scholarly journals On the spectral analysis of second-order Markov chains

2013 ◽  
Vol 22 (3) ◽  
pp. 573-621 ◽  
Author(s):  
Persi Diaconis ◽  
Laurent Miclo
Keyword(s):  
Spectral Analysis ◽  
Markov Chains ◽  
Second Order

Experimental Study of Slow-Drift Ship Motions in Shallow Water Random Waves

2011 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Trygve Kristiansen
Keyword(s):  
Spectral Analysis ◽  
Shallow Water ◽  
Transfer Functions ◽  
Second Order ◽  
Ship Motions ◽  
Random Wave ◽  
Random Waves ◽  
Low Frequencies ◽  
Wave Basin ◽  
Drift Forces

Slowly varying motions and drift forces of a large moored ship in random waves at 35m water depth are investigated by an experimental wave basin study in scale 1:50. A simple horizontal mooring set-up is used. A second-order wave correction is applied to minimize “parasitic” long waves. The effect on the ship motion from the correction is clearly seen, although less in random wave spectra than in pure bi-chromatic waves. Empirical quadratic transfer functions (QTFs) of the surge drift force are found by use of cross-bi-spectral analysis, in two different spectra have been obtained. The QTF levels increase significantly with lower wave frequencies (except at the diagonal), which is special for finite and shallow water. Furthermore, the QTF levels frequencies at low frequencies increase significantly out from the QTF diagonal. Thus Newman’s approximation should preferrably not be used in these cases. Using the LF waves as a direct excitation in a “linear” ship force analysis gives random records that compare reasonably well with those from the cross-bi-spectral analysis. This confirms the idea that the drift forces in shallow water are closely correlated to the second-order potential, and thereby by the second-order LF waves.

scholarly journals The rhythms of rhythm

2021 ◽  
pp. 1-33
Author(s):  
Dafydd Gibbon
Keyword(s):  
Spectral Analysis ◽  
Quantitative Analysis ◽  
Low Frequency ◽  
Second Order ◽  
Read Aloud ◽  
Unified Theory ◽  
New Concepts ◽  
Formant Analysis ◽  
Selection Of

The low frequency (LF) spectral analysis or ‘rhythm spectrum’ approach to the quantitative analysis and comparison of speech rhythms is extended beyond syllable or word rhythms to ‘rhetorical rhythms’ in read-aloud narratives, in a selection of exploratory scenarios, with the aim of developing a unified theory of speech rhythms. Current methodologies in the field are first discussed, then the choice of data is motivated and the modulation-theoretic rhythm spectrum and rhythm spectrogram approach is applied to the amplitude modulation (AM) and frequency modulation (FM) of speech. New concepts of rhythm formant, rhythm spectrogram and rhythm formant trajectory are introduced in the Rhythm Formant Theory (RFT) framework with its associated methodology Rhythm Formant Analysis (RFA) in order to capture second order regularities in the temporal variation of rhythms. The interaction of AM and FM rhythm factors is explored, contrasting English with Mandarin Chinese. The LF rhythm spectrogram is introduced in order to recover temporal information about long-term rhythms, and to investigate the configurative function of rhythm. The trajectory of highest magnitude frequencies through the component spectra of the LF spectrogram is extracted and applied in classifying readings in different languages and individual speaking styles using distance-based hierarchical clustering, and the existence of long-term second order ‘rhythms of rhythm’ in long narratives is shown. In the conclusion, pointers are given to the extension of this exploratory RFT rhythm approach for future quantitative confirmatory investigations.

CTCS Schemes for Second Order Wave Equation: Numerical Results and Spectral Analysis

2021 ◽  
Vol 55 ◽  
pp. 47-65
Author(s):  
Appanah Rao Appadu ◽  
Gysbert Nicolaas de Waal
Keyword(s):  
Spectral Analysis ◽  
Wave Equation ◽  
Numerical Experiments ◽  
Finite Difference Methods ◽  
Second Order ◽  
Numerical Results ◽  
Order Accuracy ◽  
Constant Coefficients ◽  
Second Order Wave Equation ◽  
The One

IIn this paper, two finite difference methods are used to solve the one-dimensional second order wave equation with constant coefficients subject to specified initial and boundary conditions. Two numerical experiments are considered. The two methods are Central in Time and Central in Space scheme with second order accuracy in both time and space, abbreviated as CTCS (2,2) and Central in Time and Central in Space scheme with second order accuracy in time and fourth order accuracy in space, abbreviated as CTCS (2,4). Properties such as consistency and stability are studied. We also perform spectral analysis of dispersive and dissipative properties of the two methods. Two numerical experiments are considered, and the numerical results are displayed.

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