scholarly journals Scaling collapse and structure functions: identifying self-affinity in finite length time series

2005 ◽  
Vol 12 (6) ◽  
pp. 767-774 ◽  
Author(s):  
S. C. Chapman ◽  
B. Hnat ◽  
G. Rowlands ◽  
N. W. Watkins
Keyword(s):  
Time Series ◽  
Finite Length ◽  
Planck Equation ◽  
Structure Functions ◽  
Affine Scaling ◽  
Theoretical Understanding ◽  
Scaling Properties ◽  
Formidable Challenge ◽  
Special Case

Abstract. Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. We consider a method of conditioning that recovers the underlying self affine scaling in a finite length time series, and illustrate it using a Lévy flight.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

New determinations of tides on the north-western Ross Ice Shelf

2020 ◽  
pp. 1-14
Author(s):  
Richard D. Ray ◽  
Kristine M. Larson ◽  
Bruce J. Haines
Keyword(s):  
Time Series ◽  
Tide Gauge ◽  
High Rate ◽  
Ice Shelf ◽  
Ross Ice Shelf ◽  
The North ◽  
Global Positioning ◽  
North Western

Abstract New determinations of ocean tides are extracted from high-rate Global Positioning System (GPS) solutions at nine stations sitting on the Ross Ice Shelf. Five are multi-year time series. Three older time series are only 2–3 weeks long. These are not ideal, but they are still useful because they provide the only in situ tide observations in that sector of the ice shelf. The long tide-gauge observations from Scott Base and Cape Roberts are also reanalysed. They allow determination of some previously neglected tidal phenomena in this region, such as third-degree tides, and they provide context for analysis of the shorter datasets. The semidiurnal tides are small at all sites, yet M2 undergoes a clear seasonal cycle, which was first noted by Sir George Darwin while studying measurements from the Discovery expedition. Darwin saw a much larger modulation than we observe, and we consider possible explanations - instrumental or climatic - for this difference.

scholarly journals Landslide geometry and activity in Villa de la Independencia (Bolivia) revealed by InSAR and seismic noise measurements

Landslides ◽  
2021 ◽  
Author(s):  
Chuang Song ◽  
Chen Yu ◽  
Zhenhong Li ◽  
Veronica Pazzi ◽  
Matteo Del Soldato ◽  
...  
Keyword(s):  
Time Series ◽  
Seismic Noise ◽  
Slip Surface ◽  
Inversion Method ◽  
Subsurface Structures ◽  
Slip Surfaces ◽  
Landslide Volume ◽  
Noise Measurements ◽  
Landslide Body

AbstractInterferometric Synthetic Aperture Radar (InSAR) enables detailed investigation of surface landslide movements, but it cannot provide information about subsurface structures. In this work, InSAR measurements were integrated with seismic noise in situ measurements to analyse both the surface and subsurface characteristics of a complex slow-moving landslide exhibiting multiple failure surfaces. The landslide body involves a town of around 6000 inhabitants, Villa de la Independencia (Bolivia), where extensive damages to buildings have been observed. To investigate the spatial-temporal characteristics of the landslide motion, Sentinel-1 displacement time series from October 2014 to December 2019 were produced. A new geometric inversion method is proposed to determine the best-fit sliding direction and inclination of the landslide. Our results indicate that the landslide is featured by a compound movement where three different blocks slide. This is further evidenced by seismic noise measurements which identified that the different dynamic characteristics of the three sub-blocks were possibly due to the different properties of shallow and deep slip surfaces. Determination of the slip surface depths allows for estimating the overall landslide volume (9.18 · 107 m3). Furthermore, Sentinel-1 time series show that the landslide movements manifest substantial accelerations in early 2018 and 2019, coinciding with increased precipitations in the late rainy season which are identified as the most likely triggers of the observed accelerations. This study showcases  the potential of integrating InSAR and seismic noise techniques to understand the landslide mechanism from ground to subsurface.

scholarly journals How to correctly apply Gaussian statistics in a non-stationary climate?

2021 ◽  
Author(s):  
Reinhold Steinacker
Keyword(s):  
Time Series ◽  
Actual Data ◽  
Temperature Record ◽  
Positive Trend ◽  
Positive Temperature ◽  
Climatic Trend ◽  
Filter Methods ◽  
Periodic Time Series ◽  
Past Data

AbstractTime series with a significant trend, as is now being the case for the temperature in the course of climate change, need a careful approach for statistical evaluations. Climatological means and moments are usually taken from past data which means that the statistics does not fit to actual data anymore. Therefore, we need to determine the long-term trend before comparing actual data with the actual climate. This is not an easy task, because the determination of the signal—a climatic trend—is influenced by the random scatter of observed data. Different filter methods are tested upon their quality to obtain realistic smoothed trends of observed time series. A new method is proposed, which is based on a variational principle. It outperforms other conventional methods of smoothing, especially if periodic time series are processed. This new methodology is used to test, how extreme the temperature of 2018 in Vienna actually was. It is shown that the new annual temperature record of 2018 is not too extreme, if we consider the positive trend of the last decades. Also, the daily mean temperatures of 2018 are not found to be really extreme according to the present climate. The real extreme of the temperature record of Vienna—and many other places around the world—is the strongly increased positive temperature trend over the last years.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

Determination of scaling properties of randomly branched polycyanurates by combined SEC/LALLS/VISC

1993 ◽  
Vol 26 (12) ◽  
pp. 3103-3107 ◽  
Author(s):  
Joerg Bauer ◽  
Walther Burchard
Keyword(s):  
Scaling Properties

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

On the estimation of a harmonic component in a time series with stationary dependent residuals

1973 ◽  
Vol 5 (02) ◽  
pp. 217-241 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Harmonic Component ◽  
Asymptotic Distributions ◽  
Finite Variance ◽  
Rigorous Derivation ◽  
Image Position ◽  
Vector Valued ◽  
Special Case

Let observations (X 1, X 2, …, Xn ) be obtained from a time series {Xt } such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu (θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu (θ) = 0 for u > 0, the parameter θ thus being absent.

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