A controlled fractal interpolation method based on random midpoint displacement for coastline

GEOMATICA ◽  
2017 ◽  
Vol 71 (2) ◽  
pp. 89-99
Author(s):  
Baode Jiang ◽  
Dongqi Wei ◽  
Zhong Xie ◽  
Zhanlong Chen
Keyword(s):  
Spatial Data ◽  
Interpolation Method ◽  
Fractal Interpolation ◽  
Quality Requirements ◽  
One Dimensional ◽  
Fractal Characteristic ◽  
Fractal Interpolation Function ◽  
Proper Order ◽  
Fractal Characteristics ◽  
Original Scale

Coastline has different geographical bending characteristics in different coastal geomorphic regions. The existing fractal interpolation methods for coastline mostly focus on how to simulate its fractal characteristic but neglect the geographical bending characteristic. This study presents an improved controlled fractal inter polation method based on one-dimensional Random Midpoint Displacement (RMD) that aims to preserve both the bending characteristics and fractal characteristics of coastline. First, the coastline is divided into sev eral parts based on its bending characteristics, in order to conserve the geographical bending struc ture of the coastline and change the uncontrollable general fractal interpolation into a combination of sev er al piece-wise interpolation units. Second, the fractal interpolation function of one-dimensional RMD is used for each divided bending unit of the coastline, and the parameters of RMD function are restricted by the con straints of each unit bending characteristics. Third, the results of fractal interpolation of each unit are linked together in proper order to obtain the approximate coastline. The experiments show that this method can maintain the geographical bending characteristics and fractal characteristics of coastline, and when the ratio of target scale to the original scale is not more than 3 times, the accuracy of interpolation spatial coor di nates can meet the quality requirements of spatial data.

scholarly journals A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 767
Author(s):  
Alexandra Băicoianu ◽  
Cristina Maria Păcurar ◽  
Marius Păun
Keyword(s):  
Approximation Method ◽  
Finite System ◽  
Countable System ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Finite Systems ◽  
Fractal Interpolation Function ◽  
Fractal Interpolation Functions ◽  
Finite Set ◽  
Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .

Study on Fractal Elastic Damage Constitutive Law for Concrete Material under Static Load

2011 ◽  
Vol 138-139 ◽  
pp. 1269-1273
Author(s):  
Ming Xie ◽  
Shan Suo Zheng
Keyword(s):  
Fracture Surface ◽  
Damage Mechanics ◽  
Constitutive Law ◽  
Uniaxial Test ◽  
Fractal Characteristic ◽  
Mechanics Model ◽  
Evolution Characteristics ◽  
Mesoscopic Level ◽  
Fractal Characteristics ◽  
Stochastic Properties

The stochastic properties and discreteness of macroscopic property for concrete appear on mechanical property and fracture surface. In consideration of stochastik and discreteness of fracture surface, a class of mesoscopic damage mechanics model of concrete based on spring model, are put forward to understand the real damage evolution characteristics of concrete at the level of constitutional law. A kind of spring-slipper model is introduced to reflect the elastic-plastic damage behavior. It has been confirmed that fracture surface of concrete has self-affine fractal characteristic only on a certain spatial scale, but the actual fracture surface of concrete is a stochastic surface with multi-fractal characteristics. Uniaxial test was operated, combined with the Computerized Tomography test of concrete, to study the evolution of crack surface from mesoscopic level to macroscopic level. Compared with the existing damage constitutive law and experimental results preliminarily, the feasibility of fractal damage constitutive law is verified.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

scholarly journals An Exploration of Fractal Based Prognostic Model and Comparative Analysis for Second Wave of COVID-19 Diffusion

2021 ◽  
Author(s):  
Easwaramoorthy D. ◽  
Gowrisankar A. ◽  
Manimaran A. ◽  
Nandhini S. ◽  
Santo Banerjee ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Death Rate ◽  
Transmission Rate ◽  
The United States ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Statistical Tool ◽  
Dimension Estimate ◽  
Fractal Interpolation Function ◽  
Second Wave

Abstract The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being carried out worldwide by scientists to understand the nature of this catastrophic virus and find a potential vaccine for it. The most possible efforts have been taken to present this paper as a form of contribution to the understanding of this lethal virus in the first and second wave. This paper presents a unique technique for the methodical comparison of disastrous virus dissemination in two waves amid five most infested countries and the death rate of the virus in order to attain a clear view on the behaviour of the spread of the disease. For this study, the dataset of the number of deaths per day and the number of infected cases per day of the most affected countries, The United States of America, Brazil, Russia, India, and The United Kingdom have been considered in first and second wave. The correlation fractal dimension has been estimated for the prescribed datasets of COVID-19 and the rate of death has been compared based on the correlation fractal dimension estimate curve. The statistical tool, analysis of variance has also been used to support the performance of the proposed method. Further, the prediction of the daily death rate has been demonstrated through the autoregressive moving average model. In addition, this study also emphasis a feasible reconstruction of the death rate based on the fractal interpolation function. Subsequently, the normal probability plot is portrayed for the original data and the predicted data, derived through the fractal interpolation function to estimate the accuracy of the prediction. Finally, this paper neatly summarized with the comparison and prediction of epidemic curve of the first and second waves of COVID-19 pandemic to picturize the transmission rate in the both times.

The Offshore Wave Simulation Based on the Improved P-M Spectrum and Multiple Fractal Interpolation

2014 ◽  
Vol 1030-1032 ◽  
pp. 1832-1836
Author(s):  
Ying Li ◽  
Rui Zhou ◽  
Hao Kuan Li ◽  
Ming Wang
Keyword(s):  
Shallow Water ◽  
Interpolation Method ◽  
Fractal Interpolation ◽  
Fractal Method ◽  
Growth State ◽  
Water Factor ◽  
Proposed Model ◽  
Simulation Based ◽  
Offshore Wave ◽  
The Waves

The Pierson - Moskowitz model is only applicable to full growth state of the waves, and it has low authenticity and hopping phenomenon under the condition of offshore shallow water. This paper proposes a simulation model of offshore wave based on the improved P-M spectrum and multiple fractal interpolation methods. In order to calculate the sea wave with shallow water, a spectrum peak regulation factor and a depth of the water factor are introduced to the P - M spectrum model. Based on this model, the wavelength and wave speed are used as the initial values of wave height. Then, the amplitude and the number of iterations in diamond square fractal method are controlled to obtain the fractal static sea. In order to reduce the influence of the hopping phenomenon to the simulation authenticity, meanwhile, a multiple dynamic non-uniform interpolation method is proposed. The experimental results show that the proposed model can simulate offshore wave with better effect and in real time.

A Flow-Condition-Based Interpolation Method Combined with Splitting Algorithm for Wind Field Calculation

2013 ◽  
Vol 671-674 ◽  
pp. 1578-1582
Author(s):  
Bo Su ◽  
Xiang Ke Han
Keyword(s):  
Wind Field ◽  
Flow Condition ◽  
Interpolation Method ◽  
Solution Procedure ◽  
Field Calculation ◽  
Splitting Algorithm ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Finite Element Procedure ◽  
Interpolation Functions

Wind field calculation is a research focus for wind disaster prevention in Civil Engineering. A new finite element procedure using flow-condition-based interpolation method combined with splitting algorithm is proposed in the paper. It used the analytical solution of one-dimensional advection–diffusion equation, and naturally introduced upwind effect in element interpolation functions. Further, combined with splitting algorithm, the element interpolation functions of velocity and pressure have concise format without meet Babuska-Brezzi condition. A two dimension four-node bilateral fluid element was constructed using flow-condition-based interpolation method and a corresponding program was developed. The solution procedure was discussed in detail and the numerical example solution was given to illustrate the capabilities of the procedure

scholarly journals Sustainable Development: Evaluating Optimal Technique for Spatial Data Forecast

Proceedings ◽  
2018 ◽  
Vol 2 (22) ◽  
pp. 1371
Author(s):  
Gaurav Kumar ◽  
Rajiv Gupta
Keyword(s):  
Information System ◽  
Spatial Data ◽  
Satellite Images ◽  
Moving Average ◽  
Vegetation Indices ◽  
Geographical Information ◽  
One Dimensional ◽  
Regression Methods ◽  
Gis Tools ◽  
Normalized Difference Vegetation Indices

This paper is an approach to forecast the spatial data in time series domain. Normally in GIS (Geographical Information System), we need raster forecasting. Moving average, exponential smoothing, and linear regression methods of forecasting are used over one-dimensional data. Present work concentrates on using these methods on satellite images applying them from pixel to pixel of historical temporal satellite data. An example set of satellite images from years 2011 to 2015 has been used to forecast the image in the year 2016. GIS tools have been developed in ArcGIS 10.1 using python to implement the methods of forecasting. Forecasted and actual images of the year 2016 have been compared by calculating the Normalized Difference Vegetation Indices (NDVI) and change detection to identify the best method.

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