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Full-Text Articles in Physical Sciences and Mathematics
Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan
Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan
Electronic Theses and Dissertations
In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …
Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati
Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati
Electronic Theses and Dissertations
In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.