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Scaling Collapse and Structure Functions: Identifying Self-affinit...

By: G. Rowlands; N. W. Watkins; B. Hnat; S. C. Chapman

Description: Space and Astrophysics, University of Warwick, UK. Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) att...

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Kernel Estimation and Display of a Five-dimensional Conditional In...

By: G. Adelfio

Description: Dipartimento di Scienze Statistiche e Matematiche Silvio Vianelli, University of Palermo, Palermo, Italy. The aim of this paper is to find a convenient and effective method of displaying some second order properties in a neighbourhood of a selected point of the process. The used techniques are based on very general high-dimensional nonparametric smoothing developed to define a more general version of the conditional intensity function introduced in earli...

Adelfio, G.: An analysis of earthquakes clustering based on a second-order diagnostic approach, in: Data Analysis and Classification, Studies in Classification, Data Analysis, and Knowledge Organization, edited by: Palumbo, F., Greenacre, M., and Lauro, C. N., Springer-Verlag, 309–317, 2010.; Adelfio, G. and Chiodi, M.: Second-order diagnostics for space-time point processes with application to seismic events, Environmetrics, 20, 895–911, 2009.; Adelfio, G., Chiodi, M., ...

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The Predictability of Large-scale Wind-driven Flows : Volume 8, Is...

By: P. Malanotte-rizzoli; J. Lu; S. P. Meacham; A. Mahadevan

Description: Ocean Process Analysis Laboratory, University of New Hampshire, Durham, NH 03824, USA. The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and sing...

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On the Separation of Timescales in Spring-block Earthquake Models ...

By: S. Hergarten; F. Jansen

Description: Institute of Geology, University of Bonn, Germany. One of the most widespread spring-block earthquake models, the Olami-Feder-Christensen model, is investigated without making the assumption that the duration of individual earthquakes is negligible. While the Gutenberg-Richter law for the size distribution of earthquakes is preserved qualitatively for earthquakes of finite duration, the b-value decreases with increasing earthquake duration. The effect ...

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Diagnosing Non-gaussianity of Forecast and Analysis Errors in a Co...

By: T. Montmerle; Y. Michel; R. Legrand

Description: Centre National de Recherches Météorologiques (CNRM), Toulouse, France. In numerical weather prediction, the problem of estimating initial conditions is usually based on a Bayesian framework. Two common derivations respectively lead to the Kalman filter and to variational approaches. They rely on either assumptions of linearity or assumptions of Gaussianity of the probability density functions of both observation and background errors. In practice, lin...

Anderson, E. and Jarvinen, H.: Variational quality control, Q. J. Roy. Meteorol. Soc., 125, 697–722, doi:10.1002/qj.49712555416, 1999.; Anderson, T. W. and Darling, D. A.: A test of goodness of fit, J. Am. Stat. Assoc., 49, 765–769, 1954.; Auligné, T., Lorenc, A., Michel, Y., Montmerle, T., Jones, A., Hu, M., and Dudhia, J.: Toward a new cloud analysis and prediction system, B. Am. Meteorol. Soc., 92, 207–210, 2011.; B...

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Modeling Nonlinear Compressional Waves in Marine Sediments : Volum...

By: B. E. McDonald

Description: US Naval Research Lab, Washington DC, 20375, USA. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm ...

Hovem, J.: The nonlinearity parameter of saturated marine sediments, J. Acoust. Soc. Am., 66, 1463–1467, 1979.; Bailey, M. R., Blackstock, D. T., Cleveland, R. O., and Crum, L. A.: Comparison of electrohydraulic lithotripters with rigid and pressure-release ellipsoidal reflectors, I. Acoustic fields, J. Acoust. Soc. Am., 104, 2517–2524, 1998.; Beyer, R. T.: Nonlinear Acoustics, Acoustical Society of America, Huntington, NY, 435~pp., 1997.; Bjorno, L.: Finite amplitude wa...

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Response of an Ocean-atmosphere Climate Model to Milankovic Forcin...

By: E. S. Posmentier

Description: Southhampton College of long Island University, Southhampton, NY 11968, USA. There is considerable evidence in support of Milankovic's theory that variations in high-latitude summer insolation caused by Earth orbital variations are the cause of the Pleistocene ice cycles. The enigmatic discrepancy between the spectra of Milankovic forcing and of Pleistocene climate variations is believed to be resolved by the slow, nonlinear response of ice sheets to cha...

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Cyclic Markov Chains with an Application to an Intermediate Enso M...

By: A. Timmermann; R. A. Pasmanter

Description: KNMI, Postbus 201, 3730 AE De Bilt, the Netherlands. We develop the theory of cyclic Markov chains and apply it to the El Niño-Southern Oscillation (ENSO) predictability problem. At the core of Markov chain modelling is a partition of the state space such that the transition rates between different state space cells can be computed and used most efficiently. We apply a partition technique, which divides the state space into multidimen...

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Unified Multifractal Atmospheric Dynamics Tested in the Tropics: P...

By: S. Lovejoy; A. Lazarev; A. Ordanovich; D. Schertzer; Y. Chigirinskaya

Description: Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France. In this paper we test the Unified Mulifractal model of atmospheric dynamics in the tropics. In the first part, we empirically investigate the scaling behaviour along the horizontal, in the second part along the vertical. Here we concentrate on the presentation of basic multifractal notions and techniques and on how they give rise to sel...

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Microstructure Induced Nonlinearity of Unconsolidated Rocks as Rel...

By: L. A. Ostrovsky; V. Yu. Zaitsev; I. Yu. Belyaeva

Description: Institute of Applied Physics, Russian Academy of Sciences, 46 Uljanov Str., 603600 Nizhny Novogorod, Russia. Manifestations of the so-called structure induced nonlinearity are considered for the case of a granular medium, the latter being a generally accepted model of nonconsolidated rocks in seismics. The consideration is carried out using the medium model in the form of the ideal random packing of spherical elastic gran...

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Multiplicative Cascade Processes and Information Integration for P...

By: Q. Cheng

Description: State Key Lab of Geological Processes and Mineral Resources, China University of Geosciences, Beijing 100083, Wuhan 430074, China. This paper presents a new model proposed on the basis of multiplicative cascade process (MCP) theory for integrating spatial information to be used for mineral resources prediction and environmental impact assessment. Probability of a spatial point event is defined as the probability that a small map calculating unit (map uni...

Blenkinsop, T. G.: The Fractal Distribution of Gold Deposits, in: Fractals and Dynamic Systems in Geoscience, edited by: Kruhl, J. H., Springer-Verlag, 247–258, 1994.; Agterberg, F. P.: Computer programs for exploration, Science, 245, 76–81, 1989a.; Agterberg, F. P.: Systematic approach to dealing with uncertainty of geoscience information in mineral exploration, in: Application of Computers and Operations in the mineral industry, edited by: Weiss, A., Proc. 21st APCOM S...

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Cosmic Ray Momentum Diffusion in the Presence of Nonlinear Alfvén ...

By: G. Michałek; M. Ostrowsky

Description: Obserwatorium Astronomiczne, Uniwersytet Jagielloński, ul. Orla 171, 30-244 Kraków, Poland. The relation between the spatial diffusion coefficient along the magnetic field, kII, and the momentum diffusion coefficient, Dp, for relativistic cosmic ray particles is modelled using Monte Carlo simulations. Wave fields with vanishing wave helicity and cross-helicity, constructed by superpos...

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A Note on Chaotic Vs. Stochastic Behavior of the High-latitude Ion...

By: K. C. Yeh; A. W. Wernik

Description: Space Research Center, Polish Academy of Sciences, ul. Bartycka 18a, Warsaw, Poland. Four data sets of density fluctuations measured in-situ by the Dynamics Explorer (DE 2) were analyzed in an attempt to study chaotic nature of the high-latitude turbulence and, in this way to complement the conventional spectral analysis. It has been found that the probability distribution function of density differences is far from ...

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Multifractal Magnetic Susceptibility Distribution Models of Hydrot...

By: M. E. Gettings

Description: US Geological Survey, 520 N. Park Ave., Rm. 355, Tucson, Arizona 85719, USA. Magnetic susceptibility was measured for 700 samples of drill core from thirteen drill holes in the porphyry copper-molybdenum deposit of the Stinkingwater mining district in the Absaroka Mountains, Wyoming. The magnetic susceptibility measurements, chemical analyses, and alteration class provided a database for study of magnetic susceptibility in these altered rocks. The distr...

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On the Identification of Dragon Kings Among Extreme-valued Outlier...

By: S. P. Neuman; A. Guadagnini; M. Riva

Description: Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milan, Italy. Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extre...

Ailliot, P., Thompson, C., and Thomson, P.: Mixed methods for fitting the GEV distribution, Water Resour. Res., 47, W05551, doi:10.1029/2010WR009417, 2011.; Akaev, A., Sadovnichy, V., and Korotayev, A.: On the dynamics of the world demographic transition and financial-economic crises forecast, Eur. Phys. J.-Spec. Top., 205, 355–373, doi:10.1140/epjst/e2012-01578-2...

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Rossby-wave Turbulence in a Rapidly Rotating Sphere : Volume 12, I...

By: P. Cardin; N. Schaeffer

Description: LGIT, Observatoire de Grenoble, Universit\'e Joseph Fourier, Grenoble, France. We use a quasi-geostrophic numerical model to study the turbulence of rotating flows in a sphere, with realistic Ekman friction and bulk viscous dissipation. The forcing is caused by the destabilization of an axisymmetric Stewartson shear layer, generated by differential rotation, resulting in a forcing at rather large scales.
The equilibrium regime is strongly anisotr...

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Chaotic Ray Propagation in Corrugated Layers : Volume 12, Issue 6 ...

By: C. Godano; M. Falanga; M. Bottiglieri; S. De Martino

Description: Environmental Department, Second University of Naples, via Vivaldi 43, 81100 Caserta and CNISM, Italy. The aim of this paper is to study the effects of a corrugated wall on the behaviour of propagating rays. Different types of corrugation are considered, using different distributions of the corrugation heights: white Gaussian, power law, self-affine perturbation. In phase space, a prevalent chaotic behaviour of rays, and the presence of a lot of caustic...

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Insight Into Earthquake Sequencing: Analysis and Interpretation of...

By: K. Vasudevan; M. S. Cavers

Description: Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada. Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time-series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthq...

Allan, D. W.: Statistics of atomic frequency standards, Ptoc. IEEE, 54, 221–230, 1966.; Barnes, J. A. and Allan, D. W.: A statistical model of flicker noise, Ptoc. IEEE, 54, 176–178, 1966.; Bird, P.: An updated digital model of plate boundaries, Geochem. Geophy. Geosy., 4, 1027, doi:10.1029/2001GC000252, 2003.; Bohnenstiehl, D. R., Tolstoy, M., Smith, D. K., Fox, C. G., and Dziak, R. P.: Time-clustering behavior of sprea...

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Integrable, Oblique Travelling Waves in Quasi-charge-neutral Two-f...

By: J. F. McKenzie; R. L. MacE; C. M. Ko; G. P. Zank; G. M. Webb

Description: Institute of Geophysics and Planetary Physics, University of California Riverside, Riverside CA 92521, USA. A Hamiltonian description of oblique travelling waves in a two-fluid, charge-neutral, electron-proton plasma reveals that the transverse momentum equations for the electron and proton fluids are exactly integrable in cases where the total transverse momentum flux integrals, Py(d) and Pz

Abramowitz, M. and Stegun, I. A.: Handbook of Mathematical Functions, (Dover: New York), 589 pp., 1965.; Bridges, T. J.: Spatial Hamiltonian structure, energy flux and the water wave problem, Proc. Roy. Soc. Lond. A, 439, 297–315, 1992.; Bridges, T. J.: Multi-symplectic structures and wave propagation, Math. Proc. Camb. Philos. Soc., 121, 147–190, 1997a.; Magri, F.: A simple model of the integrable Hamiltonian equation, J. Math. Phys., 19, 5, 1156–1162, 1978.; Bridges, T...

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Internal Solitary Waves: Propagation, Deformation and Disintegrati...

By: O. Kurkina; E. Pelinovsky; T. Talipova; R. Grimshaw

Description: Department of Mathematical Sciences, Loughborough University, Leicestershire, UK. In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate large-amplitude, horizontally propagating internal solitary waves. Typically these waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of th...

Apel, J., Ostrovsky, L. A., Stepanyants, Y. A., and Lynch, J. F.: Internal solitons in the ocean and their effect on underwater sound, J. Acoust. Soc. Am., 121, 695–722, 2007.; Benjamin, T. B.: Internal waves of finite amplitude and permanent form, J. Fluid Mech., 25, 241–270, 1966.; Benney, D. J.: Long non-linear waves in fluid flows, J. Math. Phys., 45, 52–63, 1966.; Bourgault, D., Blokhina, M. D., Mirchak, R., and Kelly, D. E.: Evolution of a shoaling internal solitar...

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