankfurt am Main : Universitätsbibliothek Johann Christian Senckenberg, 2016. http://d-nb.info/1117647943/34.
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Deshayes, Aurélia. "Modèles de croissance aléatoire et théorèmes de forme asymptotique : les processus de contact." Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0168/document.
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Cette thèse s'inscrit dans l'étude des systèmes de particules en interaction et plus précisément dans celle des modèles de croissance aléatoire qui représentent un quantité qui grandit au cours du temps et s'étend sur un réseau. Ce type de processus apparaît naturellement quand on regarde la croissance d'un cristal ou bien la propagation d'une épidémie. Cette dernière est bien modélisée par le processus de contact introduit en 1974 par Harris. Le processus de contact est un des plus simples systèmes de particules en interaction présentant une transition de phase et l'on connaît maintenant bien son comportement sur ses phases. De nombreuses questions ouvertes sur ses extensions, notamment celles de formes asymptotiques, ont motivé ce travail. Après la présentation de ce processus et de certaines de ses extensions, nous introduisons et étudions une nouvelle variante: le processus de contact avec vieillissement où les particules ont un âge qui influence leur capacité à donner naissance à leurs voisines. Nous effectuerons pour ce modèle un couplage avec une percolation orientée inspiré de celui de Bezuidenhout-Grimmett et nous montrerons la croissance d'ordre linéaire de ce processus. Dans la dernière partie de la thèse, nous nous intéressons à la preuve d'un théorème de forme asymptotique pour des modèles généraux de croissance aléatoire grâce à des techniques sous-Additives, parfois complexes à mettre en place à cause de la non 'survie presque sûre' de nos modèles. Nous en concluons en particulier que le processus de contact avec vieillissement, le processus de contact en environnement dynamique, la percolation orientée avec immigration hostile, et le processus de contact avec sensibilisation vérifient des résultats de forme asymptotiqueThis thesis is a contribution to the mathematical study of interacting particles systems which include random growth models representing a spreading shape over time in the cubic lattice. These processes are used to model the crystal growth or the spread of an infection. In particular, Harris introduced in 1974 the contact process to represent such a spread. It is one of the simplest interacting particles systems which exhibits a critical phenomenon and today, its behaviour is well-Known on each phase. Many questions about its extensions remain open and motivated our work, especially the one on the asymptotic shape. After the presentation of the contact process and its extensions, we introduce a new one: the contact process with aging where each particle has an age age that influences its ability to give birth to its neighbours. We build a coupling between our process and a supercritical oriented percolation adapted from Bezuidenhout-Grimmett's construction and we establish the 'at most linear' growth of our process. In the last part of this work, we prove an asymptotic shape theorem for general random growth models thanks to subadditive techniques, which can be complicated in the case of non-Permanent models conditioned to survive. We conclude that the process with aging, the contact process in randomly evolving environment, the oriented percolation with hostile immigration and the bounded modified contact process satisfy asymptotic shape results
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Grigg, John Antony Hugh. "Superconductive Effects in Thin Cluster Films." Thesis, University of Canterbury. Department of Physics and Astronomy, 2012. http://hdl.handle.net/10092/10376.
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In this thesis, the superconductive and superresistive properties of thin percolating films of lead nanoclusters are presented. The samples were created by depositing clusters from an inert gas aggregation cluster source onto substrates held at either room temperature or 10K.
Observations of the characteristic behaviours of the samples were made through R(T ) and V (I) measurements. Several interesting features were observed - smooth and discrete steps in the R(I) curves, hysteresis between increasing and decreasing bias currents, and non-zero resistances at superconducting temperatures. Explanations are proposed in terms of theoretical models of several phenomena - phase slips, phase slip centres and hotspots - which have seen little prior application to percolating systems in literature.
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Laugier, Jean-Marie. "Modelisation des proprietes electriques de systemes desordonnes : conductivite - constante dielectrique - bruit." Aix-Marseille 1, 1987. http://www.theses.fr/1987AIX11092.
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Etude par les modeles du milieu effectif, des matrices de transfert, du reseau fractal deterministe et du melange de deux types de poudres spheriques. Determination directe de l'angle de percolation. Description d'un banc d'essai permettant la mesure du bruit electrique
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Mohee, Lakshana. "Collagen scaffolds for tissue engineering : the relationship between microstructure, fluid dynamics, mechanics and scaffold deformation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/276980.
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Collagen scaffolds are porous structures which are used in bioreactors and in a wide range of tissue engineering applications. In these contexts, the scaffolds may be subjected to conditions in which fluid is forced through the structure and the scaffold is simultaneously compressed. It is clear that fluid transport within collagen scaffolds, and the inter-relationships between permeability, scaffold structure, fluid pressure and scaffold deformation are of key importance. However, these relationships remain poorly understood. In this thesis, a series of isotropic collagen structures were produced using a freeze-drying technique from aqueous slurry concentrations 0.5, 0.75 and 1 wt%, and fully characterised using X-ray micro-tomography and compression testing. It was found that collagen wt% influenced structural parameters such as pore size, porosity, relative density and mechanical properties. Percolation theory was used to investigate the pore interconnectivity of each scaffold. Structures with lower collagen fraction resulted in larger percolation diameters, but lower mechanical stiffness. Aligned collagen scaffolds were also produced by altering the freeze-drying protocol and using different types of mould materials and designs. It was found that a polycarbonate mould with stainless base resulted in vertically aligned structures with low angular variation. When compared with isotropic scaffolds from slurry of the same concentration, aligned scaffolds had a larger percolation diameter. Tortuosity was used as a mathematical tool to characterise the interconnected pathways within each porous structure. The effect of the size of the region of interest (ROI) chosen and the size of the virtual probe particle used in the analysis on the values of tortuosity calculated were determined and an optimised calculation methodology developed. Increasing the collagen fraction within isotropic scaffolds increased the tortuosity, and aligned structures had smaller tortuosity values than their isotropic counterparts. Permeability studies were conducted using two complementary experimental rigs designed to cover a range of pressure regimes and the results were compared with predictions from mathematical models and computational simulations. At low pressures, it was found that the lower collagen fraction structures, which had more open morphologies, had higher permeabilities. Alignment of the structure also enhanced permeability. The scaffolds all experienced deformation at high pressures resulting in a restriction of fluid flow. The lower collagen fraction scaffolds experienced a sharper decrease in permeability with increased pressure and aligned structures were more responsive to deformation than their isotropic counterparts. The inter-relationships between permeability, scaffold structure, fluid pressure and deformation of collagen scaffolds were explored. For isotropic samples, permeability followed a broad $(1- \epsilon)^2$ behaviour with strain as predicted by a tetrakaidecahedral structural model, with the constant of proportionality changing with collagen fraction. In contrast, the aligned structures did not follow this behaviour with the permeability dropping much more sharply in the early stages of compression. Open-cell polyurethane (PU) foams, sometimes used as dressings in wound healing applications, are often compared with collagen scaffolds in permeability models and were used in this thesis as a comparison structure. The foam had a higher permeability than the scaffolds due to its larger pore sizes and higher interconnectivity. In the light of the effects of compression on permeability, the changes in porous structure with compression were explored in isotropic and aligned 0.75 wt% scaffolds. Unlike the fluid flow experiments, these experiments were carried out in the dry state. Deformation in simple linear compression and in step-wise compression was studied, and the stress relaxation behaviour of the scaffolds characterised. A methodology was developed to characterise the structural changes accompanying compression using X-ray micro-tomography with an in situ compression stage. The methodology accounted for the need for samples to remain unchanged during the scan collection period for stable image reconstruction. The scaffolds were studied in uniaxial compression and biaxial compression and it was found that pore size and percolation diameter decreased with increasing compressive strain, while the tortuosity increased. The aligned structure was less affected than the isotropic at low compressions, in contrast to the results from the permeability study in which the aligned structure was more responsive to strain. This suggests that the degree of hydration may affect the structural changes observed. The insights gained in this study of the inter-relationships between microstructure, fluid dynamics and deformation in collagen scaffolds are of relevance to the informed design of porous structures for medical applications.
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Flandin, Lionel. "Étude expérimentale et modélisation microstructurale de l'évolution des propriétés électriques d'un matériau composite en cours de déformation." Université Joseph Fourier (Grenoble ; 1971-2015), 1998. http://www.theses.fr/1998GRE10024.
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L'essentiel de ce travail a porte sur l'etude des relations entre la microstructure et les proprietes macroscopiques de composites particulaires a proprietes electriques contrastees. L'objectif etait de mettre au point une methode de suivi in situ de l'evolution de microstructure de tels materiaux. Pour ce faire, ce travail s'est deroule suivant trois axes principaux. Dans un premier temps, de nouveaux composites ont ete mis en uvre dont les phases presentent un contraste eleve du point de vue de leurs proprietes electriques et mecaniques. Ces materiaux ont ete elabores en associant un latex filmogene et une suspension de polymere conducteur intrinseque (le polypyrrole). Les charges conductrices ont ete obtenues par polymerisation du pyrrole en milieu aqueux par voie chimique. Celles-ci presentent, au choix, un facteur de forme eleve ou egal a un, grace, respectivement, a une polymerisation originale a la surface de monocristaux de cellulose et une polymerisation plus classique, conduite en presence d'un stabilisant. Dans un deuxieme temps, une simulation numerique a ete developpee qui permet de rendre compte des proprietes de transport electriques de ces milieux en courant alternatif. Cette simulation est basee sur le modele rc decrit dans la litterature a laquelle une echelle de longueur dans la definition des resistances et des capacites des circuits modelisant les composites a ete ajoutee. Dans un troisieme temps, une methode de suivi de l'endommagement du squelette percolant de ces materiaux par une mesure des proprietes electriques a ete mise au point. Une evolution des proprietes electriques contradictoire avec un endommagement purement limite au reseau percolant, a pu etre comprise qualitativement, comme resultant d'un effet geometrique de rearrangement des charges. Afin d'eliminer cet effet nous avons decide d'effectuer des mesures similaires sur des composites particulaires presentant une matrice rigide. Cette etude de composites a matrice epoxy charges en noir de carbone a montre, dans l'etat non deforme, un desaccord flagrant avec les predictions du modele statistique de percolation. Une transition brutale entre un etat isolant avec une faible permittivite et un autre a conductivite elevee a, en particulier, ete mesuree et reliee a une evolution drastique de microstructure. Cette transition a pu etre verifiee par des observations microstructurales et comprises qualitativement a l'aide de potentiels d'interaction empruntes a la science des colloides.
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Xulvi-Brunet, Ramon. "Structural properties of scale-free networks." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2007. http://dx.doi.org/10.18452/15608.
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Netzwerke sind überall, von der elektrischen Stromversorgung über die Biochemie der Zellen, das Internet bis hin zu sozialen Netzen. Netzwerke als mathematisches Konzept haben sich in den letzten Jahren zu einem wichtigen Werkzeug der Beschreibung komplexer Systeme entwickelt. Ihre grundlegende Eigenschaft ist, dass sie aus einer grö{ss}en Anzahl dynamischer Elemente bestehen, die sich gegenseitig beeinflussen und dabei nicht linear gekoppelt sind. Die moderne Netzwerkwissenschaft will die Wechselwirkung zwischen den einzelnen Untereinheiten erklären und davon ausgehend verständlich machen, auf welche Weise Prozesse auf einem Netzwerk stattfinden können. Zum Beispiel wird untersucht, wie die Struktur sozialer Netze die Ausbreitung von Information oder von Krankheiten beeinflusst, wie die Topologie des World Wide Web das Surf-Verhalten oder die Funktionalität von Suchmaschinen beeinträchtigt oder welche Auswirkungen die Hierarchie in ökologischen Nischen auf die Populationsdynamik der einzelnen Spezies hat. Darüber hinaus gilt es herauszufinden, welche grundlegenden Prinzipien der Evolution realer Netzwerke zugrunde liegen, das heißt nach welchen Regeln sich einerseits die Untereinheiten entwickeln und welchen Einfluss andererseits deren Vernetzung hat. Die vorliegende Dissertation beschäftigt sich sowohl mit der Topologie verschiedener Netzwerke als auch mit den der Evolution zugrunde liegenden Prinzipien. Schwerpunkte liegen dabei auf den folgenden zwei Aspekten: erstens dem Einfluss von so gennanten ``vertex-pair correlations'''', das heißt Korrelationen zwischen den Untereinheiten, auf die Topologie und zweitens der Auswirkung der Geographie auf die Netzwerkentwicklung. Es wird der bedeutende Einfluss aufgezeigt, den die Korrelationen auf wichtige statistische Größen der Netzwerke haben. Weiterhin analysieren wir die Perkolationseigenschaften, die Aufschluss über die Empfindlichkeit gegenüber Störungen in der Vernetzung geben. Damit können zum Beispiel Fragen aus der Epidemiologie diskutiert werden. Es zeigt sich, dass die Topologie vieler Netzwerke und ihre Perkolationseigenschaften deutlich von Korrelationen beeinflusst werden. Schließlich untersuchen wir im letzten Teil dieser Arbeit, wie die Einbettung von Netzwerken in eine endlich-dimensionale Geographie auf die Modellierung und Entwicklung Web-ähnlicher Systeme Einfluss nimmt.Networks are all around us, from electrical power grids to the biochemistry of cells, from the Internet to social webs. The mathematical concept of network has recently been turned into an important tool for describing complex systems, whose principal characteristic is that they consist of a large number of mutually interacting dynamical parts which are coupled in a nonlinear fashion. Modern network science attempts to explain the structure of interactions between the subunits of a system in order to understand their functioning and the processes taking place in them. It tries, for instance, to grasp how the structure of social networks affects the spread of information or human diseases, how the structure of the World Wide Web influences the search engines and surfing behavior, or how the hierarchy of ecological niches affects population dynamics. Beyond this, the ultimate goal of network science is to discover what generating principles exist behind the evolution of real systems. It tries to find the fundamental principles under which the subunits evolve, and the wiring of interactions. This thesis centres both on the study of the topological structure of networks and the analysis of the underlying principles responsible for their evolution. More specifically, it concentrates on the following aspects: the influence of vertex-pair correlations on network topology, the network percolation problem, which is closely related to the spreading of epidemics and the robustness of networks, and the effects of geography as a generating element. We show that important topological and percolation properties change considerably when modifying the connection probabilities between vertices, and that geography as well plays a crucial role in the modeling of evolving real web-like systems.
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McAndrew, Thomas Charles. "Weighted Networks: Applications from Power grid construction to crowd control." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/668.
Full textAbstract:
Since their discovery in the 1950's by Erdos and Renyi, network theory (the study of objects and their associations) has blossomed into a full-fledged branch of mathematics.
Due to the network's flexibility, diverse scientific problems can be reformulated as networks and studied using a common set of tools.
I define a network G = (V,E) composed of two parts: (i) the set of objects V, called nodes, and (ii) set of relationships (associations) E, called links, that connect objects in V.
We can extend the classic network of nodes and links by describing the intensity of these associations with weights.
More formally, weighted networks augment the classic network with a function f(e) from links to the real line, uncovering powerful ways to model real-world applications.
This thesis studies new ways to construct robust micro powergrids, mine people's perceptions of causality on a social network, and proposes a new way to analyze crowdsourcing all in the context of the weighted network model.
The current state of Earth's ecosystem and intensifying climate calls on scientists to find new ways to harvest clean affordable energy.
A microgrid, or neighborhood-scale powergrid built using renewable energy sources attached to personal homes, suggest one way to ameliorate this energy crisis.
We can study the stability (robustness) of such a small-scale system with weighted networks.
A novel use of weighted networks and percolation theory guides the safe and efficient construction of power lines (links, E) connecting a small set of houses (nodes, V) to one another and weights each power line by the distance between houses.
This new look at the robustness of microgrid structures calls into question the efficacy of the traditional utility.
The next study uses the twitter social network to compare and contrast causal language from everyday conversation.
Collecting a set of 1 million tweets, we find a set of words (unigrams), parts of speech, named entities, and sentiment signal the use of informal causal language.
Breaking a problem difficult for a computer to solve into many parts and distributing these tasks to a group of humans to solve is called Crowdsourcing.
My final project asks volunteers to 'reply' to questions asked of them and 'supply' novel questions for others to answer.
I model this 'reply and supply' framework as a dynamic weighted network, proposing new theories about this network's behavior and how to steer it toward worthy goals.
This thesis demonstrates novel uses of, enhances the current scientific literature on, and presents novel methodology for, weighted networks.
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Lechtenfeld, Markus. "Auswertung der rheologischen und optischen Untersuchungen während der Gelierung des Systems Gelatine / Wasser mit Hilfe der Perkolationstheorie - Evaluation of rheological and optical investigations during the gelation of the system gelatin/water using the percolation theory." Gerhard-Mercator-Universitaet Duisburg, 2001. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-08022001-100118/.
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In the thesis the gelation of the system gelatin / water was investigated by use of rheological and optical methods. The rheological properties were taken to describe the gelation in terms of the percolation theory. In order to determine the gel point and the critical exponents a potential law found by Stauffer and de Gennes that describes the development of the storage and loss modulus was used to express normalized percolation approches. This normalized percolation ansatzes delivers a single very exact gelation time and the information which range should be taken for the evaluation. Combining the storage and the loss modulus symmetrically around the gel point novel so called combined percolation functions were formulated. From these combined functions the critical exponents could likewise be determined. The simultaneous measurements of the rheological and optical properties clearly show that close to the gel point the loss and the storage modulus as a function of time as well as a function of the optical rotation could be described in terms of the percolation theory. Furthermore an aggregation model was formulated that describes the development of the storage modulus close and far away from the gel point, respectively.
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Noel, Jonathan A. "Extremal combinatorics, graph limits and computational complexity." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:8743ff27-b5e9-403a-a52a-3d6299792c7b.
Full textAbstract:
This thesis is primarily focused on problems in extremal combinatorics, although we will also consider some questions of analytic and algorithmic nature. The d-dimensional hypercube is the graph with vertex set {0,1}d where two vertices are adjacent if they differ in exactly one coordinate. In Chapter 2 we obtain an upper bound on the 'saturation number' of Qm in Qd. Specifically, we show that for m ≥ 2 fixed and d large there exists a subgraph G of Qd of bounded average degree such that G does not contain a copy of Qm but, for every G' such that G ⊊ G' ⊆ Qd, the graph G' contains a copy of Qm. This result answers a question of Johnson and Pinto and is best possible up to a factor of O(m). In Chapter 3, we show that there exists ε > 0 such that for all k and for n sufficiently large there is a collection of at most 2(1-ε)k subsets of [n] which does not contain a chain of length k+1 under inclusion and is maximal subject to this property. This disproves a conjecture of Gerbner, Keszegh, Lemons, Palmer, Pálvölgyi and Patkós. We also prove that there exists a constant c ∈ (0,1) such that the smallest such collection is of cardinality 2(1+o(1))ck for all k. In Chapter 4, we obtain an exact expression for the 'weak saturation number' of Qm in Qd. That is, we determine the minimum number of edges in a spanning subgraph G of Qd such that the edges of E(Qd)\E(G) can be added to G, one edge at a time, such that each new edge completes a copy of Qm. This answers another question of Johnson and Pinto. We also obtain a more general result for the weak saturation of 'axis aligned' copies of a multidimensional grid in a larger grid. In the r-neighbour bootstrap process, one begins with a set A0 of 'infected' vertices in a graph G and, at each step, a 'healthy' vertex becomes infected if it has at least r infected neighbours. If every vertex of G is eventually infected, then we say that A0 percolates. In Chapter 5, we apply ideas from weak saturation to prove that, for fixed r ≥ 2, every percolating set in Qd has cardinality at least (1+o(1))(d choose r-1)/r. This confirms a conjecture of Balogh and Bollobás and is asymptotically best possible. In addition, we determine the minimum cardinality exactly in the case r=3 (the minimum cardinality in the case r=2 was already known). In Chapter 6, we provide a framework for proving lower bounds on the number of comparable pairs in a subset S of a partially ordered set (poset) of prescribed size. We apply this framework to obtain an explicit bound of this type for the poset 𝒱(q,n) consisting of all subspaces of 𝔽qnordered by inclusion which is best possible when S is not too large. In Chapter 7, we apply the result from Chapter 6 along with the recently developed 'container method,' to obtain an upper bound on the number of antichains in 𝒱(q,n) and a bound on the size of the largest antichain in a p-random subset of 𝒱(q,n) which holds with high probability for p in a certain range. In Chapter 8, we construct a 'finitely forcible graphon' W for which there exists a sequence (εi)∞i=1 tending to zero such that, for all i ≥ 1, every weak εi-regular partition of W has at least exp(εi-2/25log∗εi-2) parts. This result shows that the structure of a finitely forcible graphon can be much more complex than was anticipated in a paper of Lovász and Szegedy. For positive integers p,q with p/q ❘≥ 2, a circular (p,q)-colouring of a graph G is a mapping V(G) → ℤp such that any two adjacent vertices are mapped to elements of ℤp at distance at least q from one another. The reconfiguration problem for circular colourings asks, given two (p,q)-colourings f and g of G, is it possible to transform f into g by recolouring one vertex at a time so that every intermediate mapping is a p,q-colouring? In Chapter 9, we show that this question can be answered in polynomial time for 2 ≤ p/q < 4 and is PSPACE-complete for p/q ≥ 4.
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Topal, Sebahattin. "Multi-robot Coordination Control Methodology For Search And Rescue Operations." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613841/index.pdf.
Full textAbstract:
This dissertation presents a novel multi-robot coordination control algorithm for search
and rescue (SAR) operations. Continuous and rapid coverage of the unstructured and
complex disaster areas in search of possible buried survivors is a time critical operation
where prior information about the environment is either not available or very
limited. Human navigation of such areas is definitely dangerous due to the nature
of the debris. Hence, exploration of unknown disaster environments with a team of
robots is gaining importance day by day to increase the efficiency of SAR operations.
Localization of possible survivors necessitates uninterrupted navigation of robotic
aiding devices within the rubbles without getting trapped into dead ends. In this
work, a novel goal oriented prioritized exploration and map merging methodologies
are proposed to generate efficient multi-robot coordination control strategy. These
two methodologies are merged to make the proposed methodology more realistic for
real world applications.
Prioritized exploration of an environment is the first important task of the efficient coordination control algorithm for multi-robots. A goal oriented and prioritized exploration
approach based on a percolation model for victim search operation in unknown
environments is presented in this work. The percolation model is used to describe
the behavior of liquid in random media. In our approach robots start prioritized exploration
beginning from regions of the highest likelihood of finding victims using
percolation model inspired controller.
A novel map merging algorithm is presented to increase the performance of the SAR
operation in the sense of time and energy. The problem of merging partial occupancy
grid environment maps which are extracted independently by individual robot units
during search and rescue (SAR) operations is solved for complex disaster environments.
Moreover, these maps are combined using intensity and area based features
without knowing the initial position and orientation of the robots. The proposed approach
handles the limitation of existing works in the literature such aslimited overlapped area between partial maps of robots is sufficient for good merging performance and unstructured partial environment maps can be merged efficiently. These abilities allow multi-robot teams to efficiently generate the occupancy grid map of catastrophe areas and localize buried victim in the debris efficiently.
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Risi, Celso Luis Sigoli. "Influência nas propriedades elétricas devido ao alinhamento de nanotubos de carbono em matriz epóxi utilizando campo elétrico." Universidade do Estado de Santa Catarina, 2010. http://tede.udesc.br/handle/handle/1755.
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Multi-walled carbon nanotubos dispersed in epoxy matrix (DGEBA) were aligned by a sinusoidal electric field with amplitude of 300 V / cm and frequency 1 kHz, during curing of the nanocomposites. Nanocomposites were subjected to the electric field (aligned nanotubes) and samples cured without the presence of the field (with nanotubes dispersed randomly) and NC concentration equal to 0.05, 0.1, 0.25 and 0.5% (m / m). The morphologies of aligned carbon nanotubes networks, in samples submitted to the electric field were characterized by means transmitted light optical microscopy analysis. It was observed that the geometry of the networks is strongly influenced by the concentration of nanotubes. The monitoring of electrical conductivity during the curing of the samples, allowed us to identify the three main stages of formation of networks. The first is related to the alignment and clustering of NCPM, the second is related to the stability of the network and the third to the cure of epoxy matrix. The Classical Percolation Theory has been used to relate the electrical conductivity (dc) to the content of NCPM, and allowed to determine the exponent of the electrical conductivity and percolation threshold of aligned samples and samples without alignment. The trend of increase in the electrical conductivity exponent in the aligned samples indicates the formation of an anisotropic network, since the conductivity is favored in the direction of alignment. The percolation threshold showed a decrease in the sample aligned, which may relate to the facilitation of the electric conduction process through the material. As for the dielectric properties, nanocomposites analyzed showed a behavior similar to the dielectric described by the first order Debye dielectric dispersion model. Both samples type showed a relaxation time of electric dipoles in the order of milliseconds, typical of interfacial polarization. The permittivity of aligned samples exhibited a magnitude increase in frequency of 200 Hz. This behavior may be related to the increased ability to trap electrical charges due to the formation of the network carbon nanotubes. The DMA and DIL analysis showed that Tg of the aligned samples decrease, indicating that the alignment affect the restriction on the movement of polymer chains. The micro-hardness analysis was not sensitive enough to characterize the hardness anisotropy, depending on the alignment of NCPM dispersed in the matrix. In the other hand, it was revealed that the incorporation of nanotubes creates free volume within the material, which reduces the hardness of the nanocomposites compared with pure epoxy.
Nanotubos de paredes múltiplas (NCPM) dispersos em matriz epóxi (DGEBA) foram alinhados com o auxilio de um campo elétrico senoidal, de amplitude de 300 V/cm e freqüência de 1 kHz, durante a cura dos nanocompósitos. Foram fabricados nanocompósitos submetidos ao campo elétrico (nanotubos alinhados) e amostras curadas sem a presença do campo (com nanotubos dispersos de modo aleatório), com teores de NCPM iguais a 0,05; 0,1; 0,25 e 0,5 % (m/m). As morfologias das redes alinhadas, nas amostras submetidas ao campo, foram caracterizadas por meio das analises de microscopia óptica de luz transmitida. Foi possível notar que a geometria das redes e fortemente influenciada pela concentração de nanotubos. O monitoramento da condutividade elétrica, durante a cura das amostras linhadas, permitiu identificar as três principais etapas de formação das redes. A primeira esta relacionada com o processo de alinhamento e aglomeração lateral dos NCPM, a segunda esta relacionada com a estabilidade da rede e a terceira com a cura da matriz epóxi. A Teoria da Percolação Clássica foi utilizada para descrever a condutividade elétrica (cc) em função do teor de NCPM, e permitiu determinar o expoente de condutividade elétrica e o limiar de percolação das amostras alinhadas e das amostras sem alinhamento. A tendência de acréscimo do expoente de condutividade elétrica nas amostras alinhadas indica a formação de uma rede anisotrópica, uma vez que o fluxo elétrico e favorecido na direção do alinhamento. O limiar de percolação apresentou uma diminuição nas amostras alinhadas, que pode estar relacionado com a facilitação do processo de condução através do material. Como relação as propriedades dielétricas, os nanocompósitos analisados (0,5 % m/m, alinhados e sem alinhamento) apresentaram um comportamento similar aos dielétricos descritos pelo modelo de dispersão dielétrica de primeira ordem de Debye. Ambas as amostras apresentaram um tempo de relaxação dos dipolos elétricos na ordem de milissegundos, característico de polarização interfacial. Na freqüência de 200 Hz a permissividade elétrica exibiu um aumento na ordem de grandeza, nas amostras alinhadas. Este comportamento pode estar relacionado com o aumento da capacidade de aprisionar cargas elétricas, devido a formação da rede. As analises de DMA e DIL mostraram que a Tg das amostras alinhadas diminuem, indicando que o alinhamento prejudica a restrição dos movimentos das cadeias poliméricas. Já a analise de microdureza Vickers nao se mostrou sensível o bastante para caracterizar a anisotropia de tal propriedade, em função do alinhamento dos NCPM dispersos na matriz. Em contra partida, foi possível perceber que a incorporação de nanotubos gera volumes livres no interior do material, que diminui a dureza dos nanocompósitos, quando comparado com o epóxi puro.