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multifractality
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Scaling Properties and Conformal Invariance of the Critical Wave Functions at 2D Anderson Transition in the Spin-Orbit Symmetry Class
, M.Sc. Thesis Sharif University of Technology ; Jafari, Akbar (Supervisor) ; Saberi, Abbas Ali (Supervisor)
Abstract
In this thesis, first of all we introduce the Anderson model, Multifractality, and conformal field theory. Then we try to determine some critical and scaling quantities for the critical wave functions in the 2D systems with spin-orbit interactions We implement a correction-to-scaling analysis by introducing an irrelevant exponent which leads to a proper and sharp evaluation of the critical parameters including correlation exponent, rescaled localization length and the critical disorder. Then, we survey the multifractal properties of this model and obtain some multifractal exponent in the critical point. Finally, we will survey the existence of the conformal invariance symmetry in it. Our...
Analysis of Well log Data Using Detrended Fluctuation Analysis and its Comparison with Other Methods (Multifractal Analysis of Well Log Data)
, M.Sc. Thesis Sharif University of Technology ; Sahimi, Mohammad (Supervisor) ; Massihi, Mohsen (Supervisor) ; Jafari, Gholam Reza (Supervisor)
Abstract
One of the main challenges in characterization and simulation of larg scale porous media is spatial heterogeneity and variability of porous media properties such as porosity, density, and lithology at different scales. These information can be achieved at different scale from coring, well logging or seismic data. Well logs are an efficient way to obtain rock and fluid properties of geological patterns specially water resources and hydrocarbon reservoirs. One of the characteristics of geophysical well logs is their complex behavior which seems to imply a multifractal nature.In this study we investigate multifractality and presence of long range correlations in petrophysical well log data such...