Non-linearity consideration when analyzing reactor noise statistical characteristics. [BWR
Energy Technology Data Exchange (ETDEWEB)
Kebadze, B V; Adamovski, L A
1975-06-01
Statistical characteristics of boiling water reactor noise in the vicinity of stability threshold are studied. The reactor is considered as a non-linear system affected by random perturbations. To solve a non-linear problem the principle of statistical linearization is used. It is shown that the halfwidth of resonance peak in neutron power noise spectrum density as well as the reciprocal of noise dispersion, which are used in predicting a stable operation theshold, are different from zero both within and beyond the stability boundary the determination of which was based on linear criteria.
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical ...
Nonlinear wave chaos: statistics of second harmonic fields.
Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M
2017-10-01
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.
Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro
2014-05-01
This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if khthe aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.
Statistical approach of weakly nonlinear ablative Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Garnier, J.; Masse, L.
2005-01-01
A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1λ for long wavelengths, but higher for short instable wavelengths in the ablative regime
Image statistics and nonlinear artifacts in composed transmission x-ray tomography
International Nuclear Information System (INIS)
Duerinckx, A.J.G.
1979-01-01
Knowledge of the image quality and image statistics in Computed Tomography (CT) images obtained with transmission x-ray CT scanners can increase the amount of clinically useful information that can be retrieved. Artifacts caused by nonlinear shadows are strongly object-dependent and are visible over larger areas of the image. No simple technique exists for their complete elimination. One source of artifacts in the first order statistics is the nonlinearities in the measured shadow or projection data used to reconstruct the image. One of the leading causes is the polychromaticity of the x-ray beam used in transmission CT scanners. Ways to improve the resulting image quality and techniques to extract additional information using dual energy scanning are discussed. A unique formalism consisting of a vector representation of the material dependence of the photon-tissue interactions is generalized to allow an in depth analysis. Poly-correction algorithms are compared using this analytic approach. Both quantum and detector electronic noise decrease the quality or information content of first order statistics. Preliminary results are presented using an heuristic adaptive nonlinear noise filter system for projection data. This filter system can be improved and/or modified to remove artifacts in both first and second order image statistics. Artifacts in the second order image statistics arise from the contribution of quantum noise. This can be described with a nonlinear detection equivalent model, similar to the model used to study artifacts in first order statistics. When analyzing these artifacts in second order statistics, one can divide them into linear artifacts, which do not present any problem of interpretation, and nonlinear artifacts, referred to as noise artifacts. A study of noise artifacts is presented together with a discussion of their relative importance in diagnostic radiology
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
A comparison of linear and nonlinear statistical techniques in performance attribution.
Chan, N H; Genovese, C R
2001-01-01
Performance attribution is usually conducted under the linear framework of multifactor models. Although commonly used by practitioners in finance, linear multifactor models are known to be less than satisfactory in many situations. After a brief survey of nonlinear methods, nonlinear statistical techniques are applied to performance attribution of a portfolio constructed from a fixed universe of stocks using factors derived from some commonly used cross sectional linear multifactor models. By rebalancing this portfolio monthly, the cumulative returns for procedures based on standard linear multifactor model and three nonlinear techniques-model selection, additive models, and neural networks-are calculated and compared. It is found that the first two nonlinear techniques, especially in combination, outperform the standard linear model. The results in the neural-network case are inconclusive because of the great variety of possible models. Although these methods are more complicated and may require some tuning, toolboxes are developed and suggestions on calibration are proposed. This paper demonstrates the usefulness of modern nonlinear statistical techniques in performance attribution.
Nonlinear acoustics of water-saturated marine sediments
DEFF Research Database (Denmark)
Jensen, Leif Bjørnø
1976-01-01
Interest in the acoustic qualities of water-saturated marine sediments has increased considerably during recent years. The use of sources of high-intensity sound in oil propsecting, in geophysical and geological studies of bottom and subbottom materials and profiles and recently in marine...... archaeology has emphasized the need of information about the nonlinear acoustic qualities of water-saturated marine sediments. While the acoustic experiments and theoretical investigations hitherto performed have concentrated on a determination of the linear acoustic qualities of water-saturated marine...... sediments, their parameters of nonlinear acoustics are still unexplored. The strong absorption, increasing about linearly with frequency, found in most marine sediments and the occurrence of velocity dispersion by some marine sediments restrict the number of nonlinear acoustic test methods traditionally...
Statistics of peaks in cosmological nonlinear density fields
International Nuclear Information System (INIS)
Suginohara, Tatsushi; Suto, Yasushi.
1990-06-01
Distribution of the high-density peaks in the universe is examined using N-body simulations. Nonlinear evolution of the underlying density field significantly changes the statistical properties of the peaks, compared with the analytic results valid for the random Gaussian field. In particular, the abundances and correlations of the initial density peaks are discussed in the context of biased galaxy formation theory. (author)
Role of statistical linearization in the solution of nonlinear stochastic equations
International Nuclear Information System (INIS)
Budgor, A.B.
1977-01-01
The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables
Statistical properties of nonlinear one-dimensional wave fields
Directory of Open Access Journals (Sweden)
D. Chalikov
2005-01-01
Full Text Available A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Statistical properties of nonlinear one-dimensional wave fields
Chalikov, D.
2005-06-01
A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Hu, Juju; Hu, Haijiang; Ji, Yinghua
2010-03-15
Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.
Nonlinear water waves: introduction and overview
Constantin, A.
2017-12-01
For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.
International Nuclear Information System (INIS)
Harlim, John; Mahdi, Adam; Majda, Andrew J.
2014-01-01
A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Nonlinear Dielectric Response of Water Treed XLPE Cable Insulation
Energy Technology Data Exchange (ETDEWEB)
Hvidsten, Sverre
1999-07-01
Condition assessment of XLPE power cables is becoming increasingly important for the utilities, due to a large number of old cables in service with high probability of failure caused by water tree degradation. The commercial available techniques are generally based upon measurements of the dielectric response, either by time (polarisation/depolarisation current or return voltage) or frequency domain measurements. Recently it has been found that a high number of water trees in XLPE insulated cables causes the dielectric response to increase more than linearly with increasing test voltage. This nonlinear feature of water tree degraded XLPE insulation has been suggested to be of a great importance, both for diagnostic purposes, and for fundamental understanding of the water tree phenomenon itself. The main purpose of this thesis have been to study the nonlinear feature of the dielectric response measured on watertreed XLPE insulation. This has been performed by dielectric response measurements in both time and frequency domain, numerical calculations of losses of simplified water tree models, and fmally water content and water permeation measurements on single water trees. The dielectric response measurements were performed on service aged cable samples and laboratory aged Rogowski type objects. The main reason for performing laboratory ageing was to facilitate diagnostic testing as a function of ageing time of samples containing mainly vented water trees. A new method, based upon inserting NaC1 particles at the interface between the upper semiconductive screen and the insulation, was found to successfully enhance initiation and growth of vented water trees. AC breakdown strength testing show that it is the vented water trees that reduce the breakdown level of both the laboratory aged test objects and service aged cable samples. Vented water treeing was found to cause the dielectric response to become nonlinear at a relatively low voltage level. However, the measured
Visual aftereffects and sensory nonlinearities from a single statistical framework
Laparra, Valero; Malo, Jesús
2015-01-01
When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are
Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.
Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J
2016-10-03
Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.
Topological and statistical properties of nonlinear force-free fields
Mangalam, A.; Prasad, A.
2018-01-01
We use our semi-analytic solution of the nonlinear force-free field equation to construct three-dimensional magnetic fields that are applicable to the solar corona and study their statistical properties for estimating the degree of braiding exhibited by these fields. We present a new formula for calculating the winding number and compare it with the formula for the crossing number. The comparison is shown for a toy model of two helices and for realistic cases of nonlinear force-free fields; conceptually the formulae are nearly the same but the resulting distributions calculated for a given topology can be different. We also calculate linkages, which are useful topological quantities that are independent measures of the contribution of magnetic braiding to the total free energy and relative helicity of the field. Finally, we derive new analytical bounds for the free energy and relative helicity for the field configurations in terms of the linking number. These bounds will be of utility in estimating the braided energy available for nano-flares or for eruptions.
Kim, Seongho; Li, Lang
2014-02-01
The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiability of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Characterizing the Statistics of a Bunch of Optical Pulses Using a Nonlinear Optical Loop Mirror
Directory of Open Access Journals (Sweden)
Olivier Pottiez
2015-01-01
Full Text Available We propose in this work a technique for determining the amplitude distribution of a wave packet containing a large number of short optical pulses with different amplitudes. The technique takes advantage of the fast response of the optical Kerr effect in a fiber nonlinear optical loop mirror (NOLM. Under some assumptions, the statistics of the pulses can be determined from the energy transfer characteristic of the packet through the NOLM, which can be measured with a low-frequency detection setup. The statistical distribution is retrieved numerically by approximating the solution of a system of nonlinear algebraic equations using the least squares method. The technique is demonstrated numerically in the case of a packet of solitons.
Foundations of Complex Systems Nonlinear Dynamics, Statistical Physics, and Prediction
Nicolis, Gregoire
2007-01-01
Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, h
Identification of nonlinear coupling in wave turbulence at the surface of water
Campagne, Antoine; Hassaini, Roumaissa; Redor, Ivan; Aubourg, Quentin; Sommeria, Joël; Mordant, Nicolas
2017-11-01
The Weak Turbulence Theory is a theory, in the limit of vanishing nonlinearity, that derive analytically statistical features of wave turbulence. The stationary spectrum for the surface elevation in the case of gravity waves, is predicted to E(k) k - 5 / 2 . This spectral exponent -5/2 remains elusive in all experiments. in which the measured exponent is systematically lower than the prediction. Furthermore in the experiments the weaker the nonlinearity the further the spectral exponent is from the prediction. In order to investigate the reason for this observation we developed an experiment in the CORIOLIS facility in Grenoble. It is a 13m-diameter circular pool filled with water with a 70 cm depth. We generate wave turbulence by using two wedge wavemakers. Surface elevation measurements are performed by a stereoscopic optical technique and by capacitive probes. The nonlinear coupling at work in this system are analyzed by computing 3- and 4-wave correlations of the Fourier wave amplitudes in frequency. Theory predicts that coupling should occur through 4-wave resonant interaction. In our data, strong 3-wave correlations are observed in addition to the 4-wave correlation. Most our observations are consistent with field observation in the Black Sea (Leckler et al. 2015). This project has received funding from the European Research Council (ERC, Grant Agreement No 647018-WATU).
Hamiltonian formulation and statistics of an attracting system of nonlinear oscillators
International Nuclear Information System (INIS)
Tasso, H.
1987-10-01
An attracting system of r nonlinear oscillators of an extended van der Pol type was investigated with respect to Hamiltonian formulation. The case of r=2 is rather simple, though nontrivial. For r>2 the tests with Jacobi's identity and Frechet derivatives are negative if Hamiltonians in the natural variables are looked for. Independently, a Liouville theorem is proved and equilibrium statistics is made possible, which leads to a Gaussian distribution in the natural variables. (orig.)
An efficient flexible-order model for 3D nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole
2009-01-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal......, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental...
NONLINEAR EVOLUTION OF GLOBAL HYDRODYNAMIC SHALLOW-WATER INSTABILITY IN THE SOLAR TACHOCLINE
International Nuclear Information System (INIS)
Dikpati, Mausumi
2012-01-01
We present a fully nonlinear hydrodynamic 'shallow-water' model of the solar tachocline. The model consists of a global spherical shell of differentially rotating fluid, which has a deformable top, thus allowing motions in radial directions along with latitudinal and longitudinal directions. When the system is perturbed, in the course of its nonlinear evolution it can generate unstable low-frequency shallow-water shear modes from the differential rotation, high-frequency gravity waves, and their interactions. Radiative and overshoot tachoclines are characterized in this model by high and low effective gravity values, respectively. Building a semi-implicit spectral scheme containing very low numerical diffusion, we perform nonlinear evolution of shallow-water modes. Our first results show that (1) high-latitude jets or polar spin-up occurs due to nonlinear evolution of unstable hydrodynamic shallow-water disturbances and differential rotation, (2) Reynolds stresses in the disturbances together with changing shell thickness and meridional flow are responsible for the evolution of differential rotation, (3) disturbance energy primarily remains concentrated in the lowest longitudinal wavenumbers, (4) an oscillation in energy between perturbed and unperturbed states occurs due to evolution of these modes in a nearly dissipation-free system, and (5) disturbances are geostrophic, but occasional nonadjustment in geostrophic balance can occur, particularly in the case of high effective gravity, leading to generation of gravity waves. We also find that a linearly stable differential rotation profile remains nonlinearly stable.
Identification of mine waters by statistical multivariate methods
Energy Technology Data Exchange (ETDEWEB)
Mali, N [IGGG, Ljubljana (Slovenia)
1992-01-01
Three water-bearing aquifers are present in the Velenje lignite mine. The aquifer waters have differing chemical composition; a geochemical water analysis can therefore determine the source of mine water influx. Mine water samples from different locations in the mine were analyzed, the results of chemical content and of electric conductivity of mine water were statistically processed by means of MICROGAS, SPSS-X and IN STATPAC computer programs, which apply three multivariate statistical methods (discriminate, cluster and factor analysis). Reliability of calculated values was determined with the Kolmogorov and Smirnov tests. It is concluded that laboratory analysis of single water samples can produce measurement errors, but statistical processing of water sample data can identify origin and movement of mine water. 15 refs.
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....
DEFF Research Database (Denmark)
Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel
2011-01-01
Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number...... of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages ofADMB are flexibility...
Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.
Yagasaki, Takuma; Saito, Shinji
2009-09-15
Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is
Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems
Marston, J. B.; Hastings, M. B.
2005-03-01
The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.
Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe
Directory of Open Access Journals (Sweden)
M. Vrac
2007-12-01
Full Text Available Local-scale climate information is increasingly needed for the study of past, present and future climate changes. In this study we develop a non-linear statistical downscaling method to generate local temperatures and precipitation values from large-scale variables of a Earth System Model of Intermediate Complexity (here CLIMBER. Our statistical downscaling scheme is based on the concept of Generalized Additive Models (GAMs, capturing non-linearities via non-parametric techniques. Our GAMs are calibrated on the present Western Europe climate. For this region, annual GAMs (i.e. models based on 12 monthly values per location are fitted by combining two types of large-scale explanatory variables: geographical (e.g. topographical information and physical (i.e. entirely simulated by the CLIMBER model.
To evaluate the adequacy of the non-linear transfer functions fitted on the present Western European climate, they are applied to different spatial and temporal large-scale conditions. Local projections for present North America and Northern Europe climates are obtained and compared to local observations. This partially addresses the issue of spatial robustness of our transfer functions by answering the question "does our statistical model remain valid when applied to large-scale climate conditions from a region different from the one used for calibration?". To asses their temporal performances, local projections for the Last Glacial Maximum period are derived and compared to local reconstructions and General Circulation Model outputs.
Our downscaling methodology performs adequately for the Western Europe climate. Concerning the spatial and temporal evaluations, it does not behave as well for Northern America and Northern Europe climates because the calibration domain may be too different from the targeted regions. The physical explanatory variables alone are not capable of downscaling realistic values. However, the inclusion of
Farrell, Brian; Ioannou, Petros; Nikolaidis, Marios-Andreas
2017-11-01
While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field, nonlinearity is also known to play an essential role in sustaining turbulence. We report a study based on the statistical state dynamics of Couette flow turbulence with the goal of better understanding the role of nonlinearity in sustaining turbulence. The statistical state dynamics implementations used are ensemble closures at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. Two fundamentally non-normal mechanisms potentially contributing to maintaining the second cumulant are identified. These are essentially parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of selectively including these mechanisms parametric growth is found to maintain the perturbation field in the turbulent state while the more commonly invoked mechanism associated with transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation variance. Funded by ERC Coturb Madrid Summer Program and NSF AGS-1246929.
Water Fluoridation Statistics - Percent of PWS population receiving fluoridated water
U.S. Department of Health & Human Services — 2000-2014. Water Fluoridation Statistics is a biennial report of the percentage and number of people receiving fluoridated water from 2000 through 2014, originally...
Water Fluoridation Statistics - Percent of PWS population receiving fluoridated water
U.S. Department of Health & Human Services — 2000-2014 Water Fluoridation Statistics is a biennial report of the percentage and number of people receiving fluoridated water from 2000 through 2014, originally...
Nonlinear dynamics of boiling water reactors
International Nuclear Information System (INIS)
March-Leuba, J.; Cacuci, D.G.; Perez, R.B.
1983-01-01
Recent stability tests in Boiling Water Reactors (BWRs) have indicated that these reactors can exhibit the special nonlinear behavior of following a closed trajectory called limit cycle. The existence of a limit cycle corresponds to an oscillation of fixed amplitude and period. During these tests, such oscillations had their amplitudes limited to about +- 15% of the operating power. Since limit cycles are fairly insensitive to parameter variations, it is possible to operate a BWR under conditions that sustain a limit cycle (of fixed amplitude and period) over a finite range of reactor parameters
Water Quality attainment Information from Clean Water Act Statewide Statistical Surveys
U.S. Environmental Protection Agency — Designated uses assessed by statewide statistical surveys and their state and national attainment categories. Statewide statistical surveys are water quality...
Water Quality Stressor Information from Clean Water Act Statewide Statistical Surveys
U.S. Environmental Protection Agency — Stressors assessed by statewide statistical surveys and their state and national attainment categories. Statewide statistical surveys are water quality assessments...
International Nuclear Information System (INIS)
Budgor, A.B.; West, B.J.
1978-01-01
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation
Energy Technology Data Exchange (ETDEWEB)
Chabchoub, A., E-mail: achabchoub@swin.edu.au [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia); Kibler, B.; Finot, C.; Millot, G. [Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 21078 Dijon (France); Onorato, M. [Dipartimento di Fisica, Università degli Studi di Torino, Torino 10125 (Italy); Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, Torino 10125 (Italy); Dudley, J.M. [Institut FEMTO-ST, UMR 6174 CNRS- Université de Franche-Comté, 25030 Besançon (France); Babanin, A.V. [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia)
2015-10-15
The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.
Nonlinear dead water resistance at subcritical speed
Grue, John
2015-08-01
The dead water resistance F 1 = /1 2 C d w ρ S U 2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0-0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ˜ 0.875-1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.
Computation of nonlinear water waves with a high-order Boussinesq model
DEFF Research Database (Denmark)
Fuhrman, David R.; Madsen, Per A.; Bingham, Harry
2005-01-01
Computational highlights from a recently developed high-order Boussinesq model are shown. The model is capable of treating fully nonlinear waves (up to the breaking point) out to dimensionless depths of (wavenumber times depth) kh \\approx 25. Cases considered include the study of short......-crested waves in shallow/deep water, resulting in hexagonal/rectangular surface patterns; crescent waves, resulting from unstable perturbations of plane progressive waves; and highly-nonlinear wave-structure interactions. The emphasis is on physically demanding problems, and in eachcase qualitative and (when...
The use of machine learning and nonlinear statistical tools for ADME prediction.
Sakiyama, Yojiro
2009-02-01
Absorption, distribution, metabolism and excretion (ADME)-related failure of drug candidates is a major issue for the pharmaceutical industry today. Prediction of ADME by in silico tools has now become an inevitable paradigm to reduce cost and enhance efficiency in pharmaceutical research. Recently, machine learning as well as nonlinear statistical tools has been widely applied to predict routine ADME end points. To achieve accurate and reliable predictions, it would be a prerequisite to understand the concepts, mechanisms and limitations of these tools. Here, we have devised a small synthetic nonlinear data set to help understand the mechanism of machine learning by 2D-visualisation. We applied six new machine learning methods to four different data sets. The methods include Naive Bayes classifier, classification and regression tree, random forest, Gaussian process, support vector machine and k nearest neighbour. The results demonstrated that ensemble learning and kernel machine displayed greater accuracy of prediction than classical methods irrespective of the data set size. The importance of interaction with the engineering field is also addressed. The results described here provide insights into the mechanism of machine learning, which will enable appropriate usage in the future.
Several Dynamical Properties for a Nonlinear Shallow Water Equation
Directory of Open Access Journals (Sweden)
Ls Yong
2014-01-01
Full Text Available A nonlinear third order dispersive shallow water equation including the Degasperis-Procesi model is investigated. The existence of weak solutions for the equation is proved in the space L1(R∩BV (R under certain assumptions. The Oleinik type estimate and L2N(R (N is a natural number estimate for the solution are obtained.
Nonlinear optical effects from Au nanoparticles prepared by laser plasmas in water
Energy Technology Data Exchange (ETDEWEB)
Fazio, E., E-mail: enfazio@unime.it [Dipartimento di Fisica della Materia e Ingegneria Elettronica, Universitá di Messina, V.le F. Stagno d’Alcontres 31, I-98166, Messina (Italy); Neri, F. [Dipartimento di Fisica della Materia e Ingegneria Elettronica, Universitá di Messina, V.le F. Stagno d’Alcontres 31, I-98166, Messina (Italy)
2013-05-01
The optical limiting properties of Au nanoparticles prepared by laser generated plasmas in water were investigated. The ablation processes were carried out irradiating an Au target with the second harmonic (532 nm) output of a Nd:YAG laser, changing the water level above the target, the lens position and the laser pulse energy. Different surface morphologies, from isolated nearly spherical nanoparticles to elongated structures, were observed by TEM imaging. A significant nonlinear optical response was probed by the Z-scan technique. The efficiency and the nature of the nonlinear response are found to be strongly dependent on the morphological properties of the nanostructures. The third order optical susceptibility χ{sup (3)} assumes the values of 1.83 × 10{sup −6} esu and 6.34 × 10{sup −6} esu for the smaller nanoparticles size obtained at the lower ablation energies (10–20 mJ), 8.25 × 10{sup −6} esu and 2.13 × 10{sup −5} esu for the particles agglomerations obtained at the higher ablation energies (50–100 mJ). The high value of χ{sup (3)} and the possibility to tailor the nonlinear optical response by changing the morphological properties of the Au nanostructures make them interesting materials for potential applications in the nonlinear optics field.
Non-linear analysis in Light Water Reactor design
International Nuclear Information System (INIS)
Rashid, Y.R.; Sharabi, M.N.; Nickell, R.E.; Esztergar, E.P.; Jones, J.W.
1980-03-01
The results obtained from a scoping study sponsored by the US Department of Energy (DOE) under the Light Water Reactor (LWR) Safety Technology Program at Sandia National Laboratories are presented. Basically, this project calls for the examination of the hypothesis that the use of nonlinear analysis methods in the design of LWR systems and components of interest include such items as: the reactor vessel, vessel internals, nozzles and penetrations, component support structures, and containment structures. Piping systems are excluded because they are being addressed by a separate study. Essentially, the findings were that nonlinear analysis methods are beneficial to LWR design from a technical point of view. However, the costs needed to implement these methods are the roadblock to readily adopting them. In this sense, a cost-benefit type of analysis must be made on the various topics identified by these studies and priorities must be established. This document is the complete report by ANATECH International Corporation
Study on statistical analysis of nonlinear and nonstationary reactor noises
International Nuclear Information System (INIS)
Hayashi, Koji
1993-03-01
For the purpose of identification of nonlinear mechanism and diagnosis of nuclear reactor systems, analysis methods for nonlinear reactor noise have been studied. By adding newly developed approximate response function to GMDH, a conventional nonlinear identification method, a useful method for nonlinear spectral analysis and identification of nonlinear mechanism has been established. Measurement experiment and analysis were performed on the reactor power oscillation observed in the NSRR installed at the JAERI and the cause of the instability was clarified. Furthermore, the analysis and data recording methods for nonstationary noise have been studied. By improving the time resolution of instantaneous autoregressive spectrum, a method for monitoring and diagnosis of operational status of nuclear reactor has been established. A preprocessing system for recording of nonstationary reactor noise was developed and its usability was demonstrated through a measurement experiment. (author) 139 refs
Nonlinear Statistical Signal Processing: A Particle Filtering Approach
International Nuclear Information System (INIS)
Candy, J.
2007-01-01
A introduction to particle filtering is discussed starting with an overview of Bayesian inference from batch to sequential processors. Once the evolving Bayesian paradigm is established, simulation-based methods using sampling theory and Monte Carlo realizations are discussed. Here the usual limitations of nonlinear approximations and non-gaussian processes prevalent in classical nonlinear processing algorithms (e.g. Kalman filters) are no longer a restriction to perform Bayesian inference. It is shown how the underlying hidden or state variables are easily assimilated into this Bayesian construct. Importance sampling methods are then discussed and shown how they can be extended to sequential solutions implemented using Markovian state-space models as a natural evolution. With this in mind, the idea of a particle filter, which is a discrete representation of a probability distribution, is developed and shown how it can be implemented using sequential importance sampling/resampling methods. Finally, an application is briefly discussed comparing the performance of the particle filter designs with classical nonlinear filter implementations
An efficient flexible-order model for 3D nonlinear water waves
Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.
2009-04-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.
An efficient flexible-order model for 3D nonlinear water waves
International Nuclear Information System (INIS)
Engsig-Karup, A.P.; Bingham, H.B.; Lindberg, O.
2009-01-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature
Directory of Open Access Journals (Sweden)
Li Gang
2016-01-01
Full Text Available This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.
Schamel, Hans; Eliasson, Bengt
2016-05-01
Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
Hanamura, Eiichi; Yamanaka, Akio
2007-01-01
This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.
Nonlinear dynamics aspects of particle accelerators
International Nuclear Information System (INIS)
Jowett, J.M.; Turner, S.; Month, M.
1986-01-01
These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI)
Quilty, J.; Adamowski, J. F.
2015-12-01
Urban water supply systems are often stressed during seasonal outdoor water use as water demands related to the climate are variable in nature making it difficult to optimize the operation of the water supply system. Urban water demand forecasts (UWD) failing to include meteorological conditions as inputs to the forecast model may produce poor forecasts as they cannot account for the increase/decrease in demand related to meteorological conditions. Meteorological records stochastically simulated into the future can be used as inputs to data-driven UWD forecasts generally resulting in improved forecast accuracy. This study aims to produce data-driven UWD forecasts for two different Canadian water utilities (Montreal and Victoria) using machine learning methods by first selecting historical UWD and meteorological records derived from a stochastic weather generator using nonlinear input variable selection. The nonlinear input variable selection methods considered in this work are derived from the concept of conditional mutual information, a nonlinear dependency measure based on (multivariate) probability density functions and accounts for relevancy, conditional relevancy, and redundancy from a potential set of input variables. The results of our study indicate that stochastic weather inputs can improve UWD forecast accuracy for the two sites considered in this work. Nonlinear input variable selection is suggested as a means to identify which meteorological conditions should be utilized in the forecast.
The genetic algorithm for the nonlinear programming of water pollution control system
Energy Technology Data Exchange (ETDEWEB)
Wei, J.; Zhang, J. [China University of Geosciences (China)
1999-08-01
In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.
International Nuclear Information System (INIS)
Doering, C.R.
1985-01-01
Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory
Alvarez, Diego A.; Hurtado, Jorge E.; Bedoya-Ruíz, Daniel Alveiro
2012-07-01
Despite technological advances in seismic instrumentation, the assessment of the intensity of an earthquake using an observational scale as given, for example, by the modified Mercalli intensity scale is highly useful for practical purposes. In order to link the qualitative numbers extracted from the acceleration record of an earthquake and other instrumental data such as peak ground velocity, epicentral distance, and moment magnitude on the one hand and the modified Mercalli intensity scale on the other, simple statistical regression has been generally employed. In this paper, we will employ three methods of nonlinear regression, namely support vector regression, multilayer perceptrons, and genetic programming in order to find a functional dependence between the instrumental records and the modified Mercalli intensity scale. The proposed methods predict the intensity of an earthquake while dealing with nonlinearity and the noise inherent to the data. The nonlinear regressions with good estimation results have been performed using the "Did You Feel It?" database of the US Geological Survey and the database of the Center for Engineering Strong Motion Data for the California region.
Nonlinear dynamics of rotating shallow water methods and advances
Zeitlin, Vladimir
2007-01-01
The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa
Statistics for long irregular wave run-up on a plane beach from direct numerical simulations
Didenkulova, Ira; Senichev, Dmitry; Dutykh, Denys
2017-04-01
Very often for global and transoceanic events, due to the initial wave transformation, refraction, diffraction and multiple reflections from coastal topography and underwater bathymetry, the tsunami approaches the beach as a very long wave train, which can be considered as an irregular wave field. The prediction of possible flooding and properties of the water flow on the coast in this case should be done statistically taking into account the formation of extreme (rogue) tsunami wave on a beach. When it comes to tsunami run-up on a beach, the most used mathematical model is the nonlinear shallow water model. For a beach of constant slope, the nonlinear shallow water equations have rigorous analytical solution, which substantially simplifies the mathematical formulation. In (Didenkulova et al. 2011) we used this solution to study statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. The influence of the wave nonlinearity was approached by considering modifications of probability distribution of the moving shoreline and its horizontal velocity for waves of different amplitudes. It was shown that wave nonlinearity did not affect the probability distribution of the velocity of the moving shoreline, while the vertical displacement of the moving shoreline was affected substantially demonstrating the longer duration of coastal floods with an increase in the wave nonlinearity. However, this analysis did not take into account the actual transformation of irregular wave field offshore to oscillations of the moving shoreline on a slopping beach. In this study we would like to cover this gap by means of extensive numerical simulations. The modeling is performed in the framework of nonlinear shallow water equations, which are solved using a modern shock-capturing finite volume method. Although the shallow water model does not pursue the wave breaking and bore formation in a general sense (including the water surface
Nonlinear response of tropical lower-stratospheric temperature and water vapor to ENSO
Directory of Open Access Journals (Sweden)
C. I. Garfinkel
2018-04-01
Full Text Available A series of simulations using the NASA Goddard Earth Observing System Chemistry–Climate Model are analyzed in order to aid in the interpretation of observed interannual and sub-decadal variability in the tropical lower stratosphere over the past 35 years. The impact of El Niño–Southern Oscillation on temperature and water vapor in this region is nonlinear in boreal spring. While moderate El Niño events lead to cooling in this region, strong El Niño events lead to warming, even as the response of the large-scale Brewer–Dobson circulation appears to scale nearly linearly with El Niño. This nonlinearity is shown to arise from the response in the Indo-West Pacific to El Niño: strong El Niño events lead to tropospheric warming extending into the tropical tropopause layer and up to the cold point in this region, where it allows for more water vapor to enter the stratosphere. The net effect is that both strong La Niña and strong El Niño events lead to enhanced entry water vapor and stratospheric moistening in boreal spring and early summer. These results lead to the following interpretation of the contribution of sea surface temperatures to the decline in water vapor in the early 2000s: the very strong El Niño event in 1997/1998, followed by more than 2 consecutive years of La Niña, led to enhanced lower-stratospheric water vapor. As this period ended in early 2001, entry water vapor concentrations declined. This effect accounts for approximately one-quarter of the observed drop.
Nonlinear response of tropical lower-stratospheric temperature and water vapor to ENSO
Garfinkel, Chaim I.; Gordon, Amit; Oman, Luke D.; Li, Feng; Davis, Sean; Pawson, Steven
2018-04-01
A series of simulations using the NASA Goddard Earth Observing System Chemistry-Climate Model are analyzed in order to aid in the interpretation of observed interannual and sub-decadal variability in the tropical lower stratosphere over the past 35 years. The impact of El Niño-Southern Oscillation on temperature and water vapor in this region is nonlinear in boreal spring. While moderate El Niño events lead to cooling in this region, strong El Niño events lead to warming, even as the response of the large-scale Brewer-Dobson circulation appears to scale nearly linearly with El Niño. This nonlinearity is shown to arise from the response in the Indo-West Pacific to El Niño: strong El Niño events lead to tropospheric warming extending into the tropical tropopause layer and up to the cold point in this region, where it allows for more water vapor to enter the stratosphere. The net effect is that both strong La Niña and strong El Niño events lead to enhanced entry water vapor and stratospheric moistening in boreal spring and early summer. These results lead to the following interpretation of the contribution of sea surface temperatures to the decline in water vapor in the early 2000s: the very strong El Niño event in 1997/1998, followed by more than 2 consecutive years of La Niña, led to enhanced lower-stratospheric water vapor. As this period ended in early 2001, entry water vapor concentrations declined. This effect accounts for approximately one-quarter of the observed drop.
Statistical study of the non-linear propagation of a partially coherent laser beam
International Nuclear Information System (INIS)
Ayanides, J.P.
2001-01-01
This research thesis is related to the LMJ project (Laser MegaJoule) and thus to the study and development of thermonuclear fusion. It reports the study of the propagation of a partially-coherent laser beam by using a statistical modelling in order to obtain mean values for the field, and thus bypassing a complex and costly calculation of deterministic quantities. Random fluctuations of the propagated field are supposed to comply with a Gaussian statistics; the laser central wavelength is supposed to be small with respect with fluctuation magnitude; a scale factor is introduced to clearly distinguish the scale of the random and fast variations of the field fluctuations, and the scale of the slow deterministic variations of the field envelopes. The author reports the study of propagation through a purely linear media and through a non-dispersive media, and then through slow non-dispersive and non-linear media (in which the reaction time is large with respect to grain correlation duration, but small with respect to the variation scale of the field macroscopic envelope), and thirdly through an instantaneous dispersive and non linear media (which instantaneously reacts to the field) [fr
Nonlinear dynamics aspects of particle accelerators. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Jowett, J M; Turner, S; Month, M
1986-01-01
These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI).
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
Energy Technology Data Exchange (ETDEWEB)
Jiménez, N.; Picó, R. [Instituto de Investigación para la Gestión Integrada de zonas Costeras, Universitat Politècnica de València, Paranimf 1, 46730 Grao de Gandia, València (Spain); Romero-García, V. [LUNAM Université, Université du Maine, LAUM UMR CNRS 6613, Av. O. Messiaen, 72085 Le Mans (France); Garcia-Raffi, L. M. [Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València (Spain); Staliunas, K. [ICREA, Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom, 11, E-08222 Terrassa, Barcelona (Spain)
2015-11-16
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
Classifying hot water chemistry: Application of MULTIVARIATE STATISTICS
Sumintadireja, Prihadi; Irawan, Dasapta Erwin; Rezky, Yuanno; Gio, Prana Ugiana; Agustin, Anggita
2016-01-01
This file is the dataset for the following paper "Classifying hot water chemistry: Application of MULTIVARIATE STATISTICS". Authors: Prihadi Sumintadireja1, Dasapta Erwin Irawan1, Yuano Rezky2, Prana Ugiana Gio3, Anggita Agustin1
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
Two statistical approaches, weighted regression on time, discharge, and season and generalized additive models, have recently been used to evaluate water quality trends in estuaries. Both models have been used in similar contexts despite differences in statistical foundations and...
Nonlinear analysis of gas-water/oil-water two-phase flow in complex networks
Gao, Zhong-Ke; Wang, Wen-Xu
2014-01-01
Understanding the dynamics of multi-phase flows has been a challenge in the fields of nonlinear dynamics and fluid mechanics. This chapter reviews our work on two-phase flow dynamics in combination with complex network theory. We systematically carried out gas-water/oil-water two-phase flow experiments for measuring the time series of flow signals which is studied in terms of the mapping from time series to complex networks. Three network mapping methods were proposed for the analysis and identification of flow patterns, i.e. Flow Pattern Complex Network (FPCN), Fluid Dynamic Complex Network (FDCN) and Fluid Structure Complex Network (FSCN). Through detecting the community structure of FPCN based on K-means clustering, distinct flow patterns can be successfully distinguished and identified. A number of FDCN’s under different flow conditions were constructed in order to reveal the dynamical characteristics of two-phase flows. The FDCNs exhibit universal power-law degree distributions. The power-law exponent ...
Directory of Open Access Journals (Sweden)
T. Hayat
2018-03-01
Full Text Available Here modeling and computations are presented to introduce the novel concept of Darcy-Forchheimer three-dimensional flow of water-based carbon nanotubes with nonlinear thermal radiation and heat generation/absorption. Bidirectional stretching surface induces the flow. Darcy’s law is commonly replace by Forchheimer relation. Xue model is implemented for nonliquid transport mechanism. Nonlinear formulation based upon conservation laws of mass, momentum and energy is first modeled and then solved by optimal homotopy analysis technique. Optimal estimations of auxiliary variables are obtained. Importance of influential variables on the velocity and thermal fields is interpreted graphically. Moreover velocity and temperature gradients are discussed and analyzed. Physical interpretation of influential variables is examined. Keywords: Porous medium, Heat generation/absorption, SWCNTs and MWCNTs, Nonlinear radiation
2013-01-01
This book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores. The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical s
Uhlemann, C.; Feix, M.; Codis, S.; Pichon, C.; Bernardeau, F.; L'Huillier, B.; Kim, J.; Hong, S. E.; Laigle, C.; Park, C.; Shin, J.; Pogosyan, D.
2018-02-01
Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model to relate the log-densities of dark matter to those of mass-weighted dark haloes in real and redshift space. The validity of the parametrized bias model is established using a parametrization-independent extraction of the bias function. This average bias model is then combined with the dark matter PDF, neglecting any scatter around it: it nevertheless yields an excellent model for densities-in-cells statistics of mass tracers that is parametrized in terms of the underlying dark matter variance and three bias parameters. The procedure is validated on measurements of both the one- and two-point statistics of subhalo densities in the state-of-the-art Horizon Run 4 simulation showing excellent agreement for measured dark matter variance and bias parameters. Finally, it is demonstrated that this formalism allows for a joint estimation of the non-linear dark matter variance and the bias parameters using solely the statistics of subhaloes. Having verified that galaxy counts in hydrodynamical simulations sampled on a scale of 10 Mpc h-1 closely resemble those of subhaloes, this work provides important steps towards making theoretical predictions for density-in-cells statistics applicable to upcoming galaxy surveys like Euclid or WFIRST.
Sokolov, Alexei V; Naveira, Lucas M; Poudel, Milan P; Strohaber, James; Trendafilova, Cynthia S; Buck, William C; Wang, Jieyu; Strycker, Benjamin D; Wang, Chao; Schuessler, Hans; Kolomenskii, Alexandre; Kattawar, George W
2010-01-20
We study propagation of short laser pulses through water and use a spectral hole filling technique to essentially perform a sensitive balanced comparison of absorption coefficients for pulses of different duration. This study is motivated by an alleged violation of the Bouguer-Lambert-Beer law at low light intensities, where the pulse propagation is expected to be linear, and by a possible observation of femtosecond optical precursors in water. We find that at low intensities, absorption of laser light is determined solely by its spectrum and does not directly depend on the pulse duration, in agreement with our earlier work and in contradiction to some work of others. However, as the laser fluence is increased, interaction of light with water becomes nonlinear, causing energy exchange among the pulse's spectral components and resulting in peak-intensity dependent (and therefore pulse-duration dependent) transmission. For 30 fs pulses at 800 nm center wavelength, we determine the onset of nonlinear propagation effects to occur at a peak value of about 0.12 mJ/cm(2) of input laser energy fluence.
Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping
2018-01-01
An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.
Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.
Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland
2013-05-10
We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Diamond, Jared M.
1966-01-01
1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254
Hein, H.; Mai, S.; Mayer, B.; Pohlmann, T.; Barjenbruch, U.
2012-04-01
The interactions of tides, external surges, storm surges and waves with an additional role of the coastal bathymetry define the probability of extreme water levels at the coast. Probabilistic analysis and also process based numerical models allow the estimation of future states. From the physical point of view both, deterministic processes and stochastic residuals are the fundamentals of high water statistics. This study uses a so called model chain to reproduce historic statistics of tidal high water levels (Thw) as well as the prediction of future statistics high water levels. The results of the numerical models are post-processed by a stochastic analysis. Recent studies show, that for future extrapolation of extreme Thw nonstationary parametric approaches are required. With the presented methods a better prediction of time depended parameter sets seems possible. The investigation region of this study is the southern German Bright. The model-chain is the representation of a downscaling process, which starts with an emissions scenario. Regional atmospheric and ocean models refine the results of global climate models. The concept of downscaling was chosen to resolve coastal topography sufficiently. The North Sea and estuaries are modeled with the three-dimensional model HAMburg Shelf Ocean Model. The running time includes 150 years (1950 - 2100). Results of four different hindcast runs and also of one future prediction run are validated. Based on multi-scale analysis and the theory of entropy we analyze whether any significant periodicities are represented numerically. Results show that also hindcasting the climate of Thw with a model chain for the last 60 years is a challenging task. For example, an additional modeling activity must be the inclusion of tides into regional climate ocean models. It is found that the statistics of climate variables derived from model results differs from the statistics derived from measurements. E.g. there are considerable shifts in
Janssen, T.T.; Herbers, T.H.C.; Battjes, J.A.
2008-01-01
We present a stochastic model for the evolution of random ocean surface waves in coastal waters with complex seafloor topography. First, we derive a deterministic coupled-mode model based on a forward scattering approximation of the nonlinear mild slope equation; this model describes the evolution
Nonlinear dynamics and stability of boiling water reactors: qualitative and quantitative analyses
International Nuclear Information System (INIS)
March-Leuba, J.; Cacuci, D.G.; Perez, R.B.
1985-01-01
A phenomenological model has been developed to simulate the qualitative behavior of boiling water reactors (BWRs) in the nonlinear regime under deterministic and stochastic excitations. After the linear stability threshold is crossed, limit cycle oscillations appear due to interactions between two unstable equilibrium points and the phase-space trajectories. This limit cycle becomes unstable when the feedback gain exceeds a certain critical value. Subsequent limit cycle instabilities produce a cascade of period-doubling bifurcations that leads to a periodic pulsed behavior. Under stochastic excitations, BWRs exhibit a single characteristic resonance, at approx.0.5 Hz, in the linear regime. By contrast, this work shows that harmonics of this characteristic frequency appear in the nonlinear regime. Furthermore, this work also demonstrates that amplitudes of the limit cycle oscillations do not depend on the variance of the stochastic excitation and remain bounded at all times. A physical model of nonlinear BWR dynamics has also been developed and employed to calculate the amplitude of limit cycle oscillations and their effects on fuel integrity over a wide range of operating conditions in the Vermont Yankee reactor. These calculations have confirmed that, beyond the threshold for linear stability, the reactor's state variable undergo limit cycle oscillations
Analysis of efficient preconditioned defect correction methods for nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2014-01-01
Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow...... equations. We present new detailed fundamental analysis using finite-amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high-order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow...
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
International Nuclear Information System (INIS)
Cui Weiguang; Zhang Pengjie; Yang Xiaohu
2010-01-01
A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter ζ, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (ζ=1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < or approx. 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < or approx. 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance of including the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size, and initial redshift). We find that, the nonlinear power spectra can differ by ∼30% for 10% deviation from GR (|ζ-1|=0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.
Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.; Zaigham Zia, Q. M.
2018-03-01
Here modeling and computations are presented to introduce the novel concept of Darcy-Forchheimer three-dimensional flow of water-based carbon nanotubes with nonlinear thermal radiation and heat generation/absorption. Bidirectional stretching surface induces the flow. Darcy's law is commonly replace by Forchheimer relation. Xue model is implemented for nonliquid transport mechanism. Nonlinear formulation based upon conservation laws of mass, momentum and energy is first modeled and then solved by optimal homotopy analysis technique. Optimal estimations of auxiliary variables are obtained. Importance of influential variables on the velocity and thermal fields is interpreted graphically. Moreover velocity and temperature gradients are discussed and analyzed. Physical interpretation of influential variables is examined.
Cameron, Enrico; Pilla, Giorgio; Stella, Fabio A.
2018-01-01
The application of statistical classification methods is investigated—in comparison also to spatial interpolation methods—for predicting the acceptability of well-water quality in a situation where an effective quantitative model of the hydrogeological system under consideration cannot be developed. In the example area in northern Italy, in particular, the aquifer is locally affected by saline water and the concentration of chloride is the main indicator of both saltwater occurrence and groundwater quality. The goal is to predict if the chloride concentration in a water well will exceed the allowable concentration so that the water is unfit for the intended use. A statistical classification algorithm achieved the best predictive performances and the results of the study show that statistical classification methods provide further tools for dealing with groundwater quality problems concerning hydrogeological systems that are too difficult to describe analytically or to simulate effectively.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Single-step emulation of nonlinear fiber-optic link with gaussian mixture model
DEFF Research Database (Denmark)
Borkowski, Robert; Doberstein, Andy; Haisch, Hansjörg
2015-01-01
We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission.......We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission....
Energy Technology Data Exchange (ETDEWEB)
Chandra, J; Scott, A C
1983-01-01
Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.
Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition
Kwon, H.; Khalil, A.; Brown, C.; Lall, U.; Ahn, H.; Moon, Y.
2005-12-01
Traditionally forecasting and characterizations of hydrologic systems is performed utilizing many techniques. Stochastic linear methods such as AR and ARIMA and nonlinear ones such as statistical learning theory based tools have been extensively used. The common difficulty to all methods is the determination of sufficient and necessary information and predictors for a successful prediction. Relationships between hydrologic variables are often highly nonlinear and interrelated across the temporal scale. A new hybrid approach is proposed for the simulation of hydrologic time series combining both the wavelet transform and the nonlinear model. The present model employs some merits of wavelet transform and nonlinear time series model. The Wavelet Transform is adopted to decompose a hydrologic nonlinear process into a set of mono-component signals, which are simulated by nonlinear model. The hybrid methodology is formulated in a manner to improve the accuracy of a long term forecasting. The proposed hybrid model yields much better results in terms of capturing and reproducing the time-frequency properties of the system at hand. Prediction results are promising when compared to traditional univariate time series models. An application of the plausibility of the proposed methodology is provided and the results conclude that wavelet based time series model can be utilized for simulating and forecasting of hydrologic variable reasonably well. This will ultimately serve the purpose of integrated water resources planning and management.
A statistical approach for water movement in the unsaturated zone
International Nuclear Information System (INIS)
Tielin Zang.
1991-01-01
This thesis presents a statistical approach for estimating and analyzing the downward transport pattern and distribution of soil water by the use of pattern analysis of space-time correlation structures. This approach, called the Space-time-Correlation Field, is mainly based on the analyses of correlation functions simultaneously in the space and time domain. The overall purpose of this work is to derive an alternative statistical procedure in soil moisture analysis without involving detailed information on hydraulic parameters and to visualize the dynamics of soil water variability in the space and time domains. A numerical model using method of characteristics is employed to provide hypothetical time series to use in the statistical method, which is, after the verification and calibration, applied to the field measured time series. The results of the application show that the space-time correlation fields reveal effects of soil layers with different hydraulic properties and boundaries between them. It is concluded that the approach poses special advantages when visualizing time and space dependent properties simultaneously. It can be used to investigate the hydrological response of soil water dynamics and characteristics in different dimensions (space and time) and scales. This approach can be used to identify the dominant component in unsaturated flow systems. It is possible to estimate the pattern and the propagation rate downwards of moisture movement in the soil profile. Small-scale soil heterogeneities can be identified by the correlation field. Since the correlation field technique give a statistical measure of the dependent property that varies within the space-time field, it is possible to interpolate the fields to points where observations are not available, estimating spatial or temporal averages from discrete observations. (au)
Nonlinear analysis of pupillary dynamics.
Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo
2016-02-01
Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (pnonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.
Directory of Open Access Journals (Sweden)
S. Mirzaee
2016-02-01
Full Text Available Introduction: The infiltration process is one of the most important components of the hydrologic cycle. Quantifying the infiltration water into soil is of great importance in watershed management. Prediction of flooding, erosion and pollutant transport all depends on the rate of runoff which is directly affected by the rate of infiltration. Quantification of infiltration water into soil is also necessary to determine the availability of water for crop growth and to estimate the amount of additional water needed for irrigation. Thus, an accurate model is required to estimate infiltration of water into soil. The ability of physical and empirical models in simulation of soil processes is commonly measured through comparisons of simulated and observed values. For these reasons, a large variety of indices have been proposed and used over the years in comparison of infiltration water into soil models. Among the proposed indices, some are absolute criteria such as the widely used root mean square error (RMSE, while others are relative criteria (i.e. normalized such as the Nash and Sutcliffe (1970 efficiency criterion (NSE. Selecting and using appropriate statistical criteria to evaluate and interpretation of the results for infiltration water into soil models is essential because each of the used criteria focus on specific types of errors. Also, descriptions of various goodness of fit indices or indicators including their advantages and shortcomings, and rigorous discussions on the suitability of each index are very important. The objective of this study is to compare the goodness of different statistical criteria to evaluate infiltration of water into soil models. Comparison techniques were considered to define the best models: coefficient of determination (R2, root mean square error (RMSE, efficiency criteria (NSEI and modified forms (such as NSEjI, NSESQRTI, NSElnI and NSEiI. Comparatively little work has been carried out on the meaning and
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 64; Issue 3 ... Keywords. Nonlinear dynamics; logistic map; -deformation; Tsallis statistics. ... As a specific example, a -deformation procedure is applied to the logistic map. Compared ...
Statistical distributions of earthquakes and related non-linear features in seismic waves
International Nuclear Information System (INIS)
Apostol, B.-F.
2006-01-01
A few basic facts in the science of the earthquakes are briefly reviewed. An accumulation, or growth, model is put forward for the focal mechanisms and the critical focal zone of the earthquakes, which relates the earthquake average recurrence time to the released seismic energy. The temporal statistical distribution for average recurrence time is introduced for earthquakes, and, on this basis, the Omori-type distribution in energy is derived, as well as the distribution in magnitude, by making use of the semi-empirical Gutenberg-Richter law relating seismic energy to earthquake magnitude. On geometric grounds, the accumulation model suggests the value r = 1/3 for the Omori parameter in the power-law of energy distribution, which leads to β = 1,17 for the coefficient in the Gutenberg-Richter recurrence law, in fair agreement with the statistical analysis of the empirical data. Making use of this value, the empirical Bath's law is discussed for the average magnitude of the aftershocks (which is 1.2 less than the magnitude of the main seismic shock), by assuming that the aftershocks are relaxation events of the seismic zone. The time distribution of the earthquakes with a fixed average recurrence time is also derived, the earthquake occurrence prediction is discussed by means of the average recurrence time and the seismicity rate, and application of this discussion to the seismic region Vrancea, Romania, is outlined. Finally, a special effect of non-linear behaviour of the seismic waves is discussed, by describing an exact solution derived recently for the elastic waves equation with cubic anharmonicities, its relevance, and its connection to the approximate quasi-plane waves picture. The properties of the seismic activity accompanying a main seismic shock, both like foreshocks and aftershocks, are relegated to forthcoming publications. (author)
Hydration, phase separation and nonlinear rheology of temperature-sensitive water-soluble polymers
Energy Technology Data Exchange (ETDEWEB)
Tanaka, Fumihiko; Koga, Tsuyoshi [Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510 (Japan); Kaneda, Isamu [Department of Food Science, Rakuno Gakuen University, Ebetsu, Hokkaido 069-8501 (Japan); Winnik, Francoise M, E-mail: ftanaka@phys.polym.kyoto-u.ac.jp [Department of Chemistry and Faculty of Pharmacy, University of Montreal, Montreal, H3C 3J7 (Canada)
2011-07-20
The collapse of a poly(N-isopropylacrylamide) (PNIPAM) chain upon heating and the phase diagrams of aqueous PNIPAM solutions with a very flat lower critical solution temperature (LCST) phase separation line are theoretically studied on the basis of cooperative dehydration (simultaneous dissociation of bound water molecules in a group of correlated sequence), and compared with the experimental observation of temperature-induced coil-globule transition by light scattering methods. The transition becomes sharper with the cooperativity parameter {sigma} of hydration. The reentrant coil-globule-coil transition and cononsolvency in a mixed solvent of water and methanol are also studied from the viewpoint of competitive hydrogen bonds between polymer-water and polymer-methanol. The downward shift of the cloud-point curves (LCST cononsolvency) with the mol fraction of methanol due to the competition is calculated and compared with the experimental data. Aqueous solutions of hydrophobically modified PNIPAM carrying short alkyl chains at both chain ends (telechelic PNIPAM) are theoretically and experimentally studied. The LCST of these solutions is found to shift downward along the sol-gel transition curve as a result of end-chain association (association-induced phase separation), and separate from the coil-globule transition line. Associated structures in the solution, such as flower micelles, mesoglobules, and higher fractal assembly, are studied by ultra small-angle neutron scattering with theoretical modeling of the scattering function. Dynamic-mechanical modulus, nonlinear stationary viscosity, and stress build-up in start-up shear flows of the associated networks are studied on the basis of the affine and non-affine transient network theory. The molecular conditions for thickening, strain hardening, and stress overshoot are found in terms of the nonlinear amplitude A of the chain tension and the tension-dissociation coupling constant g.
Mueller, Amy V; Hemond, Harold F
2016-05-18
Knowledge of ionic concentrations in natural waters is essential to understand watershed processes. Inorganic nitrogen, in the form of nitrate and ammonium ions, is a key nutrient as well as a participant in redox, acid-base, and photochemical processes of natural waters, leading to spatiotemporal patterns of ion concentrations at scales as small as meters or hours. Current options for measurement in situ are costly, relying primarily on instruments adapted from laboratory methods (e.g., colorimetric, UV absorption); free-standing and inexpensive ISE sensors for NO3(-) and NH4(+) could be attractive alternatives if interferences from other constituents were overcome. Multi-sensor arrays, coupled with appropriate non-linear signal processing, offer promise in this capacity but have not yet successfully achieved signal separation for NO3(-) and NH4(+)in situ at naturally occurring levels in unprocessed water samples. A novel signal processor, underpinned by an appropriate sensor array, is proposed that overcomes previous limitations by explicitly integrating basic chemical constraints (e.g., charge balance). This work further presents a rationalized process for the development of such in situ instrumentation for NO3(-) and NH4(+), including a statistical-modeling strategy for instrument design, training/calibration, and validation. Statistical analysis reveals that historical concentrations of major ionic constituents in natural waters across New England strongly covary and are multi-modal. This informs the design of a statistically appropriate training set, suggesting that the strong covariance of constituents across environmental samples can be exploited through appropriate signal processing mechanisms to further improve estimates of minor constituents. Two artificial neural network architectures, one expanded to incorporate knowledge of basic chemical constraints, were tested to process outputs of a multi-sensor array, trained using datasets of varying degrees of
Statistical models for the analysis of water distribution system pipe break data
International Nuclear Information System (INIS)
Yamijala, Shridhar; Guikema, Seth D.; Brumbelow, Kelly
2009-01-01
The deterioration of pipes leading to pipe breaks and leaks in urban water distribution systems is of concern to water utilities throughout the world. Pipe breaks and leaks may result in reduction in the water-carrying capacity of the pipes and contamination of water in the distribution systems. Water utilities incur large expenses in the replacement and rehabilitation of water mains, making it critical to evaluate the current and future condition of the system for maintenance decision-making. This paper compares different statistical regression models proposed in the literature for estimating the reliability of pipes in a water distribution system on the basis of short time histories. The goals of these models are to estimate the likelihood of pipe breaks in the future and determine the parameters that most affect the likelihood of pipe breaks. The data set used for the analysis comes from a major US city, and these data include approximately 85,000 pipe segments with nearly 2500 breaks from 2000 through 2005. The results show that the set of statistical models previously proposed for this problem do not provide good estimates with the test data set. However, logistic generalized linear models do provide good estimates of pipe reliability and can be useful for water utilities in planning pipe inspection and maintenance
Nonlinearity and disorder: Theory and applications
DEFF Research Database (Denmark)
Bang, Ole; Sørensen, Mads Peter
Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...... of the photorefractive solitons. Another very fast growing area induced by the technological development is statistical phenomena in nonlinear pulse propagation in optical fibers. Intrinsic randomness of existing optical communication systems has an important impact on the performance of planned soliton communication...
Predicting long-term catchment nutrient export: the use of nonlinear time series models
Valent, Peter; Howden, Nicholas J. K.; Szolgay, Jan; Komornikova, Magda
2010-05-01
After the Second World War the nitrate concentrations in European water bodies changed significantly as the result of increased nitrogen fertilizer use and changes in land use. However, in the last decades, as a consequence of the implementation of nitrate-reducing measures in Europe, the nitrate concentrations in water bodies slowly decrease. This causes that the mean and variance of the observed time series also changes with time (nonstationarity and heteroscedascity). In order to detect changes and properly describe the behaviour of such time series by time series analysis, linear models (such as autoregressive (AR), moving average (MA) and autoregressive moving average models (ARMA)), are no more suitable. Time series with sudden changes in statistical characteristics can cause various problems in the calibration of traditional water quality models and thus give biased predictions. Proper statistical analysis of these non-stationary and heteroscedastic time series with the aim of detecting and subsequently explaining the variations in their statistical characteristics requires the use of nonlinear time series models. This information can be then used to improve the model building and calibration of conceptual water quality model or to select right calibration periods in order to produce reliable predictions. The objective of this contribution is to analyze two long time series of nitrate concentrations of the rivers Ouse and Stour with advanced nonlinear statistical modelling techniques and compare their performance with traditional linear models of the ARMA class in order to identify changes in the time series characteristics. The time series were analysed with nonlinear models with multiple regimes represented by self-exciting threshold autoregressive (SETAR) and Markov-switching models (MSW). The analysis showed that, based on the value of residual sum of squares (RSS) in both datasets, SETAR and MSW models described the time-series better than models of the
Physics constrained nonlinear regression models for time series
International Nuclear Information System (INIS)
Majda, Andrew J; Harlim, John
2013-01-01
A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)
New methods of testing nonlinear hypothesis using iterative NLLS estimator
Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.
2017-11-01
This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Detecting nonlinear structure in time series
International Nuclear Information System (INIS)
Theiler, J.
1991-01-01
We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of ''surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs
International Nuclear Information System (INIS)
Egerton, B.; Barnett, S.; Vella, G.
1994-01-01
Diagnostic ultrasound is an established imaging modality without any documented harmful effects. New developments such as pulsed Doppler and intracavity investigations may result in increases in ultrasound exposures which could cause harm. Thermal mechanisms and cavitation may become relevant sources of bioeffects. The preliminary study described here investigates the distribution and amplitude of harmonics generated through nonlinear propagation of ultrasound in water. Knowledge of harmonic attenuation will help predict sites of enhanced heating and enable accurate modelling of clinical situations. This presentation is concerned with thermal safety guidelines, their relationship to a typical ultrasound beam profile for a single, medium focussed, transducer operating in water and possible sites of enhanced heating due to nonlinear propagation effects. Measurements were made of the amplitudes of the harmonics generated by the nonlinear propagation of ultrasound in water. The amplitudes of the harmonics were detected up to frequencies of 35 MHz and displayed using Fast Fourier Transform facilities within the oscilloscope. The nonlinearity parameter of the ultrasonic waveforms has been identified as an important factor in thermal effects of ultrasound interactions. The appearance of nonlinear distortion is shown to be dependant on the peak compressional pressure and distance from the ultrasound source. 20 refs., 2 figs
Non-linear time series extreme events and integer value problems
Turkman, Kamil Feridun; Zea Bermudez, Patrícia
2014-01-01
This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time ...
Multivariate Statistical Analysis of Water Quality data in Indian River Lagoon, Florida
Sayemuzzaman, M.; Ye, M.
2015-12-01
The Indian River Lagoon, is part of the longest barrier island complex in the United States, is a region of particular concern to the environmental scientist because of the rapid rate of human development throughout the region and the geographical position in between the colder temperate zone and warmer sub-tropical zone. Thus, the surface water quality analysis in this region always brings the newer information. In this present study, multivariate statistical procedures were applied to analyze the spatial and temporal water quality in the Indian River Lagoon over the period 1998-2013. Twelve parameters have been analyzed on twelve key water monitoring stations in and beside the lagoon on monthly datasets (total of 27,648 observations). The dataset was treated using cluster analysis (CA), principle component analysis (PCA) and non-parametric trend analysis. The CA was used to cluster twelve monitoring stations into four groups, with stations on the similar surrounding characteristics being in the same group. The PCA was then applied to the similar groups to find the important water quality parameters. The principal components (PCs), PC1 to PC5 was considered based on the explained cumulative variances 75% to 85% in each cluster groups. Nutrient species (phosphorus and nitrogen), salinity, specific conductivity and erosion factors (TSS, Turbidity) were major variables involved in the construction of the PCs. Statistical significant positive or negative trends and the abrupt trend shift were detected applying Mann-Kendall trend test and Sequential Mann-Kendall (SQMK), for each individual stations for the important water quality parameters. Land use land cover change pattern, local anthropogenic activities and extreme climate such as drought might be associated with these trends. This study presents the multivariate statistical assessment in order to get better information about the quality of surface water. Thus, effective pollution control/management of the surface
Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.
Deng, Xiaogang; Tian, Xuemin; Chen, Sheng; Harris, Chris J
2018-03-01
Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.
The Nonlinear Statistics of High-contrast Patches in Natural Images
DEFF Research Database (Denmark)
Lee, Ann; Pedersen, Kim Steenstrup; Mumford, David
2003-01-01
described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely sparse with the majority of the data points concentrated in clusters and non-linear low...
Statistical inference for noisy nonlinear ecological dynamic systems.
Wood, Simon N
2010-08-26
Chaotic ecological dynamic systems defy conventional statistical analysis. Systems with near-chaotic dynamics are little better. Such systems are almost invariably driven by endogenous dynamic processes plus demographic and environmental process noise, and are only observable with error. Their sensitivity to history means that minute changes in the driving noise realization, or the system parameters, will cause drastic changes in the system trajectory. This sensitivity is inherited and amplified by the joint probability density of the observable data and the process noise, rendering it useless as the basis for obtaining measures of statistical fit. Because the joint density is the basis for the fit measures used by all conventional statistical methods, this is a major theoretical shortcoming. The inability to make well-founded statistical inferences about biological dynamic models in the chaotic and near-chaotic regimes, other than on an ad hoc basis, leaves dynamic theory without the methods of quantitative validation that are essential tools in the rest of biological science. Here I show that this impasse can be resolved in a simple and general manner, using a method that requires only the ability to simulate the observed data on a system from the dynamic model about which inferences are required. The raw data series are reduced to phase-insensitive summary statistics, quantifying local dynamic structure and the distribution of observations. Simulation is used to obtain the mean and the covariance matrix of the statistics, given model parameters, allowing the construction of a 'synthetic likelihood' that assesses model fit. This likelihood can be explored using a straightforward Markov chain Monte Carlo sampler, but one further post-processing step returns pure likelihood-based inference. I apply the method to establish the dynamic nature of the fluctuations in Nicholson's classic blowfly experiments.
Crucifix, Michel; Wilkinson, Richard; Carson, Jake; Preston, Simon; Alemeida, Carlos; Rougier, Jonathan
2013-04-01
The existence of an action of astronomical forcing on the Pleistocene climate is almost undisputed. However, quantifying this action is not straightforward. In particular, the phenomenon of deglaciation is generally interpreted as a manifestation of instability, which is typical of non-linear systems. As a consequence, explaining the Pleistocene climate record as the addition of an astronomical contribution and noise-as often done using harmonic analysis tools-is potentially deceptive. Rather, we advocate a methodology in which non-linear stochastic dynamical systems are calibrated on the Pleistocene climate record. The exercise, though, requires careful statistical reasoning and state-of-the-art techniques. In fact, the problem has been judged to be mathematically 'intractable and unsolved' and some pragmatism is justified. In order to illustrate the methodology we consider one dynamical system that potentially captures four dynamical features of the Pleistocene climate : the existence of a saddle-node bifurcation in at least one of its slow components, a time-scale separation between a slow and a fast component, the action of astronomical forcing, and the existence a stochastic contribution to the system dynamics. This model is obviously not the only possible representation of Pleistocene dynamics, but it encapsulates well enough both our theoretical and empirical knowledge into a very simple form to constitute a valid starting point. The purpose of this poster is to outline the practical challenges in calibrating such a model on paleoclimate observations. Just as in time series analysis, there is no one single and universal test or criteria that would demonstrate the validity of an approach. Several methods exist to calibrate the model and judgement develops by the confrontation of the results of the different methods. In particular, we consider here the Kalman filter variants, the Particle Monte-Carlo Markov Chain, and two other variants of Sequential Monte
Statistical mechanics of nonequilibrium liquids
Evans, Denis J; Craig, D P; McWeeny, R
1990-01-01
Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory. In discussing the framework of nonequilibrium statistical mechanics, the book explains the derivation of a nonequilibrium analogue of the Gibbsian basis for equilibrium statistical mechanics. The book reviews the linear irreversible thermodynamics, the Liouville equation, and the Irving-Kirkwood procedure. The text then explains the Green-Kubo relations used in linear transport coefficients, the linear response theory,
Hacker, Joshua; Vandenberghe, Francois; Jung, Byoung-Jo; Snyder, Chris
2017-04-01
Effective assimilation of cloud-affected radiance observations from space-borne imagers, with the aim of improving cloud analysis and forecasting, has proven to be difficult. Large observation biases, nonlinear observation operators, and non-Gaussian innovation statistics present many challenges. Ensemble-variational data assimilation (EnVar) systems offer the benefits of flow-dependent background error statistics from an ensemble, and the ability of variational minimization to handle nonlinearity. The specific benefits of ensemble statistics, relative to static background errors more commonly used in variational systems, have not been quantified for the problem of assimilating cloudy radiances. A simple experiment framework is constructed with a regional NWP model and operational variational data assimilation system, to provide the basis understanding the importance of ensemble statistics in cloudy radiance assimilation. Restricting the observations to those corresponding to clouds in the background forecast leads to innovations that are more Gaussian. The number of large innovations is reduced compared to the more general case of all observations, but not eliminated. The Huber norm is investigated to handle the fat tails of the distributions, and allow more observations to be assimilated without the need for strict background checks that eliminate them. Comparing assimilation using only ensemble background error statistics with assimilation using only static background error statistics elucidates the importance of the ensemble statistics. Although the cost functions in both experiments converge to similar values after sufficient outer-loop iterations, the resulting cloud water, ice, and snow content are greater in the ensemble-based analysis. The subsequent forecasts from the ensemble-based analysis also retain more condensed water species, indicating that the local environment is more supportive of clouds. In this presentation we provide details that explain the
Spatiotemporal drought forecasting using nonlinear models
Vasiliades, Lampros; Loukas, Athanasios
2010-05-01
Spatiotemporal data mining is the extraction of unknown and implicit knowledge, structures, spatiotemporal relationships, or patterns not explicitly stored in spatiotemporal databases. As one of data mining techniques, forecasting is widely used to predict the unknown future based upon the patterns hidden in the current and past data. In order to achieve spatiotemporal forecasting, some mature analysis tools, e.g., time series and spatial statistics are extended to the spatial dimension and the temporal dimension, respectively. Drought forecasting plays an important role in the planning and management of natural resources and water resource systems in a river basin. Early and timelines forecasting of a drought event can help to take proactive measures and set out drought mitigation strategies to alleviate the impacts of drought. Despite the widespread application of nonlinear mathematical models, comparative studies on spatiotemporal drought forecasting using different models are still a huge task for modellers. This study uses a promising approach, the Gamma Test (GT), to select the input variables and the training data length, so that the trial and error workload could be greatly reduced. The GT enables to quickly evaluate and estimate the best mean squared error that can be achieved by a smooth model on any unseen data for a given selection of inputs, prior to model construction. The GT is applied to forecast droughts using monthly Standardized Precipitation Index (SPI) timeseries at multiple timescales in several precipitation stations at Pinios river basin in Thessaly region, Greece. Several nonlinear models have been developed efficiently, with the aid of the GT, for 1-month up to 12-month ahead forecasting. Several temporal and spatial statistical indices were considered for the performance evaluation of the models. The predicted results show reasonably good agreement with the actual data for short lead times, whereas the forecasting accuracy decreases with
A Fast GPU-accelerated Mixed-precision Strategy for Fully NonlinearWater Wave Computations
DEFF Research Database (Denmark)
Glimberg, Stefan Lemvig; Engsig-Karup, Allan Peter; Madsen, Morten G.
2011-01-01
We present performance results of a mixed-precision strategy developed to improve a recently developed massively parallel GPU-accelerated tool for fast and scalable simulation of unsteady fully nonlinear free surface water waves over uneven depths (Engsig-Karup et.al. 2011). The underlying wave......-preconditioned defect correction method. The improved strategy improves the performance by exploiting architectural features of modern GPUs for mixed precision computations and is tested in a recently developed generic library for fast prototyping of PDE solvers. The new wave tool is applicable to solve and analyze...
An introduction to complex systems society, ecology, and nonlinear dynamics
Fieguth, Paul
2017-01-01
This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or per...
A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves
Directory of Open Access Journals (Sweden)
Justin R. Davis
2014-02-01
Full Text Available We describe the numerical implementation of a phase-resolving, nonlinear spectral model for shoaling directional waves over a mild sloping beach with straight parallel isobaths. The model accounts for non-linear, quadratic (triad wave interactions as well as shoaling and refraction. The model integrates the coupled, nonlinear hyperbolic evolution equations that describe the transformation of the complex Fourier amplitudes of the deep-water directional wave field. Because typical directional wave spectra (observed or produced by deep-water forecasting models such as WAVEWATCH III™ do not contain phase information, individual realizations are generated by associating a random phase to each Fourier mode. The approach provides a natural extension to the deep-water spectral wave models, and has the advantage of fully describing the shoaling wave stochastic process, i.e., the evolution of both the variance and higher order statistics (phase correlations, the latter related to the evolution of the wave shape. The numerical implementation (a Fortran 95/2003 code includes unidirectional (shore-perpendicular propagation as a special case. Interoperability, both with post-processing programs (e.g., MATLAB/Tecplot 360 and future model coupling (e.g., offshore wave conditions from WAVEWATCH III™, is promoted by using NetCDF-4/HD5 formatted output files. The capabilities of the model are demonstrated using a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation. The simulated wave transformation under combined shoaling, refraction and nonlinear interactions shows the expected generation of directional harmonics of the spectral peak and of infragravity (frequency <0.05 Hz waves. Current development efforts focus on analytic testing, development of additional physics modules essential for applications and validation with laboratory and field observations.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates
International Nuclear Information System (INIS)
Yang-Yih, Chen; Hung-Chu, Hsu
2009-01-01
Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor's series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level. (general)
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Statistical analysis of brake squeal noise
Oberst, S.; Lai, J. C. S.
2011-06-01
Despite substantial research efforts applied to the prediction of brake squeal noise since the early 20th century, the mechanisms behind its generation are still not fully understood. Squealing brakes are of significant concern to the automobile industry, mainly because of the costs associated with warranty claims. In order to remedy the problems inherent in designing quieter brakes and, therefore, to understand the mechanisms, a design of experiments study, using a noise dynamometer, was performed by a brake system manufacturer to determine the influence of geometrical parameters (namely, the number and location of slots) of brake pads on brake squeal noise. The experimental results were evaluated with a noise index and ranked for warm and cold brake stops. These data are analysed here using statistical descriptors based on population distributions, and a correlation analysis, to gain greater insight into the functional dependency between the time-averaged friction coefficient as the input and the peak sound pressure level data as the output quantity. The correlation analysis between the time-averaged friction coefficient and peak sound pressure data is performed by applying a semblance analysis and a joint recurrence quantification analysis. Linear measures are compared with complexity measures (nonlinear) based on statistics from the underlying joint recurrence plots. Results show that linear measures cannot be used to rank the noise performance of the four test pad configurations. On the other hand, the ranking of the noise performance of the test pad configurations based on the noise index agrees with that based on nonlinear measures: the higher the nonlinearity between the time-averaged friction coefficient and peak sound pressure, the worse the squeal. These results highlight the nonlinear character of brake squeal and indicate the potential of using nonlinear statistical analysis tools to analyse disc brake squeal.
Effect of bottom slope on the nonlinear triad interactions in shallow water
Chen, Hongzhou; Tang, Xiaocheng; Zhang, Ri; Gao, Junliang
2018-05-01
This paper aims at investigating the effect of bottom slope to the nonlinear triad interactions for irregular waves propagating in shallow water. The physical experiments are conducted in a wave flume with respect to the transformation of waves propagating on three bottom slopes ( β = 1/15, 1/30, and 1/45). Irregular waves with different type of breaking that are mechanically generated based on JONSWAP spectra are used for the test. The obviously different variations of spectra measured on each bottom reveal a crucial role of slope effect in the energy transfer between harmonics. The wavelet-based bispectrum were used to examine the bottom slope effect on the nonlinear triad interactions. Results show that the different bottom slopes which waves are propagated on will cause a significant discrepancy of triad interactions. Then, the discussions on the summed bicoherence which denote the distribution of phase coupling on each frequency further clarify the effect of bottom slope. Furthermore, the summed of the real and imaginary parts of bispectrum which could reflect the intensity of frequency components participating in the wave skewness and asymmetry were also investigated. Results indicate that the value of these parameters will increase as the bottom slope gets steeper.
Non-linear multi-objective model for planning water-energy modes of Novosibirsk Hydro Power Plant
Alsova, O. K.; Artamonova, A. V.
2018-05-01
This paper presents a non-linear multi-objective model for planning and optimizing of water-energy modes for the Novosibirsk Hydro Power Plant (HPP) operation. There is a very important problem of developing a strategy to improve the scheme of water-power modes and ensure the effective operation of hydropower plants. It is necessary to determine the methods and criteria for the optimal distribution of water resources, to develop a set of models and to apply them to the software implementation of a DSS (decision-support system) for managing Novosibirsk HPP modes. One of the possible versions of the model is presented and investigated in this paper. Experimental study of the model has been carried out with 2017 data and the task of ten-day period planning from April to July (only 12 ten-day periods) was solved.
QSPR Study of the Retention/release Property of Odorant Molecules in Water Using Statistical Methods
Directory of Open Access Journals (Sweden)
Assia Belhassan
2017-10-01
Full Text Available An integrated approach physicochemistry and structures property relationships has been carried out to study the odorant molecules retention/release phenomenon in the water. This study aimed to identify the molecular properties (molecular descriptors that govern this phenomenon assuming that modifying the structure leads automatically to a change in the retention/release property of odorant molecules. ACD/ChemSketch, MarvinSketch, and ChemOffice programs were used to calculate several molecular descriptors of 51 odorant molecules (15 alcohols, 11 aldehydes, 9 ketones and 16 esters. A total of 37 molecules (2/3 of the data set were placed in the training set to build the QSPR models, whereas the remaining, 14 molecules (1/3 of the data set constitute the test set. The best descriptors were selected to establish the quantitative structure property relationship (QSPR of the retention/release property of odorant molecules in water using multiple linear regression (MLR, multiple non-linear regression (MNLR and an artificial neural network (ANN methods. We propose a quantitative model according to these analyses. The models were used to predict the retention/release property of the test set compounds, and agreement between the experimental and predicted values was verified. The descriptors showed by QSPR study are used for study and designing of new compounds. The statistical results indicate that the predicted values are in good agreement with the experimental results. To validate the predictive power of the resulting models, external validation multiple correlation coefficient was calculated and has both in addition to a performant prediction power, a favorable estimation of stability. DOI: http://dx.doi.org/10.17807/orbital.v9i4.978
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
A Neural-Network-Based Nonlinear Adaptive State-Observer for Pressurized Water Reactors
Directory of Open Access Journals (Sweden)
Zhe Dong
2013-10-01
Full Text Available Although there have been some severe nuclear accidents such as Three Mile Island (USA, Chernobyl (Ukraine and Fukushima (Japan, nuclear fission energy is still a source of clean energy that can substitute for fossil fuels in a centralized way and in a great amount with commercial availability and economic competitiveness. Since the pressurized water reactor (PWR is the most widely used nuclear fission reactor, its safe, stable and efficient operation is meaningful to the current rebirth of the nuclear fission energy industry. Power-level regulation is an important technique which can deeply affect the operation stability and efficiency of PWRs. Compared with the classical power-level controllers, the advanced power-level regulators could strengthen both the closed-loop stability and control performance by feeding back the internal state-variables. However, not all of the internal state variables of a PWR can be obtained directly by measurements. To implement advanced PWR power-level control law, it is necessary to develop a state-observer to reconstruct the unmeasurable state-variables. Since a PWR is naturally a complex nonlinear system with parameters varying with power-level, fuel burnup, xenon isotope production, control rod worth and etc., it is meaningful to design a nonlinear observer for the PWR with adaptability to system uncertainties. Due to this and the strong learning capability of the multi-layer perceptron (MLP neural network, an MLP-based nonlinear adaptive observer is given for PWRs. Based upon Lyapunov stability theory, it is proved theoretically that this newly-built observer can provide bounded and convergent state-observation. This observer is then applied to the state-observation of a special PWR, i.e., the nuclear heating reactor (NHR, and numerical simulation results not only verify its feasibility but also give the relationship between the observation performance and observer parameters.
Non-gaussianity versus nonlinearity of cosmological perturbations.
Verde, L
2001-06-01
Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.
Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion
International Nuclear Information System (INIS)
Wabnitz, Stefan
2013-01-01
In analogy with ocean waves running up towards the beach, shoaling of pre-chirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion. (paper)
SWToolbox: A surface-water tool-box for statistical analysis of streamflow time series
Kiang, Julie E.; Flynn, Kate; Zhai, Tong; Hummel, Paul; Granato, Gregory
2018-03-07
This report is a user guide for the low-flow analysis methods provided with version 1.0 of the Surface Water Toolbox (SWToolbox) computer program. The software combines functionality from two software programs—U.S. Geological Survey (USGS) SWSTAT and U.S. Environmental Protection Agency (EPA) DFLOW. Both of these programs have been used primarily for computation of critical low-flow statistics. The main analysis methods are the computation of hydrologic frequency statistics such as the 7-day minimum flow that occurs on average only once every 10 years (7Q10), computation of design flows including biologically based flows, and computation of flow-duration curves and duration hydrographs. Other annual, monthly, and seasonal statistics can also be computed. The interface facilitates retrieval of streamflow discharge data from the USGS National Water Information System and outputs text reports for a record of the analysis. Tools for graphing data and screening tests are available to assist the analyst in conducting the analysis.
Nonlinear Pricing in Energy and Environmental Markets
Ito, Koichiro
This dissertation consists of three empirical studies on nonlinear pricing in energy and environmental markets. The first investigates how consumers respond to multi-tier nonlinear price schedules for residential electricity. Chapter 2 asks a similar research question for residential water pricing. Finally, I examine the effect of nonlinear financial rewards for energy conservation by applying a regression discontinuity design to a large-scale electricity rebate program that was implemented in California. Economic theory generally assumes that consumers respond to marginal prices when making economic decisions, but this assumption may not hold for complex price schedules. The chapter "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing" provides empirical evidence that consumers respond to average price rather than marginal price when faced with nonlinear electricity price schedules. Nonlinear price schedules, such as progressive income tax rates and multi-tier electricity prices, complicate economic decisions by creating multiple marginal prices for the same good. Evidence from laboratory experiments suggests that consumers facing such price schedules may respond to average price as a heuristic. I empirically test this prediction using field data by exploiting price variation across a spatial discontinuity in electric utility service areas. The territory border of two electric utilities lies within several city boundaries in southern California. As a result, nearly identical households experience substantially different nonlinear electricity price schedules. Using monthly household-level panel data from 1999 to 2008, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. I show that even though this sub-optimizing behavior has a minimal impact on individual welfare, it can critically alter the policy implications of nonlinear pricing. The second chapter " How Do
Spectral statistics of chaotic many-body systems
International Nuclear Information System (INIS)
Dubertrand, Rémy; Müller, Sebastian
2016-01-01
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (paper)
Even and odd combinations of nonlinear coherent states
International Nuclear Information System (INIS)
De los Santos-Sanchez, O; Recamier, J
2011-01-01
In this work we present some statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials; one supporting a finite number of bound states and the other supporting an infinite number of bound states, within the framework of an f-deformed algebra. We calculate their normalized variance and the temporal evolution of their dispersion relations using nonlinear coherent states defined as (a) eigensates of the deformed annihilation operator and (b) those states created by the application of a deformed displacement operator upon the ground state of the oscillator.
Edjah, Adwoba; Stenni, Barbara; Cozzi, Giulio; Turetta, Clara; Dreossi, Giuliano; Tetteh Akiti, Thomas; Yidana, Sandow
2017-04-01
Adwoba Kua- Manza Edjaha, Barbara Stennib,c,Giuliano Dreossib, Giulio Cozzic, Clara Turetta c,T.T Akitid ,Sandow Yidanae a,eDepartment of Earth Science, University of Ghana Legon, Ghana West Africa bDepartment of Enviromental Sciences, Informatics and Statistics, Ca Foscari University of Venice, Italy cInstitute for the Dynamics of Environmental Processes, CNR, Venice, Italy dDepartment of Nuclear Application and Techniques, Graduate School of Nuclear and Allied Sciences University of Ghana Legon This research is part of a PhD research work "Hydrogeological Assessment of the Lower Tano river basin for sustainable economic usage, Ghana, West - Africa". In this study, the researcher investigated surface water and groundwater quality in the Lower Tano river basin. This assessment was based on some selected sampling sites associated with mining activities, and the development of oil and gas. Statistical approach was applied to characterize the quality of surface water and groundwater. Also, water stable isotopes, which is a natural tracer of the hydrological cycle was used to investigate the origin of groundwater recharge in the basin. The study revealed that Pb and Ni values of the surface water and groundwater samples exceeded the WHO standards for drinking water. In addition, water quality index (WQI), based on physicochemical parameters(EC, TDS, pH) and major ions(Ca2+, Na+, Mg2+, HCO3-,NO3-, CL-, SO42-, K+) exhibited good quality water for 60% of the sampled surface water and groundwater. Other statistical techniques, such as Heavy metal pollution index (HPI), degree of contamination (Cd), and heavy metal evaluation index (HEI), based on trace element parameters in the water samples, reveal that 90% of the surface water and groundwater samples belong to high level of pollution. Principal component analysis (PCA) also suggests that the water quality in the basin is likely affected by rock - water interaction and anthropogenic activities (sea water intrusion). This
Nonlinear Finite Strain Consolidation Analysis with Secondary Consolidation Behavior
Directory of Open Access Journals (Sweden)
Jieqing Huang
2014-01-01
Full Text Available This paper aims to analyze nonlinear finite strain consolidation with secondary consolidation behavior. On the basis of some assumptions about the secondary consolidation behavior, the continuity equation of pore water in Gibson’s consolidation theory is modified. Taking the nonlinear compressibility and nonlinear permeability of soils into consideration, the governing equation for finite strain consolidation analysis is derived. Based on the experimental data of Hangzhou soft clay samples, the new governing equation is solved with the finite element method. Afterwards, the calculation results of this new method and other two methods are compared. It can be found that Gibson’s method may underestimate the excess pore water pressure during primary consolidation. The new method which takes the secondary consolidation behavior, the nonlinear compressibility, and nonlinear permeability of soils into consideration can precisely estimate the settlement rate and the final settlement of Hangzhou soft clay sample.
Functional integral approach to classical statistical dynamics
International Nuclear Information System (INIS)
Jensen, R.V.
1980-04-01
A functional integral method is developed for the statistical solution of nonlinear stochastic differential equations which arise in classical dynamics. The functional integral approach provides a very natural and elegant derivation of the statistical dynamical equations that have been derived using the operator formalism of Martin, Siggia, and Rose
A non-linear state space approach to model groundwater fluctuations
Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.
2006-01-01
A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual
Directory of Open Access Journals (Sweden)
G. P. Pavlos
1999-01-01
Full Text Available A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper and dynamical characteristics (Part II, which is the work a separate paper, and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Mavukkandy, Musthafa Odayooth; Karmakar, Subhankar; Harikumar, P S
2014-09-01
The establishment of an efficient surface water quality monitoring (WQM) network is a critical component in the assessment, restoration and protection of river water quality. A periodic evaluation of monitoring network is mandatory to ensure effective data collection and possible redesigning of existing network in a river catchment. In this study, the efficacy and appropriateness of existing water quality monitoring network in the Kabbini River basin of Kerala, India is presented. Significant multivariate statistical techniques like principal component analysis (PCA) and principal factor analysis (PFA) have been employed to evaluate the efficiency of the surface water quality monitoring network with monitoring stations as the evaluated variables for the interpretation of complex data matrix of the river basin. The main objective is to identify significant monitoring stations that must essentially be included in assessing annual and seasonal variations of river water quality. Moreover, the significance of seasonal redesign of the monitoring network was also investigated to capture valuable information on water quality from the network. Results identified few monitoring stations as insignificant in explaining the annual variance of the dataset. Moreover, the seasonal redesign of the monitoring network through a multivariate statistical framework was found to capture valuable information from the system, thus making the network more efficient. Cluster analysis (CA) classified the sampling sites into different groups based on similarity in water quality characteristics. The PCA/PFA identified significant latent factors standing for different pollution sources such as organic pollution, industrial pollution, diffuse pollution and faecal contamination. Thus, the present study illustrates that various multivariate statistical techniques can be effectively employed in sustainable management of water resources. The effectiveness of existing river water quality monitoring
International Nuclear Information System (INIS)
Brekke, L.; Imbo, T.D.
1992-01-01
The authors study the inequivalent quantizations of (1 + 1)-dimensional nonlinear sigma models with space manifold S 1 and target manifold X. If x is multiply connected, these models possess topological solitons. After providing a definition of spin and statistics for these solitons and demonstrating a spin-statistics correlation, we give various examples where the solitons can have exotic statistics. In some of these models, the solitons may obey a generalized version of fractional statistics called ambistatistics. In this paper the relevance of these 2d models to the statistics of vortices in (2 + 1)-dimensional spontaneously broken gauge theories is discussed. The authors close with a discussion concerning the extension of our results to higher dimensions
Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation.
Brito, Carlos S N; Gerstner, Wulfram
2016-09-01
The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.
Zhang, Y.; Li, F.; Zhang, S.; Hao, W.; Zhu, T.; Yuan, L.; Xiao, F.
2017-09-01
In this paper, Statistical Distribution based Conditional Random Fields (STA-CRF) algorithm is exploited for improving marginal ice-water classification. Pixel level ice concentration is presented as the comparison of methods based on CRF. Furthermore, in order to explore the effective statistical distribution model to be integrated into STA-CRF, five statistical distribution models are investigated. The STA-CRF methods are tested on 2 scenes around Prydz Bay and Adélie Depression, where contain a variety of ice types during melt season. Experimental results indicate that the proposed method can resolve sea ice edge well in Marginal Ice Zone (MIZ) and show a robust distinction of ice and water.
Advanced data analysis in neuroscience integrating statistical and computational models
Durstewitz, Daniel
2017-01-01
This book is intended for use in advanced graduate courses in statistics / machine learning, as well as for all experimental neuroscientists seeking to understand statistical methods at a deeper level, and theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical estimation and test theory, linear and nonlinear approaches for regression and classification, to model selection and methods for dimensionality reduction, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective, based on which it aims to convey an understanding also of the dynamical mechanisms that could have generated observed time series. Further, it integrates computational modeling of behavioral and neural dynamics with statistical estimation and hypothesis testing. This way computational models in neuroscience are not only explanat ory frameworks, but become powerfu...
DEFF Research Database (Denmark)
Lindström, Erik; Madsen, Henrik; Nielsen, Jan Nygaard
Statistics for Finance develops students’ professional skills in statistics with applications in finance. Developed from the authors’ courses at the Technical University of Denmark and Lund University, the text bridges the gap between classical, rigorous treatments of financial mathematics...... that rarely connect concepts to data and books on econometrics and time series analysis that do not cover specific problems related to option valuation. The book discusses applications of financial derivatives pertaining to risk assessment and elimination. The authors cover various statistical...... and mathematical techniques, including linear and nonlinear time series analysis, stochastic calculus models, stochastic differential equations, Itō’s formula, the Black–Scholes model, the generalized method-of-moments, and the Kalman filter. They explain how these tools are used to price financial derivatives...
Computational statistics handbook with Matlab
Martinez, Wendy L
2007-01-01
Prefaces Introduction What Is Computational Statistics? An Overview of the Book Probability Concepts Introduction Probability Conditional Probability and Independence Expectation Common Distributions Sampling Concepts Introduction Sampling Terminology and Concepts Sampling Distributions Parameter Estimation Empirical Distribution Function Generating Random Variables Introduction General Techniques for Generating Random Variables Generating Continuous Random Variables Generating Discrete Random Variables Exploratory Data Analysis Introduction Exploring Univariate Data Exploring Bivariate and Trivariate Data Exploring Multidimensional Data Finding Structure Introduction Projecting Data Principal Component Analysis Projection Pursuit EDA Independent Component Analysis Grand Tour Nonlinear Dimensionality Reduction Monte Carlo Methods for Inferential Statistics Introduction Classical Inferential Statistics Monte Carlo Methods for Inferential Statist...
Is there a statistical mechanics of turbulence?
International Nuclear Information System (INIS)
Kraichnan, R.H.; Chen, S.Y.
1988-09-01
The statistical-mechanical treatment of turbulence is made questionable by strong nonlinearity and strong disequilibrium that result in the creation of ordered structures imbedded in disorder. Model systems are described which may provide some hope that a compact, yet faithful, statistical description of turbulence nevertheless is possible. Some essential dynamic features of the models are captured by low-order statistical approximations despite strongly non-Gaussian behavior. 31 refs., 5 figs
Prinos, Scott T.; Dixon, Joann F.
2016-02-25
Statistical analyses and maps representing mean, high, and low water-level conditions in the surface water and groundwater of Miami-Dade County were made by the U.S. Geological Survey, in cooperation with the Miami-Dade County Department of Regulatory and Economic Resources, to help inform decisions necessary for urban planning and development. Sixteen maps were created that show contours of (1) the mean of daily water levels at each site during October and May for the 2000–2009 water years; (2) the 25th, 50th, and 75th percentiles of the daily water levels at each site during October and May and for all months during 2000–2009; and (3) the differences between mean October and May water levels, as well as the differences in the percentiles of water levels for all months, between 1990–1999 and 2000–2009. The 80th, 90th, and 96th percentiles of the annual maximums of daily groundwater levels during 1974–2009 (a 35-year period) were computed to provide an indication of unusually high groundwater-level conditions. These maps and statistics provide a generalized understanding of the variations of water levels in the aquifer, rather than a survey of concurrent water levels. Water-level measurements from 473 sites in Miami-Dade County and surrounding counties were analyzed to generate statistical analyses. The monitored water levels included surface-water levels in canals and wetland areas and groundwater levels in the Biscayne aquifer.
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Eskilsson, Claes
2016-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description...... at different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental...... benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained...
Li, Mo; Fu, Qiang; Singh, Vijay P.; Ma, Mingwei; Liu, Xiao
2017-12-01
Water scarcity causes conflicts among natural resources, society and economy and reinforces the need for optimal allocation of irrigation water resources in a sustainable way. Uncertainties caused by natural conditions and human activities make optimal allocation more complex. An intuitionistic fuzzy multi-objective non-linear programming (IFMONLP) model for irrigation water allocation under the combination of dry and wet conditions is developed to help decision makers mitigate water scarcity. The model is capable of quantitatively solving multiple problems including crop yield increase, blue water saving, and water supply cost reduction to obtain a balanced water allocation scheme using a multi-objective non-linear programming technique. Moreover, it can deal with uncertainty as well as hesitation based on the introduction of intuitionistic fuzzy numbers. Consideration of the combination of dry and wet conditions for water availability and precipitation makes it possible to gain insights into the various irrigation water allocations, and joint probabilities based on copula functions provide decision makers an average standard for irrigation. A case study on optimally allocating both surface water and groundwater to different growth periods of rice in different subareas in Heping irrigation area, Qing'an County, northeast China shows the potential and applicability of the developed model. Results show that the crop yield increase target especially in tillering and elongation stages is a prevailing concern when more water is available, and trading schemes can mitigate water supply cost and save water with an increased grain output. Results also reveal that the water allocation schemes are sensitive to the variation of water availability and precipitation with uncertain characteristics. The IFMONLP model is applicable for most irrigation areas with limited water supplies to determine irrigation water strategies under a fuzzy environment.
Y. Hu; M. Vaughan; C. McClain; M. Behrenfeld; H. Maring; D. Anderson; S. Sun-Mack; D. Flittner; J. Huang; B. Wielicki; P. Minnis; C. Weimer; C. Trepte; R. Kuehn
2007-01-01
International audience; This study presents an empirical relation that links layer integrated depolarization ratios, the extinction coefficients, and effective radii of water clouds, based on Monte Carlo simulations of CALIPSO lidar observations. Combined with cloud effective radius retrieved from MODIS, cloud liquid water content and effective number density of water clouds are estimated from CALIPSO lidar depolarization measurements in this study. Global statistics of the cloud liquid water...
International Nuclear Information System (INIS)
Doherty, W.
2013-01-01
A nebulizer-centric response function model of the analytical inductively coupled argon plasma ion source was used to investigate the statistical frequency distributions and noise reduction factors of simultaneously measured flicker noise limited isotope ion signals and their ratios. The response function model was extended by assuming i) a single gaussian distributed random noise source (nebulizer gas pressure fluctuations) and ii) the isotope ion signal response is a parabolic function of the nebulizer gas pressure. Model calculations of ion signal and signal ratio histograms were obtained by applying the statistical method of translation to the non-linear response function model of the plasma. Histograms of Ni, Cu, Pr, Tl and Pb isotope ion signals measured using a multi-collector plasma mass spectrometer were, without exception, negative skew. Histograms of the corresponding isotope ratios of Ni, Cu, Tl and Pb were either positive or negative skew. There was a complete agreement between the measured and model calculated histogram skew properties. The nebulizer-centric response function model was also used to investigate the effect of non-linear response functions on the effectiveness of noise cancellation by signal division. An alternative noise correction procedure suitable for parabolic signal response functions was derived and applied to measurements of isotope ratios of Cu, Ni, Pb and Tl. The largest noise reduction factors were always obtained when the non-linearity of the response functions was taken into account by the isotope ratio calculation. Possible applications of the nebulizer-centric response function model to other types of analytical instrumentation, large amplitude signal noise sources (e.g., lasers, pumped nebulizers) and analytical error in isotope ratio measurements by multi-collector plasma mass spectrometry are discussed. - Highlights: ► Isotope ion signal noise is modelled as a parabolic transform of a gaussian variable. ► Flicker
International Nuclear Information System (INIS)
Adcock, T. A. A.; Taylor, P. H.
2016-01-01
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum
UN Data- Environmental Statistics: Waste
World Wide Human Geography Data Working Group — The Environment Statistics Database contains selected water and waste statistics by country. Statistics on water and waste are based on official statistics supplied...
UN Data: Environment Statistics: Waste
World Wide Human Geography Data Working Group — The Environment Statistics Database contains selected water and waste statistics by country. Statistics on water and waste are based on official statistics supplied...
An efficient soil water balance model based on hybrid numerical and statistical methods
Mao, Wei; Yang, Jinzhong; Zhu, Yan; Ye, Ming; Liu, Zhao; Wu, Jingwei
2018-04-01
Most soil water balance models only consider downward soil water movement driven by gravitational potential, and thus cannot simulate upward soil water movement driven by evapotranspiration especially in agricultural areas. In addition, the models cannot be used for simulating soil water movement in heterogeneous soils, and usually require many empirical parameters. To resolve these problems, this study derives a new one-dimensional water balance model for simulating both downward and upward soil water movement in heterogeneous unsaturated zones. The new model is based on a hybrid of numerical and statistical methods, and only requires four physical parameters. The model uses three governing equations to consider three terms that impact soil water movement, including the advective term driven by gravitational potential, the source/sink term driven by external forces (e.g., evapotranspiration), and the diffusive term driven by matric potential. The three governing equations are solved separately by using the hybrid numerical and statistical methods (e.g., linear regression method) that consider soil heterogeneity. The four soil hydraulic parameters required by the new models are as follows: saturated hydraulic conductivity, saturated water content, field capacity, and residual water content. The strength and weakness of the new model are evaluated by using two published studies, three hypothetical examples and a real-world application. The evaluation is performed by comparing the simulation results of the new model with corresponding results presented in the published studies, obtained using HYDRUS-1D and observation data. The evaluation indicates that the new model is accurate and efficient for simulating upward soil water flow in heterogeneous soils with complex boundary conditions. The new model is used for evaluating different drainage functions, and the square drainage function and the power drainage function are recommended. Computational efficiency of the new
Hu, Y.; Vaughan, M.; McClain, C.; Behrenfeld, M.; Maring, H.; Anderson, D.; Sun-Mack, S.; Flittner, D.; Huang, J.; Wielicki, B.; Minnis, P.; Weimer, C.; Trepte, C.; Kuehn, R.
2007-03-01
This study presents an empirical relation that links layer integrated depolarization ratios, the extinction coefficients, and effective radii of water clouds, based on Monte Carlo simulations of CALIPSO lidar observations. Combined with cloud effective radius retrieved from MODIS, cloud liquid water content and effective number density of water clouds are estimated from CALIPSO lidar depolarization measurements in this study. Global statistics of the cloud liquid water content and effective number density are presented.
Separation of variables for the nonlinear wave equation in polar coordinates
International Nuclear Information System (INIS)
Shermenev, Alexander
2004-01-01
Some classical types of nonlinear wave motion in polar coordinates are studied within quadratic approximation. When the nonlinear quadratic terms in the wave equation are arbitrary, the usual perturbation techniques used in polar coordinates leads to overdetermined systems of linear algebraic equations for the unknown coefficients. However, we show that these overdetermined systems are compatible with the special case of the nonlinear shallow water equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear shallow water equation that are periodic in time and found with the same accuracy as the equation is derived
International Nuclear Information System (INIS)
Garcia, Francisco; Palacio, Carlos; Garcia, Uriel
2012-01-01
Multivariate statistical techniques were used to investigate the temporal and spatial variations of water quality at the Santa Marta coastal area where a submarine out fall that discharges 1 m3/s of domestic wastewater is located. Two-way analysis of variance (ANOVA), cluster and principal component analysis and Krigging interpolation were considered for this report. Temporal variation showed two heterogeneous periods. From December to April, and July, where the concentration of the water quality parameters is higher; the rest of the year (May, June, August-November) were significantly lower. The spatial variation reported two areas where the water quality is different, this difference is related to the proximity to the submarine out fall discharge.
Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.
Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté
2015-12-24
Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.
Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation.
Directory of Open Access Journals (Sweden)
Carlos S N Brito
2016-09-01
Full Text Available The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.
Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview
Directory of Open Access Journals (Sweden)
Fernando D. Nobre
2017-01-01
Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.
Wali, F.; Knotter, D. Martin; Wortelboer, Ronald; Mud, Auke
2007-01-01
Ultra pure water supplied inside the Fab is used in different tools at different stages of processing. Data of the particles measured in ultra pure water was compared with the defect density on wafers processed on these tools and a statistical relation is found Keywords— Yield, defect density,
Nonlinear structural damage detection using support vector machines
Xiao, Li; Qu, Wenzhong
2012-04-01
An actual structure including connections and interfaces may exist nonlinear. Because of many complicated problems about nonlinear structural health monitoring (SHM), relatively little progress have been made in this aspect. Statistical pattern recognition techniques have been demonstrated to be competitive with other methods when applied to real engineering datasets. When a structure existing 'breathing' cracks that open and close under operational loading may cause a linear structural system to respond to its operational and environmental loads in a nonlinear manner nonlinear. In this paper, a vibration-based structural health monitoring when the structure exists cracks is investigated with autoregressive support vector machine (AR-SVM). Vibration experiments are carried out with a model frame. Time-series data in different cases such as: initial linear structure; linear structure with mass changed; nonlinear structure; nonlinear structure with mass changed are acquired.AR model of acceleration time-series is established, and different kernel function types and corresponding parameters are chosen and compared, which can more accurate, more effectively locate the damage. Different cases damaged states and different damage positions have been recognized successfully. AR-SVM method for the insufficient training samples is proved to be practical and efficient on structure nonlinear damage detection.
Phase locking and quantum statistics in a parametrically driven nonlinear resonator
Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.
2016-01-01
We discuss phase-locking phenomena at low-level of quanta for parametrically driven nonlinear Kerr resonator (PDNR) in strong quantum regime. Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the Wigner functions of cavity mode showing two-fold symmetry in phase space and analyse formation of phase-locked states in the regular as well as the quantum chaotic regime.
International Nuclear Information System (INIS)
Gershgorin, B.; Majda, A.J.
2011-01-01
A statistically exactly solvable model for passive tracers is introduced as a test model for the authors' Nonlinear Extended Kalman Filter (NEKF) as well as other filtering algorithms. The model involves a Gaussian velocity field and a passive tracer governed by the advection-diffusion equation with an imposed mean gradient. The model has direct relevance to engineering problems such as the spread of pollutants in the air or contaminants in the water as well as climate change problems concerning the transport of greenhouse gases such as carbon dioxide with strongly intermittent probability distributions consistent with the actual observations of the atmosphere. One of the attractive properties of the model is the existence of the exact statistical solution. In particular, this unique feature of the model provides an opportunity to design and test fast and efficient algorithms for real-time data assimilation based on rigorous mathematical theory for a turbulence model problem with many active spatiotemporal scales. Here, we extensively study the performance of the NEKF which uses the exact first and second order nonlinear statistics without any approximations due to linearization. The role of partial and sparse observations, the frequency of observations and the observation noise strength in recovering the true signal, its spectrum, and fat tail probability distribution are the central issues discussed here. The results of our study provide useful guidelines for filtering realistic turbulent systems with passive tracers through partial observations.
Directory of Open Access Journals (Sweden)
Farshad Fathian
2017-02-01
Full Text Available Introduction: Time series models are one of the most important tools for investigating and modeling hydrological processes in order to solve problems related to water resources management. Many hydrological time series shows nonstationary and nonlinear behaviors. One of the important hydrological modeling tasks is determining the existence of nonstationarity and the way through which we can access the stationarity accordingly. On the other hand, streamflow processes are usually considered as nonlinear mechanisms while in many studies linear time series models are used to model streamflow time series. However, it is not clear what kind of nonlinearity is acting underlying the streamflowprocesses and how intensive it is. Materials and Methods: Streamflow time series of 6 hydro-gauge stations located in the upstream basin rivers of ZarrinehRoud dam (located in the southern part of Urmia Lake basin have been considered to investigate stationarity and nonlinearity. All data series used here to startfrom January 1, 1997, and end on December 31, 2011. In this study, stationarity is tested by ADF and KPSS tests and nonlinearity is tested by BDS, Keenan and TLRT tests. The stationarity test is carried out with two methods. Thefirst one method is the augmented Dickey-Fuller (ADF unit root test first proposed by Dickey and Fuller (1979 and modified by Said and Dickey (1984, which examinsthe presence of unit roots in time series.The second onemethod is KPSS test, proposed by Kwiatkowski et al. (1992, which examinesthestationarity around a deterministic trend (trend stationarity and the stationarity around a fixed level (level stationarity. The BDS test (Brock et al., 1996 is a nonparametric method for testing the serial independence and nonlinear structure in time series based on the correlation integral of the series. The null hypothesis is the time series sample comes from an independent identically distributed (i.i.d. process. The alternative hypothesis
Decoupling Linear and Nonlinear Associations of Gene Expression
Itakura, Alan
2013-05-01
The FANTOM consortium has generated a large gene expression dataset of different cell lines and tissue cultures using the single-molecule sequencing technology of HeliscopeCAGE. This provides a unique opportunity to investigate novel associations between gene expression over time and different cell types. Here, we create a MatLab wrapper for a powerful and computationally intensive set of statistics known as Maximal Information Coefficient, and then calculate this statistic for a large, comprehensive dataset containing gene expression of a variety of differentiating tissues. We then distinguish between linear and nonlinear associations, and then create gene association networks. Following this analysis, we are then able to identify clusters of linear gene associations that then associate nonlinearly with other clusters of linearity, providing insight to much more complex connections between gene expression patterns than previously anticipated.
Decoupling Linear and Nonlinear Associations of Gene Expression
Itakura, Alan
2013-01-01
The FANTOM consortium has generated a large gene expression dataset of different cell lines and tissue cultures using the single-molecule sequencing technology of HeliscopeCAGE. This provides a unique opportunity to investigate novel associations between gene expression over time and different cell types. Here, we create a MatLab wrapper for a powerful and computationally intensive set of statistics known as Maximal Information Coefficient, and then calculate this statistic for a large, comprehensive dataset containing gene expression of a variety of differentiating tissues. We then distinguish between linear and nonlinear associations, and then create gene association networks. Following this analysis, we are then able to identify clusters of linear gene associations that then associate nonlinearly with other clusters of linearity, providing insight to much more complex connections between gene expression patterns than previously anticipated.
Digital Repository Service at National Institute of Oceanography (India)
Padma, P.; Sheela, V.S.; Suryakumari, S.; Jayalakshmy, K.V.; Nair, S.M.; Kumar, N.C.
stream_size 64084 stream_content_type text/plain stream_name Water_Qual_Expos_Health_5_197.pdf.txt stream_source_info Water_Qual_Expos_Health_5_197.pdf.txt Content-Encoding UTF-8 Content-Type text/plain; charset=UTF-8... Water Qual Expo Health DOI 10.1007/s12403-014-0115-9 ORIGINAL PAPER Assessment of Water Quality of a River-Dominated Estuary with Hydrochemical Parameters: A Statistical Approach P. Padma · V. S. Sheela · S. Suryakumari · K. V. Jayalakshmy · S. M. Nair...
A non-linear reduced order methodology applicable to boiling water reactor stability analysis
International Nuclear Information System (INIS)
Prill, Dennis Paul
2013-01-01
Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character
Costa, Marco; A. Manuela Gonçalves
2012-01-01
In this work are discussed some statistical approaches that combine multivariate statistical techniques and time series analysis in order to describe and model spatial patterns and temporal evolution by observing hydrological series of water quality variables recorded in time and space. These approaches are illustrated with a data set collected in the River Ave hydrological basin located in the Northwest region of Portugal.
Directory of Open Access Journals (Sweden)
M. Bauwens
2010-11-01
Full Text Available A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ^{18}O carbonate. It is problematic in the case of freshwater influenced environments because the δ^{18}O isotopic composition of the ambient water (related to salinity needs to be known. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization (WDMR to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information for other trace elements in multi-proxy models. Although the models presented here are black-box models that do not use any prior knowledge about the proxies, the comparison of model reconstruction performances based on different proxy combinations do yield useful information about proxy characteristics. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enables a temperature reconstruction with a root mean squared error of ± 2.19 °C for a salinity range between 15 and 32.
Wang, Hao; Wang, Qunwei; He, Ming
2018-05-01
In order to investigate and improve the level of detection technology of water content in liquid chemical reagents of domestic laboratories, proficiency testing provider PT0031 (CNAS) has organized proficiency testing program of water content in toluene, 48 laboratories from 18 provinces/cities/municipals took part in the PT. This paper introduces the implementation process of proficiency testing for determination of water content in toluene, including sample preparation, homogeneity and stability test, the results of statistics of iteration robust statistic technique and analysis, summarized and analyzed those of the different test standards which are widely used in the laboratories, put forward the technological suggestions for the improvement of the test quality of water content. Satisfactory results were obtained by 43 laboratories, amounting to 89.6% of the total participating laboratories.
Nonlinear Fokker-Planck Equations Fundamentals and Applications
Frank, Till Daniel
2005-01-01
Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...
Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment
Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos
2013-01-01
In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…
Poullis, Michael
2014-11-01
EuroSCORE II, despite improving on the original EuroSCORE system, has not solved all the calibration and predictability issues. Recursive, non-linear and mixed recursive and non-linear regression analysis were assessed with regard to sensitivity, specificity and predictability of the original EuroSCORE and EuroSCORE II systems. The original logistic EuroSCORE, EuroSCORE II and recursive, non-linear and mixed recursive and non-linear regression analyses of these risk models were assessed via receiver operator characteristic curves (ROC) and Hosmer-Lemeshow statistic analysis with regard to the accuracy of predicting in-hospital mortality. Analysis was performed for isolated coronary artery bypass grafts (CABGs) (n = 2913), aortic valve replacement (AVR) (n = 814), mitral valve surgery (n = 340), combined AVR and CABG (n = 517), aortic (n = 350), miscellaneous cases (n = 642), and combinations of the above cases (n = 5576). The original EuroSCORE had an ROC below 0.7 for isolated AVR and combined AVR and CABG. None of the methods described increased the ROC above 0.7. The EuroSCORE II risk model had an ROC below 0.7 for isolated AVR only. Recursive regression, non-linear regression, and mixed recursive and non-linear regression all increased the ROC above 0.7 for isolated AVR. The original EuroSCORE had a Hosmer-Lemeshow statistic that was above 0.05 for all patients and the subgroups analysed. All of the techniques markedly increased the Hosmer-Lemeshow statistic. The EuroSCORE II risk model had a Hosmer-Lemeshow statistic that was significant for all patients (P linear regression failed to improve on the original Hosmer-Lemeshow statistic. The mixed recursive and non-linear regression using the EuroSCORE II risk model was the only model that produced an ROC of 0.7 or above for all patients and procedures and had a Hosmer-Lemeshow statistic that was highly non-significant. The original EuroSCORE and the EuroSCORE II risk models do not have adequate ROC and Hosmer
Statistical inference for financial engineering
Taniguchi, Masanobu; Ogata, Hiroaki; Taniai, Hiroyuki
2014-01-01
This monograph provides the fundamentals of statistical inference for financial engineering and covers some selected methods suitable for analyzing financial time series data. In order to describe the actual financial data, various stochastic processes, e.g. non-Gaussian linear processes, non-linear processes, long-memory processes, locally stationary processes etc. are introduced and their optimal estimation is considered as well. This book also includes several statistical approaches, e.g., discriminant analysis, the empirical likelihood method, control variate method, quantile regression, realized volatility etc., which have been recently developed and are considered to be powerful tools for analyzing the financial data, establishing a new bridge between time series and financial engineering. This book is well suited as a professional reference book on finance, statistics and statistical financial engineering. Readers are expected to have an undergraduate-level knowledge of statistics.
Toward a scalable flexible-order model for 3D nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Ducrozet, Guillaume; Bingham, Harry B.
For marine and coastal applications, current work are directed toward the development of a scalable numerical 3D model for fully nonlinear potential water waves over arbitrary depths. The model is high-order accurate, robust and efficient for large-scale problems, and support will be included...... for flexibility in the description of structures by the use of curvilinear boundary-fitted meshes. The mathematical equations for potential waves in the physical domain is transformed through $\\sigma$-mapping(s) to a time-invariant boundary-fitted domain which then becomes a basis for an efficient solution...... strategy on a time-invariant mesh. The 3D numerical model is based on a finite difference method as in the original works \\cite{LiFleming1997,BinghamZhang2007}. Full details and other aspects of an improved 3D solution can be found in \\cite{EBL08}. The new and improved approach for three...
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
bathymetric profile also compare well with the measured values. The statistical distributions of the free surface elevation and wave height, calculated from the simulated time series, are compared to those of the measurements, with particular attention paid to the extreme waves. To use this model for realistic cases with complex bathymetric variations and multidirectional wave fields, the model has been extended to two horizontal dimensions (2DH). The spectral approach in the vertical dimension is retained, while the horizontal plane is discretized with scattered nodes to maintain the model's flexibility. The horizontal derivatives are estimated with finite-difference type formulas using Radial Basis Functions (Wright and Fornberg, 2006). The 2DH version of the code is applied to simulate the propagation of regular waves over a semi-circular step, which acts as a focusing lens. The simulation results are compared to the experimental data set of Whalin (1971). The evolution of the higher harmonic amplitudes in the shallow-water zone demonstrates the ability of the model to simulate wave propagation over complex 2DH coastal bathymetries. References: Becq-Girard F., Forget P., Benoit M. (1999) Non-linear propagation of unidirectional wave fields over varying topography. Coastal Eng., 38, 91-113. Tian Y., Sato S. (2008) A numerical model on the interaction between nearshore nonlinear waves and strong currents. Coast. Eng. Journal, 50(4), 369-395. Whalin R.W. (1971) The limit of applicability of linear wave refraction theory in a convergence zone. Technical report, DTIC Documents. Wright G.B., Fornberg B. (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comp. Phys., 212, 99-123. Yates M.L., Benoit M. (2015) Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves. Int. J. Numer. Meth. Fluids, 77, 616-640. Zakharov V.E. (1968) Stability of periodic
Moderately nonlinear ultrasound propagation in blood-mimicking fluid.
Kharin, Nikolay A; Vince, D Geoffrey
2004-04-01
In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.
Three-point phase correlations: A new measure of non-linear large-scale structure
Wolstenhulme, Richard; Obreschkow, Danail
2015-01-01
We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the non-linear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F_2, which governs the non-linear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a very good agreement for separations r>20 Mpc/h. Fitting formulae for the power spectrum and the non-linear coupling kernel at small scales allow us to extend our prediction into the strongly non-linear regime. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the linear bias. Furtherm...
On nonequilibrium many-body systems III: nonlinear transport theory
International Nuclear Information System (INIS)
Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.
1986-01-01
A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt
Nonlinear GARCH model and 1 / f noise
Kononovicius, A.; Ruseckas, J.
2015-06-01
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Tao, Chenyang; Feng, Jianfeng
2016-03-15
Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications. Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples. NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts. In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present. Copyright © 2016 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Vahid Reza Jalali
2017-10-01
water was taken from Maharlu Lake, Fars province, Iran. This natural and highly saline water with electrical conductivity of 512 dS/m diluted with fresh water to obtain the designated saline waters required for the experimental treatments. The designed experimental treatments were consisted of a non-saline water and five salinity levels of 2, 4, 6, 8 and 10 dS/m with three replicates. Three statistics of modified coefficient efficiency (E', modified index of agreement (d' and coefficient of residual mass (CRM were used to compare the used models and to assess their performances. Results and discussion Comparing the relative performance of models based on statistical indices of Modified Coefficient Efficiency (E' and Modified Index of agreement (d' indicated that the nonlinear model of Homaee et al. is most accurate between process-physical models and Modified Gompertz Function is most accurate between statistical-experimental models. Comparison assessment of all models based on statistical index indicated that Homaee et al. model was the most accurate model for simulation of durum wheat yield. This is while the parameters of Homaee et al. equation is well-defined concept and is easily measurable, but in statistical-experimental models, parameters of each model have no biophysical concept and the absolute values of each parameter do not express any information about development status of the plant. So, the nonlinear model of Homaee et al. was chosen as the optimal model in this research. Conclusion Most of the plants such as wheat, are sensitive to salinity and by increasing the age, their sensitivity to salinity are reduced. Based on the obtained results of this study, by knowing and quantitative assessment of the dominant cultivars sensitivity of each region, as well as using appropriate simulation models, one can use brackish or saline waters to partly compensate fresh water shortage for scientific and extension Agricultural programs.
Tavakoli, Ali; Nikoo, Mohammad Reza; Kerachian, Reza; Soltani, Maryam
2015-04-01
In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.
Nonlinear aspects of quantum plasma physics
International Nuclear Information System (INIS)
Shukla, Padma K; Eliasson, B
2010-01-01
Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects (e.g., the interior of white dwarf stars, in magnetars, etc.), in semiconductors and micromechanical systems, as well as in the next-generation intense laser-solid density plasma interaction experiments and in quantum X-ray free-electron lasers. In contrast to classical plasmas, quantum plasmas have extremely high plasma number densities and low temperatures. Quantum plasmas are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, and holes) obey the Fermi-Dirac statistics. In quantum plasmas, there are new forces associated with (i) quantum statistical electron and positron pressures, (ii) electron and positron tunneling through the Bohm potential, and (iii) electron and positron angular momentum spin. Inclusion of these quantum forces allows the existence of very high-frequency dispersive electrostatic and electromagnetic waves (e.g., in the hard X-ray and gamma-ray regimes) with extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave-wave and wave-electron interactions in dense quantum plasmas. Specifically, we focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of three-dimensional quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase-space kinetic structures and mechanisms that can generate quasistationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed. Finally, future perspectives of the nonlinear quantum plasma physics are highlighted. (reviews of topical problems)
Note: Nonpolar solute partial molar volume response to attractive interactions with water
Energy Technology Data Exchange (ETDEWEB)
Williams, Steven M.; Ashbaugh, Henry S., E-mail: hanka@tulane.edu [Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118 (United States)
2014-01-07
The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.
Note: Nonpolar solute partial molar volume response to attractive interactions with water.
Williams, Steven M; Ashbaugh, Henry S
2014-01-07
The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.
Entropy and convexity for nonlinear partial differential equations.
Ball, John M; Chen, Gui-Qiang G
2013-12-28
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.
Linear and Nonlinear Analysis of Brain Dynamics in Children with Cerebral Palsy
Sajedi, Firoozeh; Ahmadlou, Mehran; Vameghi, Roshanak; Gharib, Masoud; Hemmati, Sahel
2013-01-01
This study was carried out to determine linear and nonlinear changes of brain dynamics and their relationships with the motor dysfunctions in CP children. For this purpose power of EEG frequency bands (as a linear analysis) and EEG fractality (as a nonlinear analysis) were computed in eyes-closed resting state and statistically compared between 26…
Statistical field theory of futures commodity prices
Baaquie, Belal E.; Yu, Miao
2018-02-01
The statistical theory of commodity prices has been formulated by Baaquie (2013). Further empirical studies of single (Baaquie et al., 2015) and multiple commodity prices (Baaquie et al., 2016) have provided strong evidence in support the primary assumptions of the statistical formulation. In this paper, the model for spot prices (Baaquie, 2013) is extended to model futures commodity prices using a statistical field theory of futures commodity prices. The futures prices are modeled as a two dimensional statistical field and a nonlinear Lagrangian is postulated. Empirical studies provide clear evidence in support of the model, with many nontrivial features of the model finding unexpected support from market data.
Multiple scaling behaviour and nonlinear traits in music scores
González-Espinoza, Alfredo; Larralde, Hernán; Martínez-Mekler, Gustavo; Müller, Markus
2017-12-01
We present a statistical analysis of music scores from different composers using detrended fluctuation analysis (DFA). We find different fluctuation profiles that correspond to distinct autocorrelation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear autocorrelations by estimating the DFA of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.
A nonlinear model for the fluidization of marine mud by waves
Energy Technology Data Exchange (ETDEWEB)
Foda, M.A.; Hunt, J.R.; Chou, Hsien-Ter (Univ. of California, Berkeley (United States))
1993-04-15
The authors consider the problem of fluidization of mud deposits in shallow waters due to interactions with water waves. This is of increasing interest because of concerns that water pollutants, including heavy metals, pesticides, etc., are often found near surfaces of mud deposits. The authors look at the question of whether the cohesive properties of mud deposits exhibit nonlinear properties when they experience strains from water wave interactions. It is obvious that with large enough wave interactions the deposits become fluidized, and are not in that case truly nonlinear. In their modeling efforts they try to incorporate these ideas into a cohesive model where the magnitude of the water wave-sediment interaction has an influence on the type of response within the system.
Direct approach for solving nonlinear evolution and two-point ...
Indian Academy of Sciences (India)
2013-12-01
Dec 1, 2013 ... 1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong,. NSW 2522 ... the nonlinear phenomena as well as their further applications in the real-life situations, it is ... concentration gradient. Thus ...
Observing and modeling nonlinear dynamics in an internal combustion engine
International Nuclear Information System (INIS)
Daw, C.S.; Kennel, M.B.; Finney, C.E.; Connolly, F.T.
1998-01-01
We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model close-quote s simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. copyright 1998 The American Physical Society
Directory of Open Access Journals (Sweden)
Y. Hu
2007-06-01
Full Text Available This study presents an empirical relation that links the volume extinction coefficients of water clouds, the layer integrated depolarization ratios measured by lidar, and the effective radii of water clouds derived from collocated passive sensor observations. Based on Monte Carlo simulations of CALIPSO lidar observations, this method combines the cloud effective radius reported by MODIS with the lidar depolarization ratios measured by CALIPSO to estimate both the liquid water content and the effective number concentration of water clouds. The method is applied to collocated CALIPSO and MODIS measurements obtained during July and October of 2006, and January 2007. Global statistics of the cloud liquid water content and effective number concentration are presented.
Hu, Y.; Vaughan, M.; McClain, C.; Behrenfeld, M.; Maring, H.; Anderson, D.; Sun-Mack, S.; Flittner, D.; Huang, J.; Wielicki, B.; Minnis, P.; Weimer, C.; Trepte, C.; Kuehn, R.
2007-06-01
This study presents an empirical relation that links the volume extinction coefficients of water clouds, the layer integrated depolarization ratios measured by lidar, and the effective radii of water clouds derived from collocated passive sensor observations. Based on Monte Carlo simulations of CALIPSO lidar observations, this method combines the cloud effective radius reported by MODIS with the lidar depolarization ratios measured by CALIPSO to estimate both the liquid water content and the effective number concentration of water clouds. The method is applied to collocated CALIPSO and MODIS measurements obtained during July and October of 2006, and January 2007. Global statistics of the cloud liquid water content and effective number concentration are presented.
Nonlinear dynamical system identification using unscented Kalman filter
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
Statistical and Biophysical Models for Predicting Total and Outdoor Water Use in Los Angeles
Mini, C.; Hogue, T. S.; Pincetl, S.
2012-04-01
Modeling water demand is a complex exercise in the choice of the functional form, techniques and variables to integrate in the model. The goal of the current research is to identify the determinants that control total and outdoor residential water use in semi-arid cities and to utilize that information in the development of statistical and biophysical models that can forecast spatial and temporal urban water use. The City of Los Angeles is unique in its highly diverse socio-demographic, economic and cultural characteristics across neighborhoods, which introduces significant challenges in modeling water use. Increasing climate variability also contributes to uncertainties in water use predictions in urban areas. Monthly individual water use records were acquired from the Los Angeles Department of Water and Power (LADWP) for the 2000 to 2010 period. Study predictors of residential water use include socio-demographic, economic, climate and landscaping variables at the zip code level collected from US Census database. Climate variables are estimated from ground-based observations and calculated at the centroid of each zip code by inverse-distance weighting method. Remotely-sensed products of vegetation biomass and landscape land cover are also utilized. Two linear regression models were developed based on the panel data and variables described: a pooled-OLS regression model and a linear mixed effects model. Both models show income per capita and the percentage of landscape areas in each zip code as being statistically significant predictors. The pooled-OLS model tends to over-estimate higher water use zip codes and both models provide similar RMSE values.Outdoor water use was estimated at the census tract level as the residual between total water use and indoor use. This residual is being compared with the output from a biophysical model including tree and grass cover areas, climate variables and estimates of evapotranspiration at very high spatial resolution. A
Directory of Open Access Journals (Sweden)
Chen-Lin Soo
2017-01-01
Full Text Available The study on Sarawak coastal water quality is scarce, not to mention the application of the multivariate statistical approach to investigate the spatial variation of water quality and to identify the pollution source in Sarawak coastal water. Hence, the present study aimed to evaluate the spatial variation of water quality along the coastline of the southwestern region of Sarawak using multivariate statistical techniques. Seventeen physicochemical parameters were measured at 11 stations along the coastline with approximately 225 km length. The coastal water quality showed spatial heterogeneity where the cluster analysis grouped the 11 stations into four different clusters. Deterioration in coastal water quality has been observed in different regions of Sarawak corresponding to land use patterns in the region. Nevertheless, nitrate-nitrogen exceeded the guideline value at all sampling stations along the coastline. The principal component analysis (PCA has determined a reduced number of five principal components that explained 89.0% of the data set variance. The first PC indicated that the nutrients were the dominant polluting factors, which is attributed to the domestic, agricultural, and aquaculture activities, followed by the suspended solids in the second PC which are related to the logging activities.
Ageing of the nonlinear optical susceptibility in soft matter
International Nuclear Information System (INIS)
Ghofraniha, N; Conti, C; Leonardo, R Di; Ruzicka, B; Ruocco, G
2007-01-01
We investigate the nonlinear optics response of a colloidal dispersion undergoing dynamics slowing down with age, by using Z-scan and dynamic light scattering measurements. We study the high optical nonlinearity of an organic dye (rhodamine B) dispersed in a water-clay (laponite) suspension. We consider different clay concentrations (2.0-2.6 wt%) experiencing dynamics arrest. We find that (i) the concentration dependent exponential growth of both mean relaxation time and nonlinear absorption coefficient can be individually scaled to a master curve and (ii) the scaling times are the same for the two physical quantities. These findings indicate that the optical nonlinear susceptibility exhibits the same ageing universal scaling behaviour, typical of disordered out of equilibrium systems
Applied statistics for social and management sciences
Miah, Abdul Quader
2016-01-01
This book addresses the application of statistical techniques and methods across a wide range of disciplines. While its main focus is on the application of statistical methods, theoretical aspects are also provided as fundamental background information. It offers a systematic interpretation of results often discovered in general descriptions of methods and techniques such as linear and non-linear regression. SPSS is also used in all the application aspects. The presentation of data in the form of tables and graphs throughout the book not only guides users, but also explains the statistical application and assists readers in interpreting important features. The analysis of statistical data is presented consistently throughout the text. Academic researchers, practitioners and other users who work with statistical data will benefit from reading Applied Statistics for Social and Management Sciences. .
Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant
Directory of Open Access Journals (Sweden)
Xiangjie Liu
2014-01-01
Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.
Exact nonparametric inference for detection of nonlinear determinism
Luo, Xiaodong; Zhang, Jie; Small, Michael; Moroz, Irene
2005-01-01
We propose an exact nonparametric inference scheme for the detection of nonlinear determinism. The essential fact utilized in our scheme is that, for a linear stochastic process with jointly symmetric innovations, its ordinary least square (OLS) linear prediction error is symmetric about zero. Based on this viewpoint, a class of linear signed rank statistics, e.g. the Wilcoxon signed rank statistic, can be derived with the known null distributions from the prediction error. Thus one of the ad...
Directory of Open Access Journals (Sweden)
Vujović Svetlana R.
2013-01-01
Full Text Available This paper illustrates the utility of multivariate statistical techniques for analysis and interpretation of water quality data sets and identification of pollution sources/factors with a view to get better information about the water quality and design of monitoring network for effective management of water resources. Multivariate statistical techniques, such as factor analysis (FA/principal component analysis (PCA and cluster analysis (CA, were applied for the evaluation of variations and for the interpretation of a water quality data set of the natural water bodies obtained during 2010 year of monitoring of 13 parameters at 33 different sites. FA/PCA attempts to explain the correlations between the observations in terms of the underlying factors, which are not directly observable. Factor analysis is applied to physico-chemical parameters of natural water bodies with the aim classification and data summation as well as segmentation of heterogeneous data sets into smaller homogeneous subsets. Factor loadings were categorized as strong and moderate corresponding to the absolute loading values of >0.75, 0.75-0.50, respectively. Four principal factors were obtained with Eigenvalues >1 summing more than 78 % of the total variance in the water data sets, which is adequate to give good prior information regarding data structure. Each factor that is significantly related to specific variables represents a different dimension of water quality. The first factor F1 accounting for 28 % of the total variance and represents the hydrochemical dimension of water quality. The second factor F2 accounting for 18% of the total variance and may be taken factor of water eutrophication. The third factor F3 accounting 17 % of the total variance and represents the influence of point sources of pollution on water quality. The fourth factor F4 accounting 13 % of the total variance and may be taken as an ecological dimension of water quality. Cluster analysis (CA is an
Statistical Validation of Engineering and Scientific Models: Background
International Nuclear Information System (INIS)
Hills, Richard G.; Trucano, Timothy G.
1999-01-01
A tutorial is presented discussing the basic issues associated with propagation of uncertainty analysis and statistical validation of engineering and scientific models. The propagation of uncertainty tutorial illustrates the use of the sensitivity method and the Monte Carlo method to evaluate the uncertainty in predictions for linear and nonlinear models. Four example applications are presented; a linear model, a model for the behavior of a damped spring-mass system, a transient thermal conduction model, and a nonlinear transient convective-diffusive model based on Burger's equation. Correlated and uncorrelated model input parameters are considered. The model validation tutorial builds on the material presented in the propagation of uncertainty tutoriaI and uses the damp spring-mass system as the example application. The validation tutorial illustrates several concepts associated with the application of statistical inference to test model predictions against experimental observations. Several validation methods are presented including error band based, multivariate, sum of squares of residuals, and optimization methods. After completion of the tutorial, a survey of statistical model validation literature is presented and recommendations for future work are made
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Megalopoulos, Fivos A; Ochsenkuehn-Petropoulou, Maria T
2015-01-01
A statistical model based on multiple linear regression is developed, to estimate the bromine residual that can be expected after the bromination of cooling water. Make-up water sampled from a power plant in the Greek territory was used for the creation of the various cooling water matrices under investigation. The amount of bromine fed to the circuit, as well as other important operational parameters such as concentration at the cooling tower, temperature, organic load and contact time are taken as the independent variables. It is found that the highest contribution to the model's predictive ability comes from cooling water's organic load concentration, followed by the amount of bromine fed to the circuit, the water's mean temperature, the duration of the bromination period and finally its conductivity. Comparison of the model results with the experimental data confirms its ability to predict residual bromine given specific bromination conditions.
Statistical aspects of fish stock assessment
DEFF Research Database (Denmark)
Berg, Casper Willestofte
for stock assessment by application of state-of-the-art statistical methodology. The main contributions are presented in the form of six research papers. The major part of the thesis deals with age-structured assessment models, which is the most common approach. Conversion from length to age distributions...... statistical aspects of fish stocks assessment, which includes topics such as time series analysis, generalized additive models (GAMs), and non-linear state-space/mixed models capable of handling missing data and a high number of latent states and parameters. The aim is to improve the existing methods...
Statistical analysis of lineaments of Goa, India
Digital Repository Service at National Institute of Oceanography (India)
Iyer, S.D.; Banerjee, G.; Wagle, B.G.
statistically to obtain the nonlinear pattern in the form of a cosine wave. Three distinct peaks were found at azimuths of 40-45 degrees, 90-95 degrees and 140-145 degrees, which have peak values of 5.85, 6.80 respectively. These three peaks are correlated...
Directory of Open Access Journals (Sweden)
Md. Bodrud-Doza
2016-04-01
Full Text Available This study investigates the groundwater quality in the Faridpur district of central Bangladesh based on preselected 60 sample points. Water evaluation indices and a number of statistical approaches such as multivariate statistics and geostatistics are applied to characterize water quality, which is a major factor for controlling the groundwater quality in term of drinking purposes. The study reveal that EC, TDS, Ca2+, total As and Fe values of groundwater samples exceeded Bangladesh and international standards. Ground water quality index (GWQI exhibited that about 47% of the samples were belonging to good quality water for drinking purposes. The heavy metal pollution index (HPI, degree of contamination (Cd, heavy metal evaluation index (HEI reveal that most of the samples belong to low level of pollution. However, Cd provide better alternative than other indices. Principle component analysis (PCA suggests that groundwater quality is mainly related to geogenic (rock–water interaction and anthropogenic source (agrogenic and domestic sewage in the study area. Subsequently, the findings of cluster analysis (CA and correlation matrix (CM are also consistent with the PCA results. The spatial distributions of groundwater quality parameters are determined by geostatistical modeling. The exponential semivariagram model is validated as the best fitted models for most of the indices values. It is expected that outcomes of the study will provide insights for decision makers taking proper measures for groundwater quality management in central Bangladesh.
THREE-POINT PHASE CORRELATIONS: A NEW MEASURE OF NONLINEAR LARGE-SCALE STRUCTURE
Energy Technology Data Exchange (ETDEWEB)
Wolstenhulme, Richard; Bonvin, Camille [Kavli Institute for Cosmology Cambridge and Institute of Astronomy, Madingley Road, Cambridge CB3 OHA (United Kingdom); Obreschkow, Danail [International Centre for Radio Astronomy Research (ICRAR), M468, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009 (Australia)
2015-05-10
We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the nonlinear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F{sub 2}, which governs the nonlinear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1σ agreement for separations r ≳ 30 h{sup −1} Mpc. Fitting formulae for the power spectrum and the nonlinear coupling kernel at small scales allow us to extend our prediction into the strongly nonlinear regime, where we find a 1σ agreement with the simulations for r ≳ 2 h{sup −1} Mpc. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the nonlinear regime of gravity, with less contamination from the power spectrum variance.
Linking structure and activity in nonlinear spiking networks.
Directory of Open Access Journals (Sweden)
Gabriel Koch Ocker
2017-06-01
Full Text Available Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.
Linking structure and activity in nonlinear spiking networks.
Ocker, Gabriel Koch; Josić, Krešimir; Shea-Brown, Eric; Buice, Michael A
2017-06-01
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.
Directory of Open Access Journals (Sweden)
Yolanda Escalante
2012-09-01
Full Text Available The aims of this study were (i to compare women's water polo game-related statistics by match outcome (winning and losing teams and phase (preliminary, classificatory, and semi-final/bronze medal/gold medal, and (ii identify characteristics that discriminate performances for each phase. The game-related statistics of the 124 women's matches played in five International Championships (World and European Championships were analyzed. Differences between winning and losing teams in each phase were determined using the chi-squared. A discriminant analysis was then performed according to context in each of the three phases. It was found that the game-related statistics differentiate the winning from the losing teams in each phase of an international championship. The differentiating variables were both offensive (centre goals, power-play goals, counterattack goal, assists, offensive fouls, steals, blocked shots, and won sprints and defensive (goalkeeper-blocked shots, goalkeeper-blocked inferiority shots, and goalkeeper-blocked 5-m shots. The discriminant analysis showed the game-related statistics to discriminate performance in all phases: preliminary, classificatory, and final phases (92%, 90%, and 83%, respectively. Two variables were discriminatory by match outcome (winning or losing teams in all three phases: goals and goalkeeper-blocked shots
Digital Repository Service at National Institute of Oceanography (India)
Pankajakshan, T.; Shikauchi, A; Sugimori, Y.; Kubota, M.
-T a and precipitable water. The rms errors of the SSMI-T a , in this case are found to be reduced to 1.0°C. 1. Introduction Satellite derived surface-level meteorological parameters are considered to be a better alternative to sparse ship... Vol. 49, pp. 551 to 558. 1993 A Statistical Method to Get Surface Level Air-Temperature from Satellite Observations of Precipitable Water PANKAJAKSHAN THADATHIL*, AKIRA SHIKAUCHI, YASUHIRO SUGIMORI and MASAHISA KUBOTA School of Marine Science...
Sapsis, Themistoklis P; Majda, Andrew J
2013-08-20
A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.
Temporal aspects of surface water quality variation using robust statistical tools.
Mustapha, Adamu; Aris, Ahmad Zaharin; Ramli, Mohammad Firuz; Juahir, Hafizan
2012-01-01
Robust statistical tools were applied on the water quality datasets with the aim of determining the most significance parameters and their contribution towards temporal water quality variation. Surface water samples were collected from four different sampling points during dry and wet seasons and analyzed for their physicochemical constituents. Discriminant analysis (DA) provided better results with great discriminatory ability by using five parameters with (P < 0.05) for dry season affording more than 96% correct assignation and used five and six parameters for forward and backward stepwise in wet season data with P-value (P < 0.05) affording 68.20% and 82%, respectively. Partial correlation results revealed that there are strong (r(p) = 0.829) and moderate (r(p) = 0.614) relationships between five-day biochemical oxygen demand (BOD(5)) and chemical oxygen demand (COD), total solids (TS) and dissolved solids (DS) controlling for the linear effect of nitrogen in the form of ammonia (NH(3)) and conductivity for dry and wet seasons, respectively. Multiple linear regression identified the contribution of each variable with significant values r = 0.988, R(2) = 0.976 and r = 0.970, R(2) = 0.942 (P < 0.05) for dry and wet seasons, respectively. Repeated measure t-test confirmed that the surface water quality varies significantly between the seasons with significant value P < 0.05.
Chiou, C.T.; Kile, D.E.; Rutherford, D.W.; Sheng, G.; Boyd, S.A.
2000-01-01
The sorption isotherms of ethylene dibromide (EDB), diuron (DUN), and 3,5-dichlorophenol (DCP) from water on the humic acid and humin fractions of a peat soil and on the humic-acid of a muck soil have been measured. The data were compared with those of the solutes with the whole peat from which the humic-acid (HA) and humin (HM) fractions were derived and on which the sorption of the solutes exhibited varying extents of nonlinear capacities at low relative concentrations (C(e)/S(w)). The HA fraction as prepared by the density-fractionated method is relatively pure and presumably free of high- surface-area carbonaceous material (HSACM) that is considered to be responsible for the observed nonlinear sorption for nonpolar solutes (e.g., EDB) on the peat; conversely, the base-insoluble HM fraction as prepared is presumed to be enriched with HSACM, as manifested by the greatly higher BET- (N2) surface area than that of the whole peat. The sorption of EDB on HA exhibits no visible nonlinear effect, whereas the sorption on HM shows an enhanced nonlinearity over that on the whole peat. The sorption of polar DUN and DCP on HA and HM display nonlinear effects comparable with those on the whole peat; the effects are much more significant than those with nonpolar EDB. These results conform to the hypothesis that adsorption onto a small amount of strongly adsorbing HSACM is largely responsible for the nonlinear sorption of nonpolar solutes on soils and that additional specific interactions with the active groups of soil organic matter are responsible for the generally higher nonlinear sorption of the polar solutes.
Linear theory for filtering nonlinear multiscale systems with model error.
Berry, Tyrus; Harlim, John
2014-07-08
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering
Modeling the SAR Signature of Nonlinear Internal Waves
National Research Council Canada - National Science Library
Lettvin, Ellen E
2008-01-01
Nonlinear Internal Waves are pervasive globally, particularly in coastal waters. The currents and displacements associated with internal waves influence acoustic propagation and underwater navigation, as well as ocean transport and mixing...
Yuldashev, Petr V; Ollivier, Sébastien; Karzova, Maria M; Khokhlova, Vera A; Blanc-Benon, Philippe
2017-12-01
Linear and nonlinear propagation of high amplitude acoustic pulses through a turbulent layer in air is investigated using a two-dimensional KZK-type (Khokhlov-Zabolotskaya-Kuznetsov) equation. Initial waves are symmetrical N-waves with shock fronts of finite width. A modified von Kármán spectrum model is used to generate random wind velocity fluctuations associated with the turbulence. Physical parameters in simulations correspond to previous laboratory scale experiments where N-waves with 1.4 cm wavelength propagated through a turbulence layer with the outer scale of about 16 cm. Mean value and standard deviation of peak overpressure and shock steepness, as well as cumulative probabilities to observe amplified peak overpressure and shock steepness, are analyzed. Nonlinear propagation effects are shown to enhance pressure level in random foci for moderate initial amplitudes of N-waves thus increasing the probability to observe highly peaked waveforms. Saturation of the pressure level is observed for stronger nonlinear effects. It is shown that in the linear propagation regime, the turbulence mainly leads to the smearing of shock fronts, thus decreasing the probability to observe high values of steepness, whereas nonlinear effects dramatically increase the probability to observe steep shocks.
Nonlinear Relaxation in Population Dynamics
Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.
Faes, Luca; Zhao, He; Chon, Ki H; Nollo, Giandomenico
2009-03-01
We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discriminating statistic. Analysis of simulated time series showed that using TIV surrogates, linear nonstationary time series may be erroneously regarded as nonlinear and weak TV nonlinearities may remain unrevealed, while the use of TV AR surrogates markedly increases the probability of a correct interpretation. Application to short (500 beats) heart rate variability (HRV) time series recorded at rest (R), after head-up tilt (T), and during paced breathing (PB) showed: 1) modifications of the SE statistic that were well interpretable with the known cardiovascular physiology; 2) significant contribution of nonlinear dynamics to HRV in all conditions, with significant increase during PB at 0.2 Hz respiration rate; and 3) a disagreement between TV AR surrogates and TIV surrogates in about a quarter of the series, suggesting that nonstationarity may affect HRV recordings and bias the outcome of the traditional surrogate-based nonlinearity test.
Malkyarenko, Dariya I; Chenevert, Thomas L
2014-12-01
To describe an efficient procedure to empirically characterize gradient nonlinearity and correct for the corresponding apparent diffusion coefficient (ADC) bias on a clinical magnetic resonance imaging (MRI) scanner. Spatial nonlinearity scalars for individual gradient coils along superior and right directions were estimated via diffusion measurements of an isotropicic e-water phantom. Digital nonlinearity model from an independent scanner, described in the literature, was rescaled by system-specific scalars to approximate 3D bias correction maps. Correction efficacy was assessed by comparison to unbiased ADC values measured at isocenter. Empirically estimated nonlinearity scalars were confirmed by geometric distortion measurements of a regular grid phantom. The applied nonlinearity correction for arbitrarily oriented diffusion gradients reduced ADC bias from 20% down to 2% at clinically relevant offsets both for isotropic and anisotropic media. Identical performance was achieved using either corrected diffusion-weighted imaging (DWI) intensities or corrected b-values for each direction in brain and ice-water. Direction-average trace image correction was adequate only for isotropic medium. Empiric scalar adjustment of an independent gradient nonlinearity model adequately described DWI bias for a clinical scanner. Observed efficiency of implemented ADC bias correction quantitatively agreed with previous theoretical predictions and numerical simulations. The described procedure provides an independent benchmark for nonlinearity bias correction of clinical MRI scanners.
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes....
International Nuclear Information System (INIS)
Gallaher, B.; Mercier, T.; Black, P.; Mullen, K.
2000-01-01
Four governmental agencies conducted a round of groundwater, surface water, and spring water sampling at the Los Alamos National Laboratory during 1998. Samples were split among the four parties and sent to independent analytical laboratories. Results from three of the agencies were available for this study. Comparisons of analytical results that were paired by location and date were made between the various analytical laboratories. The results for over 50 split samples analyzed for inorganic chemicals, metals, and radionuclides were compared. Statistical analyses included non-parametric (sign test and signed-ranks test) and parametric (paired t-test and linear regression) methods. The data pairs were tested for statistically significant differences, defined by an observed significance level, or p-value, less than 0.05. The main conclusion is that the laboratories' performances are similar across most of the analytes that were measured. In some 95% of the laboratory measurements there was agreement on whether contaminant levels exceeded regulatory limits. The most significant differences in performance were noted for the radioactive suite, particularly for gross alpha particle activity and Sr-90
Tellinghuisen, Joel
2008-01-01
The method of least squares is probably the most powerful data analysis tool available to scientists. Toward a fuller appreciation of that power, this work begins with an elementary review of statistics fundamentals, and then progressively increases in sophistication as the coverage is extended to the theory and practice of linear and nonlinear least squares. The results are illustrated in application to data analysis problems important in the life sciences. The review of fundamentals includes the role of sampling and its connection to probability distributions, the Central Limit Theorem, and the importance of finite variance. Linear least squares are presented using matrix notation, and the significance of the key probability distributions-Gaussian, chi-square, and t-is illustrated with Monte Carlo calculations. The meaning of correlation is discussed, including its role in the propagation of error. When the data themselves are correlated, special methods are needed for the fitting, as they are also when fitting with constraints. Nonlinear fitting gives rise to nonnormal parameter distributions, but the 10% Rule of Thumb suggests that such problems will be insignificant when the parameter is sufficiently well determined. Illustrations include calibration with linear and nonlinear response functions, the dangers inherent in fitting inverted data (e.g., Lineweaver-Burk equation), an analysis of the reliability of the van't Hoff analysis, the problem of correlated data in the Guggenheim method, and the optimization of isothermal titration calorimetry procedures using the variance-covariance matrix for experiment design. The work concludes with illustrations on assessing and presenting results.
Gohil, B. S.; Hariharan, T. A.; Sharma, A. K.; Pandey, P. C.
1982-01-01
The 19.35 GHz and 22.235 GHz passive microwave radiometers (SAMIR) on board the Indian satellite Bhaskara have provided very useful data. From these data has been demonstrated the feasibility of deriving atmospheric and ocean surface parameters such as water vapor content, liquid water content, rainfall rate and ocean surface winds. Different approaches have been tried for deriving the atmospheric water content. The statistical and empirical methods have been used by others for the analysis of the Nimbus data. A simulation technique has been attempted for the first time for 19.35 GHz and 22.235 GHz radiometer data. The results obtained from three different methods are compared with radiosonde data. A case study of a tropical depression has been undertaken to demonstrate the capability of Bhaskara SAMIR data to show the variation of total water vapor and liquid water contents.
Impact of Seawater Nonlinearities on Nordic Seas Circulation
Helber, R. W.; Wallcraft, A. J.; Shriver, J. F.
2017-12-01
The Nordic Seas (Greenland, Iceland, and Norwegian Seas) form an ocean basin important for Arctic-mid-latitude climate linkages. Cold fresh water from the Arctic Ocean and warm salty water from the North Atlantic Ocean meet in the Nordic Seas, where a delicate balance between temperature and salinity variability results in deep water formation. Seawater non-linearities are stronger at low temperatures and salinities making high-latitude oceans highly subject to thermbaricity and cabbeling. This presentation highlights and quantifies the impact of seawater non-linearities on the Nordic Seas circulation. We use two layered ocean circulation models, the Hybrid Coordinate Ocean Model (HYOCM) and the Modular Ocean Model version 6 (MOM6), that enable accurate representation of processes along and across density or neutral density surfaces. Different equations-of-state and vertical coordinates are evaluated to clarify the impact of seawater non-linearities. Present Navy systems, however, do not capture some features in the Nrodic Seas vertical structure. For example, observations from the Greenland Sea reveal a subsurface temperature maximum that deepens from approximately 1500 m during 1998 to 1800 m during 2005. We demonstrate that in terms of density, salinity is the largest source of error in Nordic Seas Navy forecasts, regional scale models can represent mesoscale features driven by thermobaricity, vertical coordinates are a critical issue in Nordic Sea circulation modeling.
Breaking of ensembles of linear and nonlinear oscillators
International Nuclear Information System (INIS)
Buts, V.A.
2016-01-01
Some results concerning the study of the dynamics of ensembles of linear and nonlinear oscillators are stated. It is shown that, in general, a stable ensemble of linear oscillator has a limited number of oscillators. This number has been defined for some simple models. It is shown that the features of the dynamics of linear oscillators can be used for conversion of the low-frequency energy oscillations into high frequency oscillations. The dynamics of coupled nonlinear oscillators in most cases is chaotic. For such a case, it is shown that the statistical characteristics (moments) of chaotic motion can significantly reduce potential barriers that keep the particles in the capture region
Linear and nonlinear kinetic-stability studies in tokamaks
International Nuclear Information System (INIS)
Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.
1982-09-01
This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Generation of Caustics and Rogue Waves from Nonlinear Instability.
Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W
2017-11-17
Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.
SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix
Energy Technology Data Exchange (ETDEWEB)
Michalski, D; Huq, M; Bednarz, G; Lalonde, R; Yang, Y; Heron, D [University of Pittsburgh Medical Center, Pittsburgh, PA (United States)
2014-06-01
Purpose: To quantify respiratory signal of patients in BodyFix undergoing 4DCT scan with and without immobilization cover. Methods: 20 pairs of respiratory tracks recorded with RPM system during 4DCT scan were analyzed. Descriptive statistic was applied to selected parameters of exhale-inhale decomposition. Standardized signals were used with the delay method to build orbits in embedded space. Nonlinear behavior was tested with surrogate data. Sample entropy SE, Lempel-Ziv complexity LZC and the largest Lyapunov exponents LLE were compared. Results: Statistical tests show difference between scans for inspiration time and its variability, which is bigger for scans without cover. The same is for variability of the end of exhalation and inhalation. Other parameters fail to show the difference. For both scans respiratory signals show determinism and nonlinear stationarity. Statistical test on surrogate data reveals their nonlinearity. LLEs show signals chaotic nature and its correlation with breathing period and its embedding delay time. SE, LZC and LLE measure respiratory signal complexity. Nonlinear characteristics do not differ between scans. Conclusion: Contrary to expectation cover applied to patients in BodyFix appears to have limited effect on signal parameters. Analysis based on trajectories of delay vectors shows respiratory system nonlinear character and its sensitive dependence on initial conditions. Reproducibility of respiratory signal can be evaluated with measures of signal complexity and its predictability window. Longer respiratory period is conducive for signal reproducibility as shown by these gauges. Statistical independence of the exhale and inhale times is also supported by the magnitude of LLE. The nonlinear parameters seem more appropriate to gauge respiratory signal complexity since its deterministic chaotic nature. It contrasts with measures based on harmonic analysis that are blind for nonlinear features. Dynamics of breathing, so crucial for
SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix
International Nuclear Information System (INIS)
Michalski, D; Huq, M; Bednarz, G; Lalonde, R; Yang, Y; Heron, D
2014-01-01
Purpose: To quantify respiratory signal of patients in BodyFix undergoing 4DCT scan with and without immobilization cover. Methods: 20 pairs of respiratory tracks recorded with RPM system during 4DCT scan were analyzed. Descriptive statistic was applied to selected parameters of exhale-inhale decomposition. Standardized signals were used with the delay method to build orbits in embedded space. Nonlinear behavior was tested with surrogate data. Sample entropy SE, Lempel-Ziv complexity LZC and the largest Lyapunov exponents LLE were compared. Results: Statistical tests show difference between scans for inspiration time and its variability, which is bigger for scans without cover. The same is for variability of the end of exhalation and inhalation. Other parameters fail to show the difference. For both scans respiratory signals show determinism and nonlinear stationarity. Statistical test on surrogate data reveals their nonlinearity. LLEs show signals chaotic nature and its correlation with breathing period and its embedding delay time. SE, LZC and LLE measure respiratory signal complexity. Nonlinear characteristics do not differ between scans. Conclusion: Contrary to expectation cover applied to patients in BodyFix appears to have limited effect on signal parameters. Analysis based on trajectories of delay vectors shows respiratory system nonlinear character and its sensitive dependence on initial conditions. Reproducibility of respiratory signal can be evaluated with measures of signal complexity and its predictability window. Longer respiratory period is conducive for signal reproducibility as shown by these gauges. Statistical independence of the exhale and inhale times is also supported by the magnitude of LLE. The nonlinear parameters seem more appropriate to gauge respiratory signal complexity since its deterministic chaotic nature. It contrasts with measures based on harmonic analysis that are blind for nonlinear features. Dynamics of breathing, so crucial for
International Nuclear Information System (INIS)
Aminu Ibrahim; Hafizan Juahir; Mohd Ekhwan Toriman; Mustapha, A.; Azman Azid; Isiyaka, H.A.
2015-01-01
Multivariate Statistical techniques including cluster analysis, discriminant analysis, and principal component analysis/factor analysis were applied to investigate the spatial variation and pollution sources in the Terengganu river basin during 5 years of monitoring 13 water quality parameters at thirteen different stations. Cluster analysis (CA) classified 13 stations into 2 clusters low polluted (LP) and moderate polluted (MP) based on similar water quality characteristics. Discriminant analysis (DA) rendered significant data reduction with 4 parameters (pH, NH 3 -NL, PO 4 and EC) and correct assignation of 95.80 %. The PCA/ FA applied to the data sets, yielded in five latent factors accounting 72.42 % of the total variance in the water quality data. The obtained varifactors indicate that parameters in charge for water quality variations are mainly related to domestic waste, industrial, runoff and agricultural (anthropogenic activities). Therefore, multivariate techniques are important in environmental management. (author)
Directory of Open Access Journals (Sweden)
Voza Danijela
2015-12-01
Full Text Available The aim of this article is to evaluate the quality of the Danube River in its course through Serbia as well as to demonstrate the possibilities for using three statistical methods: Principal Component Analysis (PCA, Factor Analysis (FA and Cluster Analysis (CA in the surface water quality management. Given that the Danube is an important trans-boundary river, thorough water quality monitoring by sampling at different distances during shorter and longer periods of time is not only ecological, but also a political issue. Monitoring was carried out at monthly intervals from January to December 2011, at 17 sampling sites. The obtained data set was treated by multivariate techniques in order, firstly, to identify the similarities and differences between sampling periods and locations, secondly, to recognize variables that affect the temporal and spatial water quality changes and thirdly, to present the anthropogenic impact on water quality parameters.
Nonlinear unitary quantum collapse model with self-generated noise
Geszti, Tamás
2018-04-01
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.
An Entropy-Based Statistic for Genomewide Association Studies
Zhao, Jinying; Boerwinkle, Eric; Xiong, Momiao
2005-01-01
Efficient genotyping methods and the availability of a large collection of single-nucleotide polymorphisms provide valuable tools for genetic studies of human disease. The standard χ2 statistic for case-control studies, which uses a linear function of allele frequencies, has limited power when the number of marker loci is large. We introduce a novel test statistic for genetic association studies that uses Shannon entropy and a nonlinear function of allele frequencies to amplify the difference...
Photon statistics, antibunching and squeezed states
International Nuclear Information System (INIS)
Leuchs, G.
1986-01-01
This paper attempts to describe the status and addresses future prospects of experiments regarding photon antibunching, and squeezed states. Light correlation is presented in the framework of classical electrodynamics. The extension to quantized radiation fields is discussed and an introduction to the basic principles related to photon statistics, antibunching and squeezed states are presented. The effect of linear attenuation (beam splitters, neutral density filters, and detector quantum efficiency) on the detected signal is discussed. Experiments on the change of photon statistics by the nonlinear interaction of radiation fields with matter are described and some experimental observations of antibunching and sub-Poissonian photon statistics in resonance fluorescence and with possible schemes for the generation and detection of squeezed states are examined
Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation
Vitanov, Nikolay K.; Dimitrova, Zlatinka I.
2018-03-01
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...... symmetric non-linear error correction considered. A simulation study shows that the fi…nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...... symmetric non-linear error correction are considered. A simulation study shows that the finite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....
Lee, Cameron C.; Sheridan, Scott C.; Barnes, Brian B.; Hu, Chuanmin; Pirhalla, Douglas E.; Ransibrahmanakul, Varis; Shein, Karsten
2017-10-01
The coastal waters of the southeastern USA contain important protected habitats and natural resources that are vulnerable to climate variability and singular weather events. Water clarity, strongly affected by atmospheric events, is linked to substantial environmental impacts throughout the region. To assess this relationship over the long-term, this study uses an artificial neural network-based time series modeling technique known as non-linear autoregressive models with exogenous input (NARX models) to explore the relationship between climate and a water clarity index (KDI) in this area and to reconstruct this index over a 66-year period. Results show that synoptic-scale circulation patterns, weather types, and precipitation all play roles in impacting water clarity to varying degrees in each region of the larger domain. In particular, turbid water is associated with transitional weather and cyclonic circulation in much of the study region. Overall, NARX model performance also varies—regionally, seasonally and interannually—with wintertime estimates of KDI along the West Florida Shelf correlating to the actual KDI at r > 0.70. Periods of extreme (high) KDI in this area coincide with notable El Niño events. An upward trend in extreme KDI events from 1948 to 2013 is also present across much of the Florida Gulf coast.
A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter
Brigo, D.; Hanzon, B.; LeGland, F.
1998-01-01
This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is
Nonlinear spin-up in a circular cylinder
van de Konijnenberg, J.A.; Heijst, van G.J.F.
1995-01-01
Nonlinear spin-up in a circular cylindrical tank is investigated experimentally and compared with the Wedemeyer model. The experiments were performed with water, using tracer particles floating at the free surface in order to visualize the flow field. The experimentally determined vorticity profiles
Non-linear dielectric spectroscopy of microbiological suspensions
Treo, Ernesto F; Felice, Carmelo J
2009-01-01
Background Non-linear dielectric spectroscopy (NLDS) of microorganism was characterized by the generation of harmonics in the polarization current when a microorganism suspension was exposed to a sinusoidal electric field. The biological nonlinear response initially described was not well verified by other authors and the results were susceptible to ambiguous interpretation. In this paper NLDS was performed to yeast suspension in tripolar and tetrapolar configuration with a recently developed analyzer. Methods Tripolar analysis was carried out by applying sinusoidal voltages up to 1 V at the electrode interface. Tetrapolar analysis was carried on with sinusoidal field strengths from 0.1 V cm-1 to 70 V cm-1. Both analyses were performed within a frequency range from 1 Hz through 100 Hz. The harmonic amplitudes were Fourier-analyzed and expressed in dB. The third harmonic, as reported previously, was investigated. Statistical analysis (ANOVA) was used to test the effect of inhibitor an activator of the plasma membrane enzyme in the measured response. Results No significant non-linearities were observed in tetrapolar analysis, and no observable changes occurred when inhibitor and activator were added to the suspension. Statistical analysis confirmed these results. When a pure sinus voltage was applied to an electrode-yeast suspension interface, variations higher than 25 dB for the 3rd harmonic were observed. Variation higher than 20 dB in the 3rd harmonics has also been found when adding an inhibitor or activator of the membrane-bounded enzymes. These variations did not occur when the suspension was boiled. Discussion The lack of result in tetrapolar cells suggest that there is no, if any, harmonic generation in microbiological bulk suspension. The non-linear response observed was originated in the electrode-electrolyte interface. The frequency and voltage windows observed in previous tetrapolar analysis were repeated in the tripolar measurements, but maximum were not
Non-linear dielectric spectroscopy of microbiological suspensions
Directory of Open Access Journals (Sweden)
Felice Carmelo J
2009-09-01
Full Text Available Abstract Background Non-linear dielectric spectroscopy (NLDS of microorganism was characterized by the generation of harmonics in the polarization current when a microorganism suspension was exposed to a sinusoidal electric field. The biological nonlinear response initially described was not well verified by other authors and the results were susceptible to ambiguous interpretation. In this paper NLDS was performed to yeast suspension in tripolar and tetrapolar configuration with a recently developed analyzer. Methods Tripolar analysis was carried out by applying sinusoidal voltages up to 1 V at the electrode interface. Tetrapolar analysis was carried on with sinusoidal field strengths from 0.1 V cm-1 to 70 V cm-1. Both analyses were performed within a frequency range from 1 Hz through 100 Hz. The harmonic amplitudes were Fourier-analyzed and expressed in dB. The third harmonic, as reported previously, was investigated. Statistical analysis (ANOVA was used to test the effect of inhibitor an activator of the plasma membrane enzyme in the measured response. Results No significant non-linearities were observed in tetrapolar analysis, and no observable changes occurred when inhibitor and activator were added to the suspension. Statistical analysis confirmed these results. When a pure sinus voltage was applied to an electrode-yeast suspension interface, variations higher than 25 dB for the 3rd harmonic were observed. Variation higher than 20 dB in the 3rd harmonics has also been found when adding an inhibitor or activator of the membrane-bounded enzymes. These variations did not occur when the suspension was boiled. Discussion The lack of result in tetrapolar cells suggest that there is no, if any, harmonic generation in microbiological bulk suspension. The non-linear response observed was originated in the electrode-electrolyte interface. The frequency and voltage windows observed in previous tetrapolar analysis were repeated in the tripolar
Energy Technology Data Exchange (ETDEWEB)
Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)
2016-11-15
Highlights: • Simplified models with inclusion of the clad temperature are considered. • Boiling nonlinearity and core power removal have been modeled. • Method of multiple time scales has been used for nonlinear analysis to get the nature and amplitude of oscillations. • Incorporation of modeling complexities enhances the stability of system. • We find that reactors with higher nominal power are more desirable from the point of view of global stability. - Abstract: We study the effect of including boiling nonlinearity, clad temperature and void-dependent power removal from the primary loop in the mathematical modeling of a boiling water reactor (BWR) on its dynamic characteristics. The advanced heavy water reactor (AHWR) is taken as a case study. Towards this end, we have analyzed two different simplified models with different handling of the clad temperature. Each of these models has the necessary modifications pertaining to boiling nonlinearity and power removal from the primary loop. These simplified models incorporate the neutronics and thermal–hydraulic coupling. The effect of successive changes in the modeling assumptions on the linear stability of the reactor has been studied and we find that incorporation of each of these complexities in the model increases the stable operating region of the reactor. Further, the method of multiple time scales (MMTS) is exploited to carry out the nonlinear analysis with a view to predict the bifurcation characteristics of the reactor. Both subcritical and supercritical Hopf bifurcations are present in each model depending on the choice of operating parameters. These analytical observations from MMTS have been verified against numerical simulations. A parametric study on the effect of changing the nominal reactor power on the regions in the parametric space of void coefficient of reactivity and fuel temperature coefficient of reactivity with sub- and super-critical Hopf bifurcations has been performed for all
Qi, D.; Majda, A.
2017-12-01
A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with
Statistical modelling of transcript profiles of differentially regulated genes
Directory of Open Access Journals (Sweden)
Sergeant Martin J
2008-07-01
Full Text Available Abstract Background The vast quantities of gene expression profiling data produced in microarray studies, and the more precise quantitative PCR, are often not statistically analysed to their full potential. Previous studies have summarised gene expression profiles using simple descriptive statistics, basic analysis of variance (ANOVA and the clustering of genes based on simple models fitted to their expression profiles over time. We report the novel application of statistical non-linear regression modelling techniques to describe the shapes of expression profiles for the fungus Agaricus bisporus, quantified by PCR, and for E. coli and Rattus norvegicus, using microarray technology. The use of parametric non-linear regression models provides a more precise description of expression profiles, reducing the "noise" of the raw data to produce a clear "signal" given by the fitted curve, and describing each profile with a small number of biologically interpretable parameters. This approach then allows the direct comparison and clustering of the shapes of response patterns between genes and potentially enables a greater exploration and interpretation of the biological processes driving gene expression. Results Quantitative reverse transcriptase PCR-derived time-course data of genes were modelled. "Split-line" or "broken-stick" regression identified the initial time of gene up-regulation, enabling the classification of genes into those with primary and secondary responses. Five-day profiles were modelled using the biologically-oriented, critical exponential curve, y(t = A + (B + CtRt + ε. This non-linear regression approach allowed the expression patterns for different genes to be compared in terms of curve shape, time of maximal transcript level and the decline and asymptotic response levels. Three distinct regulatory patterns were identified for the five genes studied. Applying the regression modelling approach to microarray-derived time course data
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem
2018-01-01
In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Directory of Open Access Journals (Sweden)
Azmat Ullah
Full Text Available In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA with Interior Point Algorithm (IPA is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Modern applied statistics with s-plus
Venables, W N
1997-01-01
S-PLUS is a powerful environment for the statistical and graphical analysis of data. It provides the tools to implement many statistical ideas which have been made possible by the widespread availability of workstations having good graphics and computational capabilities. This book is a guide to using S-PLUS to perform statistical analyses and provides both an introduction to the use of S-PLUS and a course in modern statistical methods. S-PLUS is available for both Windows and UNIX workstations, and both versions are covered in depth. The aim of the book is to show how to use S-PLUS as a powerful and graphical system. Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS, and both students and researchers using statistics. Throughout, the emphasis is on presenting practical problems and full analyses of real data sets. Many of the methods discussed are state-of-the-art approaches to topics such as linear and non-linear regression models, robust a...
STREAMFLOW AND WATER QUALITY REGRESSION MODELING ...
African Journals Online (AJOL)
... downstream Obigbo station show: consistent time-trends in degree of contamination; linear and non-linear relationships for water quality models against total dissolved solids (TDS), total suspended sediment (TSS), chloride, pH and sulphate; and non-linear relationship for streamflow and water quality transport models.
On the pressure field of nonlinear standing water waves
Schwartz, L. W.
1980-01-01
The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.
International Nuclear Information System (INIS)
El-Tawil, M A; Al-Jihany, A S
2008-01-01
In this paper, nonlinear oscillators under quadratic nonlinearity with stochastic inputs are considered. Different methods are used to obtain first order approximations, namely, the WHEP technique, the perturbation method, the Pickard approximations, the Adomian decompositions and the homotopy perturbation method (HPM). Some statistical moments are computed for the different methods using mathematica 5. Comparisons are illustrated through figures for different case-studies
Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Vitanov Nikolay K.
2018-03-01
Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.
Signaling on the continuous spectrum of nonlinear optical fiber.
Tavakkolnia, Iman; Safari, Majid
2017-08-07
This paper studies different signaling techniques on the continuous spectrum (CS) of nonlinear optical fiber defined by nonlinear Fourier transform. Three different signaling techniques are proposed and analyzed based on the statistics of the noise added to CS after propagation along the nonlinear optical fiber. The proposed methods are compared in terms of error performance, distance reach, and complexity. Furthermore, the effect of chromatic dispersion on the data rate and noise in nonlinear spectral domain is investigated. It is demonstrated that, for a given sequence of CS symbols, an optimal bandwidth (or symbol rate) can be determined so that the temporal duration of the propagated signal at the end of the fiber is minimized. In effect, the required guard interval between the subsequently transmitted data packets in time is minimized and the effective data rate is significantly enhanced. Moreover, by selecting the proper signaling method and design criteria a distance reach of 7100 km is reported by only singling on CS at a rate of 9.6 Gbps.
Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations
Kanoglu, U.; Aydin, B.
2014-12-01
The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV
Noise and non-linearities in high-throughput data
International Nuclear Information System (INIS)
Nguyen, Viet-Anh; Lió, Pietro; Koukolíková-Nicola, Zdena; Bagnoli, Franco
2009-01-01
High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Eisenhart, T.; Josset, L.; Rising, J. A.; Devineni, N.; Lall, U.
2017-12-01
In the wake of recent water crises, the need to understand and predict the risk of water stress in urban and rural areas has grown. This understanding has the potential to improve decision making in public resource management, policy making, risk management and investment decisions. Assuming an underlying relationship between urban and rural water stress and observable features, we apply Deep Learning and Supervised Learning models to uncover hidden nonlinear patterns from spatiotemporal datasets. Results of interest includes prediction accuracy on extreme categories (i.e. urban areas highly prone to water stress) and not solely the average risk for urban or rural area, which adds complexity to the tuning of model parameters. We first label urban water stressed counties using annual water quality violations and compile a comprehensive spatiotemporal dataset that captures the yearly evolution of climatic, demographic and economic factors of more than 3,000 US counties over the 1980-2010 period. As county-level data reporting is not done on a yearly basis, we test multiple imputation methods to get around the issue of missing data. Using Python libraries, TensorFlow and scikit-learn, we apply and compare the ability of, amongst other methods, Recurrent Neural Networks (testing both LSTM and GRU cells), Convolutional Neural Networks and Support Vector Machines to predict urban water stress. We evaluate the performance of those models over multiple time spans and combine methods to diminish the risk of overfitting and increase prediction power on test sets. This methodology seeks to identify hidden nonlinear patterns to assess the predominant data features that influence urban and rural water stress. Results from this application at the national scale will assess the performance of deep learning models to predict water stress risk areas across all US counties and will highlight a predominant Machine Learning method for modeling water stress risk using spatiotemporal
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of
Mons, M.N.; Wielen, J.M.L. van der; Blokker, E.J.M.; Sinclair, M.I.; Hulshof, K.F.A.M.; Dangendorf, F.; Hunter, P.R.; Medema, G.J.
2007-01-01
The volume of cold tap water consumed is an essential element in quantitative microbial risk assessment. This paper presents a review of tap water consumption studies. Study designs were evaluated and statistical distributions were fitted to water consumption data from The Netherlands, Great
Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures
International Nuclear Information System (INIS)
Zhao, Y.
1996-01-01
Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed
Predicting radiotherapy outcomes using statistical learning techniques
International Nuclear Information System (INIS)
El Naqa, Issam; Bradley, Jeffrey D; Deasy, Joseph O; Lindsay, Patricia E; Hope, Andrew J
2009-01-01
Radiotherapy outcomes are determined by complex interactions between treatment, anatomical and patient-related variables. A common obstacle to building maximally predictive outcome models for clinical practice is the failure to capture potential complexity of heterogeneous variable interactions and applicability beyond institutional data. We describe a statistical learning methodology that can automatically screen for nonlinear relations among prognostic variables and generalize to unseen data before. In this work, several types of linear and nonlinear kernels to generate interaction terms and approximate the treatment-response function are evaluated. Examples of institutional datasets of esophagitis, pneumonitis and xerostomia endpoints were used. Furthermore, an independent RTOG dataset was used for 'generalizabilty' validation. We formulated the discrimination between risk groups as a supervised learning problem. The distribution of patient groups was initially analyzed using principle components analysis (PCA) to uncover potential nonlinear behavior. The performance of the different methods was evaluated using bivariate correlations and actuarial analysis. Over-fitting was controlled via cross-validation resampling. Our results suggest that a modified support vector machine (SVM) kernel method provided superior performance on leave-one-out testing compared to logistic regression and neural networks in cases where the data exhibited nonlinear behavior on PCA. For instance, in prediction of esophagitis and pneumonitis endpoints, which exhibited nonlinear behavior on PCA, the method provided 21% and 60% improvements, respectively. Furthermore, evaluation on the independent pneumonitis RTOG dataset demonstrated good generalizabilty beyond institutional data in contrast with other models. This indicates that the prediction of treatment response can be improved by utilizing nonlinear kernel methods for discovering important nonlinear interactions among model
Quantum statistics and squeezing for a microwave-driven interacting magnon system.
Haghshenasfard, Zahra; Cottam, Michael G
2017-02-01
Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.
Nonlinear optical properties of colloidal silver nanoparticles produced by laser ablation in liquids
International Nuclear Information System (INIS)
Karavanskii, V A; Krasovskii, V I; Ivanchenko, P V; Simakin, Aleksandr V
2004-01-01
The optical and nonlinear optical properties of colloidal solutions of silver obtained by laser ablation in water and ethanol are studied. It is shown that freshly prepared colloids experience a full or partial sedimentation by changing their nonlinear optical properties. Aqueous colloids undergo a partial sedimentation and their nonlinear optical absorption changes to nonlinear optical transmission. The obtained results are interpreted using the Drude model for metal particles taking the particle size into account and can be explained by the sedimentation of larger silver particles accompanied by the formation of a stable colloid containing silver nanoparticles with a tentatively silver oxide shell. The characteristic size of particles forming such a stable colloid is determined and its optical nonlinearity is estimated. (nonlinear optical phenomena)
Preface "Nonlinear processes in oceanic and atmospheric flows"
Directory of Open Access Journals (Sweden)
E. García-Ladona
2010-05-01
Full Text Available Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows" contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Niño Southern Oscillation.
Nonlinear Magnetic Phenomena in Highly Polarized Target Materials
Kiselev, Yu F
2007-01-01
The report introduces and surveys nonlinear magnetic phenomena which have been observed at high nuclear polarizations in polarized targets of the SMC and of the COMPASS collaborations at CERN. Some of these phenomena, namely the frequency modulation eect and the distortion of the NMR line shape, promote the development of the polarized target technique. Others, as the spin-spin cross-relaxation between spin subsystems can be used for the development of quantum statistical physics. New findings bear on an electromagnetic noise and the spectrally resolved radiation from LiD with negatively polarized nuclei detected by low temperature bolometers. These nonlinear phenomena need to be taken into account for achieving the ultimate polarizations.
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1992-12-01
Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science
Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems
He, Yuning; Davies, Misty Dawn
2014-01-01
The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.
International Nuclear Information System (INIS)
Outeda, R.; D'Onofrio, A.; El Hasi, C.; Zalts, A.
2014-01-01
Density driven instabilities produced by CO 2 (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO 2 pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO 2 pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm −1 ) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO 2 pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator
Dry Sliding Wear Behavior of Super Duplex Stainless Steel AISI 2507: a Statistical Approach
Directory of Open Access Journals (Sweden)
Davanageri M.
2016-12-01
Full Text Available The dry sliding wear behavior of heat-treated super duplex stainless steel AISI 2507 was examined by taking pin-on-disc type of wear-test rig. Independent parameters, namely applied load, sliding distance, and sliding speed, influence mainly the wear rate of super duplex stainless steel. The said material was heat treated to a temperature of 850°C for 1 hour followed by water quenching. The heat treatment was carried out to precipitate the secondary sigma phase formation. Experiments were conducted to study the influence of independent parameters set at three factor levels using the L27 orthogonal array of the Taguchi experimental design on the wear rate. Statistical significance of both individual and combined factor effects was determined for specific wear rate. Surface plots were drawn to explain the behavior of independent variables on the measured wear rate. Statistically, the models were validated using the analysis of variance test. Multiple non-linear regression equations were derived for wear rate expressed as non-linear functions of independent variables. Further, the prediction accuracy of the developed regression equation was tested with the actual experiments. The independent parameters responsible for the desired minimum wear rate were determined by using the desirability function approach. The worn-out surface characteristics obtained for the minimum wear rate was examined using the scanning electron microscope. The desired smooth surface was obtained for the determined optimal condition by desirability function approach.
Preliminary Test for Nonlinear Input Output Relations in SISO Systems
DEFF Research Database (Denmark)
Knudsen, Torben
2000-01-01
This paper discusses and develops preliminary statistical tests for detecting nonlinearities in the deterministic part of SISO systems with noise. The most referenced method is unreliable for common noise processes as e.g.\\ colored. Therefore two new methods based on superposition and sinus input...
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
Energy Technology Data Exchange (ETDEWEB)
Yoshimoto, H. [Ship Research Inst., Tokyo (Japan)
1996-12-31
Since ocean waves encountered by ocean vessels or offshore structures in actual sea areas present extremely irregular variations, a stochastic method is necessary to estimate their statistical properties. This paper first shows a calculation method for probability density function for water level variation which strictly incorporates a secondary non-linear effect containing directional dispersibility by modeling ocean waves as short-crested irregular waves. Then, the paper specifically elucidates effects of the directional dispersibility of ocean waves on statistical amount of amplitudes by deriving the statistical amount of the amplitudes based on the probability density function of the water level variation and by using a numerical simulation. The paper finally takes up data of waves in stormy sea observed in an experiment in an actual sea area, compares the result with that of theoretical calculations, and evaluates reasonability of this method. With this estimation method, individual secondary components or components of difference and sum may be subjected to influence of the directional dispersibility, but they do not differ much from the case of long-crested irregular waves on the whole. 21 refs., 11 figs., 2 tabs.
Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models
Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric D.; Naranjo, Ramon C.; Huntington, Justin
2018-01-01
The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.
Nonlinear wave collapse and strong turbulence
International Nuclear Information System (INIS)
Robinson, P.A.
1997-01-01
The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Zhang Xiwen; He Feng; Hao Pengfei; Wang Xuefang
2000-01-01
Based on the elaborate force and moment analysis with characteristics method and control-volume integrating method for the piping system of primary loop under pressurized water reactor' loss of coolant accident (LOCA) conditions, the nonlinear dynamic response of this system is calculated by the updated Lagrangian formulation (ADINA code). The piping system and virtual underpinning are specially processed, the move displacement of the broken pipe with time is accurately acquired, which is very important and useful for the design of piping system and virtual underpinning
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
Zhang, Yu; Jiang, Jack J.
2008-09-01
Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.
Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan
2018-05-01
Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.
Energy Technology Data Exchange (ETDEWEB)
Jiang, Qingchao; Yan, Xuefeng; Lv, Zhaomin; Guo, Meijin [East China University of Science and Technology, Shanghai (China)
2013-06-15
Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring.
International Nuclear Information System (INIS)
Jiang, Qingchao; Yan, Xuefeng; Lv, Zhaomin; Guo, Meijin
2013-01-01
Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring
Discriminatory power of water polo game-related statistics at the 2008 Olympic Games.
Escalante, Yolanda; Saavedra, Jose M; Mansilla, Mirella; Tella, Victor
2011-02-01
The aims of this study were (1) to compare water polo game-related statistics by context (winning and losing teams) and sex (men and women), and (2) to identify characteristics discriminating the performances for each sex. The game-related statistics of the 64 matches (44 men's and 20 women's) played in the final phase of the Olympic Games held in Beijing in 2008 were analysed. Unpaired t-tests compared winners and losers and men and women, and confidence intervals and effect sizes of the differences were calculated. The results were subjected to a discriminant analysis to identify the differentiating game-related statistics of the winning and losing teams. The results showed the differences between winning and losing men's teams to be in both defence and offence, whereas in women's teams they were only in offence. In men's games, passing (assists), aggressive play (exclusions), centre position effectiveness (centre shots), and goalkeeper defence (goalkeeper-blocked 5-m shots) predominated, whereas in women's games the play was more dynamic (possessions). The variable that most discriminated performance in men was goalkeeper-blocked shots, and in women shooting effectiveness (shots). These results should help coaches when planning training and competition.
Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim
2014-05-01
The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX
Nonlinear physics of twisted magnetic field lines
International Nuclear Information System (INIS)
Yoshida, Zensho
1998-01-01
Twisted magnetic field lines appear commonly in many different plasma systems, such as magnetic ropes created through interactions between the magnetosphere and the solar wind, magnetic clouds in the solar wind, solar corona, galactic jets, accretion discs, as well as fusion plasma devices. In this paper, we study the topological characterization of twisted magnetic fields, nonlinear effect induced by the Lorentz back reaction, length-scale bounds, and statistical distributions. (author)
Nonlinear acoustic propagation of launch vehicle and military jet aircraft noise
Gee, Kent L.
2010-10-01
The noise from launch vehicles and high-performance military jet aircraft has been shown to travel nonlinearly as a result of an amplitude-dependent speed of sound. Because acoustic pressure compressions travel faster than rarefactions, the waveform steepens and shocks form. This process results in a very different (and readily audible) noise signature and spectrum than predicted by linear models. On-going efforts to characterize the nonlinearity using statistical and spectral measures are described with examples from recent static tests of solid rocket boosters and the F-22 Raptor.
Monte Carlo simulation of nonlinear reactive contaminant transport in unsaturated porous media
International Nuclear Information System (INIS)
Giacobbo, F.; Patelli, E.
2007-01-01
In the current proposed solutions of radioactive waste repositories, the protective function against the radionuclide water-driven transport back to the biosphere is to be provided by an integrated system of engineered and natural geologic barriers. The occurrence of several nonlinear interactions during the radionuclide migration process may render burdensome the classical analytical-numerical approaches. Moreover, the heterogeneity of the barriers' media forces approximations to the classical analytical-numerical models, thus reducing their fidelity to reality. In an attempt to overcome these difficulties, in the present paper we adopt a Monte Carlo simulation approach, previously developed on the basis of the Kolmogorov-Dmitriev theory of branching stochastic processes. The approach is here extended for describing transport through unsaturated porous media under transient flow conditions and in presence of nonlinear interchange phenomena between the liquid and solid phases. This generalization entails the determination of the functional dependence of the parameters of the proposed transport model from the water content and from the contaminant concentration, which change in space and time during the water infiltration process. The corresponding Monte Carlo simulation approach is verified with respect to a case of nonreactive transport under transient unsaturated flow and to a case of nonlinear reactive transport under stationary saturated flow. Numerical applications regarding linear and nonlinear reactive transport under transient unsaturated flow are reported
International Nuclear Information System (INIS)
Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru
2011-01-01
A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.
On nonequilibrium many-body systems. 1: The nonequilibrium statistical operator method
International Nuclear Information System (INIS)
Algarte, A.C.S.; Vasconcellos, A.R.; Luzzi, R.; Sampaio, A.J.C.
1985-01-01
The theoretical aspects involved in the treatment of many-body systems strongly departed from equilibrium are discussed. The nonequilibrium statistical operator (NSO) method is considered in detail. Using Jaynes' maximum entropy formalism complemented with an ad hoc hypothesis a nonequilibrium statistical operator is obtained. This approach introduces irreversibility from the outset and we recover statistical operators like those of Green-Mori and Zubarev as particular cases. The connection with Generalized Thermodynamics and the construction of nonlinear transport equations are briefly described. (Author) [pt
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Dumedah, Gift; Walker, Jeffrey P.; Chik, Li
2014-07-01
Soil moisture information is critically important for water management operations including flood forecasting, drought monitoring, and groundwater recharge estimation. While an accurate and continuous record of soil moisture is required for these applications, the available soil moisture data, in practice, is typically fraught with missing values. There are a wide range of methods available to infilling hydrologic variables, but a thorough inter-comparison between statistical methods and artificial neural networks has not been made. This study examines 5 statistical methods including monthly averages, weighted Pearson correlation coefficient, a method based on temporal stability of soil moisture, and a weighted merging of the three methods, together with a method based on the concept of rough sets. Additionally, 9 artificial neural networks are examined, broadly categorized into feedforward, dynamic, and radial basis networks. These 14 infilling methods were used to estimate missing soil moisture records and subsequently validated against known values for 13 soil moisture monitoring stations for three different soil layer depths in the Yanco region in southeast Australia. The evaluation results show that the top three highest performing methods are the nonlinear autoregressive neural network, rough sets method, and monthly replacement. A high estimation accuracy (root mean square error (RMSE) of about 0.03 m/m) was found in the nonlinear autoregressive network, due to its regression based dynamic network which allows feedback connections through discrete-time estimation. An equally high accuracy (0.05 m/m RMSE) in the rough sets procedure illustrates the important role of temporal persistence of soil moisture, with the capability to account for different soil moisture conditions.
A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation
Rajeswaran, Jeevanantham; Blackstone, Eugene H.
2014-01-01
In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830
Directory of Open Access Journals (Sweden)
Xiangyu Mu
2014-09-01
Full Text Available Natural factors and anthropogenic activities both contribute dissolved chemical loads to lakes and streams. Mineral solubility, geomorphology of the drainage basin, source strengths and climate all contribute to concentrations and their variability. Urbanization and agriculture waste-water particularly lead to aquatic environmental degradation. Major contaminant sources and controls on water quality can be asssessed by analyzing the variability in proportions of major and minor solutes in water coupled to mutivariate statistical methods. The demand for freshwater needed for increasing crop production puulation and industrialization occurs almost everywhere in in China and these conflicting needs have led to widespread water contamination. Because of heavy nutrient loadings from all of these sources, Lake Taihu (eastern China notably suffers periodic hyper-eutrophication and drinking water deterioration, which has led to shortages of freshwater for the City of Wuxi and other nearby cities. This lake, the third largest freshwater body in China, has historically beeen considered a cultural treasure of China, and has supported long-term fisheries. The is increasing pressure to remediate the present contamination which compromises both aquiculture and the prior economic base centered on tourism. However, remediation cannot be effectively done without first characterizing the broad nature of the non-point source pollution. To this end, we investigated the hydrochemical setting of Lake Taihu to determine how different land use types influence the variability of surface water chemistry in different water sources to the lake. We found that waters broadly show wide variability ranging from calcium-magnesium-bicarbonate hydrochemical facies type to mixed sodium-sulfate-chloride type. Principal components analysis produced three principal components that explained 78% of the variance in the water quality and reflect three major types of water
Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas
International Nuclear Information System (INIS)
Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.
1996-01-01
A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, δf = f - f 0 , from an initial analytic distribution f 0 . High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question
A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
International Nuclear Information System (INIS)
Johnson, Jay R.; Wing, Simon
2004-01-01
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach
DEFF Research Database (Denmark)
Vich, Catalina; Berg, Rune W.; Guillamon, Antoni
2017-01-01
Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo...... recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical...... models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures...
Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.
Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji
2016-09-01
It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.
Statistical and trend analysis of water quality and quantity data for the Strymon River in Greece
Directory of Open Access Journals (Sweden)
V. Z. Antonopoulos
2001-01-01
Full Text Available Strymon is a transboundary river of Greece, Bulgaria and Former Yugoslav Republic of Macedonia (FYROM in southeastern Europe. Water quality parameters and the discharge have been monitored each month just 10 km downstream of the river’s entry into Greece. The data of nine water quality variables (T, ECw, DO, SO42-, Na++K+, Mg2+ , Ca2+, NO3‾, TP and the discharge for the period 1980-1997 were selected for this analysis. In this paper a the time series of monthly values of water quality parameters and the discharge were analysed using statistical methods, b the existence of trends and the evaluation of the best fitted models were performed and c the relationships between concentration and loads of constituents both with the discharge were also examined. Boxplots for summarising the distribution of a data set were used. The ◈-test and the Kolmogorov-Smirnov test were used to select the theoretical distribution which best fitted the data. Simple regression was used to examine the concentration-discharge and the load-discharge relationships. According to the correlation coefficient (r values the relation between concentrations and discharge is weak (r 0.902. Trends were detected using the nonparametric Spearman’s criterion upon the data for the variables: Q, ECw, DO, SO42-, Na++K+ and NO3‾ on which temporal trend analysis was performed. Keywords: Strymon river, water quality, discharge, concentration, load, statistics, trends
Optimal Design and Related Areas in Optimization and Statistics
Pronzato, Luc
2009-01-01
This edited volume, dedicated to Henry P. Wynn, reflects his broad range of research interests, focusing in particular on the applications of optimal design theory in optimization and statistics. It covers algorithms for constructing optimal experimental designs, general gradient-type algorithms for convex optimization, majorization and stochastic ordering, algebraic statistics, Bayesian networks and nonlinear regression. Written by leading specialists in the field, each chapter contains a survey of the existing literature along with substantial new material. This work will appeal to both the
Nonlinear flow model for well production in an underground formation
Directory of Open Access Journals (Sweden)
J. C. Guo
2013-05-01
Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.
International Nuclear Information System (INIS)
Jovic, V.; Afgan, N.; Jovic, L.; Spasojevic, D.
1993-01-01
The paper presents results of the experimental and theoretical analyses of linear and nonlinear characteristics of adiabatic two-phase water-air flow in vertical parallel channels. Regime character changes and linear to nonlinear dynamic characteristics transfer conditions were defined. (author)
Leppäranta, Matti; Lewis, John E; Heini, Anniina; Arvola, Lauri
2018-06-04
Spatial variability, an essential characteristic of lake ecosystems, has often been neglected in field research and monitoring. In this study, we apply spatial statistical methods for the key physics and chemistry variables and chlorophyll a over eight sampling dates in two consecutive years in a large (area 103 km 2 ) eutrophic boreal lake in southern Finland. In the four summer sampling dates, the water body was vertically and horizontally heterogenic except with color and DOC, in the two winter ice-covered dates DO was vertically stratified, while in the two autumn dates, no significant spatial differences in any of the measured variables were found. Chlorophyll a concentration was one order of magnitude lower under the ice cover than in open water. The Moran statistic for spatial correlation was significant for chlorophyll a and NO 2 +NO 3 -N in all summer situations and for dissolved oxygen and pH in three cases. In summer, the mass centers of the chemicals were within 1.5 km from the geometric center of the lake, and the 2nd moment radius ranged in 3.7-4.1 km respective to 3.9 km for the homogeneous situation. The lateral length scales of the studied variables were 1.5-2.5 km, about 1 km longer in the surface layer. The detected spatial "noise" strongly suggests that besides vertical variation also the horizontal variation in eutrophic lakes, in particular, should be considered when the ecosystems are monitored.
Sadeghi, Fatemeh; Nasseri, Simin; Mosaferi, Mohammad; Nabizadeh, Ramin; Yunesian, Masud; Mesdaghinia, Alireza
2017-05-01
In this research, probable arsenic contamination in drinking water in the city of Ardabil was studied in 163 samples during four seasons. In each season, sampling was carried out randomly in the study area. Results were analyzed statistically applying SPSS 19 software, and the data was also modeled by Arc GIS 10.1 software. The maximum permissible arsenic concentration in drinking water defined by the World Health Organization and Iranian national standard is 10 μg/L. Statistical analysis showed 75, 88, 47, and 69% of samples in autumn, winter, spring, and summer, respectively, had concentrations higher than the national standard. The mean concentrations of arsenic in autumn, winter, spring, and summer were 19.89, 15.9, 10.87, and 14.6 μg/L, respectively, and the overall average in all samples through the year was 15.32 μg/L. Although GIS outputs indicated that the concentration distribution profiles changed in four consecutive seasons, variance analysis of the results showed that statistically there is no significant difference in arsenic levels in four seasons.
DEFF Research Database (Denmark)
Malaguerra, Flavio
The access to safe drinking water is essential for the well being of the population. The spread of micropollutant contamination jeopardise many freshwater reservoirs, and is a serious threat for human health, especially because of its long-term effects. To asses the threat of contamination, models...... to model. The identification of dominant processes is an essential step in the understanding of system behaviour, because it enables the development of simplified models that can approximate the fate of contaminants with the best trade-off between model complexity and reliability of results. In this thesis......, global sensitivity analysis techniques are used to assess detailed models in order to identify the main processes involved in the degradation of chlorinated solvents in the subsurface, and in the transport of pesticides from surface water into nearby wells in confined aquifers. Statistical techniques...
Study nonlinear dynamics of stratospheric ozone concentration at Pakistan Terrestrial region
Jan, Bulbul; Zai, Muhammad Ayub Khan Yousuf; Afradi, Faisal Khan; Aziz, Zohaib
2018-03-01
This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.
Hoyer, Dirk; Leder, Uwe; Hoyer, Heike; Pompe, Bernd; Sommer, Michael; Zwiener, Ulrich
2002-01-01
The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.
Joint management of water and electricity in State Water Project
Yang, T.
2013-12-01
Understanding the relationship between California's water and electrical power is important for improving the management and planning of these two vital resources to the state's economy development and people's well-being. It is often unclear for consumers, managers and decision-makers that water and electricity in California are inextricably connected. In the past, insufficient considerations of electricity production, consumption and cost in the State Water Project (SWP) - the world's largest publicly built and operated water and power development and conveyance system-has led to significant water rate and electricity rate increase. An innovative concept of this proposed study is developing new technology capable of managing and planning water and power jointly in SWP to promote its operation efficiency, sustainability and resilience to potential water shortage caused by climate change and population increase. To achieve this goal, a nonlinear, two-fold network model describing water delivery in company with power consumption and generation will be constructed, and a multi-objective optimization scheme is to be used to resolve this complex nonlinear network problem.
Effective potentials in nonlinear polycrystals and quadrature formulae
Michel, Jean-Claude; Suquet, Pierre
2017-08-01
This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.
International Nuclear Information System (INIS)
2012-01-01
This report evaluates the chemistry of seep water occurring in three desert drainages near Shiprock, New Mexico: Many Devils Wash, Salt Creek Wash, and Eagle Nest Arroyo. Through the use of geochemical plotting tools and multivariate statistical analysis techniques, analytical results of samples collected from the three drainages are compared with the groundwater chemistry at a former uranium mill in the Shiprock area (the Shiprock site), managed by the U.S. Department of Energy Office of Legacy Management. The objective of this study was to determine, based on the water chemistry of the samples, if statistically significant patterns or groupings are apparent between the sample populations and, if so, whether there are any reasonable explanations for those groupings.
Energy Technology Data Exchange (ETDEWEB)
None, None
2012-12-31
This report evaluates the chemistry of seep water occurring in three desert drainages near Shiprock, New Mexico: Many Devils Wash, Salt Creek Wash, and Eagle Nest Arroyo. Through the use of geochemical plotting tools and multivariate statistical analysis techniques, analytical results of samples collected from the three drainages are compared with the groundwater chemistry at a former uranium mill in the Shiprock area (the Shiprock site), managed by the U.S. Department of Energy Office of Legacy Management. The objective of this study was to determine, based on the water chemistry of the samples, if statistically significant patterns or groupings are apparent between the sample populations and, if so, whether there are any reasonable explanations for those groupings.
Sub-Poissonian statistics in order-to-chaos transition
International Nuclear Information System (INIS)
Kryuchkyan, Gagik Yu.; Manvelyan, Suren B.
2003-01-01
We study the phenomena at the overlap of quantum chaos and nonclassical statistics for the time-dependent model of nonlinear oscillator. It is shown in the framework of Mandel Q parameter and Wigner function that the statistics of oscillatory excitation numbers is drastically changed in the order-to-chaos transition. The essential improvement of sub-Poissonian statistics in comparison with an analogous one for the standard model of driven anharmonic oscillator is observed for the regular operational regime. It is shown that in the chaotic regime, the system exhibits the range of sub-Poissonian and super-Poissonian statistics which alternate one to other depending on time intervals. Unusual dependence of the variance of oscillatory number on the external noise level for the chaotic dynamics is observed. The scaling invariance of the quantum statistics is demonstrated and its relation to dissipation and decoherence is studied
DEFF Research Database (Denmark)
Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak
2016-01-01
A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...
Comparison of three nonlinear filters for fault detection in continuous glucose monitors.
Mahmoudi, Zeinab; Wendt, Sabrina Lyngbye; Boiroux, Dimitri; Hagdrup, Morten; Norgaard, Kirsten; Poulsen, Niels Kjolstad; Madsen, Henrik; Jorgensen, John Bagterp
2016-08-01
The purpose of this study is to compare the performance of three nonlinear filters in online drift detection of continuous glucose monitors. The nonlinear filters are the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the particle filter (PF). They are all based on a nonlinear model of the glucose-insulin dynamics in people with type 1 diabetes. Drift is modelled by a Gaussian random walk and is detected based on the statistical tests of the 90-min prediction residuals of the filters. The unscented Kalman filter had the highest average F score of 85.9%, and the smallest average detection delay of 84.1%, with the average detection sensitivity of 82.6%, and average specificity of 91.0%.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Statistical perspectives on inverse problems
DEFF Research Database (Denmark)
Andersen, Kim Emil
of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...
Statistical physics of vaccination
Wang, Zhen; Bauch, Chris T.; Bhattacharyya, Samit; d'Onofrio, Alberto; Manfredi, Piero; Perc, Matjaž; Perra, Nicola; Salathé, Marcel; Zhao, Dawei
2016-12-01
Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination-one of the most important preventive measures of modern times-is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.
DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.
2008-01-01
equations in complex and curvilinear geometries which amends the application range of previous numerical models that have been based on structured Cartesian grids. The Boussinesq method provides the basis for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep...... waters within the breaking limit. To demonstrate the current applicability of the model both linear and mildly nonlinear test cases are considered in two horizontal dimensions where the water waves interact with bottom-mounted fully reflecting structures. It is established that, by simple symmetry...... considerations combined with a mirror principle, it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated...
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....
Multiple (G /G)-expansion method and its applications to nonlinear ...
Indian Academy of Sciences (India)
to nonlinear evolution equations in mathematical physics ... recent years, due to the availability of symbolic computation systems like Mathematica ..... In this subsection we study the generalized shallow water wave (GSWW) equation [12,. 40],.
Coastal tomographic mapping of nonlinear tidal currents and residual currents
Zhu, Ze-Nan; Zhu, Xiao-Hua; Guo, Xinyu
2017-07-01
Depth-averaged current data, which were obtained by coastal acoustic tomography (CAT) July 12-13, 2009 in Zhitouyang Bay on the western side of the East China Sea, are used to estimate the semidiurnal tidal current (M2) as well as its first two overtide currents (M4 and M6). Spatial mean amplitude ratios M2:M4:M6 in the bay are 1.00:0.15:0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, where water depths are larger than 60 m, M4 velocity amplitudes measured by CAT agree well with those predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. In addition, dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents. This is the first ever nonlinear tidal current study by CAT.
Regression modeling of ground-water flow
Cooley, R.L.; Naff, R.L.
1985-01-01
Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)
Directory of Open Access Journals (Sweden)
Catalina Vich
2017-07-01
Full Text Available Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nonlinear propagation of phase-conjugate focused sound beams in water
Brysev, A. P.; Krutyansky, L. M.; Preobrazhensky, V. L.; Pyl'nov, Yu. V.; Cunningham, K. B.; Hamilton, M. F.
2000-07-01
Nonlinear propagation of phase-conjugate, focused, ultrasound beams is studied. Measurements are presented of harmonic amplitudes along the axis and in the focal plane of the conjugate beam, and of the waveform and spectrum at the focus. A maximum peak pressure of 3.9 MPa was recorded in the conjugate beam. The measurements are compared with simulations based on the KZK equation, and satisfactory agreement is obtained.
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
Information theory and stochastics for multiscale nonlinear systems
Majda, Andrew J; Grote, Marcus J
2005-01-01
This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...
Unit Root Testing and Estimation in Nonlinear ESTAR Models with Normal and Non-Normal Errors.
Directory of Open Access Journals (Sweden)
Umair Khalil
Full Text Available Exponential Smooth Transition Autoregressive (ESTAR models can capture non-linear adjustment of the deviations from equilibrium conditions which may explain the economic behavior of many variables that appear non stationary from a linear viewpoint. Many researchers employ the Kapetanios test which has a unit root as the null and a stationary nonlinear model as the alternative. However this test statistics is based on the assumption of normally distributed errors in the DGP. Cook has analyzed the size of the nonlinear unit root of this test in the presence of heavy-tailed innovation process and obtained the critical values for both finite variance and infinite variance cases. However the test statistics of Cook are oversized. It has been found by researchers that using conventional tests is dangerous though the best performance among these is a HCCME. The over sizing for LM tests can be reduced by employing fixed design wild bootstrap remedies which provide a valuable alternative to the conventional tests. In this paper the size of the Kapetanios test statistic employing hetroscedastic consistent covariance matrices has been derived and the results are reported for various sample sizes in which size distortion is reduced. The properties for estimates of ESTAR models have been investigated when errors are assumed non-normal. We compare the results obtained through the fitting of nonlinear least square with that of the quantile regression fitting in the presence of outliers and the error distribution was considered to be from t-distribution for various sample sizes.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2017-04-15
The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.
General renormalized statistical approach with finite cross-field correlations
International Nuclear Information System (INIS)
Vakulenko, M.O.
1992-01-01
The renormalized statistical approach is proposed, accounting for finite correlations of potential and magnetic fluctuations. It may be used for analysis of a wide class of nonlinear model equations describing the cross-correlated plasma states. The influence of a cross spectrum on stationary potential and magnetic ones is investigated. 10 refs. (author)
Workshop on Nonlinear Phenomena in Complex Systems
1989-01-01
This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.
Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility
International Nuclear Information System (INIS)
El-Sabbagh, Mostafa F.; Ahmad, Ali T.
2011-01-01
The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries. (general)
International Nuclear Information System (INIS)
Alvarez R, J.T.
1998-01-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Depression of Nonlinearity in Decaying Isotropic MHD Turbulence
International Nuclear Information System (INIS)
Servidio, S.; Matthaeus, W. H.; Dmitruk, P.
2008-01-01
Spectral method simulations show that undriven magnetohydrodynamic turbulence spontaneously generates coherent spatial correlations of several types, associated with local Beltrami fields, directional alignment of velocity and magnetic fields, and antialignment of magnetic and fluid acceleration components. These correlations suppress nonlinearity to levels lower than what is obtained from Gaussian fields, and occur in spatial patches. We suggest that this rapid relaxation leads to non-Gaussian statistics and spatial intermittency
Evaluation of non-linear blending in dual-energy computed tomography
International Nuclear Information System (INIS)
Holmes, David R.; Fletcher, Joel G.; Apel, Anja; Huprich, James E.; Siddiki, Hassan; Hough, David M.; Schmidt, Bernhard; Flohr, Thomas G.; Robb, Richard; McCollough, Cynthia; Wittmer, Michael; Eusemann, Christian
2008-01-01
Dual-energy CT scanning has significant potential for disease identification and classification. However, it dramatically increases the amount of data collected and therefore impacts the clinical workflow. One way to simplify image review is to fuse CT datasets of different tube energies into a unique blended dataset with desirable properties. A non-linear blending method based on a modified sigmoid function was compared to a standard 0.3 linear blending method. The methods were evaluated in both a liver phantom and patient study. The liver phantom contained six syringes of known CT contrast which were placed in a bovine liver. After scanning at multiple tube currents (45, 55, 65, 75, 85, 95, 105, and 115 mAs for the 140-kV tube), the datasets were blended using both methods. A contrast-to-noise (CNR) measure was calculated for each syringe. In addition, all eight scans were normalized using the effective dose and statistically compared. In the patient study, 45 dual-energy CT scans were retrospectively mixed using the 0.3 linear blending and modified sigmoid blending functions. The scans were compared visually by two radiologists. For the 15, 45, and 64 HU syringes, the non-linear blended images exhibited similar CNR to the linear blended images; however, for the 79, 116, and 145 HU syringes, the non-linear blended images consistently had a higher CNR across dose settings. The radiologists qualitatively preferred the non-linear blended images of the phantom. In the patient study, the radiologists preferred non-linear blending in 31 of 45 cases with a strong preference in bowel and liver cases. Non-linear blending of dual energy data can provide an improvement in CNR over linear blending and is accompanied by a visual preference for non-linear blended images. Further study on selection of blending parameters and lesion conspicuity in non-linear blended images is being pursued
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk
2015-01-01
Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics
International Nuclear Information System (INIS)
Fossum, Kristian; Mannseth, Trond
2014-01-01
We assess and compare parameter sampling capabilities of one sequential and one simultaneous Bayesian, ensemble-based, joint state-parameter (JS) estimation method. In the companion paper, part I (Fossum and Mannseth 2014 Inverse Problems 30 114002), analytical investigations lead us to propose three claims, essentially stating that the sequential method can be expected to outperform the simultaneous method for weakly nonlinear forward models. Here, we assess the reliability and robustness of these claims through statistical analysis of results from a range of numerical experiments. Samples generated by the two approximate JS methods are compared to samples from the posterior distribution generated by a Markov chain Monte Carlo method, using four approximate measures of distance between probability distributions. Forward-model nonlinearity is assessed from a stochastic nonlinearity measure allowing for sufficiently large model dimensions. Both toy models (with low computational complexity, and where the nonlinearity is fairly easy to control) and two-phase porous-media flow models (corresponding to down-scaled versions of problems to which the JS methods have been frequently applied recently) are considered in the numerical experiments. Results from the statistical analysis show strong support of all three claims stated in part I. (paper)
Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel
2015-10-01
A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).
Layer contributions to the nonlinear acoustic radiation from stratified media.
Vander Meulen, François; Haumesser, Lionel
2016-12-01
This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects. Copyright © 2016 Elsevier B.V. All rights reserved.
Theories of quantum dissipation and nonlinear coupling bath descriptors
Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing
2018-03-01
The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....
Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.
Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo
2007-10-01
Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.
A Statistical Model for the Estimation of Natural Gas Consumption
Czech Academy of Sciences Publication Activity Database
Vondráček, Jiří; Pelikán, Emil; Konár, Ondřej; Čermáková, Jana; Eben, Kryštof; Malý, Marek; Brabec, Marek
2008-01-01
Roč. 85, c. 5 (2008), s. 362-370 ISSN 0306-2619 R&D Projects: GA AV ČR 1ET400300513 Institutional research plan: CEZ:AV0Z10300504 Keywords : nonlinear regression * gas consumption modeling Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.371, year: 2008
Ooi, Kelvin J. A.; Tan, Dawn T. H.
2017-10-01
The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.
A Statistical Framework for Automatic Leakage Detection in Smart Water and Gas Grids
Directory of Open Access Journals (Sweden)
Marco Fagiani
2016-08-01
Full Text Available In the last few years, due to the technological improvement of advanced metering infrastructures, water and natural gas grids can be regarded as smart-grids, similarly to power ones. However, considering the number of studies related to the application of computational intelligence to distribution grids, the gap between power grids and water/gas grids is notably wide. For this purpose, in this paper, a framework for leakage identification is presented. The framework is composed of three sections aimed at the extraction and the selection of features and at the detection of leakages. A variation of the Sequential Feature Selection (SFS algorithm is used to select the best performing features within a set, including, also, innovative temporal ones. The leakage identification is based on novelty detection and exploits the characterization of a normality model. Three statistical approaches, The Gaussian Mixture Model (GMM, Hidden Markov Model (HMM and One-Class Support Vector Machine (OC-SVM, are adopted, under a comparative perspective. Both residential and office building environments are investigated by means of two datasets. One is the Almanac of Minutely Power dataset (AMPds, and it provides water and gas data consumption at 1, 10 and 30 min of time resolution; the other is the Department of International Development (DFID dataset, and it provides water and gas data consumption at 30 min of time resolution. The achieved performance, computed by means of the Area Under the Curve (AUC, reaches 90 % in the office building case study, thus confirming the suitability of the proposed approach for applications in smart water and gas grids.
A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data
DEFF Research Database (Denmark)
Raket, Lars Lau; Sommer, Stefan Horst; Markussen, Bo
2014-01-01
We consider misaligned functional data, where data registration is necessary for proper statistical analysis. This paper proposes to treat misalignment as a nonlinear random effect, which makes simultaneous likelihood inference for horizontal and vertical effects possible. By simultaneously fitti...
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
Nonlinear waves and pattern dynamics
Pelinovsky, Efim; Mutabazi, Innocent
2018-01-01
This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2016-01-01
The response of an offshore wind turbine tower and its monopile foundation has been investigated when exposed to linear and fully nonlinear irregular waves on four different water depths. The investigation focuses on the consequences of including full nonlinearity in the wave kinematics. The line...
Volume fraction dependence of transient absorption signal and nonlinearities in metal nanocolloids
International Nuclear Information System (INIS)
Jayabalan, J; Singh, Asha; Khan, Salahuddin; Chari, Rama
2013-01-01
Electron–lattice thermalization dynamics in metal nanoparticles or in bulk metal is usually estimated by measuring the decay time of the change in transmission following an optical excitation. Such measurements can be performed in transient absorption geometry using a femtosecond laser. We find that for silver nanoplatelet/water colloids, the decay time of the transient absorption depends on the volume fraction of silver in water. By estimating the volume fraction dependence of nonlinearities in the same samples, we show that the variation in the measured decay time is due to pump-depletion effects present in the sample. The correct correction factor for taking into account pump-depletion effects in fifth- and higher-order nonlinearities is also presented. (paper)
Nonlinear optical properties of ZnO/poly (vinyl alcohol) nanocomposite films
International Nuclear Information System (INIS)
Jeeju, P. P.; Jayalekshmi, S.; Chandrasekharan, K.
2014-01-01
Extensive studies have already been reported on the optical characteristics of ZnO/polymer nanocomposite films, using a variety of polymers including transparent polymers such as polystyrene, polymethyl methacrylate etc and many interesting results have been established regarding the non linear optical characteristics of these systems. Poly (vinyl alcohol)(PVA) is a water soluble polymer. Though the structural and optical studies of ZnO/PVA nanocomposite films have already been investigated, there are no detailed reports on the nonlinear optical characteristics of ZnO/PVA nanocomposite films, irrespective of the fact that these nanocomposite films can be synthesized using quite easy and cost effective methods. The present work is an attempt to study in detail the nonlinear optical behaviour of ZnO/PVA nanocomposite films using Z-scan technique. Highly transparent ZnO/PVA nanocomposite films were prepared from the ZnO incorporated PVA solution in water using spin coating technique. The ZnO nanoparticles were synthesized by the simple chemical route at room temperature. High-resolution transmission electron microscopy studies show that the ZnO nanoparticles are of size around 10 nm. The ZnO/PVA nanocomposite films were structurally characterized by X-ray diffraction technique, from which the presence of both PVA and ZnO in the nanocomposite was established. The optical absorptive nonlinearity in the nanocomposite films was investigated using open aperture Z-scan technique. The results indicate optical limiting type nonlinearity in the films due to two photon absorption in ZnO with efficiency more than 50%. These films also show a self defocusing type negative nonlinear refraction in closed aperture Z-scan experiment. The present studies indicate that, highly transparent and homogeneous films of ZnO/PVA nanocomposite can be obtained on glass substrates using simple methods, in a highly cost effective way, since PVA is water soluble. These nanocomposite films offer
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
2007-01-01
In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Energy Technology Data Exchange (ETDEWEB)
Outeda, R.; D' Onofrio, A. [Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, C1063ACV Buenos Aires (Argentina); El Hasi, C.; Zalts, A. [Instituto de Ciencias, Universidad Nacional General Sarmiento, J. M. Gutiérrez 1150, B1613GSX, Los Polvorines, Provincia de Buenos Aires (Argentina)
2014-03-15
Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.
Statistical analysis of random pulse trains
International Nuclear Information System (INIS)
Da Costa, G.
1977-02-01
Some experimental and theoretical results concerning the statistical properties of optical beams formed by a finite number of independent pulses are presented. The considered waves (corresponding to each pulse) present important spatial variations of the illumination distribution in a cross-section of the beam, due to the time-varying random refractive index distribution in the active medium. Some examples of this kind of emission are: (a) Free-running ruby laser emission; (b) Mode-locked pulse trains; (c) Randomly excited nonlinear media
Statistical modelling in biostatistics and bioinformatics selected papers
Peng, Defen
2014-01-01
This book presents selected papers on statistical model development related mainly to the fields of Biostatistics and Bioinformatics. The coverage of the material falls squarely into the following categories: (a) Survival analysis and multivariate survival analysis, (b) Time series and longitudinal data analysis, (c) Statistical model development and (d) Applied statistical modelling. Innovations in statistical modelling are presented throughout each of the four areas, with some intriguing new ideas on hierarchical generalized non-linear models and on frailty models with structural dispersion, just to mention two examples. The contributors include distinguished international statisticians such as Philip Hougaard, John Hinde, Il Do Ha, Roger Payne and Alessandra Durio, among others, as well as promising newcomers. Some of the contributions have come from researchers working in the BIO-SI research programme on Biostatistics and Bioinformatics, centred on the Universities of Limerick and Galway in Ireland and fu...
Evaluation of ECC bypass data with a nonlinear constrained MLE technique
International Nuclear Information System (INIS)
Bishop, T.A.; Collier, R.P.; Kurth, R.E.
1980-01-01
Recently, Battelle's Columbus Laboratories have been involved in scale-model tests of emergency core cooling (ECC) systems for hypothesized loss-of-coolant accidents in pressurized water reactors (PWR). These tests are intended to increase our understanding of ECC bypass, which can occur when steam flow from the reactor core causes the emergency coolant to bypass the core and flow directly to the break. One objective of these experiments is the development of a correlation which relates the flow rate of water penetrating to the core to the steam flow rate. This correlation is derived from data obtained from a 2/15 scale model PWR at various ECC water injection rates, subcoolings, pressures, and steam flows. The general form of the correlation being studied is a modification of the correlation first proposed by Wallis. The correlation model is inherently nonlinear and implicit in form, and the model variables are all subject to error. Therefore, the usual nonlinear analysis techniques are inappropriate. A nonlinear constrained maximum-likelihood-estimation technique has been used to obtain estimates of the model parameters, and a Battelle-developed code, NLINMLE, has been used to analyze the data. The application of this technique is illustrated by sample calculations of estimates of the model parameters and their associated confidence intervals for selected experimental data sets. 5 figures, 7 tables
Hash function based on piecewise nonlinear chaotic map
International Nuclear Information System (INIS)
Akhavan, A.; Samsudin, A.; Akhshani, A.
2009-01-01
Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.
Nonlinear and non-Gaussian Bayesian based handwriting beautification
Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua
2013-03-01
A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.
Nonlinear processes of magnons in insulating ferromagnetic materials
International Nuclear Information System (INIS)
Araujo, C.B. de.
1975-04-01
The representation of coherent states is used to investigate the excitation of magnons by 'parallel pumping', 'perpendicular pumping' and 'phonon pumping'. The stationary regime of the processes is studied with respect to the magnon population and the statistic behavior of the system below and just above the threshold. Particular attention is given to the thermodynamic and the coherence properties of the parametric states. The results show that just above the threshold the generated states become coherent. Also, it is shown that the non-linear processes have characteristics of a second-order phase transition with the pumping power as the 'reservoir variable' and the transverse dynamical magnetization as the 'order parameter'. Finally, the possibilities to extend the theory, its experimental check, and its convenience to study the other nonlinear processes of magnons and phonons in magnetic insulators are discussed. (author) [pt
A nonlinear wavelet method for data smoothing of low-level gamma-ray spectra
International Nuclear Information System (INIS)
Gang Xiao; Li Deng; Benai Zhang; Jianshi Zhu
2004-01-01
A nonlinear wavelet method was designed for smoothing low-level gamma-ray spectra. The spectra of a 60 Co graduated radioactive source and a mixed soil sample were smoothed respectively according to this method and a 5 point smoothing method. The FWHM of 1,332 keV peak of 60 Co source and the absolute activities of 238 U of soil sample were calculated. The results show that the nonlinear wavelet method is better than the traditional method, with less loss of spectral peak and a more complete reduction of statistical fluctuation. (author)
Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics
Zhu, Yanqui; Cohn, Stephen E.; Todling, Ricardo
1999-01-01
The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Nonlinear analysis and dynamic structure in the energy market
Aghababa, Hajar
This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non
Irrigated Area Maps and Statistics of India Using Remote Sensing and National Statistics
Directory of Open Access Journals (Sweden)
Prasad S. Thenkabail
2009-04-01
Full Text Available The goal of this research was to compare the remote-sensing derived irrigated areas with census-derived statistics reported in the national system. India, which has nearly 30% of global annualized irrigated areas (AIAs, and is the leading irrigated area country in the World, along with China, was chosen for the study. Irrigated areas were derived for nominal year 2000 using time-series remote sensing at two spatial resolutions: (a 10-km Advanced Very High Resolution Radiometer (AVHRR and (b 500-m Moderate Resolution Imaging Spectroradiometer (MODIS. These areas were compared with the Indian National Statistical Data on irrigated areas reported by the: (a Directorate of Economics and Statistics (DES of the Ministry of Agriculture (MOA, and (b Ministry of Water Resources (MoWR. A state-by-state comparison of remote sensing derived irrigated areas when compared with MoWR derived irrigation potential utilized (IPU, an equivalent of AIA, provided a high degree of correlation with R2 values of: (a 0.79 with 10-km, and (b 0.85 with MODIS 500-m. However, the remote sensing derived irrigated area estimates for India were consistently higher than the irrigated areas reported by the national statistics. The remote sensing derived total area available for irrigation (TAAI, which does not consider intensity of irrigation, was 101 million hectares (Mha using 10-km and 113 Mha using 500-m. The AIAs, which considers intensity of irrigation, was 132 Mha using 10-km and 146 Mha using 500-m. In contrast the IPU, an equivalent of AIAs, as reported by MoWR was 83 Mha. There are “large variations” in irrigated area statistics reported, even between two ministries (e.g., Directorate of Statistics of Ministry of Agriculture and Ministry of Water Resources of the same national system. The causes include: (a reluctance on part of the states to furnish irrigated area data in view of their vested interests in sharing of water, and (b reporting of large volumes of data
Classical model of intermediate statistics
International Nuclear Information System (INIS)
Kaniadakis, G.
1994-01-01
In this work we present a classical kinetic model of intermediate statistics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as the Maxwell-Boltzmann (MD) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-inclusion principle. In our model the intermediate statistics are obtained as steady states of a system of coupled nonlinear kinetic equations, where the coupling constants are the transmutational potentials η κκ' . We show that, besides the FD-BE intermediate statistics extensively studied from the quantum point of view, we can also study the MB-FD and MB-BE ones. Moreover, our model allows us to treat the three-state mixing FD-MB-BE intermediate statistics. For boson and fermion mixing in a D-dimensional space, we obtain a family of FD-BE intermediate statistics by varying the transmutational potential η BF . This family contains, as a particular case when η BF =0, the quantum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Lett. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE statistics, we derive an analytic expression of the fraction of fermions. When the temperature T→∞, the system is composed by an equal number of bosons and fermions, regardless of the value of η BF . On the contrary, when T=0, η BF becomes important and, according to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions
Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics
Kashima, Kenji
2016-01-01
Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics. PMID:27264780
Macek-Rowland, Kathleen M.; Dressler, Valerie M.
2002-01-01
The quantity and quality of current and future water resources in the Red River of the North Basin in North Dakota, Minnesota, and South Dakota are concerns of people who reside within the basin. Additional water resources are needed because of recent growth in population, industry, and agriculture. How the management of current and future water-resources will impact water quality within the basin is a critical issue. Water-quality data, particularly for surface-water sources, will help water-resources managers make decisions about current and future water resources in the Red River of the North Basin. Statistical summaries of water-quality data for 43 streamflow-gaging stations in the Red River of the North Basin in North Dakota, Minnesota, and South Dakota are presented in this report. Statistical summaries include sample size, maximum, minimum, mean, and values for the 95th, 75th, 50th, 25th, and 5th percentiles.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Statistical Mechanics of Turbulent Flows
International Nuclear Information System (INIS)
Cambon, C
2004-01-01
This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their
Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities
Directory of Open Access Journals (Sweden)
Y. N. Pavlov
2015-01-01
Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic
Statistical mechanics, gravity, and Euclidean theory
International Nuclear Information System (INIS)
Fursaev, Dmitri V.
2002-01-01
A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigenvalue problems which depend non-linearly on the spectral parameter. We present a method to deal with such problems. In particular, we demonstrate how some results of the spectral theory of second-order elliptic operators, such as heat kernel asymptotics, can be extended to a class of non-linear spectral problems. The method is used to trace down the relation between the canonical definition of the free energy based on summation over the modes and the covariant definition given in Euclidean quantum gravity. As an application, high-temperature asymptotics of the free energy and of the thermal part of the stress-energy tensor in the presence of rotation are derived. We also discuss statistical mechanics in the presence of Killing horizons where canonical and Euclidean theories are related in a non-trivial way
Müller, M. F.; Thompson, S. E.
2015-09-01
The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash-Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drives of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by a strong wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are strongly favored over statistical models.
Nonlinear spectroscopic studies of interfacial molecular ordering
International Nuclear Information System (INIS)
Superfine, R.
1991-07-01
The second order nonlinear optical processes of second harmonic generation and sum frequency generation are powerful new probes of surfaces. They possess unusual surface sensitivity due to the symmetry properties of the nonlinear susceptibility. In particular, infrared-visible sum frequency generation (SFG) can obtain the vibrational spectrum of sub-monolayer coverages of molecules. In this thesis, we explore the unique information that can be obtained from SFG. We take advantage of the sensitivity of SFG to the conformation of alkane chains to study the interaction between adsorbed liquid crystal molecules and surfactant treated surfaces. The sign of the SFG susceptibility depends on the sign of the molecular polarizability and the orientation, up or down, of the molecule. We experimentally determine the sign of the susceptibility and use it to determine the absolute orientation to obtain the sign of the molecular polarizability and show that this quantity contains important information about the dynamics of molecular charge distributions. Finally, we study the vibrational spectra and the molecular orientation at the pure liquid/vapor interface of methanol and water and present the most detailed evidence yet obtained for the structure of the pure water surface. 32 refs., 4 figs., 2 tabs
A nonlinear isobologram model with Box-Cox transformation to both sides for chemical mixtures.
Chen, D G; Pounds, J G
1998-12-01
The linear logistical isobologram is a commonly used and powerful graphical and statistical tool for analyzing the combined effects of simple chemical mixtures. In this paper a nonlinear isobologram model is proposed to analyze the joint action of chemical mixtures for quantitative dose-response relationships. This nonlinear isobologram model incorporates two additional new parameters, Ymin and Ymax, to facilitate analysis of response data that are not constrained between 0 and 1, where parameters Ymin and Ymax represent the minimal and the maximal observed toxic response. This nonlinear isobologram model for binary mixtures can be expressed as [formula: see text] In addition, a Box-Cox transformation to both sides is introduced to improve the goodness of fit and to provide a more robust model for achieving homogeneity and normality of the residuals. Finally, a confidence band is proposed for selected isobols, e.g., the median effective dose, to facilitate graphical and statistical analysis of the isobologram. The versatility of this approach is demonstrated using published data describing the toxicity of the binary mixtures of citrinin and ochratoxin as well as a new experimental data from our laboratory for mixtures of mercury and cadmium.
THESEE-3, Orgel Reactor Performance and Statistic Hot Channel Factors
International Nuclear Information System (INIS)
Chambaud, B.
1974-01-01
1 - Nature of physical problem solved: The code applies to a heavy-water moderated organic-cooled reactor channel. Different fuel cluster models can be used (circular or hexagonal patterns). The code gives coolant temperatures and velocities and cladding temperatures throughout the channel and also channel performances, such as power, outlet temperature, boiling and burn-out safety margins (see THESEE-1). In a further step, calculations are performed with statistical values obtained by random retrieval of geometrical in- put data and taking into account construction tolerances, vibrations, etc. The code evaluates the mean value and standard deviation for the more important thermal and hydraulic parameters. 2 - Method of solution: First step calculations are performed for nominal values of parameters by solving iteratively the non-linear system of equations which give the pressure drops in subchannels of the current zone (see THESEE-1). Then a Gaussian probability distribution of possible statistical values of the geometrical input data is assumed. A random number generation routine determines the statistical case. Calculations are performed in the same way as for the nominal case. In the case of several channels, statistical performances must be adjusted to equalize the normal pressure drop. A special subroutine (AVERAGE) then determines the mean value and standard deviation, and thus probability functions of the most significant thermal and hydraulic results. 3 - Restrictions on the complexity of the problem: Maximum 7 fuel clusters, each divided into 10 axial zones. Fuel bundle geometries are restricted to the following models - circular pattern 6/7, 18/19, 36/67 rods, with or without fillers. The fuel temperature distribution is not studied. The probability distribution of the statistical input is assumed to be a Gaussian function. The principle of random retrieval of statistical values is correct, but some additional correlations could be found from a more
Dynamic statistical information theory
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel
Naro, Daniel; Rummel, Christian; Schindler, Kaspar; Andrzejak, Ralph G
2014-09-01
The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).
Nonlinear photonic metasurfaces
Li, Guixin; Zhang, Shuang; Zentgraf, Thomas
2017-03-01
Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.
Extended statistical entropy analysis as a quantitative management tool for water resource systems
Sobantka, Alicja; Rechberger, Helmut
2010-05-01
The use of entropy in hydrology and water resources has been applied to various applications. As water resource systems are inherently spatial and complex, a stochastic description of these systems is needed, and entropy theory enables development of such a description by providing determination of the least-biased probability distributions with limited knowledge and data. Entropy can also serve as a basis for risk and reliability analysis. The relative entropy has been variously interpreted as a measure freedom of choice, uncertainty and disorder, information content, missing information or information gain or loss. In the analysis of empirical data, entropy is another measure of dispersion, an alternative to the variance. Also, as an evaluation tool, the statistical entropy analysis (SEA) has been developed by previous workers to quantify the power of a process to concentrate chemical elements. Within this research programme the SEA is aimed to be extended for application to chemical compounds and tested for its deficits and potentials in systems where water resources play an important role. The extended SEA (eSEA) will be developed first for the nitrogen balance in waste water treatment plants (WWTP). Later applications on the emission of substances to water bodies such as groundwater (e.g. leachate from landfills) will also be possible. By applying eSEA to the nitrogen balance in a WWTP, all possible nitrogen compounds, which may occur during the water treatment process, are taken into account and are quantified in their impact towards the environment and human health. It has been shown that entropy reducing processes are part of modern waste management. Generally, materials management should be performed in a way that significant entropy rise is avoided. The entropy metric might also be used to perform benchmarking on WWTPs. The result out of this management tool would be the determination of the efficiency of WWTPs. By improving and optimizing the efficiency
Statistical algebraic approach to quantum mechanics
International Nuclear Information System (INIS)
Slavnov, D.A.
2001-01-01
The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru
Non-Linear Dependence and Teleconnections in Climate Data: Sources, Relevance, Nonstationarity
Czech Academy of Sciences Publication Activity Database
Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Novotná, Dagmar; Paluš, Milan
2014-01-01
Roč. 42, č. 7-8 (2014), s. 1873-1886 ISSN 0930-7575 R&D Projects: GA ČR GCP103/11/J068 Institutional support: RVO:67985807 ; RVO:68378289 Keywords : climate networks * nonlinearity * mutual information * teleconnections * seasonality in variance * nonstationarity Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.673, year: 2014
Directory of Open Access Journals (Sweden)
MANFREDI, P.
2014-11-01
Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.
Nonlinear Stochastic Models for Water Level Dynamics in Closed Lakes
Mishchenko, A.S.; Zelikin, M.I.; Zelikina, L.F.
1995-01-01
This paper presents the results of investigation of nonlinear mathematical models of the behavior of closed lakes using the example of the Caspian Sea. Forecasting the level of the Caspian Sea is crucial both for the economy of the region and for the region's environment. The Caspian Sea is a closed reservoir; it is well known that its level changes considerably due to a variety of factors including global climate change. A series of forecasts exists based on different methods and taking...
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....
Test for Nonlinear Input Output Relations in SISO Systems by Preliminary Data Analysis
DEFF Research Database (Denmark)
Knudsen, Torben
2000-01-01
This paper discusses and develops preliminary statistical tests for detecting nonlinearities in the deterministic part of SISO systems with noise. The most referenced method is unreliable for common noise processes as e.g.\\ colored. Therefore two new methods based on superposition and sinus input...
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....
Selected papers on analysis, probability, and statistics
Nomizu, Katsumi
1994-01-01
This book presents papers that originally appeared in the Japanese journal Sugaku. The papers fall into the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrödinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets and the global structure of analytic functions.
Optimal Control of Nonlinear Hydraulic Networks in the Presence of Disturbance
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Leth, John-Josef; Kallesøe, Carsten
2014-01-01
Water leakage is an important component of water loss. Many methods have emerged from urban water supply systems for leakage control, but it still remains a challenge in many countries. Pressure management is an effective way to reduce the leakage in a system. It can also reduce the power...... consumption. To this end, an optimal control strategy is proposed in this paper. In the water supply system model, the hydraulic resistance of the valve is estimated by the real data from a water supply system and it is considered to be a disturbance. The method which is used to solve the nonlinear optimal...
Directory of Open Access Journals (Sweden)
Yunhui Zhang
2018-01-01
Full Text Available The utilization for water resource has been of great concern to human life. To assess the natural water system in Kangding County, the integrated methods of hydrochemical analysis, multivariate statistics and geochemical modelling were conducted on surface water, groundwater, and thermal water samples. Surface water and groundwater were dominated by Ca-HCO3 type, while thermal water belonged to Ca-HCO3 and Na-Cl-SO4 types. The analyzing results concluded the driving factors that affect hydrochemical components. Following the results of the combined assessments, hydrochemical process was controlled by the dissolution of carbonate and silicate minerals with slight influence from anthropogenic activity. The mixing model of groundwater and thermal water was calculated using silica-enthalpy method, yielding cold-water fraction of 0.56–0.79 and an estimated reservoir temperature of 130–199 °C, respectively. δD and δ18O isotopes suggested that surface water, groundwater and thermal springs were of meteoric origin. Thermal water should have deep circulation through the Xianshuihe fault zone, while groundwater flows through secondary fractures where it recharges with thermal water. Those analytical results were used to construct a hydrological conceptual model, providing a better understanding of the natural water system in Kangding County.
Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method
Kenderi, Gábor; Fidlin, Alexander
2014-12-01
The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.
Müller, M. F.; Thompson, S. E.
2016-02-01
The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash-Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drivers of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by frequent wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are favored over statistical models.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
Cleophas, Ton J
2012-01-01
The first part of this title contained all statistical tests relevant to starting clinical investigations, and included tests for continuous and binary data, power, sample size, multiple testing, variability, confounding, interaction, and reliability. The current part 2 of this title reviews methods for handling missing data, manipulated data, multiple confounders, predictions beyond observation, uncertainty of diagnostic tests, and the problems of outliers. Also robust tests, non-linear modeling , goodness of fit testing, Bhatacharya models, item response modeling, superiority testing, variab
Energy Technology Data Exchange (ETDEWEB)
Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)
2016-09-15
Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the
Quantum theoretical physics is statistical and relativistic
International Nuclear Information System (INIS)
Harding, C.
1980-01-01
A new theoretical framework for the quantum mechanism is presented. It is based on a strict deterministic behavior of single systems. The conventional QM equation, however, is found to describe statistical results of many classical systems. It will be seen, moreover, that a rigorous synthesis of our theory requires relativistic kinematics. So, QM is not only a classical statistical theory, it is, of necessity, a relativistic theory. The equation of the theory does not just duplicate QM, it indicates an inherent nonlinearity in QM which is subject to experimental verification. It is shown, therefore, that conventional QM is a corollary of classical deterministic principles. It is suggested that this concept of nature conflicts with that prevalent in modern physics. (author)
Non-linear contributions to interactions in climate networks: sources, relevance, nonstationarity
Czech Academy of Sciences Publication Activity Database
Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Paluš, Milan
2012-01-01
Roč. 14, - (2012), s. 14274 ISSN 1607-7962. [European Geosciences Union General Assembly 2012. 22.04.2012-27.04.2012, Vienna] R&D Projects: GA ČR GCP103/11/J068 Institutional support: RVO:67985807 Keywords : correlation * mutual information * test of nonlinearity * surrogate data * complex networks * climate network Subject RIV: BB - Applied Statistics, Operational Research
Sublinear Expectation Nonlinear Regression for the Financial Risk Measurement and Management
Directory of Open Access Journals (Sweden)
Yunquan Song
2013-01-01
normality of the estimation and the mini-max property of the prediction are obtained. Finally, simulation study and real data analysis are carried out to illustrate the new model and methods. In this paper, the notions and methodological developments are nonclassical and original, and the proposed modeling and inference methods establish the foundations for nonlinear expectation statistics.
Mathematical and statistical methods for actuarial sciences and finance
Sibillo, Marilena
2014-01-01
The interaction between mathematicians and statisticians working in the actuarial and financial fields is producing numerous meaningful scientific results. This volume, comprising a series of four-page papers, gathers new ideas relating to mathematical and statistical methods in the actuarial sciences and finance. The book covers a variety of topics of interest from both theoretical and applied perspectives, including: actuarial models; alternative testing approaches; behavioral finance; clustering techniques; coherent and non-coherent risk measures; credit-scoring approaches; data envelopment analysis; dynamic stochastic programming; financial contagion models; financial ratios; intelligent financial trading systems; mixture normality approaches; Monte Carlo-based methodologies; multicriteria methods; nonlinear parameter estimation techniques; nonlinear threshold models; particle swarm optimization; performance measures; portfolio optimization; pricing methods for structured and non-structured derivatives; r...
Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity
Mostafazadeh, Ali; Oflaz, Neslihan
2017-11-01
We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.
Nonlinear Fluctuation Behavior of Financial Time Series Model by Statistical Physics System
Directory of Open Access Journals (Sweden)
Wuyang Cheng
2014-01-01
Full Text Available We develop a random financial time series model of stock market by one of statistical physics systems, the stochastic contact interacting system. Contact process is a continuous time Markov process; one interpretation of this model is as a model for the spread of an infection, where the epidemic spreading mimics the interplay of local infections and recovery of individuals. From this financial model, we study the statistical behaviors of return time series, and the corresponding behaviors of returns for Shanghai Stock Exchange Composite Index (SSECI and Hang Seng Index (HSI are also comparatively studied. Further, we investigate the Zipf distribution and multifractal phenomenon of returns and price changes. Zipf analysis and MF-DFA analysis are applied to investigate the natures of fluctuations for the stock market.
DEFF Research Database (Denmark)
Sommer, Helle Mølgaard; Holst, Helle; Spliid, Henrik
1995-01-01
Three identical microbiological experiments were carried out and analysed in order to examine the variability of the parameter estimates. The microbiological system consisted of a substrate (toluene) and a biomass (pure culture) mixed together in an aquifer medium. The degradation of the substrate...... and the growth of the biomass are described by the Monod model consisting of two nonlinear coupled first-order differential equations. The objective of this study was to estimate the kinetic parameters in the Monod model and to test whether the parameters from the three identical experiments have the same values....... Estimation of the parameters was obtained using an iterative maximum likelihood method and the test used was an approximative likelihood ratio test. The test showed that the three sets of parameters were identical only on a 4% alpha level....
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Directory of Open Access Journals (Sweden)
Do-Hwan Kim
2017-01-01
Full Text Available Large-demand customers, generally high-density dwellings and buildings, have dedicated ground or elevated water tanks to consistently supply drinking water to residents. Online field measurement for Nonsan-2 district meter area demonstrated that intermittent replenishment from large-demand customers could disrupt the normal operation of a water distribution system by taking large quantities of water in short times when filling the tanks from distribution mains. Based on the previous results of field measurement for hydraulic and water quality parameters, statistical analysis is performed for measured data in terms of autocorrelation, power spectral density, and cross-correlation. The statistical results show that the intermittent filling interval of 6.7 h and diurnal demand pattern of 23.3 h are detected through autocorrelation analyses, the similarities of the flow-pressure and the turbidity-particle count data are confirmed as a function of frequency through power spectral density analyses, and a strong cross-correlation is observed in the flow-pressure and turbidity-particle count analyses. In addition, physicochemical results show that the intermittent refill of storage tank from large-demand customers induces abnormal flow and pressure fluctuations and results in transient-induced turbid flow mainly composed of fine particles ranging within 2–4 μm and constituting Fe, Si, and Al.
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society
Statistical theory of resistive drift-wave turbulence and transport
International Nuclear Information System (INIS)
Hu, G.; Krommes, J.A.; Bowman, J.C.
1997-01-01
Resistive drift-wave turbulence in a slab geometry is studied by statistical closure methods and direct numerical simulations. The two-field Hasegawa endash Wakatani (HW) fluid model, which evolves the electrostatic potential and plasma density self-consistently, is a paradigm for understanding the generic nonlinear behavior of multiple-field plasma turbulence. A gyrokinetic derivation of the HW model is sketched. The recently developed Realizable Markovian Closure (RMC) is applied to the HW model; spectral properties, nonlinear energy transfers, and turbulent transport calculations are discussed. The closure results are also compared to direct numerical simulation results; excellent agreement is found. The transport scaling with the adiabaticity parameter, which measures the strength of the parallel electron resistivity, is analytically derived and understood through weak- and strong-turbulence analyses. No evidence is found to support previous suggestions that coherent structures cause a large depression of saturated transport from its quasilinear value in the hydrodynamic regime of the HW model. Instead, the depression of transport is well explained by the spectral balance equation of the (second-order) statistical closure when account is taken of incoherent noise. copyright 1997 American Institute of Physics
Statistics and Dynamics in the Large-scale Structure of the Universe
International Nuclear Information System (INIS)
Matsubara, Takahiko
2006-01-01
In cosmology, observations and theories are related to each other by statistics in most cases. Especially, statistical methods play central roles in analyzing fluctuations in the universe, which are seeds of the present structure of the universe. The confrontation of the statistics and dynamics is one of the key methods to unveil the structure and evolution of the universe. I will review some of the major statistical methods in cosmology, in connection with linear and nonlinear dynamics of the large-scale structure of the universe. The present status of analyses of the observational data such as the Sloan Digital Sky Survey, and the future prospects to constrain the nature of exotic components of the universe such as the dark energy will be presented
Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics
Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad
2018-05-01
The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.
International Nuclear Information System (INIS)
Chirikov, B.V.; Shepelyansky, D.L.
1983-02-01
Motion in the stochastic layer around the separatrix of a nonlinear resonance was investigated. The integral distribution function F(tau) of trajectory recurrence times tau to the center of the layer was numerically determined. It was found that the distribution F(tau) = A tau - /sup p/ is a power function, the exponent assuming two different values: for tau less than or equal to tau 0 , p = 1/2 and for tau >> tau 0 , p = 3/2 (time tau 0 is determined by the characteristics of the layer)
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity
Bache, Morten; Lavrinenko, Andrei V.
2017-09-01
Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.
Kamaraju, N.; Kumar, Sunil; Sood, A. K.; Guha, Shekhar; Krishnamurthy, Srinivasan; Rao, C. N. R.
2007-12-01
Nonlinear transmission of 80 and 140fs pulsed light with 0.79μm wavelength through single walled carbon nanotubes suspended in water containing sodium dodecyl sulfate is studied. Pulse-width independent saturation absorption and negative cubic nonlinearity are observed, respectively, in open and closed aperture z-scan experiments. The theoretical expressions derived to analyze the z-dependent transmission in the saturable limit require two photon absorption coefficient β0˜1.4cm/MW and a nonlinear index γ ˜-5.5×10-11cm2/W to fit the data.
International Nuclear Information System (INIS)
Bekiros, Stelios D.; Diks, Cees G.H.
2008-01-01
The present study investigates the linear and nonlinear causal linkages between daily spot and futures prices for maturities of one, two, three and four months of West Texas Intermediate (WTI) crude oil. The data cover two periods October 1991-October 1999 and November 1999-October 2007, with the latter being significantly more turbulent. Apart from the conventional linear Granger test we apply a new nonparametric test for nonlinear causality by Diks and Panchenko after controlling for cointegration. In addition to the traditional pairwise analysis, we test for causality while correcting for the effects of the other variables. To check if any of the observed causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VECM filtered residuals. Finally, we investigate the hypothesis of nonlinear non-causality after controlling for conditional heteroskedasticity in the data using a GARCH-BEKK model. Whilst the linear causal relationships disappear after VECM cointegration filtering, nonlinear causal linkages in some cases persist even after GARCH filtering in both periods. This indicates that spot and futures returns may exhibit asymmetric GARCH effects and/or statistically significant higher order conditional moments. Moreover, the results imply that if nonlinear effects are accounted for, neither market leads or lags the other consistently, videlicet the pattern of leads and lags changes over time. (author)
Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities
DEFF Research Database (Denmark)
Bache, Morten; Liu, Xing; Zhou, Binbin
Generating few-cycle energetic and broadband mid-IR pulses is an urgent current challenge in nonlinear optics. Cascaded second-harmonic generation (SHG) gives access to an ultrafast and octave-spanning self-defocusing nonlinearity: when ΔkL >> 2π the pump experiences a Kerr-like nonlinear index...
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
International Nuclear Information System (INIS)
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-01-01
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules
Detecting nonlinearity in run-up on a natural beach
Directory of Open Access Journals (Sweden)
K. R. Bryan
2007-07-01
Full Text Available Natural geophysical timeseries bear the signature of a number of complex, possibly inseparable, and generally unknown combination of linear, stable non-linear and chaotic processes. Quantifying the relative contribution of, in particular, the non-linear components will allow improved modelling and prediction of natural systems, or at least define some limitations on predictability. However, difficulties arise; for example, in cases where the series are naturally cyclic (e.g. water waves, it is most unclear how this cyclic behaviour impacts on the techniques commonly used to detect the nonlinear behaviour in other fields. Here a non-linear autoregressive forecasting technique which has had success in demonstrating nonlinearity in non-cyclical geophysical timeseries, is applied to a timeseries generated by videoing the waterline on a natural beach (run-up, which has some irregular oscillatory behaviour that is in part induced by the incoming wave field. In such cases, the deterministic shape of each run-up cycle has a strong influence on forecasting results, causing questionable results at small (within a cycle prediction distances. However, the technique can clearly differentiate between random surrogate series and natural timeseries at larger prediction distances (greater than one cycle. Therefore it was possible to clearly identify nonlinearity in the relationship between observed run-up cycles in that a local autoregressive model was more adept at predicting run-up cycles than a global one. Results suggest that despite forcing from waves impacting on the beach, each run-up cycle evolves somewhat independently, depending on a non-linear interaction with previous run-up cycles. More generally, a key outcome of the study is that oscillatory data provide a similar challenge to differentiating chaotic signals from correlated noise in that the deterministic shape causes an additional source of autocorrelation which in turn influences the
Statistical Physics of Neural Systems with Nonadditive Dendritic Coupling
Directory of Open Access Journals (Sweden)
David Breuer
2014-03-01
Full Text Available How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such nonadditive dendritic processing on single-neuron responses and the performance of associative-memory tasks in artificial neural networks. First, we compute the effect of random input to a neuron incorporating nonlinear dendrites. This approach is independent of the details of the neuronal dynamics. Second, we use those results to study the impact of dendritic nonlinearities on the network dynamics in a paradigmatic model for associative memory, both numerically and analytically. We find that dendritic nonlinearities maintain network convergence and increase the robustness of memory performance against noise. Interestingly, an intermediate number of dendritic branches is optimal for memory functionality.
International Nuclear Information System (INIS)
Khoroshun, L.P.
1995-01-01
The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero
Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics
Beretta, Gian Paolo
2006-01-01
We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy stat...
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
Learning Statistics - in a WEB-based and non-linear way
DEFF Research Database (Denmark)
Rootzen, Helle
2007-01-01
different from one another. They have different prior knowledge and different learning styles so it is a challenging task to teach them all in the same way. Furthermore the world of statistics has become so huge that it is impossible to cover everything. The structure imposed by the Bologna agreement gives...... can design the course – or a part of the course – so that it fits their individual learning style and their prior knowledge. Some prefer to look at examples first and afterwards look at which theories it is based on. Others want to do it the opposite way. Some wants to work with the problem themselves...
Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme
Directory of Open Access Journals (Sweden)
Lan Wang
2017-01-01
Full Text Available Quasi-linear autoregressive with exogenous inputs (Quasi-ARX models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Energy Technology Data Exchange (ETDEWEB)
Guo, Shimin, E-mail: gsm861@126.com [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands); Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, 710049 (China); Sun, Anbang [Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands)
2013-05-15
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.
International Nuclear Information System (INIS)
Guo, Shimin; Mei, Liquan; Sun, Anbang
2013-01-01
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time
Energy Technology Data Exchange (ETDEWEB)
Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)
2014-09-25
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.
International Nuclear Information System (INIS)
Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar
2014-01-01
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range
Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.
2018-07-01
We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.
Testing and inference in nonlinear cointegrating vector error correction models
DEFF Research Database (Denmark)
Kristensen, D.; Rahbek, A.
2013-01-01
We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under...... the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full...... asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap...
Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism
Directory of Open Access Journals (Sweden)
Ervin K. Lenzi
2017-01-01
Full Text Available We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.
Leydesdorff, L.
2013-01-01
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the configurations among variables can be important in addition
Nonlinear effects in the radiation force generated by amplitude-modulated focused beams
González, Nuria; Jiménez, Noé; Redondo, Javier; Roig, Bernardino; Picó, Rubén; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.; Camarena, Francisco
2012-10-01
Harmonic Motion Imaging (HMI) uses an amplitude-modulated (AM) beam to induce an oscillatory radiation force before, during and after ablation. In this paper, the findings from a numerical analysis of the effects related with the nonlinear propagation of AM focused ultrasonic beams in water on the radiation force and the location of its maxima will be presented. The numerical modeling is performed using the KZK nonlinear parabolic equation. The radiation force is generated by a focused transducer with a gain of 18, a carrier frequency of 1 MHz and a modulation frequency of 25 kHz. The modulated excitation generates a spatially-invariant force proportional to the intensity. Regarding the nonlinear wave propagation, the force is no longer proportional to the intensity, reaching a factor of eight between the nonlinear and linear estimations. Also, a 9 mm shift in the on-axis force peak occurs when the initial pressure increased from 1 to 300 kPa. This spatial shift, due to the nonlinear effects, becomes dynamic in AM focused beams, as the different signal periods have different amplitudes. This study shows that both the value and the spatial position of the force peak are affected by the nonlinear propagation of the ultrasonic waves.
A spline-based non-linear diffeomorphism for multimodal prostate registration.
Mitra, Jhimli; Kato, Zoltan; Martí, Robert; Oliver, Arnau; Lladó, Xavier; Sidibé, Désiré; Ghose, Soumya; Vilanova, Joan C; Comet, Josep; Meriaudeau, Fabrice
2012-08-01
This paper presents a novel method for non-rigid registration of transrectal ultrasound and magnetic resonance prostate images based on a non-linear regularized framework of point correspondences obtained from a statistical measure of shape-contexts. The segmented prostate shapes are represented by shape-contexts and the Bhattacharyya distance between the shape representations is used to find the point correspondences between the 2D fixed and moving images. The registration method involves parametric estimation of the non-linear diffeomorphism between the multimodal images and has its basis in solving a set of non-linear equations of thin-plate splines. The solution is obtained as the least-squares solution of an over-determined system of non-linear equations constructed by integrating a set of non-linear functions over the fixed and moving images. However, this may not result in clinically acceptable transformations of the anatomical targets. Therefore, the regularized bending energy of the thin-plate splines along with the localization error of established correspondences should be included in the system of equations. The registration accuracies of the proposed method are evaluated in 20 pairs of prostate mid-gland ultrasound and magnetic resonance images. The results obtained in terms of Dice similarity coefficient show an average of 0.980±0.004, average 95% Hausdorff distance of 1.63±0.48 mm and mean target registration and target localization errors of 1.60±1.17 mm and 0.15±0.12 mm respectively. Copyright © 2012 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Williams, Ross; Cherin, Emmanuel; Lam, Toby Y J; Tavakkoli, Jahangir; Zemp, Roger J; Foster, F Stuart
2006-01-01
Nonlinear propagation has been demonstrated to have a significant impact on ultrasound imaging. An efficient computational algorithm is presented to simulate nonlinear ultrasound propagation through layered liquid and tissue-equivalent media. Results are compared with hydrophone measurements. This study was undertaken to investigate the role of nonlinear propagation in high frequency ultrasound micro-imaging. The acoustic field of a focused transducer (20 MHz centre frequency, f-number 2.5) was simulated for layered media consisting of water and tissue-mimicking phantom, for several wide-bandwidth source pulses. The simulation model accounted for the effects of diffraction, attenuation and nonlinearity, with transmission and refraction at layer boundaries. The parameter of nonlinearity, B/A, of the water and tissue-mimicking phantom were assumed to be 5.2 and 7.4, respectively. The experimentally measured phantom B/A value found using a finite-amplitude insert-substitution method was shown to be 7.4 ± 0.6. Relative amounts of measured second and third harmonic pressures as a function of the fundamental pressures at the focus were in good agreement with simulations. Agreement within 3% was found between measurements and simulations of the beam widths of the fundamental and second harmonic signals following propagation through the tissue phantom. The results demonstrate significant nonlinear propagation effects for high frequency imaging beams
Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain
Energy Technology Data Exchange (ETDEWEB)
Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)
2010-08-15
This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to earlier studies, we model the on-off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas. Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper. Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement. (author)
Dmitriev, Egor V; Khomenko, Georges; Chami, Malik; Sokolov, Anton A; Churilova, Tatyana Y; Korotaev, Gennady K
2009-03-01
The absorption of sunlight by oceanic constituents significantly contributes to the spectral distribution of the water-leaving radiance. Here it is shown that current parameterizations of absorption coefficients do not apply to the optically complex waters of the Crimea Peninsula. Based on in situ measurements, parameterizations of phytoplankton, nonalgal, and total particulate absorption coefficients are proposed. Their performance is evaluated using a log-log regression combined with a low-pass filter and the nonlinear least-square method. Statistical significance of the estimated parameters is verified using the bootstrap method. The parameterizations are relevant for chlorophyll a concentrations ranging from 0.45 up to 2 mg/m(3).
Nonlinear dynamics of two-phase flow
International Nuclear Information System (INIS)
Rizwan-uddin
1986-01-01
Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques
Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.
2018-04-01
The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.
Non-dispersive traveling waves in inclined shallow water channels
International Nuclear Information System (INIS)
Didenkulova, Ira; Pelinovsky, Efim
2009-01-01
Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied.
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
Energy Technology Data Exchange (ETDEWEB)
McHarris, Wm C, E-mail: mcharris@chemistry.msu.edu [Departments of Chemistry and Physics/Astronomy, Michigan State University, East Lansing, MI 48824 (United States)
2011-07-08
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a definitely quantum system. As an illustration of what can go wrong when quantum effects are forced into a linear interpretation, I examine Bell-type inequalities. In conventional derivations of such inequalities, classical systems are found to impose upper limits on the statistical correlations between, say, the properties of a pair of separated but entangled particles, whereas quantum systems allow greater correlations. Numerous experiments have upheld the quantum predictions (greater statistical correlations than allowed classically), which has led to inferences such as the instantaneous transmission of information between effectively infinitely separated particles - Einstein's 'spooky action-at-a-distance', incompatible with relativity. I argue that there is nothing wrong with the quantum mechanical side of such derivations (the usual point of attack by those attempting to debunk Bell-type arguments), but implicit in the derivations on the classical side is the assumption of independent, uncorrelated particles. As a result, one is comparing uncorrelated probabilities versus conditional probabilities rather than comparing classical versus quantum mechanics, making moot the experimental inferences. Further, nonlinear classical systems are known to exhibit correlations that can easily be as great as and overlap with quantum correlations - so-called nonextensive thermodynamics with its nonadditive entropy has verified this with numerous examples. Perhaps quantum mechanics does contain fundamental nonlinear elements. Nonlinear dynamics and chaos theory could
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
International Nuclear Information System (INIS)
McHarris, Wm C
2011-01-01
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a definitely quantum system. As an illustration of what can go wrong when quantum effects are forced into a linear interpretation, I examine Bell-type inequalities. In conventional derivations of such inequalities, classical systems are found to impose upper limits on the statistical correlations between, say, the properties of a pair of separated but entangled particles, whereas quantum systems allow greater correlations. Numerous experiments have upheld the quantum predictions (greater statistical correlations than allowed classically), which has led to inferences such as the instantaneous transmission of information between effectively infinitely separated particles - Einstein's 'spooky action-at-a-distance', incompatible with relativity. I argue that there is nothing wrong with the quantum mechanical side of such derivations (the usual point of attack by those attempting to debunk Bell-type arguments), but implicit in the derivations on the classical side is the assumption of independent, uncorrelated particles. As a result, one is comparing uncorrelated probabilities versus conditional probabilities rather than comparing classical versus quantum mechanics, making moot the experimental inferences. Further, nonlinear classical systems are known to exhibit correlations that can easily be as great as and overlap with quantum correlations - so-called nonextensive thermodynamics with its nonadditive entropy has verified this with numerous examples. Perhaps quantum mechanics does contain fundamental nonlinear elements. Nonlinear dynamics and chaos theory could well provide a
Simulation of Irregular Waves and Wave Induced Loads on Wind Power Plants in Shallow Water
Energy Technology Data Exchange (ETDEWEB)
Trumars, Jenny [Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Water Environment Transport
2004-05-01
The essay gives a short introduction to waves and discusses the problem with non-linear waves in shallow water and how they effect an offshore wind energy converter. The focus is on the realisation of non-linear waves in the time domain from short-term statistics in the form of a variance density spectrum of the wave elevation. For this purpose the wave transformation from deep water to the near to shore site of a wind energy farm at Bockstigen has been calculated with the use of SWAN (Simulating Waves Near Shore). The result is a wave spectrum, which can be used as input to the realisation. The realisation of waves is done by perturbation theory to the first and second-order. The properties calculated are the wave elevation, water particle velocity and acceleration. The wave heights from the second order perturbation equations are higher than those from the first order perturbation equations. This is also the case for the water particle kinematics. The increase of variance is significant between the first order and the second order realisation. The calculated wave elevation exhibits non-linear features as the peaks become sharper and the troughs flatter. The resulting forces are calculated using Morison's equation. For second order force and base moment there is an increase in the maximum values. The force and base moment are largest approximately at the zero up and down crossing of the wave elevation. This indicates an inertia dominated wave load. So far the flexibility and the response of the structure have not been taken into account. They are, however, of vital importance. For verification of the wave model the results will later on be compared with measurements at Bockstigen off the coast of Gotland in the Baltic Sea.
Soliton excitations in a class of nonlinear field theory models
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Fedyanin, V.K.
1985-01-01
Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated
A new similarity index for nonlinear signal analysis based on local extrema patterns
Niknazar, Hamid; Motie Nasrabadi, Ali; Shamsollahi, Mohammad Bagher
2018-02-01
Common similarity measures of time domain signals such as cross-correlation and Symbolic Aggregate approximation (SAX) are not appropriate for nonlinear signal analysis. This is because of the high sensitivity of nonlinear systems to initial points. Therefore, a similarity measure for nonlinear signal analysis must be invariant to initial points and quantify the similarity by considering the main dynamics of signals. The statistical behavior of local extrema (SBLE) method was previously proposed to address this problem. The SBLE similarity index uses quantized amplitudes of local extrema to quantify the dynamical similarity of signals by considering patterns of sequential local extrema. By adding time information of local extrema as well as fuzzifying quantized values, this work proposes a new similarity index for nonlinear and long-term signal analysis, which extends the SBLE method. These new features provide more information about signals and reduce noise sensitivity by fuzzifying them. A number of practical tests were performed to demonstrate the ability of the method in nonlinear signal clustering and classification on synthetic data. In addition, epileptic seizure detection based on electroencephalography (EEG) signal processing was done by the proposed similarity to feature the potentials of the method as a real-world application tool.
PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.
Xia, Jing; Wang, Michelle Yongmei
Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.
Relations between nonlinear Riccati equations and other equations in fundamental physics
International Nuclear Information System (INIS)
Schuch, Dieter
2014-01-01
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown
International Nuclear Information System (INIS)
Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.
2002-01-01
A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed
Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints
Directory of Open Access Journals (Sweden)
Shaochong Yang
2017-01-01
Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in
Water scarcity, market-based incentives, and consumer response
Krause, K.; Chermak, J. M.; Brookshire, D. S.
2003-04-01
Water is an increasingly scarce resource and the future viability of many regions will depend in large part on how efficiently resources are utilized. A key factor to this success will be a thorough understanding of consumers and the characteristics that drive their water use. In this research test and find support for the hypothesis that residential water consumers are heterogeneous. We combine experimental and survey responses to test for statistically significant consumer characteristics that are observable factors of demand for water. Significant factors include "stage of life" (i.e., student versus workforce versus retired), as well as various social and cultural factors including age, ethnicity, political affiliation and religious affiliation. Identification of these characteristics allows us to econometrically estimate disaggregated water demand for a sample of urban water consumers in Albuquerque, New Mexico, USA. The results provide unique parameter estimates for different consumer types. Using these results we design an incentive compatible, non-linear pricing program that allows individual consumers to choose a fixed fee/commodity charge from a menu that not only allows the individual to maximize his or her utility, while meeting the conservation goals of the program. We show that this program, with the attention to consumer differences is more efficient than the traditional "one size fits all" programs commonly employed by many water utilities.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Modeling exposure–lag–response associations with distributed lag non-linear models
Gasparrini, Antonio
2014-01-01
In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094
Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models
Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.
2011-01-01
We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.
Dijkstra, T.K.; Henseler, J.
2011-01-01
The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with
FRF decoupling of nonlinear systems
Kalaycıoğlu, Taner; Özgüven, H. Nevzat
2018-03-01
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
Statistical identification of effective input variables
International Nuclear Information System (INIS)
Vaurio, J.K.
1982-09-01
A statistical sensitivity analysis procedure has been developed for ranking the input data of large computer codes in the order of sensitivity-importance. The method is economical for large codes with many input variables, since it uses a relatively small number of computer runs. No prior judgemental elimination of input variables is needed. The sceening method is based on stagewise correlation and extensive regression analysis of output values calculated with selected input value combinations. The regression process deals with multivariate nonlinear functions, and statistical tests are also available for identifying input variables that contribute to threshold effects, i.e., discontinuities in the output variables. A computer code SCREEN has been developed for implementing the screening techniques. The efficiency has been demonstrated by several examples and applied to a fast reactor safety analysis code (Venus-II). However, the methods and the coding are general and not limited to such applications
The Relationship between Nonconservative Schemes and Initial Values of Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
林万涛
2004-01-01
For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.
Wu, Hui; Hu, Liming; Wen, Qingbo
2017-06-01
Electro-osmotic consolidation is an effective method for soft ground improvement. A main limitation of previous numerical models on this technique is the ignorance of the non-linear variation of soil parameters. In the present study, a multi-field numerical model is developed with the consideration of the non-linear variation of soil parameters during electro-osmotic consolidation process. The numerical simulations on an axisymmetric model indicated that the non-linear variation of soil parameters showed remarkable impact on the development of the excess pore water pressure and degree of consolidation. A field experiment with complex geometry, boundary conditions, electrode configuration and voltage application was further simulated with the developed numerical model. The comparison between field and numerical data indicated that the numerical model coupling of the non-linear variation of soil parameters gave more reasonable results. The developed numerical model is capable to analyze engineering cases with complex operating conditions.
Chaotic synchronization of two complex nonlinear oscillators
International Nuclear Information System (INIS)
Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.
2009-01-01
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Bubble nonlinear dynamics and stimulated scattering process
Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu
2016-02-01
A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).
Reactor water level control device
International Nuclear Information System (INIS)
Hiramatsu, Yohei.
1980-01-01
Purpose: To increase the rapid response of the waterlevel control converting a reactor water level signal into a non-linear type, when the water level is near to a set value, to stabilize the water level reducting correlatively the reactor water level variation signal to stabilize greatly from the set value, and increasing the variation signal. Constitution: A main vapor flow quality transmitter detects the vapor flow generated in a reactor and introduced into a turbine. A feed water flow transmitter detects the quantity of a feed water flow from the turbine to the reactor, this detected value is sent to an addition operating apparatus. On the other hand, the power signal of the reactor water level transmitter is sent to the addition operating apparatus through a non-linear water level signal converter. The addition operation apparatus generates a signal for requesting the feed water flow quantity from both signals. Upon this occasion, the reactor water level signal converter makes small the reactor water level variation when the reactor level is close the set value, and when the water level deviates greatly from the set value, the reactor water level variation is made large thereby to improve the rapid response of the reactor coater level control. (Yoshino, Y.)
Venturi, D.; Karniadakis, G. E.
2012-08-01
By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.
National Research Council Canada - National Science Library
Reeves, Justin M
2008-01-01
...) was conducted from 13 - 15 April 2005 on the continental shelf in the northeast portion of the South China Sea to study the effects of nonlinear internal waves on the transmission of a 400-Hz signal...
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr
Apel, Heiko; Gafurov, Abror; Gerlitz, Lars; Unger-Shayesteh, Katy; Vorogushyn, Sergiy; Merkushkin, Aleksandr; Merz, Bruno
2016-04-01
The semi-arid regions of Central Asia crucially depend on the water resources supplied by the mountainous areas of the Tien-Shan and Pamirs. During the summer months the snow and glacier melt water of the rivers originating in the mountains provides the only water resource available for agricultural production but also for water collection in reservoirs for energy production in winter months. Thus a reliable seasonal forecast of the water resources is crucial for a sustainable management and planning of water resources.. In fact, seasonal forecasts are mandatory tasks of national hydro-meteorological services in the region. Thus this study aims at a statistical forecast of the seasonal water availability, whereas the focus is put on the usage of freely available data in order to facilitate an operational use without data access limitations. The study takes the Naryn basin as a test case, at which outlet the Toktogul reservoir stores the discharge of the Naryn River. As most of the water originates form snow and glacier melt, a statistical forecast model should use data sets that can serve as proxy data for the snow masses and snow water equivalent in late spring, which essentially determines the bulk of the seasonal discharge. CRU climate data describing the precipitation and temperature in the basin during winter and spring was used as base information, which was complemented by MODIS snow cover data processed through ModSnow tool, discharge during the spring and also GRACE gravimetry anomalies. For the construction of linear forecast models monthly as well as multi-monthly means over the period January to April were used to predict the seasonal mean discharge of May-September at the station Uchterek. An automatic model selection was performed in multiple steps, whereas the best models were selected according to several performance measures and their robustness in a leave-one-out cross validation. It could be shown that the seasonal discharge can be predicted with
Palozzi, Jason; Pantopoulos, George; Maravelis, Angelos G.; Nordsvan, Adam; Zelilidis, Avraam
2018-02-01
This investigation presents an outcrop-based integrated study of internal division analysis and statistical treatment of turbidite bed thickness applied to a Carboniferous deep-water channel-levee complex in the Myall Trough, southeast Australia. Turbidite beds of the studied succession are characterized by a range of sedimentary structures grouped into two main associations, a thick-bedded and a thin-bedded one, that reflect channel-fill and overbank/levee deposits, respectively. Three vertically stacked channel-levee cycles have been identified. Results of statistical analysis of bed thickness, grain-size and internal division patterns applied on the studied channel-levee succession, indicate that turbidite bed thickness data seem to be well characterized by a bimodal lognormal distribution, which is possibly reflecting the difference between deposition from lower-density flows (in a levee/overbank setting) and very high-density flows (in a channel fill setting). Power law and exponential distributions were observed to hold only for the thick-bedded parts of the succession and cannot characterize the whole bed thickness range of the studied sediments. The succession also exhibits non-random clustering of bed thickness and grain-size measurements. The studied sediments are also characterized by the presence of statistically detected fining-upward sandstone packets. A novel quantitative approach (change-point analysis) is proposed for the detection of those packets. Markov permutation statistics also revealed the existence of order in the alternation of internal divisions in the succession expressed by an optimal internal division cycle reflecting two main types of gravity flow events deposited within both thick-bedded conglomeratic and thin-bedded sandstone associations. The analytical methods presented in this study can be used as additional tools for quantitative analysis and recognition of depositional environments in hydrocarbon-bearing research of ancient
Impact of nonlinear distortion on acoustic radiation force elastography.
Draudt, Andrew B; Cleveland, Robin O
2011-11-01
High-intensity focused ultrasound (HIFU) produces an acoustic radiation force that induces tissue displacement, which can be measured by monitoring time shifts in the backscattered signals from interrogation pulses. If the pulse occurs simultaneously with the HIFU, the arrival time of the backscatter will be biased because nonlinearity associated with the HIFU changes the local sound speed. Measurements of the pressure field using 1.1 MHz HIFU and a 7.5 MHz pulse in water exhibited a nonlinearly induced apparent displacement (NIAD) that varied with the HIFU pressure, propagation distance and the timing of the pulse relative to the HIFU. Nonlinear simulations employing the KZK equation predicted NIADs that agreed with measurements. Experiments with chicken breast demonstrated a NIAD with magnitude similar to that expected from the radiation force. Finally it was shown that if two pulses were fired with different phases relative to the HIFU, then upon averaging, the NIAD could be mitigated. Copyright © 2011 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics
Zhu, Yanqiu; Cohn, Stephen E.; Todling, Ricardo
1999-01-01
The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Energy Technology Data Exchange (ETDEWEB)
Jasna M. Djinovic; Aleksandar R. Popovic [University of Belgrade, Belgrade (Serbia and Montenegro). Center of Chemistry, Institute of Chemistry, Technology and Metallurgy
2007-01-15
The aim of this study was to establish the real in situ influence of coal ash and slag transport and storage on the quality of neighboring surface and ground waters by applying correlation statistic analysis. It was found that the waste waters from the coal ash dump do not have any influence on the quality of the Danube river water. The Danube and the waste waters, however, influence the quality of the ground waters of the Petka spring. Changes in the concentrations of elements in the Danube or in the waste waters can have immediate or delayed impact on the quality of the spring waters. The immediate impact has calcium, magnesium, zinc, copper, vanadium, cobalt from Danube; magnesium, vanadium from overflow and drainage waters; copper from drainage water. And the delayed impact has calcium, magnesium, vanadium and silicon from the Danube waters, cobalt from drainage waters, chromium and silicon from overflow waters and magnesium and vanadium from both overflow and drainage waters. 20 refs., 2 figs., 4 tabs.
Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.
Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal
2017-08-18
The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.
Rego, JoãO. L.; Li, Chunyan
2010-06-01
This study applied the finite volume coastal ocean model (FVCOM) to the storm surge induced by Hurricane Rita along the Louisiana-Texas coast. The model was calibrated for tides and validated with observed water levels. Peak water levels were shown to be lower than expected for a landfall at high tide. For low- and high-tide landfalls, nonlinear effects due to tide-surge coupling were constructive and destructive to total storm tide, respectively, and their magnitude reached up to 70% of the tidal amplitude in the Rita application. Tide-surge interaction was further examined using a standard hurricane under idealized scenarios to evaluate the effects of various shelf geometries, tides, and landfall timings (relative to tide). Nonlinearity was important between landfall position and locations within 2.5 × radius of maximum winds. On an idealized wide continental shelf, nonlinear effects reached up to 80% of the tidal amplitude with an S2 tide and up to 47% with a K1 tide. Increasing average depths by 4 m reduced nonlinear effects to 41% of the tidal amplitude; increasing the slope by a factor of 3 produced nonlinearities of just 26% of tide (both with a K1 tide). The nonlinear effect was greatest for landfalls at low tide, followed by landfalls at high tide and then by landfalls at midebb or midflood.
Piezoelectric Non-linear Nanomechanical Temperature and Acceleration Intensive Clocks (PENNTAC)
2014-05-01
amplifiers”, Applied Physics Letters , vol. 96, 234101, 2010. [4] Miller, N.J. “Escape statistics for parameter sweeps through bifurcations”, Phys. Rev. E...Device Letters , Vol. 33, Issue 5, 2012, pp. 724-726. J. S.-Fernandez, G. Piazza, “Thermal Nonlinearities in Contour Mode AlN Resonators”, IEEE Journal...Rinaldi, H. Pak, D. Fry, D. Bail , D. Stevens, Gianluca Piazza, “A 586 MHz Microcontroller Compensated MEMS Oscillator Based on Ovenized Aluminum
Introductory statistics for business and economics theory, exercises and solutions
Ubøe, Jan
2017-01-01
This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor. The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.
A Statistical Model for Soliton Particle Interaction in Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans; Truelsen, J.
1986-01-01
A statistical model for soliton-particle interaction is presented. A master equation is derived for the time evolution of the particle velocity distribution as induced by resonant interaction with Korteweg-de Vries solitons. The detailed energy balance during the interaction subsequently determines...... the evolution of the soliton amplitude distribution. The analysis applies equally well for weakly nonlinear plasma waves in a strongly magnetized waveguide, or for ion acoustic waves propagating in one-dimensional systems....
Optimising the weighting of the water retention index using sensitivity analysis
Becker, William; Vandecasteele, Ine
2015-04-01
A robust composite indicator was developed to assess the capacity of the landscape to regulate and retain water passing through it at Pan-European scale. The "Water Retention Index" (WRI) takes into account the role of interception by vegetation, the water-holding capacity of the soil, and the relative capacity of the bedrock to allow percolation of water, as well as the influence of soil sealing and slope gradient. A delicate issue in composite indicators is however the relative weighting of each variable used in the indicator - strong correlations and skewness are known to cause unequal influence of the input variables, even though the weighting coefficients are equal (Paruolo et al, 2013). To understand the effects of the weightings in the WRI, penalised splines were used to calculate the first order sensitivity index of each variable used in the construction of the WRI, allowing the true influence of each input to be determined. Furthermore, the weighting coefficients were optimised using an iterative nonlinear algorithm to find the coefficients which resulted in the most equal influence of each input to the indicator. In principle, this approach can be used to improve the weighting of many different kinds of composite indicator, the results of which are often used as the basis for important policy decisions at the European level. Paruolo, Paolo, Michaela Saisana, and Andrea Saltelli. "Ratings and rankings: voodoo or science?." Journal of the Royal Statistical Society: Series A (Statistics in Society) 176.3 (2013): 609-634.
International Nuclear Information System (INIS)
Peterlin, Primoz
2010-01-01
Two methods of data analysis are compared: spreadsheet software and a statistics software suite. Their use is compared analysing data collected in three selected experiments taken from an introductory physics laboratory, which include a linear dependence, a nonlinear dependence and a histogram. The merits of each method are compared.
Observations of linear and nonlinear processes in the foreshock wave evolution
Directory of Open Access Journals (Sweden)
Y. Narita
2007-07-01
Full Text Available Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion right-hand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.
Fundamentals of nonlinear optical materials
Indian Academy of Sciences (India)
Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.
DEFF Research Database (Denmark)
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.
This paper contains an analyses of the error induced by applying the method of the equivalent statistical linearzation (ESL) to randomly-exited multi-degree-of-freedom (MDOF) geometrically nonlinear shear-frame structures as the number of degrees of freedom increases. The quantity that is analyzed...
The mechanism by which nonlinearity sustains turbulence in plane Couette flow
Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.
2018-04-01
Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.
Directory of Open Access Journals (Sweden)
Astafyeva Liudmila
2011-01-01
Full Text Available Abstract Nonlinear thermo-optical properties of two-layered spherical system of gold nanoparticle core and water vapor shell, created under laser heating of nanoparticle in water, were theoretically investigated. Vapor shell expansion leads to decreasing up to one to two orders of magnitude in comparison with initial values of scattering and extinction of the radiation with wavelengths 532 and 633 nm by system while shell radius is increased up to value of about two radii of nanoparticle. Subsequent increasing of shell radius more than two radii of nanoparticle leads to rise of scattering and extinction properties of system over initial values. The significant decrease of radiation scattering and extinction by system of nanoparticle-vapor shell can be used for experimental detection of the energy threshold of vapor shell formation and investigation of the first stages of its expansion. PACS: 42.62.BE. 78.67. BF
Muhammad, Said; Tahir Shah, M; Khan, Sardar
2010-10-01
The present study was conducted in Kohistan region, where mafic and ultramafic rocks (Kohistan island arc and Indus suture zone) and metasedimentary rocks (Indian plate) are exposed. Water samples were collected from the springs, streams and Indus river and analyzed for physical parameters, anions, cations and arsenic (As(3+), As(5+) and arsenic total). The water quality in Kohistan region was evaluated by comparing the physio-chemical parameters with permissible limits set by Pakistan environmental protection agency and world health organization. Most of the studied parameters were found within their respective permissible limits. However in some samples, the iron and arsenic concentrations exceeded their permissible limits. For health risk assessment of arsenic, the average daily dose, hazards quotient (HQ) and cancer risk were calculated by using statistical formulas. The values of HQ were found >1 in the samples collected from Jabba, Dubair, while HQ values were pollution load was also calculated by using multivariate statistical techniques like one-way ANOVA, correlation analysis, regression analysis, cluster analysis and principle component analysis. Copyright © 2010 Elsevier Ltd. All rights reserved.
Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Statistical mechanics of program systems
International Nuclear Information System (INIS)
Neirotti, Juan P; Caticha, Nestor
2006-01-01
We discuss the collective behaviour of a set of operators and variables that constitute a program and the emergence of meaningful computational properties in the language of statistical mechanics. This is done by appropriately modifying available Monte Carlo methods to deal with hierarchical structures. The study suggests, in analogy with simulated annealing, a method to automatically design programs. Reasonable solutions can be found, at low temperatures, when the method is applied to simple toy problems such as finding an algorithm that determines the roots of a function or one that makes a nonlinear regression. Peaks in the specific heat are interpreted as signalling phase transitions which separate regions where different algorithmic strategies are used to solve the problem
Nonlinear Schrödinger approach to European option pricing
Wróblewski, Marcin
2017-05-01
This paper deals with numerical option pricing methods based on a Schrödinger model rather than the Black-Scholes model. Nonlinear Schrödinger boundary value problems seem to be alternatives to linear models which better reflect the complexity and behavior of real markets. Therefore, based on the nonlinear Schrödinger option pricing model proposed in the literature, in this paper a model augmented by external atomic potentials is proposed and numerically tested. In terms of statistical physics the developed model describes the option in analogy to a pair of two identical quantum particles occupying the same state. The proposed model is used to price European call options on a stock index. the model is calibrated using the Levenberg-Marquardt algorithm based on market data. A Runge-Kutta method is used to solve the discretized boundary value problem numerically. Numerical results are provided and discussed. It seems that our proposal more accurately models phenomena observed in the real market than do linear models.
International Nuclear Information System (INIS)
Shen Yuanrang
2011-01-01
This article presents a brief introduction to the birth and early investigations of nonlinear optics, such as second harmonic generation,sum and difference frequency generation, stimulated Raman scattering,and self-action of light etc. Several important research achievements and applications of nonlinear optics are presented as well, including nonlinear optical spectroscopy, phase conjugation and adaptive optics, coherent nonlinear optics, and high-order harmonic generation. In the end, current and future research topics in nonlinear optics are summarized. (authors)