Relevant bibliographies by topics / Chaos expansion

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Chaos expansion'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Chaos expansion"

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Rahman, Sharif. "A Spline Chaos Expansion." SIAM/ASA Journal on Uncertainty Quantification 8, no. 1 (January 2020): 27–57. http://dx.doi.org/10.1137/19m1239702.

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SEPAHVAND, K., S. MARBURG, and H. J. HARDTKE. "UNCERTAINTY QUANTIFICATION IN STOCHASTIC SYSTEMS USING POLYNOMIAL CHAOS EXPANSION." International Journal of Applied Mechanics 02, no. 02 (June 2010): 305–53. http://dx.doi.org/10.1142/s1758825110000524.

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In recent years, extensive research has been reported about a method which is called the generalized polynomial chaos expansion. In contrast to the sampling methods, e.g., Monte Carlo simulations, polynomial chaos expansion is a nonsampling method which represents the uncertain quantities as an expansion including the decomposition of deterministic coefficients and random orthogonal bases. The generalized polynomial chaos expansion uses more orthogonal polynomials as the expansion bases in various random spaces which are not necessarily Gaussian. A general review of uncertainty quantification methods, the theory, the construction method, and various convergence criteria of the polynomial chaos expansion are presented. We apply it to identify the uncertain parameters with predefined probability density functions. The new concepts of optimal and nonoptimal expansions are defined and it demonstrated how we can develop these expansions for random variables belonging to the various random spaces. The calculation of the polynomial coefficients for uncertain parameters by using various procedures, e.g., Galerkin projection, collocation method, and moment method is presented. A comprehensive error and accuracy analysis of the polynomial chaos method is discussed for various random variables and random processes and results are compared with the exact solution or/and Monte Carlo simulations. The method is employed for the basic stochastic differential equation and, as practical application, to solve the stochastic modal analysis of the microsensor quartz fork. We emphasize the accuracy in results and time efficiency of this nonsampling procedure for uncertainty quantification of stochastic systems in comparison with sampling techniques, e.g., Monte Carlo simulation.
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Gaspard, P. "Quantization of Chaos: -Expansion Theory." Progress of Theoretical Physics Supplement 116 (May 16, 2013): 59–106. http://dx.doi.org/10.1143/ptp.116.59.

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Yin, Shengwen, Xiaohan Zhu, and Xiang Liu. "A Novel Sparse Polynomial Expansion Method for Interval and Random Response Analysis of Uncertain Vibro-Acoustic System." Shock and Vibration 2021 (September 23, 2021): 1–15. http://dx.doi.org/10.1155/2021/1125373.

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For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the simplicity of the traditional arbitrary polynomial chaos method, while avoiding its inefficiency. In the SGS-IRAPC, the response is approximated by the moment-based arbitrary polynomial chaos expansion and the expansion coefficient is determined by the least squares approximation method. A new sparse sampling scheme combined the sparse grids’ scheme with the sequential sampling scheme which is employed to generate the sampling points used to calculate the expansion coefficient to decrease the computational cost. The efficiency of the proposed surrogate method is demonstrated using a typical mathematical problem and an engineering application.
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Crestaux, Thierry, Olivier Le Maıˆtre, and Jean-Marc Martinez. "Polynomial chaos expansion for sensitivity analysis." Reliability Engineering & System Safety 94, no. 7 (July 2009): 1161–72. http://dx.doi.org/10.1016/j.ress.2008.10.008.

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Gayrard, Emeline, Cédric Chauvière, Hacène Djellout, and Pierre Bonnet. "MODELING EXPERIMENTAL DATA WITH POLYNOMIALS CHAOS." Probability in the Engineering and Informational Sciences 34, no. 1 (August 14, 2018): 14–26. http://dx.doi.org/10.1017/s026996481800030x.

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Given a raw data sample, the purpose of this paper is to design a numerical procedure to model this sample under the form of polynomial chaos expansion. The coefficients of the polynomial are computed as the solution to a constrained optimization problem. The procedure is first validated on samples coming from a known distribution and it is then applied to raw experimental data of unknown distribution. Numerical experiments show that only five coefficients of the Chaos expansions are required to get an accurate representation of a sample.
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Shao, Hua, Yuming Shi, and Hao Zhu. "Strong Li–Yorke Chaos for Time-Varying Discrete Dynamical Systems with A-Coupled-Expansion." International Journal of Bifurcation and Chaos 25, no. 13 (December 15, 2015): 1550186. http://dx.doi.org/10.1142/s0218127415501862.

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This paper is concerned with strong Li–Yorke chaos induced by [Formula: see text]-coupled-expansion for time-varying (i.e. nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li–Yorke are established via strict coupled-expansions for irreducible transition matrices in bounded and closed subsets of complete metric spaces and in compact subsets of metric spaces, respectively, where their conditions are weaker than those in the existing literature. One example is provided for illustration.
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Briand, Philippe, and Céline Labart. "Simulation of BSDEs by Wiener chaos expansion." Annals of Applied Probability 24, no. 3 (June 2014): 1129–71. http://dx.doi.org/10.1214/13-aap943.

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Paffrath, M., and U. Wever. "Adapted polynomial chaos expansion for failure detection." Journal of Computational Physics 226, no. 1 (September 2007): 263–81. http://dx.doi.org/10.1016/j.jcp.2007.04.011.

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Cooper, Fred, John Dawson, Salman Habib, Yuval Kluger, Dawn Meredith, and Harvey Shepard. "Semiquantum chaos and the large N expansion." Physica D: Nonlinear Phenomena 83, no. 1-3 (May 1995): 74–97. http://dx.doi.org/10.1016/0167-2789(94)00251-k.

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Dissertations / Theses on the topic "Chaos expansion"

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Szepietowska, Katarzyna. "POLYNOMIAL CHAOS EXPANSION IN BIO- AND STRUCTURAL MECHANICS." Thesis, Bourges, INSA Centre Val de Loire, 2018. http://www.theses.fr/2018ISAB0004/document.

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Cette thèse présente une approche probabiliste de la modélisation de la mécanique des matériaux et des structures. Le dimensionnement est influencé par l'incertitude des paramètres d'entrée. Le travail est interdisciplinaire et les méthodes décrites sont appliquées à des exemples de biomécanique et de génie civil. La motivation de ce travail était le besoin d'approches basées sur la mécanique dans la modélisation et la simulation des implants utilisés dans la réparation des hernies ventrales. De nombreuses incertitudes apparaissent dans la modélisation du système implant-paroi abdominale. L'approche probabiliste proposée dans cette thèse permet de propager ces incertitudes et d’étudier leurs influences respectives. La méthode du chaos polynomial basée sur la régression est utilisée dans ce travail. L'exactitude de ce type de méthodes non intrusives dépend du nombre et de l'emplacement des points de calcul choisis. Trouver une méthode universelle pour atteindre un bon équilibre entre l'exactitude et le coût de calcul est encore une question ouverte. Différentes approches sont étudiées dans cette thèse afin de choisir une méthode efficace et adaptée au cas d’étude. L'analyse de sensibilité globale est utilisée pour étudier les influences des incertitudes d'entrée sur les variations des sorties de différents modèles. Les incertitudes sont propagées aux modèles implant-paroi abdominale. Elle permet de tirer des conclusions importantes pour les pratiques chirurgicales. À l'aide de l'expertise acquise à partir de ces modèles biomécaniques, la méthodologie développée est utilisée pour la modélisation de joints de bois historiques et la simulation de leur comportement mécanique. Ce type d’étude facilite en effet la planification efficace des réparations et de la rénovation des bâtiments ayant une valeur historique
This thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair of ventral hernias. Many uncertainties appear in the modelling of the implant-abdominal wall system. The probabilistic approach proposed in this thesis enables these uncertainties to be propagated to the output of the model and the investigation of their respective influences. The regression-based polynomial chaos expansion method is used here. However, the accuracy of such non-intrusive methods depends on the number and location of sampling points. Finding a universal method to achieve a good balance between accuracy and computational cost is still an open question so different approaches are investigated in this thesis in order to choose an efficient method. Global sensitivity analysis is used to investigate the respective influences of input uncertainties on the variation of the outputs of different models. The uncertainties are propagated to the implant-abdominal wall models in order to draw some conclusions important for further research. Using the expertise acquired from biomechanical models, modelling of historic timber joints and simulations of their mechanical behaviour is undertaken. Such an investigation is important owing to the need for efficient planning of repairs and renovation of buildings of historical value
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Aït-Simmou, Abderrahmane. "Filtrage non-linéaire et expansion en chaos de Wiener /." Thèse, Trois-Rivières : Université du Québec à Trois-Rivières, 2002. http://www.uqtr.ca/biblio/notice/tablemat/03-2246353TM.html.

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Aït-Simmou, Abderrahmane. "Filtrage non-linéaire et expansion en chaos de Wiener." Thèse, Université du Québec à Trois-Rivières, 2002. http://depot-e.uqtr.ca/3992/1/000102224.pdf.

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Nydestedt, Robin. "Application of Polynomial Chaos Expansion for Climate Economy Assessment." Thesis, KTH, Optimeringslära och systemteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223985.

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In climate economics integrated assessment models (IAMs) are used to predict economic impacts resulting from climate change. These IAMs attempt to model complex interactions between human and geophysical systems to provide quantifications of economic impact, typically using the Social Cost of Carbon (SCC) which represents the economic cost of a one ton increase in carbon dioxide. Another difficulty that arises in modeling a climate economics system is that both the geophysical and economic submodules are inherently stochastic. Even in frequently cited IAMs, such as DICE and PAGE, there exists a lot of variation in the predictions of the SCC. These differences stem both from the models of the climate and economic modules used, as well as from the choice of probability distributions used for the random variables. Seeing as IAMs often take the form of optimization problems these nondeterministic elements potentially result in heavy computational costs. In this thesis a new IAM, FAIR/DICE, is introduced. FAIR/DICE is a discrete time hybrid of DICE and FAIR providing a potential improvement to DICE as the climate and carbon modules in FAIR take into account feedback coming from the climate module to the carbon module. Additionally uncertainty propagation in FAIR/DICE is analyzed using Polynomial Chaos Expansions (PCEs) which is an alternative to Monte Carlo sampling where the stochastic variables are projected onto stochastic polynomial spaces. PCEs provide better computational efficiency compared to Monte Carlo sampling at the expense of storage requirements as a lot of computations can be stored from the first simulation of the system, and conveniently statistics can be computed from the PCE coefficients without the need for sampling. A PCE overloading of FAIR/DICE is investigated where the equilibrium climate sensitivity, modeled as a four parameter Beta distribution, introduces an uncertainty to the dynamical system. Finally, results in the mean and variance obtained from the PCEs are compared to a Monte Carlo reference and avenues into future work are suggested.
Inom klimatekonomi används integrated assessment models (IAMs) för att förutspå hur klimatförändringar påverkar ekonomin. Dessa IAMs modellerar komplexa interaktioner mellan geofysiska och mänskliga system för att kunna kvantifiera till exempel kostnaden för den ökade koldioxidhalten på planeten, i.e. Social Cost of Carbon (SCC). Detta representerar den ekonomiska kostnaden som motsvaras av utsläppet av ett ton koldioxid. Faktumet att både de geofysiska och ekonomiska submodulerna är stokastiska gör att SCC-uppskattningar varierar mycket även inom väletablerade IAMs som PAGE och DICE. Variationen grundar sig i skillnader inom modellerna men också från att val av sannolikhetsfördelningar för de stokastiska variablerna skiljer sig. Eftersom IAMs ofta är formulerade som optimeringsproblem leder dessutom osäkerheterna till höga beräkningskostnader. I denna uppsats introduceras en ny IAM, FAIR/DICE, som är en diskret tids hybrid av DICE och FAIR. Den utgör en potentiell förbättring av DICE eftersom klimat- och kolmodulerna i FAIR även behandlar återkoppling från klimatmodulen till kolmodulen. FAIR/DICE är analyserad med hjälp av Polynomial Chaos Expansions (PCEs), ett alternativ till Monte Carlo-metoder. Med hjälp av PCEs kan de osäkerheter projiceras på stokastiska polynomrum vilket har fördelen att beräkningskostnader reduceras men nackdelen att lagringskraven ökar. Detta eftersom många av beräkningarna kan sparas från första simuleringen av systemet, dessutom kan statistik extraheras direkt från PCE koefficienterna utan behov av sampling. FAIR/DICE systemet projiceras med hjälp av PCEs där en osäkerhet är introducerad via equilibrium climate sensitivity (ECS), vilket i sig är ett värde på hur känsligt klimatet är för koldioxidförändringar. ECS modelleras med hjälp av en fyra-parameters Beta sannolikhetsfördelning. Avslutningsvis jämförs resultat i medelvärde och varians mellan PCE implementationen av FAIR/DICE och en Monte Carlo-baserad referens, därefter ges förslag på framtida utvecklingsområden.
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Luo, Wuan Hou Thomas Y. "Wiener chaos expansion and numerical solutions of stochastic partial differential equations /." Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05182006-173710.

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Price, Darryl Brian. "Estimation of Uncertain Vehicle Center of Gravity using Polynomial Chaos Expansions." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/33625.

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The main goal of this study is the use of polynomial chaos expansion (PCE) to analyze the uncertainty in calculating the lateral and longitudinal center of gravity for a vehicle from static load cell measurements. A secondary goal is to use experimental testing as a source of uncertainty and as a method to confirm the results from the PCE simulation. While PCE has often been used as an alternative to Monte Carlo, PCE models have rarely been based on experimental data. The 8-post test rig at the Virginia Institute for Performance Engineering and Research facility at Virginia International Raceway is the experimental test bed used to implement the PCE model. Experimental tests are conducted to define the true distribution for the load measurement systemsâ uncertainty. A method that does not require a new uncertainty distribution experiment for multiple tests with different goals is presented. Moved mass tests confirm the uncertainty analysis using portable scales that provide accurate results. The polynomial chaos model used to find the uncertainty in the center of gravity calculation is derived. Karhunen-Loeve expansions, similar to Fourier series, are used to define the uncertainties to allow for the polynomial chaos expansion. PCE models are typically computed via the collocation method or the Galerkin method. The Galerkin method is chosen as the PCE method in order to formulate a more accurate analytical result. The derivation systematically increases from one uncertain load cell to all four uncertain load cells noting the differences and increased complexity as the uncertainty dimensions increase. For each derivation the PCE model is shown and the solution to the simulation is given. Results are presented comparing the polynomial chaos simulation to the Monte Carlo simulation and to the accurate scales. It is shown that the PCE simulations closely match the Monte Carlo simulations.
Master of Science
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Cattell, Simon. "A Wiener chaos based approach to stability analysis of stochastic shear flows." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/289421.

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As the aviation industry expands, consuming oil reserves, generating carbon dioxide gas and adding to environmental concerns, there is an increasing need for drag reduction technology. The ability to maintain a laminar flow promises significant reductions in drag, with economic and environmental benefits. Whilst development of flow control technology has gained interest, few studies investigate the impacts that uncertainty, in flow properties, can have on flow stability. Inclusion of uncertainty, inherent in all physical systems, facilitates a more realistic analysis, and is therefore central to this research. To this end, we study the stability of stochastic shear flows, and adopt a framework based upon the Wiener Chaos expansion for efficient numerical computations. We explore the stability of stochastic Poiseuille, Couette and Blasius boundary layer type base flows, presenting stochastic results for both the modal and non modal problem, contrasting with the deterministic case and identifying the responsible flow characteristics. From a numerical perspective we show that the Wiener Chaos expansion offers a highly efficient framework for the study of relatively low dimensional stochastic flow problems, whilst Monte Carlo methods remain superior in higher dimensions. Further, we demonstrate that a Gaussian auto-covariance provides a suitable model for the stochasticity present in typical wind tunnel tests, at least in the case of a Blasius boundary layer. From a physical perspective we demonstrate that it is neither the number of inflection points in a defect, nor the input variance attributed to a defect, that influences the variance in stability characteristics for Poiseuille flow, but the shape/symmetry of the defect. Conversely, we show the symmetry of defects to be less important in the case of the Blasius boundary layer, where we find that defects which increase curvature in the vicinity of the critical point generally reduce stability. In addition, we show that defects which enhance gradients in the outer regions of a boundary layer can excite centre modes with the potential to significantly impact neutral curves. Such effects can lead to the development of an additional lobe at lower wave-numbers, can be related to jet flows, and can significantly reduce the critical Reynolds number.
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Song, Chen [Verfasser], and Vincent [Akademischer Betreuer] Heuveline. "Uncertainty Quantification for a Blood Pump Device with Generalized Polynomial Chaos Expansion / Chen Song ; Betreuer: Vincent Heuveline." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177252406/34.

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Langewisch, Dustin R. "Application of the polynomial chaos expansion to multiphase CFD : a study of rising bubbles and slug flow." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92097.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 157-167).
Part I of this thesis considers subcooled nucleate boiling on the microscale, focusing on the analysis of heat transfer near the Three-Phase (solid, liquid, and vapor) contact Line (TPL) region. A detailed derivation of one representative TPL model is presented. From this work, it was ultimately concluded that heat transfer in the vicinity of the TPL is rather unimportant in the overall quantification of nucleate boiling heat transfer; despite the extremely high heat fluxes that are attainable, it is limited to a very small region so the net heat transfer from this region is comparatively small. It was further concluded that many of the so-called microlayer heat transfer models appearing in the literature are actually models for TPL heat transfer; these models do not model the experimentally observed microlayer. This portion of the project was terminated early, however, in order to focus on the application of advanced computational uncertainty quantification methods to computational multiphase fluid dynamics (Part II). Part II discusses advanced uncertainty quantification (UQ) methods for long-running numerical models, namely computational multiphase fluid dynamics (CMFD) simulations. We consider the problem of how to efficiently propagate uncertainties in the model inputs (e.g., fluid properties, such as density, viscosity, etc.) through a computationally demanding model. The challenge is chiefly a matter of economics-the long run-time of these simulations limits the number of samples that one can reasonably obtain (i.e., the number of times the simulation can be run). Chapter 2 introduces the generalized Polynomial Chaos (gPC) expansion, which has shown promise for reducing the computational cost of performing UQ for a large class of problems, including heat transfer and single phase, incompressible flow simulations; example applications are demonstrated in Chapter 2. One of main objectives of this research was to ascertain whether this promise extends to realm of CMFD applications, and this is the topic of Chapters 3 and 4; Chapter 3 covers the numerical simulation of a single bubble rising in a quiescent liquid bath. The pertinent quantities from these simulations are the terminal velocity of the bubble and terminal bubble shape. the simulations were performed using the open source gerris flow solver. A handful of test cases were performed to validate the simulation results against available experimental data and numerical results from other authors; the results from gerris were found to compare favorably. Following the validation, we considered two uncertainty quantifications problems. In the first problem, the viscosity of the surrounding liquid is modeled as a uniform random variable and we quantify the resultant uncertainty in the bubbles terminal velocity. The second example is similar, except the bubble's size (diameter) is modeled as a log-normal random variable. In this case, the Hermite expansion is seen to converge almost immediately; a first-order Hermite expansion computed using 3 model evaluations is found to capture the terminal velocity distribution almost exactly. Both examples demonstrate that NISP can be successfully used to efficiently propagate uncertainties through CMFD models. Finally, we describe a simple technique to implement a moving reference frame in gerris. Chapter 4 presents an extensive study of the numerical simulation of capillary slug flow. We review existing correlations for the thickness of the liquid film surrounding a Taylor bubble and the pressure drop across the bubble. Bretherton's lubrication analysis, which yields analytical predictions for these quantities when inertial effects are negligible and Ca[beta] --> o, is considered in detail. In addition, a review is provided of film thickness correlations that are applicable for high Cab or when inertial effects are non-negligible. An extensive computational study was undertaken with gerris to simulate capillary slug flow under a variety of flow conditions; in total, more than two hundred simulations were carried out. The simulations were found to compare favorably with simulations performed previously by other authors using finite elements. The data from our simulations have been used to develop a new correlation for the film thickness and bubble velocity that is generally applicable. While similar in structure to existing film thickness correlations, the present correlation does not require the bubble velocity to be known a priori. We conclude with an application of the gPC expansion to quantify the uncertainty in the pressure drop in a channel in slug flow when the bubble size is described by a probability distribution. It is found that, although the gPC expansion fails to adequately quantify the uncertainty in field quantities (pressure and velocity) near the liquid-vapor interface, it is nevertheless capable of representing the uncertainty in other quantities (e.g., channel pressure drop) that do not depend sensitively on the precise location of the interface.
by Dustin R. Langewisch.
Ph. D.
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Koehring, Andrew. "The application of polynomial response surface and polynomial chaos expansion metamodels within an augmented reality conceptual design environment." [Ames, Iowa : Iowa State University], 2008.

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Books on the topic "Chaos expansion"

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Nicolay, David. Asymptotic Chaos Expansions in Finance. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6506-4.

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(Editor), Michele Carter, Robh Ruppel (Illustrator), Tony DiTerlizzi (Illustrator), Rob Lazzaretti (Illustrator), Dana Knutson (Illustrator), and Robin Raab (Illustrator), eds. Planes of Chaos (Advanced Dungeons & Dragons, 2nd Edition: Planescape, Campaign Expansion/2603). Wizards of the Coast, 1994.

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Christian, Houdré, Pérez-Abreu Víctor, and Workshop on Multiple Wiener-Itô and Their Applications (1992 : Centro de Investigación en Matemáticas), eds. Chaos expansions, multiple Wiener-Itô integrals and their applications. Boca Raton, FL: CRC Press, 1994.

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Peccati, Giovanni, and Matthias Reitzner. Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry. Springer, 2016.

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Peccati, Giovanni, and Matthias Reitzner. Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry. Springer, 2018.

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Orkaby, Asher. Beyond the Arab Cold War. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190618445.001.0001.

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Beyond the Arab Cold War brings the Yemen Civil War (1962–68) to the forefront of modern Middle East history, in a comprehensive account that features multilingual and multinational archives and oral histories. Throughout six years of major conflict Yemen sat at the crossroads of regional and international conflict as dozens of countries, international organizations, and individuals intervened in the local South Arabian civil war. Yemen was a showcase for a new era of UN and Red Cross peacekeeping, clandestine activity, Egypt’s counterinsurgency, and one of the first large-scale uses of poison gas since World War I. Events in Yemen were not dominated by a single power, nor were they sole products of US-Soviet or Saudi-Egyptian Arab Cold War rivalry. Rather, during the 1960s Yemen was transformed into an arena of global conflict whose ensuing chaos tore down the walls of centuries of religious rule and isolation and laid the groundwork for the next half century of Yemeni history. The end of the Yemen Civil War marked the end of both Egyptian President Nasser’s Arab nationalist colonial expansion and the British Empire in the Middle East, two of the most dominant regional forces. The legacy of the eventual northern tribal defeat and the compromised establishment of a weak and decentralized republic are at the core of modern-day conflicts in South Arabia.
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Leitch, Thomas, ed. The Oxford Handbook of Adaptation Studies. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199331000.001.0001.

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This collection of forty original essays reflects on the history of adaptation studies, surveys the current state of the field, and maps out possible futures that mobilize its unparalleled ability to bring together theorists and practitioners in different modes of discourse. Grounding contemporary adaptation studies in a series of formative debates about what adaptation is, whether its orientation should be scientific or aesthetic, and whether it is most usefully approached inductively, through close analyses of specific adaptations, or deductively, through general theories of adaptation, the volume, not so much a museum as a laboratory or a provocation, aims to foster, rather than resolve, these debates. Its seven parts focus on the historical and theoretical foundations of adaptation study, the problems raised by adapting canonical classics and the aesthetic commons, the ways different genres and presentational modes illuminate and transform the nature of adaptation, the relations between adaptation and intertextuality, the interdisciplinary status of adaptation, and the issues involved in professing adaptation, now and in the future. Embracing an expansive view of adaptation and adaptation studies, it emphasizes the area’s status as a crossroads or network that fosters interactive exchange across many disciplines and advocates continued debate on its leading questions as the best defense against the possibilities of dilution, miscommunication, and chaos that this expansive view threatens to introduce to a burgeoning field uniquely responsive to the contemporary textual landscape.
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Book chapters on the topic "Chaos expansion"

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Yokoyama, Tadashi. "Improving the Classical Expansion of the Disturbing Function." In From Newton to Chaos, 99–102. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1085-1_8.

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Wang, Chuanfu, and Qun Ding. "Camellia Key Expansion Algorithm Based on Chaos." In Advances in Intelligent Systems and Computing, 210–18. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48499-0_26.

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Rozovsky, Boris L., and Sergey V. Lototsky. "Chaos Expansion for Linear Stochastic Evolution Systems." In Stochastic Evolution Systems, 279–314. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94893-5_8.

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Levajković, Tijana, and Hermann Mena. "Equations Involving Malliavin Derivative: A Chaos Expansion Approach." In Pseudo-Differential Operators and Generalized Functions, 199–216. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14618-8_14.

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Ustunel, A. S., and M. Zakai. "The Wiener Chaos Expansion of Certain Radon-Nikodym Derivatives." In Stochastic Analysis and Related Topics, 365–69. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0373-5_10.

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Chikhaoui, K., N. Kacem, N. Bouhaddi, and M. Guedri. "Uncertainty Propagation Combining Robust Condensation and Generalized Polynomial Chaos Expansion." In Model Validation and Uncertainty Quantification, Volume 3, 225–33. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15224-0_24.

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Marchi, Mariapia, Enrico Rigoni, Rosario Russo, and Alberto Clarich. "Percentile via Polynomial Chaos Expansion: Bridging Robust Optimization with Reliability." In EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII, 57–80. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49325-1_3.

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Vibe, Alexander, and Nicole Marheineke. "Wiener Chaos Expansion for an Inextensible Kirchhoff Beam Driven by Stochastic Forces." In Progress in Industrial Mathematics at ECMI 2016, 761–68. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63082-3_112.

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Hu, Junjun, S. Lakshmivarahan, and John M. Lewis. "Quantification of Forecast Uncertainty and Data Assimilation Using Wiener’s Polynomial Chaos Expansion." In Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. III), 141–76. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43415-5_7.

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Zhao, Huan, and Zhenghong Gao. "Uncertainty-Based Design Optimization of NLF Airfoil Based on Polynomial Chaos Expansion." In Lecture Notes in Electrical Engineering, 1576–92. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3305-7_126.

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Conference papers on the topic "Chaos expansion"

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Mohammed, V. Anis, and S. T. G. Raghukanth. "Uncertainty Quantification Using Wiener Chaos Expansion." In 5th International Congress on Computational Mechanics and Simulation. Singapore: Research Publishing Services, 2014. http://dx.doi.org/10.3850/978-981-09-1139-3_455.

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Watanabe, Shinzo. "Martingale Representation Theorem and Chaos Expansion." In Proceedings of the 5th Ritsumeikan International Symposium. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774637_0007.

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Xiong, Fenfen, Bin Xue, Zhang Yan, and Shuxing Yang. "Polynomial chaos expansion based robust design optimization." In 2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE). IEEE, 2011. http://dx.doi.org/10.1109/icqr2mse.2011.5976745.

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Codecasa, Lorenzo, and Luca Di Rienzo. "Stochastic thermal modeling by polynomial chaos expansion." In 2013 19th International Workshop on Thermal Investigations of ICs and Systems (THERMINIC). IEEE, 2013. http://dx.doi.org/10.1109/therminic.2013.6675234.

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Novák, Lukáš, Miroslav Vořechovský, and Václav Sadílek. "ADAPTIVE SEQUENTIAL SAMPLING FOR POLYNOMIAL CHAOS EXPANSION." In 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Research and Development for Computational Methods in Engineering Sciences (ICMES), 2021. http://dx.doi.org/10.7712/120221.8038.18955.

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Chen, Guangsong, Linfang Qian, Jia Ma, and Lei Ji. "A new efficient adaptive polynomial chaos expansion metamodel." In 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM). IEEE, 2015. http://dx.doi.org/10.1109/aim.2015.7222702.

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Pettit, Chris, and Philip Beran. "Polynomial Chaos Expansion Applied to Airfoil Limit Cycle Oscillations." In 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-1691.

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Muhlpfordt, Tillmann, Timm Faulwasser, and Veit Hagenmeyer. "Solving stochastic AC power flow via polynomial chaos expansion." In 2016 IEEE Conference on Control Applications (CCA). IEEE, 2016. http://dx.doi.org/10.1109/cca.2016.7587824.

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Frick, Eduard, Jan B. Preibisch, Christian Seifert, Marko Lindner, and Christian Schuster. "Variability analysis of via crosstalk using polynomial chaos expansion." In 2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO). IEEE, 2017. http://dx.doi.org/10.1109/nemo.2017.7964272.

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Preibisch, Jan B., Piero Triverio, and Christian Schuster. "Sensitivity analysis of via impedance using polynomial chaos expansion." In 2015 IEEE 19th Workshop on Signal and Power Integrity (SPI). IEEE, 2015. http://dx.doi.org/10.1109/sapiw.2015.7237386.

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Reports on the topic "Chaos expansion"

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Jakeman, John, Fabian Franzelin, Akil Narayan, Michael Eldred, and Dirk Pflueger. Polynomial chaos expansions for dependent random variables. Office of Scientific and Technical Information (OSTI), May 2019. http://dx.doi.org/10.2172/1762354.

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