Anisotropic Helmholtz and wave–vortex decomposition of one-dimensional spectra

2017 ◽  
Vol 815 ◽  
pp. 361-387 ◽  
Author(s):  
Oliver Bühler ◽  
Max Kuang ◽  
Esteban G. Tabak
Keyword(s):  
Synthetic Data ◽  
Power Spectra ◽  
Statistical Correlation ◽  
Original Method ◽  
Anisotropic Flow ◽  
One Dimensional ◽  
Divergent Flow ◽  
Consistent Manner ◽  
Flow Components ◽  
The One

We present an extension to anisotropic flows of the recently developed Helmholtz and wave–vortex decomposition method for one-dimensional spectra measured along ship or aircraft tracks in Bühler et al. (J. Fluid Mech., vol. 756, 2014, pp. 1007–1026). Here, anisotropy refers to the statistical properties of the underlying flow field, which in the original method was assumed to be homogeneous and isotropic in the horizontal plane. Now, the flow is allowed to have a simple kind of horizontal anisotropy that is chosen in a self-consistent manner and can be deduced from the one-dimensional power spectra of the horizontal velocity fields and their cross-correlation. The key result is that an exact and robust Helmholtz decomposition of the horizontal kinetic energy spectrum can be achieved in this anisotropic flow setting, which then also allows the subsequent wave–vortex decomposition step. The anisotropic method is as easy to use as its isotropic counterpart and it robustly converges back to it if the observed anisotropy tends to zero. As a by-product of our analysis we also found a simple test for statistical correlation between rotational and divergent flow components. The new method is developed theoretically and tested with encouraging results on challenging synthetic data as well as on ocean data from the Gulf Stream.

scholarly journals Analysis of temporal correlation in heart rate variability through maximum entropy principle in a minimal pairwise glassy model

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Elena Agliari ◽  
Francesco Alemanno ◽  
Adriano Barra ◽  
Orazio Antonio Barra ◽  
Alberto Fachechi ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Maximum Entropy ◽  
Clinical Status ◽  
Synthetic Data ◽  
Maximum Entropy Principle ◽  
Temporal Correlation ◽  
One Dimensional ◽  
Entropy Principle ◽  
The One

Abstract In this work we apply statistical mechanics tools to infer cardiac pathologies over a sample of M patients whose heart rate variability has been recorded via 24 h Holter device and that are divided in different classes according to their clinical status (providing a repository of labelled data). Considering the set of inter-beat interval sequences $$\{\mathbf {r}(i) \} = \{ r_1(i), r_2(i), \ldots , \}$$ { r ( i ) } = { r 1 ( i ) , r 2 ( i ) , … , } , with $$i=1,\ldots ,M$$ i = 1 , … , M , we estimate their probability distribution $$P(\mathbf {r})$$ P ( r ) exploiting the maximum entropy principle. By setting constraints on the first and on the second moment we obtain an effective pairwise $$(r_n,r_m)$$ ( r n , r m ) model, whose parameters are shown to depend on the clinical status of the patient. In order to check this framework, we generate synthetic data from our model and we show that their distribution is in excellent agreement with the one obtained from experimental data. Further, our model can be related to a one-dimensional spin-glass with quenched long-range couplings decaying with the spin–spin distance as a power-law. This allows us to speculate that the 1/f noise typical of heart-rate variability may stem from the interplay between the parasympathetic and orthosympathetic systems.

scholarly journals Estimation of in Vivo Pulses in Medical Ultrasound

1994 ◽  
Vol 16 (3) ◽  
pp. 190-203 ◽  
Author(s):  
Jørgen Arendt Jensen
Keyword(s):  
Local Minimum ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Medical Ultrasound ◽  
One Dimensional ◽  
Main Application ◽  
Estimated Parameters ◽  
Ultrasound Field ◽  
The One

An algorithm for the estimation of one-dimensional in-vivo ultrasound pulses is derived. The routine estimates a set of ARMA parameters describing the pulse and uses data from a number of adjacent rf lines. Using multiple lines results in a decrease in variance on the estimated parameters and significantly reduces the risk of terminating the algorithm at a local minimum. Examples from use on synthetic data confirms the reduction in variance and increased chance of successful minimization termination. Simulations are also reported indicating the relation between the one-dimensional pulse and the three-dimensional, attenuated ultrasound field for a concave transducer. Pulses are estimated from in-vivo liver data showing good resemblance to a pulse measured as the response from a planar reflector and then properly attenuated. The main application for the algorithm is to function as a preprocessing stage for deconvolution algorithms using parametric pulses.

Including lateral velocity variations into true-amplitude common-shot wave-equation migration

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. S175-S186 ◽  
Author(s):  
Daniela Amazonas ◽  
Rafael Aleixo ◽  
Gabriela Melo ◽  
Jörg Schleicher ◽  
Amélia Novais ◽  
...  
Keyword(s):  
Wave Equations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Approximate Solutions ◽  
Vertical Gradient ◽  
Correct Description ◽  
Lateral Velocity ◽  
One Dimensional ◽  
Velocity Variations ◽  
The One

In heterogeneous media, standard one-way wave equations describe only the kinematic part of one-way wave propagation correctly. For a correct description of amplitudes, the one-way wave equations must be modified. In media with vertical velocity variations only, the resulting true-amplitude one-way wave equations can be solved analytically. In media with lateral velocity variations, these equations are much harder to solve and require sophisticated numerical techniques. We present an approach to circumvent these problems by implementing approximate solutions based on the one-dimensional analytic amplitude modifications. We use these approximations to show how to modify conventional migration methods such as split-step and Fourier finite-difference migrations in such a way that they more accurately handle migration amplitudes. Simple synthetic data examples in media with a constant vertical gradient demonstrate that the correction achieves the recovery of true migration amplitudes. Applications to the SEG/EAGE salt model and the Marmousi data show that the technique improves amplitude recovery in the migrated images in more realistic situations.

Anisotropic Statistics of Lagrangian Structure Functions and Helmholtz Decomposition

2021 ◽  
Vol 51 (5) ◽  
pp. 1375-1393
Author(s):  
Han Wang ◽  
Oliver Bühler
Keyword(s):  
Velocity Structure ◽  
Synthetic Data ◽  
Structure Functions ◽  
Separation Distance ◽  
New Method ◽  
Helmholtz Decomposition ◽  
Spatial Homogeneity ◽  
Divergent Flow ◽  
Cross Covariance ◽  
Flow Components

AbstractWe present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition into rotational and divergent components, from sparse data collected along Lagrangian observations. The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field and also in the collection of the Lagrangian data. Specifically, we assume only stationarity and spatial homogeneity of the data and that the cross covariance between the rotational and divergent flow components is either zero or a function of the separation distance only. No further assumptions are made and the anisotropy of the underlying flow components can be arbitrarily strong. We demonstrate our new method by testing it against synthetic data and applying it to the Lagrangian Submesoscale Experiment (LASER) dataset. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy.

The spectrum of temperature fluctuations in turbulent flow

1968 ◽  
Vol 34 (3) ◽  
pp. 423-442 ◽  
Author(s):  
H. L. Grant ◽  
B. A. Hughes ◽  
W. M. Vogel ◽  
A. Moilliet
Keyword(s):  
Power Spectra ◽  
Temperature Fluctuations ◽  
Inertial Subrange ◽  
Velocity Fluctuations ◽  
One Dimensional ◽  
Open Sea ◽  
Spectrum Function ◽  
Velocity Spectra ◽  
The One ◽  
Rate Of Dissipation

Temperature and velocity fluctuations have been recorded in the open sea and in a tidal channel, and power spectra have been determined from the records. The one-dimensional spectra of temperature fluctuations are found to have an inertial subrange. At larger wave-numbers the data can be fitted by Batchelor's spectrum function for the viscous-convective range. The spectra are inconsistent with the form proposed by Pao for the viscous-convective range.Estimates are given for the constants in Batchelor's spectrum function, but these depend upon knowledge of the rate of dissipation of kinetic energy, which is determined from the velocity spectra. There is doubt about the validity of some of the velocity spectra, and in other cases there is reason to suspect that the turbulence is not locally isotropic.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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