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Academic literature on the topic 'Random walks in cooling random environments'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Random walks in cooling random environments"

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Lee, P. M., and B. D. Hughes. "Random Walks and Random Environments: Vol. I, Random Walks." Journal of the Royal Statistical Society. Series A (Statistics in Society) 159, no. 3 (1996): 624. http://dx.doi.org/10.2307/2983343.

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Hughes, B. D. "Random Walks and Random Environments, Volume 1: Random Walks." Biometrics 54, no. 3 (September 1998): 1204. http://dx.doi.org/10.2307/2533883.

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Weiss, George H. "Random walks and random environments, volume 1: Random walks." Journal of Statistical Physics 82, no. 5-6 (March 1996): 1675–77. http://dx.doi.org/10.1007/bf02183400.

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Zeitouni, Ofer. "Random walks in random environments." Journal of Physics A: Mathematical and General 39, no. 40 (September 19, 2006): R433—R464. http://dx.doi.org/10.1088/0305-4470/39/40/r01.

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Douglas, Jack F. "Random walks and random environments, vol. 2, random environments." Journal of Statistical Physics 87, no. 3-4 (May 1997): 961–62. http://dx.doi.org/10.1007/bf02181260.

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Buffet, E., and P. Hannigan. "Directed random walks in random environments." Journal of Statistical Physics 65, no. 3-4 (November 1991): 645–72. http://dx.doi.org/10.1007/bf01053747.

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Holmes, Mark, and Thomas S. Salisbury. "Random Walks in Degenerate Random Environments." Canadian Journal of Mathematics 66, no. 5 (October 1, 2014): 1050–77. http://dx.doi.org/10.4153/cjm-2013-017-3.

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AbstractWe study the asymptotic behaviour of random walks in i.i.d. random environments on . The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2-valued environment, and show that this does not hold for 3-valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong but non-trivial conditions on the distribution of the environment. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience and, in 2-dimensions, the existence of a deterministic limiting velocity.
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Bricmont, J., and A. Kupiainen. "Random walks in asymmetric random environments." Communications in Mathematical Physics 142, no. 2 (December 1991): 345–420. http://dx.doi.org/10.1007/bf02102067.

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Shlesinger, Michael F. "Book Review: Random Walks and Random Environments." Fractals 04, no. 01 (March 1996): 111–12. http://dx.doi.org/10.1142/s0218348x96000145.

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Lenci, Marco. "Random walks in random environments without ellipticity." Stochastic Processes and their Applications 123, no. 5 (May 2013): 1750–64. http://dx.doi.org/10.1016/j.spa.2013.01.007.

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Dissertations / Theses on the topic "Random walks in cooling random environments"

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Buckley, Stephen Philip. "Problems in random walks in random environments." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:06a12be2-b831-4c2a-87b1-f0abccfb9b8b.

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Recent years have seen progress in the analysis of the heat kernel for certain reversible random walks in random environments. In particular the work of Barlow(2004) showed that the heat kernel for the random walk on the infinite component of supercritical bond percolation behaves in a Gaussian fashion. This heat kernel control was then used to prove a quenched functional central limit theorem. Following this work several examples have been analysed with anomalous heat kernel behaviour and, in some cases, anomalous scaling limits. We begin by generalizing the first result - looking for sufficient conditions on the geometry of the environment that ensure standard heat kernel upper bounds hold. We prove that these conditions are satisfied with probability one in the case of the random walk on continuum percolation and use the heat kernel bounds to prove an invariance principle. The random walk on dynamic environment is then considered. It is proven that if the environment evolves ergodically and is, in a certain sense, geometrically d-dimensional then standard on diagonal heat kernel bounds hold. Anomalous lower bounds on the heat kernel are also proven - in particular the random conductance model is shown to be "more anomalous" in the dynamic case than the static. Finally, the reflected random walk amongst random conductances is considered. It is shown in one dimension that under the usual scaling, this walk converges to reflected Brownian motion.
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Carigi, Giulia. "On the recurrence of random walks in Lévy random environments." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10088/.

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This thesis investigates one-dimensional random walks in random environment whose transition probabilities might have an infinite variance. The ergodicity of the dynamical system ''from the point of view of the particle'' is proved under the assumptions of transitivity and existence of an absolutely continuous steady state on the space of the environments. We show that, if the average of the local drift over the environments is summable and null, then the RWRE is recurrent. We provide an example satisfying all the hypotheses.
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Di, Stefano Andrea [Verfasser]. "Random walks interacting with evolving random environments and related kinetic equations / Andrea di Stefano." Bielefeld : Universitätsbibliothek Bielefeld, 2015. http://d-nb.info/107612478X/34.

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Yurchenko, Aleksey. "Some problems in the theory of open dynamical systems and deterministic walks in random environments." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26549.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.
Committee Chair: Bunimovich, Leonid; Committee Member: Bakhtin, Yuri; Committee Member: Cvitanovic, Predrag; Committee Member: Houdre, Christian; Committee Member: Weiss, Howard. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Zeng, Xiaolin. "Marches aléatoires renforcées et opérateurs de Schrödinger aléatoires." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10252/document.

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Cette thèse s'intéresse à deux modèles de processus auto intéagissant étroitement reliés: le processus de sauts renforcé par sites (VRJP) et la marche aléatoire renforcée par arêtes (ERRW). Nous étudions aussi les liens entre ces processus et un opérateur de Schrödinger aléatoire. Dans le chapitre 3, nous montrons que le VRJP est le seul processus satisfaisant la propriété d'échangeabilité partielle et tel que la probabilité de transition ne dépende que du temps local des voisins, sous quelques conditions techniques. Le chapitre 4 donne la transition de phase entre vitesse positive et vitesse nulle pour un VRJP transitoire sur un arbre de Galton Watson, utilisant le fait que sur un arbre, le VRJP est une marche aléatoire en milieu aléatoire. Dans le chapitre 5, une nouvelle famille exponentielle de loi est introduite et ses liens avec le VRJP sont étudiés. En particulier, nous donnons une preuve de la formule de Coppersmith et Diaconis, n'utilisant que des calculs élémentaires. Finalement, dans le chapitre 6 nous étudions la représentation du VRJP comme mélange de processus de Markov sur les graphes infinis. Nous représentons le VRJP à l'aide de la fonction de Green et d'une fonction propre généralisée d'un opérateur de Schrödinger aléatoire associé au VRJP. En conséquence, nous obtenons un principe d'invariance pour le VRJP quand le renforcement est suffisamment faible, ainsi que la récurrence du ERRW sur ℤ2 pour toute valeurs initiales des paramètres
This thesis is dedicated to the study of two closely related self-interacting processes: the vertex reinforced jump process (VRJP) and the edge reinforced random walk (ERRW). We also study the relations between these processes and a random Schrödinger operator. In Chapter 3, we prove that the VRJP is the only partially exchangeable process whose transition probability depends only on neighbor local times, under some technical conditions. Chapter 4 gives the phase transition between positive speed and null speed of a transient VRJP on a Galton Watson tree, using a representation of random walk in independent random environment. In Chapter 5, we introduce a new exponential family of probability distributions generalizing the Inverse Gaussian distribution, and we show some of its relations to the VRJP. In particular, we give an elementary proof of the formula of Coppersmith and Diaconis. Finally, we show in Chapter 6 that the VRJP on infinite graph is a mixture of Markov jump processes, by constructing the random environment using the Green function and a generalized eigenfunction related to a random Schrödinger operator associated with the VRJP. As a consequence, we obtain a central limit theorem when the reinforcement is weak enough, and also the recurrence of ERRW on ℤ2 for any initial constant weights
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Miller, Katja [Verfasser], Nina [Akademischer Betreuer] Gantert, Matthias [Gutachter] Birkner, Nina [Gutachter] Gantert, and Silke [Gutachter] Rolles. "Random walks on oriented percolation and in recurrent environments / Katja Miller ; Gutachter: Matthias Birkner, Nina Gantert, Silke Rolles ; Betreuer: Nina Gantert." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/115354573X/34.

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Miller, Katja Verfasser], Nina [Akademischer Betreuer] [Gantert, Matthias [Gutachter] Birkner, Nina [Gutachter] Gantert, and Silke [Gutachter] Rolles. "Random walks on oriented percolation and in recurrent environments / Katja Miller ; Gutachter: Matthias Birkner, Nina Gantert, Silke Rolles ; Betreuer: Nina Gantert." München : Universitätsbibliothek der TU München, 2017. http://nbn-resolving.de/urn:nbn:de:bvb:91-diss-20171023-1366085-1-2.

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Chiffaudel, Yann. "Etude de la diffusion des processus déterministes et faiblement aléatoires en environnement aléatoire." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7083.

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Cette thèse étudie la diffusion dans le modèle des miroirs, modèle inspiré de la physique et introduit en 1988 par Ruijgrok et Cohen. Ce modèle est déterministe et réversible. Pour traiter ce modèle difficile, initialement défini uniquement en dimension 2, nous l'avons d'abord généralisé pour en faire un modèle en dimension quelconque. De premières études numériques permirent de conjecturer que le modèle est diffusif en dimension supérieur ou égale à 3. Nous avons par la suite exploré une approche perturbative du coefficient de diffusion basée sur la technique de lace expansion développée par Gordon Slade pour l'étude de la marche aléatoire auto-évitante. Face à la difficulté des calculs nous avons légèrement simplifié le modèle en abandonnant la contrainte de réversibilité. Nous avons obtenu ainsi un nouveau modèle que nous nommons le modèle des permutations. Nous avons ensuite transformé ces deux modèles pour en faire des marches aléatoires en milieu aléatoire, et ce via une approche systématique et généraliste. Grâce à ces modifications nous avons pu pousser l'approche perturbative jusqu'à obtenir une approximation satisfaisante de la valeur du coefficient de diffusion dans le modèle des permutations. Le résultat principal est l'existence d'une série dont tout les termes sont bien définis et dont les premiers termes fournissent l'approximation voulue. La convergence de cette série reste un problème ouvert. Les résultats analytiques sont appuyés par une approche numérique de ces modèles, ce qui permet de voir que la lace expansion donne des résultats de qualité. De nombreuses questions restent ouvertes, notamment le calcul des termes suivants du développement perturbatif et la généralisation de cette approche au modèle des miroirs, ce qui ne saurait poser problème, puis à une classe plus large de modèles
This thesis studies the diffusion in the mirrors model, a physics-based model introduced in 1988 by Ruijgrok and Cohen. This model is deterministic and reversible. To treat this difficult model, initially defined only in dimension 2, we first generalized it to a model valid in any dimension. Initial numerical studies suggested that the model is diffusive in dimensions greater than or equal to 3. We then explored a perturbative diffusion coefficient approach based on the lace expansion technique developed by Gordon Slade for the study of self-avoiding random walk. Faced with the difficulty of the calculations, we slightly simplified the model by giving up the reversibility constraint. We thus obtained a new model that we call the permutations model. We then transformed these two models into random walks in random environment using a systematic and general approach. Thanks to these modifications, we were able to push the perturbative approach to obtain a satisfactory approximation of the value of the diffusion coefficient in the permutations model. The main result is the existence of a series in which all terms are well defined and the first terms provide the desired approximation. The convergence of this series remains an open problem. The analytical results are supported by a numerical approach to these models, which shows that the lace expansion gives quality results. Many questions remain open, including the calculation of the following terms of perturbative development and the generalization of this approach to the mirrors model -which should not be a problem- and then to a broader class of models
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Books on the topic "Random walks in cooling random environments"

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Hughes, B. D. Random walks and random environments. Oxford: Clarendon Press, 1995.

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Random walk in random and non-random environments. Hackensack, New Jersey: World Scientific, 2013.

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Random walk in random and non-random environments. Singapore: Teaneck, N.J., 1990.

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Random walk in random and non-random environments. 2nd ed. New Jersey: World Scientific, 2005.

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1966-, Ellwood D. (David), and Brazilian School of Probability (14th : 2010 : Armação dos Búzios, Brazil), eds. Probability and statistical physics in two and more dimensions: Clay Mathematics Institute Summer School and XIV Brazilian School of Probability, Búzios, Brazil, July 11-August 7, 2010. Providence, R.I: American Mathematical Society, 2012.

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Hughes, Barry D. Random Walks and Random Environments: Volume 2: Random Environments (Vol 2). Oxford University Press, USA, 1996.

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Letchikov, A. Localization of One-Dimensional Random Walks in Random Environments. Routledge, 1989.

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Yarovaya, Elena. Branching Random Walks in Nonhomogenous Environments. Wiley & Sons, Incorporated, John, 2023.

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Yarovaya, Elena. Branching Random Walks in Nonhomogenous Environments. Wiley & Sons, Incorporated, John, 2023.

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Yarovaya, Elena. Branching Random Walks in Nonhomogenous Environments. Wiley & Sons, Incorporated, John, 2023.

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Book chapters on the topic "Random walks in cooling random environments"

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Avena, Luca, and Frank den Hollander. "Random Walks in Cooling Random Environments." In Springer Proceedings in Mathematics & Statistics, 23–42. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0302-3_2.

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Kawazu, K., Y. Tamura, and H. Tanaka. "One-dimensional diffusions and random walks in random environments." In Lecture Notes in Mathematics, 170–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078472.

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Zeitouni, Ofer. "Random Walks in Random Environments in the Perturbative Regime." In New Trends in Mathematical Physics, 823–26. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2810-5_51.

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Pemantle, Robin, and Yuval Peres. "On which Graphs are All Random Walks in Random Environments Transient?" In Random Discrete Structures, 207–11. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0719-1_14.

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Liu, Xiang-dong, and Li-ye Zhu. "Asymptotic Behavior of Random Walks with Resting State in Ergodic Environments." In Lecture Notes in Electrical Engineering, 421–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-28807-4_59.

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Bogachev, L. V. "Random Walks in Random Environments." In Encyclopedia of Mathematical Physics, 353–71. Elsevier, 2006. http://dx.doi.org/10.1016/b0-12-512666-2/00063-8.

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"LIMIT THEOREMS FOR ONE-DIMENSIONAL RANDOM WALKS IN RANDOM ENVIRONMENTS." In Vol. 2, 90–96. De Gruyter, 1990. http://dx.doi.org/10.1515/9783112319024-009.

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"RANDOM WALKS WITH JUMPS IN RANDOM ENVIRONMENTS (EXAMPLES OF CYCLE AND WEIGHT REPRESENTATIONS)." In Probability Theory and Mathematical Statistics, 199–212. De Gruyter, 1999. http://dx.doi.org/10.1515/9783112313480-018.

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"Random walks with jumps in random environments (examples of cycle and weight representations)." In Probability Theory and Mathematical Statistics, 199–212. De Gruyter, 1999. http://dx.doi.org/10.1515/9783112314081-018.

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Conference papers on the topic "Random walks in cooling random environments"

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Blanchard, Ph, D. Volchenkov, Christopher C. Bernido, and M. Victoria Carpio-Bernido. "Exploring Urban Environments By Random Walks." In STOCHASTIC AND QUANTUM DYNAMICS OF BIOMOLECULAR SYSTEMS: Proceedings of the 5th Jagna International Workshop. AIP, 2008. http://dx.doi.org/10.1063/1.2956796.

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Forsyth, Peter, David R. H. Gillespie, Matthew McGilvray, and Vincent Galoul. "Validation and Assessment of the Continuous Random Walk Model for Particle Deposition in Gas Turbine Engines." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57332.

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Threats to engine integrity and life from deposition of environmental particulates that can reach the turbine cooling systems (i.e. <10 micron) have become increasing important within the aero-engine industry, with an increase of flight paths crossing sandy, tropical storm-infested, or polluted airspaces. This has led to studies in the turbomachinery community investigating environmental particulate deposition, largely applying the Discrete Random Walk (DRW) model in CFD simulations of air paths. However, this model was conceived to model droplet dispersion in bulk flow regimes, and therefore has fundamental limitations for deposition studies. One significant limitation is an insensitivity to particle size in the turbulent deposition size regime, where deposition is strongly linked to particle size. This is highlighted within this study through comparisons to published experimental data. Progress made within the wider particulate deposition community has recently led to the development and application of the Continuous Random Walk (CRW) model. This new model provides significantly improved predictions of particle deposition seen experimentally in comparison to the DRW for low temperature pipe flow experiments. However, the CRW model is not without its difficulties. This paper highlights the sensitivities within the CRW model and actions taken to alleviate them where possible. For validation of the model at gas turbine conditions, it should be assessed at engine-representative conditions. These include high-temperature and swirling flows, with thermophoretic and wall-roughness effects. Thermophoresis is a particle force experienced in the negative direction of the temperature gradient, and can strongly effect deposition efficiency from certain flows. Previous validation of the model has centred on low temperatures and pipe flow conditions. Presented here is the validation process which is currently being undertaken to assess the model at gas turbine-relevant conditions. Discussion centres on the underlying principles of the model, how to apply this model appropriately to gas turbine flows and initial assessment for flows seen in secondary air systems. Verification of model assumptions is undertaken, including demonstrating that the effect of boundary layer modelling of anisotropic turbulence is shown to be Reynolds-independent. The integration time step for numerical solution of the non-dimensional Langevin equation is redefined, showing improvement against existing definitions for the available low temperature pipe flow data. The grid dependence of particle deposition in numerical simulations is presented and shown to be more significant for particle conditions in the diffusional deposition regime. Finally, the model is applied to an engine-representative geometry to demonstrate the improvement in sensitivity to particle size that the CRW offers over the DRW for wall-bounded flows.
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Bunker, Ronald S. "Evolution of Turbine Cooling." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63205.

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Turbine cooling is a battle between the desire for greater hot section component life and the techno-economic demands of the marketplace. Surprisingly little separates the haves from the have nots. The evolution of turbine cooling is loosely analogous to that of the Darwinian theory of evolution for animals, starting from highly simplistic forms and progressing to increasingly more complex designs having greater capabilities. Yet even with the several generations of design advances, limitations are becoming apparent as complexity sometimes leads to less robust outcomes in operation. Furthermore, the changing environment for operation and servicing of cooled components, both the natural and the imposed environments, are resulting in new failure modes, higher sensitivities, and more variability in life. The present paper treats the evolution of turbine cooling in three broad aspects including the background development, the current state-of-the-art, and the prospects for the future. Unlike the Darwinian theory of evolution however, it is not feasible to implement thousands of small incremental design changes, random or not, to determine the fittest for survival and advancement. Instead, innovation and experience are utilized to direct the evolution. Over the last approximately 50 years, advances have led to an overall increase in component cooling effectiveness from 0.1 to 0.7. Innovation and invention aside, the performance of the engine has always dictated which technologies advance and which do not. Cooling technologies have been aided by complimentary and substantial advancements in materials and manufacturing. The state-of-the-art now contains dozens of internal component cooling methods with their many variations, yet still relies mainly on only a handful of basic film cooling forms that have been known for 40 years. Even so, large decreases in coolant usage, up to 50%, have been realized over time in the face of increasing turbine firing temperatures. The primary areas of greatest impact for the future of turbine cooling are discussed, these being new engine operating environments, component and systems integration effects, revolutionary turbine cooling, revolutionary manufacturing, and the quantification of unknowns. One key will be the marriage of design and manufacturing to bring about the concurrent use of engineered micro cooling or transpiration, with the ability of additive manufacturing. If successful, this combination could see a further 50% reduction in coolant usage for turbines. The other key element concerns the quantification of unknowns, which directly impacts validation and verification of current state-of-the-art and future turbine cooling. Addressing the entire scope of the challenges will require future turbine cooling to be of robust simplicity and stability, with freeform design, much as observed in the “designs” of nature.
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Mersinligil, Mehmet, Jean-Franc¸ois Brouckaert, and Julien Desset. "First Unsteady Pressure Measurements With a Fast Response Cooled Total Pressure Probe in High Temperature Gas Turbine Environments." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23630.

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This paper presents the first experimental engine and test rig results obtained from a fast response cooled total pressure probe. The first objective of the probe design was to favor continuous immersion of the probe into the engine to obtain time series of pressure with a high bandwidth and therefore statistically representative average fluctuations at the blade passing frequency. The probe is water cooled by a high pressure cooling system and uses a conventional piezo-resistive pressure sensor which yields therefore both time-averaged and time-resolved pressures. The initial design target was to gain the capability of performing measurements at the temperature conditions typically found at high pressure turbine exit (1100–1400K) with a bandwidth of at least 40kHz and in the long term at combustor exit (2000K or higher). The probe was first traversed at the turbine exit of a Rolls-Royce Viper turbojet engine, at exhaust temperatures around 750 °C and absolute pressure of 2.1bars. The probe was able to resolve the high blade passing frequency (≈23kHz) and several harmonics up to 100kHz. Besides the average total pressure distributions from the radial traverses, phase-locked averages and random unsteadiness are presented. The probe was also used in a virtual three-hole mode yielding unsteady yaw angle, static pressure and Mach number. The same probe was used for measurements in a Rolls-Royce intermediate pressure burner rig. Traverses were performed inside the flame tube of a kerosene burner at temperatures above 1600 °C. The probe successfully measured the total pressure distribution in the flame tube and typical frequencies of combustion instabilities were identified during rumble conditions. The cooling performance of the probe is compared to estimations at the design stage and found to be in good agreement. The frequency response of the probe is compared to cold shock tube results and a significant increase in the natural frequency of the line-cavity system formed by the conduction cooled screen in front of the miniature pressure sensor were observed.
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Vos, Willem, Petter Norli, and Emilie Vallee. "Application of Wide-Band Ultrasound for the Detection of Angled Crack Features in Oil and Gas Pipelines." In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/ipc2018-78521.

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This paper describes a novel technique for the detection of cracks in pipelines. The proposed in-line inspection technique has the ability to detect crack features at random angles in the pipeline, such as axial, circumferential, and any angle in between. This ability is novel to the current ILI technology offering and will also add value by detecting cracks in deformed pipes (i.e. in dents), and cracks associated with the girth weld (mid weld cracks, rapid cooling cracks and cracks parallel to the weld). Furthermore, the technology is suitable for detection of cracks in spiral welded pipes, both parallel to the spiral weld as well as perpendicular to the weld. Integrity issues around most features described above are not addressed with ILI tools, often forcing operators to perform hydrostatic tests to ensure pipeline safety. The technology described here is based on the use of wideband ultrasound inline inspection tools that are already in operation. They are designed for the inspection of structures operating in challenging environments such as offshore pipelines. Adjustments to the front-end analog system and data collection from a grid of transducers allow the tools to detect cracks in any orientation in the line. Description of changes to the test set-up are presented as well as the theoretical background behind crack detection. Historical development of the technology will be presented, such as early laboratory testing and proof of concept. The proof of concept data will be compared to the theoretical predictions. A detailed set of results are presented. These are from tests that were performed on samples sourced from North America and Europe which contain SCC features. Results from ongoing testing will be presented, which involved large-scale testing on SCC features in gas-filled pipe spools.
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