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Letteratura scientifica selezionata sul tema "Ergodic theory"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 29 luglio 2024

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Articoli di riviste sul tema "Ergodic theory"

Gray, R. M. "Ergodic theory". Proceedings of the IEEE 74, n. 2 (1986): 380. http://dx.doi.org/10.1109/proc.1986.13473.

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Kida, Yoshikata. "Ergodic group theory". Sugaku Expositions 35, n. 1 (7 aprile 2022): 103–26. http://dx.doi.org/10.1090/suga/470.

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Moore, Calvin C. "Ergodic theorem, ergodic theory, and statistical mechanics". Proceedings of the National Academy of Sciences 112, n. 7 (17 febbraio 2015): 1907–11. http://dx.doi.org/10.1073/pnas.1421798112.

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This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.

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JONES, ROGER L., ROBERT KAUFMAN, JOSEPH M. ROSENBLATT e MÁTÉ WIERDL. "Oscillation in ergodic theory". Ergodic Theory and Dynamical Systems 18, n. 4 (agosto 1998): 889–935. http://dx.doi.org/10.1017/s0143385798108349.

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In this paper we establish a variety of square function inequalities and study other operators which measure the oscillation of a sequence of ergodic averages. These results imply the pointwise ergodic theorem and give additional information such as control of the number of upcrossings of the ergodic averages. Related results for differentiation and for the connection between differentiation operators and the dyadic martingale are also established.

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Boyd, David W., Karma Dajani e Cor Kraaikamp. "Ergodic Theory of Numbers". American Mathematical Monthly 111, n. 7 (agosto 2004): 633. http://dx.doi.org/10.2307/4145181.

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Walters, Peter. "TOPICS IN ERGODIC THEORY". Bulletin of the London Mathematical Society 28, n. 2 (marzo 1996): 221–23. http://dx.doi.org/10.1112/blms/28.2.221.

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Sinai, Ya G., e Barry Simon. "Topics in Ergodic Theory". Physics Today 47, n. 10 (ottobre 1994): 74–75. http://dx.doi.org/10.1063/1.2808677.

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Barnes, Julie, Lorelei Koss e Rachel Rossetti. "The Ergodic Theory Café". Math Horizons 26, n. 3 (28 dicembre 2018): 5–9. http://dx.doi.org/10.1080/10724117.2018.1518099.

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Kozlov, V. V. "Coarsening in ergodic theory". Russian Journal of Mathematical Physics 22, n. 2 (aprile 2015): 184–87. http://dx.doi.org/10.1134/s1061920815020053.

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Jones, Roger L., Joseph M. Rosenblatt e Máté Wierdl. "Counting in Ergodic Theory". Canadian Journal of Mathematics 51, n. 5 (1 ottobre 1999): 996–1019. http://dx.doi.org/10.4153/cjm-1999-044-2.

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AbstractMany aspects of the behavior of averages in ergodic theory are a matter of counting the number of times a particular event occurs. This theme is pursued in this article where we consider large deviations, square functions, jump inequalities and related topics.

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Tesi sul tema "Ergodic theory"

Quas, Anthony Nicholas. "Some problems in ergodic theory". Thesis, University of Warwick, 1993. http://wrap.warwick.ac.uk/58569/.

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The thesis consists of a study of problems in ergodic theory relating to one-dimensional dynamical systems, Markov chains and generalizations of Markov chains. It is divided into chapters, three of which have appeared in the literature as papers. Chapter 1 looks at continuous families of circle maps and investigates conditions under which there is a weak*-continuous family of invariant measures. Sufficient conditions are exhibited and the necessity of these conditions is investigated. Chapter 2 is about expanding maps of the interval and the circle, and their relation with g-measures and generalized baker's transformations. The g-measures are generalizations of Markov chains to stochastic processes with infinite memory and generalized baker's transformations are geometric realizations of these. The chapter is based around the question of whether there exist expanding maps preserving Lebesgue measure, for which Lebesgue measure is not ergodic. Results are known if the map is sufficiently differentiable (for example C1+α), but the C1 case is still unclear. The chapter contains some partial solutions to this question. Chapter 3 is about representation of Markov chains on compact manifolds by measured collections of smooth maps. Given a measured collection of maps, a Markov chain is induced in a natural fashion. This chapter is about reversing this process. Chapter 4 describes a specialization of the setting of Chapter 3 to Markov chains on tori. In this case, it is possible to demand more of the maps of the representation than smoothness. In particular, they can be chosen to be local diffeomorphisms. The chapter also addresses the question of whether in general the maps can be taken to be diffeomorphisms and gives a counterexample showing that there exist Markov chains on tori which do not admit a representation by diffeomorphisms.

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Bulinski, Kamil. "Interactions between Ergodic Theory and Combinatorial Number Theory". Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17733.

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The seminal work of Furstenberg on his ergodic proof of Szemerédi’s Theorem gave rise to a very rich connection between Ergodic Theory and Combinatorial Number Theory (Additive Combinatorics). The former is concerned with dynamics on probability spaces, while the latter is concerned with Ramsey theoretic questions about the integers, as well as other groups. This thesis further develops this symbiosis by establishing various combinatorial results via ergodic techniques, and vice versa. Let us now briefly list some examples of such. A shorter ergodic proof of the following theorem of Magyar is given: If B Zd, where d 5, has upper Banach density at least > 0, then the set of all squared distances in B, i.e., the set fkb1 􀀀 b2k2 j b1; b2 2 Bg, contains qZ>R for some integer q = q( ) > 0 and R = R(B). Our technique also gives rise to results on the abundance of many other higher order Euclidean configurations in such sets. Next, we turn to establishing analogues of this result of Magyar, where k k2 is replaced with other quadratic forms and various other algebraic functions. Such results were initially obtained by Björklund and Fish, but their techniques involved some deep measure rigidity results of Benoist-Quint. We are able to recover many of their results and prove some completely new ones (not obtainable by their techniques) in a much more self-contained way by avoiding these deep results of Benoist-Quint and using only classical tools from Ergodic Theory. Finally, we extend some recent ergodic analogues of the classical Plünnecke inequalities for sumsets obtained by Björklund-Fish and establish some estimates of the Banach density of product sets in amenable non-abelain groups. We have aimed to make this thesis accesible to readers outside of Ergodic Theory who may be primarily interested in the arithmetic and combinatorial applications.

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Butkevich, Sergey G. "Convergence of Averages in Ergodic Theory". The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu980555965.

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Butkevich, Sergey. "Convergence of averages in Ergodic Theory /". The Ohio State University, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488196781735316.

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Johnson, Bryan R. "Unconditional convergence of differences in ergodic theory /". The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487945015615412.

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Jaššová, Alena. "On ergodic theory in non-Archimedean settings". Thesis, University of Liverpool, 2014. http://livrepository.liverpool.ac.uk/2006322/.

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Meco, Benjamin. "Ergodic Theory and Applications to Combinatorial Problems". Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-409810.

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Prabaharan, Kanagarajah. "Topics in ergodic theory : existence of invariant elements and ergodic decompositions of Banach lattices /". The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487688973685025.

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Cannizzo, Jan. "Schreier Graphs and Ergodic Properties of Boundary Actions". Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31444.

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This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary actions, and investigating various properties of Schreier graphs. Our main result concerning the former problem is that, in a variety of situations, the action of an invariant random subgroup of a group G on a boundary of G (e.g. the hyperbolic boundary, or the Poisson boundary) is conservative (there are no wandering sets). This addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda and establishes a connection between invariant random subgroups and normal subgroups. We approach the latter problem from a number of directions (in particular, both in the presence and the absence of a probability measure), with an emphasis on what we term Schreier structures (edge-labelings of a given graph which turn it into a Schreier coset graph). One of our main results is that, under mild assumptions, there exists a rich space of invariant Schreier structures over a given unimodular graph structure, in that this space contains uncountably many ergodic measures, many of which we are able to describe explicitly.

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Raissi-Dehkordi, Ramin. "Ergodic theory of dynamical systems having absolutely continuous spectrum". Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627274.

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Libri sul tema "Ergodic theory"

Assani, Idris, a cura di. Ergodic Theory. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/conm/485.

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Kerr, David, e Hanfeng Li. Ergodic Theory. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49847-8.

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Einsiedler, Manfred, e Thomas Ward. Ergodic Theory. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-021-2.

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Nadkarni, M. G. Basic Ergodic Theory. Gurgaon: Hindustan Book Agency, 2013. http://dx.doi.org/10.1007/978-93-86279-53-8.

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Nadkarni, M. G. Basic Ergodic Theory. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-8839-4.

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Nadkarni, M. G. Basic ergodic theory. 2^a ed. Basel: Birkhauser Verlag, 1995.

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Silva, César Ernesto. Invitation to ergodic theory. Providence, R.I: American Mathematical Society, 2008.

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Silva, César Ernesto. Invitation to ergodic theory. Providence, R.I: American Mathematical Society, 2008.

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Sinaĭ, Ya G. Topics in ergodic theory. Princeton, N.J: Princeton University Press, 1994.

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Idris, Assani, e Chapel Hill Ergodic Theory Workshop (2008 : University of North Carolina at Chapel Hill), a cura di. Ergodic theory: Chapel Hill Probability and Ergodic Theory Workshops 2007-2008. Providence, R.I: American Mathematical Society, 2009.

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Capitoli di libri sul tema "Ergodic theory"

Parry, William. "Ergodic Theory". In Time Series and Statistics, 73–81. London: Palgrave Macmillan UK, 1990. http://dx.doi.org/10.1007/978-1-349-20865-4_7.

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Yushida, Kôsaku, Shizuo Kakutani, Karl Petersen, W. Parry, Arshag B. Hajian, Yuji Ito e J. R. Choksi. "Ergodic Theory". In Shizuo Kakutani, 591–754. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5391-4_9.

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Klenke, Achim. "Ergodic Theory". In Probability Theory, 493–513. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56402-5_20.

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Sinai, Ya G. "Ergodic Theory". In Mathematics and Its Applications, 247–50. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-2973-4_20.

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Nikolaev, Igor. "Ergodic Theory". In Foliations on Surfaces, 241–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04524-4_8.

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Ito, Yuji. "Ergodic Theory". In Kôsaku Yosida Collected Papers, 147–260. Tokyo: Springer Japan, 1992. http://dx.doi.org/10.1007/978-4-431-65859-7_3.

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Radin, Charles. "Ergodic theory". In Miles of Tiles, 17–54. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/stml/001/02.

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Taylor, Michael. "Ergodic theory". In Graduate Studies in Mathematics, 193–205. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/gsm/076/14.

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Barreira, Luis, e Claudia Valls. "Ergodic Theory". In Dynamical Systems, 181–202. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4835-7_8.

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Knauf, Andreas. "Ergodic Theory". In UNITEXT, 191–214. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-662-55774-7_9.

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Atti di convegni sul tema "Ergodic theory"

Ruelle, David. "Ergodic Theory of Chaos". In Optical Bistability. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/obi.1985.wc1.

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Determinsistic chaos arises in a variety of nonlinear dynamical systems in physics, and in particular in optics. One has now gained a reasonable understanding of the onset of chaos in terms of the geometry of bifurcations and strange attractors. This geometric approach does not work for attractors of more than two or three dimensions. For these, however, ergodic theory provides new concepts: characteristic exponents, entropy, information dimension, which are reproducibly estimated from physical experiments. The Characteristic exponents measure the rate of divergence of nearby trajectories of a dynamical system, the entropy measures the rate of information creation by the system, and the information dimension is a fractal dimension of particular interest. There are inequalities (or even identities) relating the entropy and information dimension to the characteristic exponents. The experimental measure of these ergodic quantities provides a numerical estimate of the instability of chaotic systems, and of the number of "degrees of freedom" which they possess.

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Nazer, Bobak, Michael Gastpar, Syed Ali Jafar e Sriram Vishwanath. "Ergodic interference alignment". In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205270.

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Nakamura, M. "Ergodic theorems for algorithmically random sequences". In IEEE Information Theory Workshop, 2005. IEEE, 2005. http://dx.doi.org/10.1109/itw.2005.1531876.

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Simeone, Osvaldo, Oren Somekh, Elza Erkip, H. Vincent Poor e Shlomo Shamai. "Multirelay channel with non-ergodic link failures". In 2009 IEEE Information Theory Workshop on Networking and Information Theory (ITW). IEEE, 2009. http://dx.doi.org/10.1109/itwnit.2009.5158540.

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Ryabko, Daniil, e Boris Ryabko. "On hypotheses testing for ergodic processes". In 2008 IEEE Information Theory Workshop (ITW). IEEE, 2008. http://dx.doi.org/10.1109/itw.2008.4578669.

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Bardi, Martino, e Olivier Alvarez. "Some ergodic problems for differential games". In Control Systems: Theory, Numerics and Applications. Trieste, Italy: Sissa Medialab, 2006. http://dx.doi.org/10.22323/1.018.0025.

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Kupiainen, Antti. "Ergodic theory of SDE’s with degenerate noise". In Proceedings of a Satellite Conference of ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812791559_0003.

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Aggarwal, Vaneet, Lalitha Sankar, A. Robert Calderbank e H. Vincent Poor. "Ergodic layered erasure one-sided interference channels". In 2009 IEEE Information Theory Workshop. IEEE, 2009. http://dx.doi.org/10.1109/itw.2009.5351176.

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Nasser, Rajai. "Ergodic theory meets polarization I: A foundation of polarization theory". In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282896.

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Rajan, Adithya, e Cihan Tepedelenlioglu. "Ergodic capacity ordering of fading channels". In 2012 IEEE International Symposium on Information Theory - ISIT. IEEE, 2012. http://dx.doi.org/10.1109/isit.2012.6284686.

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Rapporti di organizzazioni sul tema "Ergodic theory"

Rupe, Adam. Ergodic Theory and Dynamical Process Modeling. Office of Scientific and Technical Information (OSTI), gennaio 2021. http://dx.doi.org/10.2172/1762707.

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Mezic, Igor. Nonlinear Dynamics and Ergodic Theory Methods in Control. Fort Belvoir, VA: Defense Technical Information Center, dicembre 2005. http://dx.doi.org/10.21236/ada451673.

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Mezic, Igor. Nonlinear Dynamics and Ergodic Theory Methods in Control. Fort Belvoir, VA: Defense Technical Information Center, gennaio 2003. http://dx.doi.org/10.21236/ada418975.

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ALMODARESI, S. A., e Ali BOLOOR. A mathematical modelling for spatio temporal substitution base on Ergodic theorem. Cogeo@oeaw-giscience, settembre 2011. http://dx.doi.org/10.5242/iamg.2011.0026.

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Houdre, Christian. On the Spectral SLLN and Pointwise Ergodic Theorem in L alpha. Fort Belvoir, VA: Defense Technical Information Center, luglio 1990. http://dx.doi.org/10.21236/ada225960.

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Stewart, Jonathan, Grace Parker, Joseph Harmon, Gail Atkinson, David Boore, Robert Darragh, Walter Silva e Youssef Hashash. Expert Panel Recommendations for Ergodic Site Amplification in Central and Eastern North America. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, marzo 2017. http://dx.doi.org/10.55461/tzsy8988.

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The U.S. Geological Survey (USGS) national seismic hazard maps have historically been produced for a reference site condition of VS30 = 760 m/sec (where VS30 is time averaged shear wave velocity in the upper 30 m of the site). The resulting ground motions are modified for five site classes (A-E) using site amplification factors for peak acceleration and ranges of short- and long-oscillator periods. As a result of Project 17 recommendations, this practice is being revised: (1) maps will be produced for a range of site conditions (as represented by VS30 ) instead of a single reference condition; and (2) the use of site factors for period ranges is being replaced with period-specific factors over the period range of interest (approximately 0.1 to 10 sec). Since the development of the current framework for site amplification factors in 1992, the technical basis for the site factors used in conjunction with the USGS hazard maps has remained essentially unchanged, with only one modification (in 2014). The approach has been to constrain site amplification for low-to-moderate levels of ground shaking using inference from observed ground motions (approximately linear site response), and to use ground response simulations (recently combined with observations) to constrain nonlinear site response. Both the linear and nonlinear site response has been based on data and geologic conditions in the western U.S. (an active tectonic region). This project and a large amount of previous and contemporaneous related research (e.g., NGA-East Geotechnical Working Group for site response) has sought to provide an improved basis for the evaluation of ergodic site amplification in central and eastern North America (CENA). The term ‘ergodic’ in this context refers to regionally-appropriate, but not site-specific, site amplification models (i.e., models are appropriate for CENA generally, but would be expected to have bias for any particular site). The specific scope of this project was to review and synthesize relevant research results so as to provide recommendations to the USGS for the modeling of ergodic site amplification in CENA for application in the next version of USGS maps. The panel assembled for this project recommends a model provided as three terms that are additive in natural logarithmic units. Two describe linear site amplification. One of these describes VS30-scaling relative to a 760 m/sec reference, is largely empirical, and has several distinct attributes relative to models for active tectonic regions. The second linear term adjusts iv site amplification from the 760 m/sec reference to the CENA reference condition (used with NGA-East ground motion models) of VS =3000 m/sec; this second term is simulation-based. The panel is also recommending a nonlinear model, which is described in a companion report [Hashash et al. 2017a]. All median model components are accompanied by models for epistemic uncertainty. The models provided in this report are recommended for application by the USGS and other entities. The models are considered applicable for VS30 = 200–2000 m/sec site conditions and oscillator periods of 0.08–5 sec. Finally, it should be understood that as ergodic models, they lack attributes that may be important for specific sites, such as resonances at site periods. Site-specific analyses are recommended to capture such effects for significant projects and for any site condition with VS30 < 200 m/sec. We recommend that future site response models for hazard applications consider a two-parameter formulation that includes a measure of site period in addition to site stiffness.

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Goulet, Christine, Yousef Bozorgnia, Nicolas Kuehn, Linda Al Atik, Robert Youngs, Robert Graves e Gail Atkinson. NGA-East Ground-Motion Models for the U.S. Geological Survey National Seismic Hazard Maps. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, marzo 2017. http://dx.doi.org/10.55461/qozj4825.

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The purpose of this report is to provide a set of ground motion models (GMMs) to be considered by the U.S. Geological Survey (USGS) for their National Seismic Hazard Maps (NSHMs) for the Central and Eastern U.S. (CEUS). These interim GMMs are adjusted and modified from a set of preliminary models developed as part of the Next Generation Attenuation for Central and Eastern North-America (CENA) project (NGA-East). The NGA-East objective was to develop a new ground-motion characterization (GMC) model for the CENA region. The GMC model consists of a set of GMMs for median and standard deviation of ground motions and their associated weights in the logic-tree for use in probabilistic seismic hazard analysis (PSHA). NGA-East is a large multidisciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER), at the University of California, Berkeley. The project has two components: (1) a set of scientific research tasks, and (2) a model-building component following the framework of the “Seismic Senior Hazard Analysis Committee (SSHAC) Level 3” [Budnitz et al. 1997; NRC 2012]. Component (2) is built on the scientific results of component (1) of the NGA-East Project. This report does not document the final NGA-East model under (2), but instead presents interim GMMs for use in the U.S. Geological Survey (USGS) National Seismic Hazard Maps. Under component (1) of NGA-East, several scientific issues were addressed, including: (a) development of a new database of empirical data recorded in CENA; (b) development of a regionalized ground-motion map for CENA, (c) definition of the reference site condition; (d) simulations of ground motions based on different methodologies, (e) development of numerous GMMs for CENA, and (f) the development of the current report. The scientific tasks of NGA- East were all documented as a series of PEER reports. This report documents the GMMs recommended by the authors for consideration by the USGS for their NSHM. The report documents the key elements involved in the development of the proposed GMMs and summarizes the median and aleatory models for ground motions along with their recommended weights. The models presented here build on the work from the authors and aim to globally represent the epistemic uncertainty in ground motions for CENA. The NGA-East models for the USGS NSHMs includes a set of 13 GMMs defined for 25 ground-motion intensity measures, applicable to CENA in the moment magnitude range of 4.0 to 8.2 and covering distances up to 1500 km. Standard deviation models are also provided for general PSHA applications (ergodic standard deviation). Adjustment factors are provided for hazard computations involving the Gulf Coast region.

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Goulet, Christine, Yousef Bozorgnia, Norman Abrahamson, Nicolas Kuehn, Linda Al Atik, Robert Youngs, Robert Graves e Gail Atkinson. Central and Eastern North America Ground-Motion Characterization - NGA-East Final Report. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, dicembre 2018. http://dx.doi.org/10.55461/wdwr4082.

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Abstract (sommario):

This document is the final project report of the Next Generation Attenuation for Central and Eastern North America (CENA) project (NGA-East). The NGA-East objective was to develop a new ground-motion characterization (GMC) model for the CENA region. The GMC model consists of a set of new ground-motion models (GMMs) for median and standard deviation of ground motions and their associated weights to be used with logic-trees in probabilistic seismic hazard analyses (PSHA). NGA-East is a large multidisciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER), at the University of California. The project has two components: (1) a set of scientific research tasks, and (2) a model-building component following the framework of the “Seismic Senior Hazard Analysis Committee (SSHAC) Level 3” (Budnitz et al. 1997; NRC 2012). Component (2) is built on the scientific results of component (1) of the NGA-East project. This report documents the tasks under component (2) of the project. Under component (1) of NGA-East, several scientific issues were addressed, including: (a) development of a new database of ground motion data recorded in CENA; (b) development of a regionalized ground-motion map for CENA, (c) definition of the reference site condition; (d) simulations of ground motions based on different methodologies; and (e) development of numerous GMMs for CENA. The scientific tasks of NGA-East were all documented as a series of PEER reports. The scope of component (2) of NGA-East was to develop the complete GMC. This component was designed as a SSHAC Level 3 study with the goal of capturing the ground motions’ center, body, and range of the technically defensible interpretations in light of the available data and models. The SSHAC process involves four key tasks: evaluation, integration, formal review by the Participatory Peer Review Panel (PPRP), and documentation (this report). Key tasks documented in this report include review and evaluation of the empirical ground- motion database, the regionalization of ground motions, and screening sets of candidate GMMs. These are followed by the development of new median and standard deviation GMMs, the development of new analyses tools for quantifying the epistemic uncertainty in ground motions, and the documentation of implementation guidelines of the complete GMC for PSHA computations. Appendices include further documentation of the relevant SSHAC process and additional supporting technical documentation of numerous sensitivity analyses results. The PEER reports documenting component (1) of NGA-East are also considered “attachments” to the current report and are all available online on the PEER website (https://peer.berkeley.edu/). The final NGA-East GMC model includes a set of 17 GMMs defined for 24 ground-motion intensity measures, applicable to CENA in the moment magnitude range of 4.0 to 8.2 and covering distances up to 1500 km. Standard deviation models are also provided for site-specific analysis (single-station standard deviation) and for general PSHA applications (ergodic standard deviation). Adjustment factors are provided for consideration of source-depth effects and hanging-wall effects, as well as for hazard computations at sites in the Gulf Coast region.

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