scholarly journals Constraining higher-order parameters for primordial non-Gaussianities from power spectra and bispectra of imaging surveys

2016 ◽  
Vol 93 (10) ◽  
Author(s):  
Ichihiko Hashimoto ◽  
Atsushi Taruya ◽  
Takahiko Matsubara ◽  
Toshiya Namikawa ◽  
Shuichiro Yokoyama
Keyword(s):  
Power Spectra ◽  
Higher Order ◽  
Order Parameters

Higher order auto‐spectra by maximum entropy method

Geophysics ◽  
1983 ◽  
Vol 48 (10) ◽  
pp. 1409-1410 ◽  
Author(s):  
Robert Owen Plaisted ◽  
Hugo Gustavo Peña
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Power Spectra ◽  
Higher Order ◽  
Linear Process ◽  
Entropy Method ◽  
Resolving Power ◽  
Energy Spectra ◽  
Nonlinear Interactions

Higher order auto‐spectra, in particular bispectra and perhaps trispectra, are being used increasingly for analyzing various nonlinear interactions in the ocean, e.g., Herring (1980) and McComas and Briscoe (1980). The resolution of these spectra, as with conventional energy spectra, is frequently limited because short data records must be used. The purpose of this note is to present a maximum entropy (MEM) representation for higher order auto‐spectra which has the advantage of the superior resolving power of the MEM technique under these circumstances. The derivation is a generalizaton of the power spectra derived for a linear process (Box and Jenkins, 1970). We derive an MEM representation for bispectra and show that this result can be generalized to auto‐spectra of any order.

scholarly journals Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

2014 ◽  
Vol 90 (6) ◽  
Author(s):  
Tao Zhu ◽  
Anzhong Wang ◽  
Gerald Cleaver ◽  
Klaus Kirsten ◽  
Qin Sheng
Keyword(s):  
Power Spectra ◽  
Quantum Effects ◽  
Higher Order ◽  
Spectral Indices ◽  
Higher Order Corrections

On higher order parameters in cracked composite plates under far‐field pure shear

2019 ◽  
Vol 43 (3) ◽  
pp. 568-585 ◽  
Author(s):  
Saeid Ghouli ◽  
Majid R. Ayatollahi ◽  
Morteza Nejati
Keyword(s):  
Pure Shear ◽  
Composite Plates ◽  
Higher Order ◽  
Order Parameters ◽  
Far Field

NMR Evidence for Higher-Order Multipole Order Parameters inNpO2

2006 ◽  
Vol 97 (25) ◽  
Author(s):  
Y. Tokunaga ◽  
D. Aoki ◽  
Y. Homma ◽  
S. Kambe ◽  
H. Sakai ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Parameters

scholarly journals BISPECTRAL AND TRISPECTRAL CHARACTERIZATION OF TRANSITION TO CHAOS IN THE DUFFING OSCILLATOR

1993 ◽  
Vol 03 (03) ◽  
pp. 551-557 ◽  
Author(s):  
VINOD CHANDRAN ◽  
STEVE ELGAR ◽  
CHARLES PEZESHKI
Keyword(s):  
Numerical Solutions ◽  
Duffing Oscillator ◽  
Broad Band ◽  
Power Spectra ◽  
Period Doubling ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Route To Chaos ◽  
Higher Order Spectra

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

scholarly journals Mechanical analysis of heterogeneous materials with higher-order parameters

2021 ◽  
Author(s):  
Bozo Vazic ◽  
Bilen Emek Abali ◽  
Hua Yang ◽  
Pania Newell
Keyword(s):  
Mechanical Properties ◽  
Porous Materials ◽  
Higher Order ◽  
Order Parameters ◽  
Constitutive Law ◽  
Porous System ◽  
First Order ◽  
Bio Engineering ◽  
The Relationship ◽  
Effective Mechanical Properties

AbstractEven though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.

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