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http://hdl.handle.net/11375/27100
Title: | Solutions and limits of the Thomas-Fermi-Dirac-Von Weizsacker energy with background potential |
Authors: | Aguirre Salazar, Lorena |
Advisor: | Bronsard, Lia Alama, Stanley |
Department: | Mathematics and Statistics |
Keywords: | calculus of variations;partial differential equations;pattern formation;nonlocal |
Publication Date: | 2021 |
Abstract: | We study energy-driven nonlocal pattern forming systems with opposing interactions. Selections are drawn from the area of Quantum Physics, and nonlocalities are present via Coulombian type interactions. More precisely, we study Thomas-Fermi-Dirac-Von Weizsacker (TFDW) type models, which are mass-constrained variational problems. The TFDW model is a physical model describing ground state electron configurations of many-body systems. First, we consider minimization problems of the TFDW type, both for general external potentials and for perturbations of the Newtonian potential satisfying mild conditions. We describe the structure of minimizing sequences, and obtain a more precise characterization of patterns in minimizing sequences for the TFDW functionals regularized by long-range perturbations. Second, we consider the TFDW model and the Liquid Drop Model with external potential, a model proposed by Gamow in the context of nuclear structure. It has been observed that the TFDW model and the Liquid Drop Model exhibit many of the same properties, especially in regard to the existence and nonexistence of minimizers. We show that, under a "sharp interface'' scaling of the coefficients, the TFDW energy with constrained mass Gamma-converges to the Liquid Drop model, for a general class of external potentials. Finally, we present some consequences for global minimizers of each model. |
URI: | http://hdl.handle.net/11375/27100 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Aguirre Salazar_Lorena_202106_PhD.pdf | 790.2 kB | Adobe PDF | View/Open |
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