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- ItemSoliton solution for the Korteweg-de Vries equation(2022) Mucalica, AnaKorteweg de Vries (KdV) model is considered quintessential in modeling the surface gravity water waves in shallow water. In this project, we are interested in starting from the Elliptic Jacobian Functions, and performing a complete analysis of these functions to discover that one can recover the soliton in the particular case, when m approaches 1, where m is a parameter between 0 and 1 in the definition of the Elliptic Jacobian Functions. This analysis will provide us with an understanding of cnoidal periodic waves and how, through them, we can derive the soliton solution. Finally, this project grants readers a deeper understanding of the origin of solitons and their applications in water wave theory.
- ItemQuantum computation and search algorithms: a historical overview and introduction(2020) Eliasson, Leif; Rezania, VahidQuantum computation is the study of the information processing tasks which may be accomplished using quantum mechanical systems. At the heart of inquiries to ascertain the potential of quantum computation is the question of whether it is possible for a quantum computer to efficiently solve computational problems which have no efficient solution on a classical computer. Pioneering work done by David Deutsch, Peter Shor, Lov Grover and others in the 1980s and 1990s established a great deal of the essential theoretical framework and results which provided answers to this question which has justified continued research and interest in quantum computing ever since. Today we will provide a brief historical and functional overview of the development of quantum computing and its applications during this time, and contrast it with classical computing, and in particular, we will examine Grover’s algorithm as an illustrative example of the potential benefits of quantum search algorithms.
- ItemNotes for slides: Quantum computation and search algorithms(2020) Eliasson, Leif; Rezania, VahidQuantum computation is the study of the information processing tasks which may be accomplished using quantum mechanical systems. At the heart of inquiries to ascertain the potential of quantum computation is the question of whether it is possible for a quantum computer to efficiently solve computational problems which have no efficient solution on a classical computer. Pioneering work done by David Deutsch, Peter Shor, Lov Grover and others in the 1980s and 1990s established a great deal of the essential theoretical framework and results which provided answers to this question which has justified continued research and interest in quantum computing ever since. Today we will provide a brief historical and functional overview of the development of quantum computing and its applications during this time, and contrast it with classical computing, and in particular, we will examine Grover’s algorithm as an illustrative example of the potential benefits of quantum search algorithms.
- ItemPopulation density analysis of a liver lobule(2015) Wisk, Sara; Rezania, Vahid; Rezania, VahidThe purpose of my research was to analyze the population densities of hepatocytes and sinusoids in the liver lobule of a real image and a simulated image. This analysis was done using Matlab. This information would then be used to make adjustments to the code in the simulated image to reflect the population density in a real image.