GENERAL CODING METHOD ON RANDOM SELF-SIMILAR TREE COMPOSED OF MULTIPLE BASIC PATTERNS

Fractals ◽  
2009 ◽  
Vol 17 (03) ◽  
pp. 283-298
Author(s):  
CHUN-PO HUNG
Keyword(s):  
Topological Distance ◽  
Tree Generation ◽  
Coding Method ◽  
Wide Range ◽  
Width Function ◽  
Instantaneous Unit Hydrograph ◽  
Character Code ◽  
Self Similar ◽  
Hydrologic Responses ◽  
Northern Taiwan

This work discusses the random self-similar tree generation by employing multiple basic patterns, and investigates the character code and standardization algorithm for multiple basic patterns. With reference to the wide range of various basic patterns in natural shapes, the general coding method and the corresponding algorithm to calculate the topological distance is developed for random self-similar tree with multiple basic patterns. To assess the adaptability of the process, the general coding method is applied to transfer the generated river network to a code series and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. Finally, the width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results reveal that the random self-similar tree with multiple basic patterns proposed in this study can be implemented successfully to calculate hydrologic responses.

CODING AND DISTANCE CALCULATING OF SEPARATELY RANDOM FRACTALS AND APPLICATION TO GENERATING RIVER NETWORKS

Fractals ◽  
2005 ◽  
Vol 13 (01) ◽  
pp. 57-71 ◽  
Author(s):  
CHUN-PO HUNG ◽  
RU-YIH WANG
Keyword(s):  
Topological Distance ◽  
Starting Point ◽  
Coding Method ◽  
Wide Range ◽  
Width Function ◽  
Instantaneous Unit Hydrograph ◽  
Fractal Patterns ◽  
Self Similar ◽  
Hydrologic Responses ◽  
Northern Taiwan

This work develops a preliminary method for coding random self-similar patterns as a series of numbers and investigates the corresponding algorithm to calculate the topological distance between starting point and the link in the generated fractal pattern from the code series. With reference to the wide range of stochastic property in natural patterns, a process for generating fractal patterns with various generating probabilities of the pattern links denoted as separately random self-similar generation or separately random fractal is proposed. To assess the adaptability of the process, the coding method is applied to the generation of a random self-similar river network and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. The width function-based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results show that the separately random self-similar generating algorithm can be implemented successfully to calculate hydrologic responses.

A GENERALIZED WIDTH FUNCTION OF FRACTAL RIVER NETWORK FOR THE CALCULATION OF HYDROLOGIC RESPONSES

Fractals ◽  
2002 ◽  
Vol 10 (02) ◽  
pp. 157-171 ◽  
Author(s):  
PENG-JUI WANG ◽  
RU-YIH WANG
Keyword(s):  
River Network ◽  
Hydrologic Response ◽  
Unit Hydrograph ◽  
Estimation Model ◽  
Analytical Results ◽  
Width Function ◽  
Instantaneous Unit Hydrograph ◽  
Self Similar ◽  
Hydrologic Responses ◽  
Northern Taiwan

An approach to apply the fractal concept to estimate hydrologic response is proposed in this paper by matching suitable self-similar networks (SSNs) to a specific watershed, and modeling the runoff with a width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH). In order to work out the identification between a specific basin and SSNs that are generated by an interior generator cooperating with an exterior generator, a generalized width function is derived. Subsequently, cumulative width functions on the basis of the derived function, as well as the informational entropies are used as criteria to decide the best patterns of the two cooperating generators for the specific watershed. The WF-GIUH model is then applied to calculate the runoff of this watershed as an outcome of the estimation. To assess the adaptability of the estimation model, San-Hsia watershed of Northern Taiwan is selected as a study area, where the analytical results of the outflow estimation indicate that the fractal algorithm has been implemented successfully for the calculation of hydrologic responses.

scholarly journals A Comparison of Some Methods of Deriving the Instantaneous Unit Hydrograph

1985 ◽  
Vol 16 (1) ◽  
pp. 1-10 ◽  
Author(s):  
V. P. Singh ◽  
C. Corradini ◽  
F. Melone
Keyword(s):  
Peak Flow ◽  
Central Italy ◽  
Effective Rainfall ◽  
Unit Hydrograph ◽  
Time To Peak ◽  
Wide Range ◽  
Instantaneous Unit Hydrograph ◽  
Similar Accuracy ◽  
Two Parameters ◽  
Range Of Values

The geomorphological instantaneous unit hydrograph (IUH) proposed by Gupta et al. (1980) was compared with the IUH derived by commonly used time-area and Nash methods. This comparison was performed by analyzing the effective rainfall-direct runoff relationship for four large basins in Central Italy ranging in area from 934 to 4,147 km2. The Nash method was found to be the most accurate of the three methods. The geomorphological method, with only one parameter estimated in advance from the observed data, was found to be little less accurate than the Nash method which has two parameters determined from observations. Furthermore, if the geomorphological and Nash methods employed the same information represented by basin lag, then they produced similar accuracy provided the other Nash parameter, expressed by the product of peak flow and time to peak, was empirically assessed within a wide range of values. It was concluded that it was more appropriate to use the geomorphological method for ungaged basins and the Nash method for gaged basins.

scholarly journals Universal void density profiles from simulation and SDSS

2014 ◽  
Vol 11 (S308) ◽  
pp. 542-545 ◽  
Author(s):  
S. Nadathur ◽  
S. Hotchkiss ◽  
J. M. Diego ◽  
I. T. Iliev ◽  
S. Gottlöber ◽  
...  
Keyword(s):  
Fundamental Property ◽  
Watershed Algorithm ◽  
Void Size ◽  
Self Similarity ◽  
Density Profiles ◽  
Watershed Transform ◽  
Future Studies ◽  
Main Galaxy ◽  
Wide Range ◽  
Self Similar

AbstractWe discuss the universality and self-similarity of void density profiles, for voids in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. Voids are identified using a modified version of the ZOBOV watershed transform algorithm, with additional selection cuts. We find that voids in simulation areself-similar, meaning that their average rescaled profile does not depend on the void size, or – within the range of the simulated catalogue – on the redshift. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The profiles of real voids also show auniversalbehaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.

scholarly journals A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees

2017 ◽  
Vol 284 (1846) ◽  
pp. 20162395 ◽  
Author(s):  
Kohei Koyama ◽  
Ken Yamamoto ◽  
Masayuki Ushio
Keyword(s):  
Lognormal Distribution ◽  
Species Abundance ◽  
Self Similarity ◽  
Lognormal Distributions ◽  
Multiplicative Effect ◽  
Wide Range ◽  
Error Distributions ◽  
Species Abundance Distributions ◽  
Self Similar ◽  
Ulmus Davidiana

Lognormal distributions and self-similarity are characteristics associated with a wide range of biological systems. The sequential breakage model has established a link between lognormal distributions and self-similarity and has been used to explain species abundance distributions. To date, however, there has been no similar evidence in studies of multicellular organismal forms. We tested the hypotheses that the distribution of the lengths of terminal stems of Japanese elm trees ( Ulmus davidiana ), the end products of a self-similar branching process, approaches a lognormal distribution. We measured the length of the stem segments of three elm branches and obtained the following results: (i) each occurrence of branching caused variations or errors in the lengths of the child stems relative to their parent stems; (ii) the branches showed statistical self-similarity; the observed error distributions were similar at all scales within each branch and (iii) the multiplicative effect of these errors generated variations of the lengths of terminal twigs that were well approximated by a lognormal distribution, although some statistically significant deviations from strict lognormality were observed for one branch. Our results provide the first empirical evidence that statistical self-similarity of an organismal form generates a lognormal distribution of organ sizes.

Modeling and Simulation of Self-Similar Traffic in Wireless IP Networks

2011 ◽  
pp. 249-265
Author(s):  
Dimitar Radev ◽  
Izabella Lokshina ◽  
Svetla Radeva
Keyword(s):  
Network Traffic ◽  
Traffic Load ◽  
Single Server ◽  
Finite Buffer ◽  
Wide Range ◽  
Telecommunications Network ◽  
Source Models ◽  
Wireless Ip ◽  
Self Similar ◽  
Markov Modulated

The paper examines self-similar properties of real telecommunications network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Simulation with stochastic and long range dependent traffic source models is performed, and the algorithms for buffer overflow simulation for finite buffer single server model under self-similar traffic load SSM/M/1/B are explained. The algorithms for modeling fixed-length sequence generators that are used to simulate self-similar behavior of wireless IP network traffic are developed and applied. Numerical examples are provided, and simulation results are analyzed.

scholarly journals An object-based approach for semi-automated landslide change detection and attribution of changes to landslide classes in northern Taiwan

2015 ◽  
Vol 8 (2) ◽  
pp. 327-335 ◽  
Author(s):  
Daniel Hölbling ◽  
Barbara Friedl ◽  
Clemens Eisank
Keyword(s):  
Change Detection ◽  
Spatial Resolution ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Remote Sensing Data ◽  
Detection Methods ◽  
Detection And Attribution ◽  
Object Based ◽  
Wide Range ◽  
Northern Taiwan

Abstract Earth observation (EO) data are very useful for the detection of landslides after triggering events, especially if they occur in remote and hardly accessible terrain. To fully exploit the potential of the wide range of existing remote sensing data, innovative and reliable landslide (change) detection methods are needed. Recently, object-based image analysis (OBIA) has been employed for EO-based landslide (change) mapping. The proposed object-based approach has been tested for a sub-area of the Baichi catchment in northern Taiwan. The focus is on the mapping of landslides and debris flows/sediment transport areas caused by the Typhoons Aere in 2004 and Matsa in 2005. For both events, pre- and post-disaster optical satellite images (SPOT-5 with 2.5 m spatial resolution) were analysed. A Digital Elevation Model (DEM) with 5 m spatial resolution and its derived products, i.e., slope and curvature, were additionally integrated in the analysis to support the semi-automated object-based landslide mapping. Changes were identified by comparing the normalised values of the Normalized Difference Vegetation Index (NDVI) and the Green Normalized Difference Vegetation Index (GNDVI) of segmentation-derived image objects between pre- and post-event images and attributed to landslide classes.

scholarly journals Multifractal analysis for the ULF geomagnetic data during the 1993 Guam earthquake

2005 ◽  
Vol 12 (2) ◽  
pp. 157-162 ◽  
Author(s):  
Y. Ida ◽  
M. Hayakawa ◽  
A. Adalev ◽  
K. Gotoh
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Multifractal Analysis ◽  
Fluctuation Analysis ◽  
Sensitive Parameter ◽  
Wide Range ◽  
Geomagnetic Data ◽  
Self Similar ◽  
Significant Change ◽  
Detrended Fluctuation

Abstract. In our previous papers we have shown that the fractal (monofractal) dimension (Do) showed a significant increase before the Guam earthquake occurred on 8 August, 1993. In order to have a further support to this precursory effect to the general rupture (earthquake) we have carried out the corresponding multifractal analysis (by means of detrended fluctuation analysis) for the same data to study the statistical self-similar properties in a wide range of scales. We have analyzed the ULF geomagnetic data (the most intense H component) observed at Guam observatory. As the result, we have found that we could observe significant changes in the multifractal parameters at Guam such that αmin showed a meaningful decrease about 25 days before the earthquake and correspondingly Δα increased because αmax exhibited no significant change at all. The most sensitive parameter seems to be non-uniformity factor Δ. Correspondingly, the generalized multifractal dimension Dq (q>1) showed a significant decrease (whereas Dq (q<0) showed no change) and D0 (=Dq (q=0) (as already found in our previous papers) is reconfirmed to increase before the earthquake. These multifractal characteristics seem to be a further support that these changes are closely associated with the earthquake as a precursor to the Guam earthquake, providing us with appreciable information on the pre-rupture evolution of the earthquake.

A simple representation of a developing contaminant concentration field

1995 ◽  
Vol 289 ◽  
pp. 141-157 ◽  
Author(s):  
B. L. Sawford ◽  
P. J. Sullivan
Keyword(s):  
Simple Form ◽  
Line Source ◽  
Concentration Field ◽  
Scalar Fields ◽  
Source Distribution ◽  
Additional Parameter ◽  
Wide Range ◽  
Observed Behaviour ◽  
Self Similar ◽  
Two Parameters

Chatwin & Sullivan (1990) have demonstrated that, for a wide range of self-similar scalar fields, the moments of the probability density function of concentration have a very simple form. Here, an extension to this simple form which takes account of the source distribution is developed. This extension has two effects. Firstly it modifies the values of the two parameters appearing in the original theory and in particular explains the observed behaviour of these parameters very near to a line source of heat in grid tubulence. Secondly, it introduces an additional parameter in the description of each moment beyond the second. It is shown that these additional parameters are necessary in order to describe measurements of the first four central moments throughout the concentration field from a continuous line source of heat in grid-generated turbulence.

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