scholarly journals Spectral Analysis of Multidimensional Stochastic Geophysical Models with an Application to Decadal ENSO Variability

2011 ◽  
Vol 68 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Richard Kleeman
Keyword(s):  
Normal Mode ◽  
Linear Models ◽  
Decadal Variability ◽  
Normal Modes ◽  
Spectral Character ◽  
Stochastic Forcing ◽  
Spectral Matrix ◽  
Enso Variability ◽  
Cross Spectrum ◽  
The Cross

Abstract Simple linear models with additive stochastic forcing have been rather successful in explaining the observed spectrum of important climate variables. Motivated by this, the authors analyze the spectral character of such a general stochastic system of finite dimension. The spectral matrix is derived in the case that the spectrum is a linear combination of dynamical variables and their stochastic forcings. It is found that the most convenient basis for analysis is provided by the normal modes. In general the spectrum consists of two pieces. The first “diagonal” piece is a symmetric Lorentzian curve centered on the normal mode frequencies with breadth and strength determined by the normal mode dissipation. The second cross-spectrum piece derives usually from the coherency of the stochastic forcing of two different normal modes. The cross-spectrum is smaller in magnitude than the corresponding two diagonal pieces. This relative magnitude is controlled by the Wiener coherency, which is equal to the magnitude of the correlation of the stochastic forcings of different normal modes. This new analysis framework is studied in detail for the ENSO case for which a two-dimensional stochastically forced oscillator has been previously suggested as a minimal model. It is found that the observed spectrum is rather easily reproduced given appropriate dissipation. Further, it is found that the cross-spectrum results in a phase-dependent enhancement or suppression of frequencies smaller than the dominant ENSO frequency. This therefore provides a new mechanism for decadal ENSO variability. Since the cross-spectrum is phase dependent, the decadal variability generated has a distinctive spatial character. The significance of the cross-spectrum depends on the Wiener coherency, which in turn depends on the statistics of the stochastic forcing.

Notes on the stability problem for inhomogeneous equilibria

1983 ◽  
Vol 29 (2) ◽  
pp. 275-286 ◽  
Author(s):  
K. R. Symon
Keyword(s):  
Growth Rate ◽  
Normal Mode ◽  
Stability Problem ◽  
Normal Modes ◽  
Electromagnetic Mode ◽  
Spectral Matrix ◽  
First Order ◽  
Real Frequency ◽  
Special Cases ◽  
The Stability

Several conclusions regarding the stability of inhomogeneous Vlasov equilibria are drawn from earlier work. A technique is presented for generating first-order formulae for the change δω in the frequency of any normal mode, when a parameter λ characterizing the equilibrium is changed slightly. Several applications are given, including a first-order calculation of the growth rate or damping of an electromagnetic mode due to the presence of plasma. A condition is derived for the existence of a normal mode with real frequency. When there are ignorable co-ordinates, the normal modes can be written in the form of waves propagating in the ignorable directions. The character of the modes depends on certain symmetries in the dynamic spectral matrix. Special cases arise when the orbits can be approximated in certain ways.

Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

scholarly journals Nonlinear modeling growth body weight of Mangalarga Marchador horses

2017 ◽  
Vol 47 (4) ◽  
Author(s):  
Felipe Amorim Caetano Souza ◽  
Tales Jesus Fernandes ◽  
Raquel Silva de Moura ◽  
Sarah Laguna Conceição Meirelles ◽  
Rafaela Aparecida Ribeiro ◽  
...  
Keyword(s):  
Body Weight ◽  
Linear Models ◽  
Nonlinear Modeling ◽  
Growth Curves ◽  
Live Weight ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Cross Sectional ◽  
Adult Body Weight ◽  
The Cross

ABSTRACT: The analysis of the growth and development of various species has been done using the growth curves of the specific animal based on non-linear models. The objective of the current study was to evaluate the fit of the Brody, Gompertz, Logistic and von Bertalanffy models to the cross-sectional data of the live weight of the MangalargaMarchador horses to identify the best model and make accurate predictions regarding the growth and maturity in the males and females of this breed. The study involved recording the weight of 214 horses, of which 94 were males and 120 were non-pregnant females, between 6 and 153 months of age. The parameters of the model were estimated by employing the method of least squares, using the iteratively regularized Gauss-Newton method and the R software package. Comparison of the models was done based on the following criteria: coefficient of determination (R²); Residual Standard Deviation (RSD); corrected Akaike Information Criterion (AICc). The estimated weight of the adult horses by the models ranged between 431kg and 439kg for males and between 416kg and 420kg for females. The growth curves were studied using the cross-sectional data collection method. For males the von Bertalanffymodel was found to be the most effective in expressing growth, while in females the Brody model was more suitable. The MangalargaMarchador females achieve adult body weight earlier than the males.

scholarly journals Computational notes on the electronic properties of carboxylic acid

2020 ◽  
Vol 9 (2) ◽  
pp. 1079-1082
Keyword(s):  
Acetic Acid ◽  
Carboxylic Acid ◽  
Electronic Properties ◽  
Carboxylic Acids ◽  
Normal Mode ◽  
Normal Modes ◽  
Carboxyl Groups ◽  
Vibrational Characteristics ◽  
Vibrational Features ◽  
Acetic Acids

The present work describing the electronic properties and vibrational characteristics of carboxylic acids. Acetic acid is chosen as model molecules then optimized at B3LYP/6-31g(d,p) level of theory. The vibrational frequencies were calculated at the same level of theory. Band assignments which were calculated as 18 normal modes were assigned as one compare the normal mode coordinates with original one. Band assignments were described indicating the directions of normal modes in terms the vibrating atoms of the acetic acids. It could be concluded that DFT could be a useful tool for elucidation both the structural and vibrational features of carboxylic acids and then further utilized for assignment of the structures contains carboxyl groups which are known as most reactive structures in chemistry, biology and environment.

scholarly journals Normal modes in thermal AdS via the Selberg zeta function

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Normal Mode ◽  
Kernel Method ◽  
Normal Modes ◽  
Quasinormal Mode ◽  
Partition Functions ◽  
Selberg Zeta Function ◽  
Exact Agreement ◽  
Spin Fields

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin ss fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z}ℍ3/ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1}AdS2n+1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z}ℍ2n+1/ℤ. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

Identification of a Significantly Non-Proportionally Damped Structure Using Force Appropriation

1995 ◽  
Author(s):  
P. S. Holmes ◽  
J. R. Wright ◽  
J. E. Cooper
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Normal Mode ◽  
Normal Modes ◽  
Dynamic Tests ◽  
High Quality ◽  
Element Analysis ◽  
Standard Curve ◽  
Complex Modes ◽  
Phase Resonance

Abstract Dynamic tests were carried out on an aluminium plate with significant non-proportional damping applied via two oil filled dampers. Normal mode force appropriation (phase resonance) methods were used to measure the undamped normal modes of the plate and the results compared with corresponding complex modes obtained using a standard curve fitting (phase separation) approach. It is demonstrated that, as long as suitable excitation positions are chosen, high quality undamped normal modes can be identified while the curve fitted modes are highly complex. A Finite Element analysis of the plate was used to show how the results of normal mode force appropriation are directly comparable, particularly when damping is non-proportional.

Earthquake site response estimation: A weak-motion case study

1992 ◽  
Vol 82 (6) ◽  
pp. 2283-2307
Author(s):  
E. H. Field ◽  
K. H. Jacob ◽  
S. E. Hough
Keyword(s):  
Site Response ◽  
Spectral Ratio ◽  
Large Degree ◽  
One Dimensional ◽  
Loma Prieta Earthquake ◽  
Cross Spectrum ◽  
Downward Bias ◽  
Dimensional Models ◽  
The Cross ◽  
Input Motion

Abstract Using weak-motion recordings of aftershocks of the 1989 Loma Prieta earthquake recorded in Oakland, California, near the failed Nimitz Freeway, two methods have been applied to estimate the site response of an alluvium site and three mud-over-alluvium sites. The first estimate is the traditional spectral ratio, and the second utilizes the cross spectrum. Recordings obtained at a nearby bedrock site are used as estimates of the sediment site input motions. While the two site response estimates produce similar peaks and troughs, there is an approximate factor of 2 difference in amplitudes. This discrepancy is evidence that there is a much greater level of noise than would be expected from the pre-event ambient noise. We interpret this as signal-generated noise produced by scattering from heterogeneities, which causes the true sediment site input to differ significantly from the bedrock site recording. Given this level of noise, the cross-spectrum estimate suffers a severe downward bias (by a factor of 2 in this study) and should probably not be used when the input motion is estimated from a bedrock site recording. The spectral-ratio estimates are relatively unbiased, but the level of noise introduces a large degree of uncertainty. Therefore, inferences about site response from individual spectral ratios should probably be avoided. On the other hand, ensemble averages of the estimates significantly reduce the scatter to reveal resonances that agree quite well in frequency and overall shape with those of one-dimensional models whose parameters were determined independently. A discrepancy of higher observed amplitudes than predicted by theory remains unexplained but most likely results from the effects of boundary layer topography, which are not accounted for by the simple one-dimensional models.

scholarly journals Use of ice-sheet normal modes for initialization and modelling small changes

1997 ◽  
Vol 25 ◽  
pp. 85-95 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Normal Mode ◽  
Time Constant ◽  
Normal Modes ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Short Term ◽  
Scale Theory ◽  
Digital Elevation ◽  
Linearized Model ◽  
Term Response

Linearizations about two horizontal-dimensional ice sheets are proposed as methods of generating normal mode initializations for ice-sheet models and for computing the short-term response. Linearized models can be generated directly from balance-flux calculations without the need for tuning the rate factor.A linearized model is compared with the Eismint Benchmark, and the normal modes for two coarse Antarctic digital elevation models are computed and compared. Volumetric relaxation spectra are presented. The slowest mode has a time constant comparable to that computed from scale theory.

Sign in / Sign up

Export Citation Format

Share Document