Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Keyword
-
- Active set method (1)
- Asymptotic methods (1)
- Continuum mechanics (1)
- Fixed-point (1)
- Graphene (1)
-
- Hopping (1)
- Incommensurate (1)
- Lattice (1)
- Low-frequency (1)
- Materials science (1)
- Memory (1)
- Newton–Kantorovich (1)
- Nonlocal model (1)
- Optimal design (1)
- Optimization (1)
- Orthogonal polynomials (1)
- Partial differential equations (1)
- Phase-field method (1)
- Quantum trees (1)
- Robin spectrum (1)
- Trilayer (1)
- Variational inequality (1)
- Wannier (1)
Articles 1 - 5 of 5
Full-Text Articles in Other Applied Mathematics
Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard
Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard
LSU Doctoral Dissertations
Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …
Quasistatic Peridynamics, Existence Of Unique Solution In The Presence Of Damage, Nuwanthi N. Samarawickrama
Quasistatic Peridynamics, Existence Of Unique Solution In The Presence Of Damage, Nuwanthi N. Samarawickrama
LSU Doctoral Dissertations
A mathematical model for damage propagation based on nonlocal potentials is developed within the framework of peridynamics. This model is applied to simulate damage evolution in cyclically loaded structures. By neglecting inertial effects, a well-posed quasistatic formulation for cyclic loading is obtained.\\ The resulting equation is expressed as a nonlocal and nonlinear integral operator that couples damage evolution to the deformation field.\\ This coupling occurs through the product of a damage factor and the derivative of a force potential. The damage factor ranges between zero and one, where one represents undamaged material and zero indicates complete damage.\\ It serves to …
Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain
Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain
LSU Doctoral Dissertations
The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …
Optimal Design Problems With State Constraints, Nha Van Tran
Optimal Design Problems With State Constraints, Nha Van Tran
LSU Doctoral Dissertations
This thesis focuses on constrained optimization problems with constraints on the state variables. When the constraints involve partial differential equations or variational inequalities, the optimization problem is also known as Mathematical Programs with Equilibrium Constraints. First, we applied active-set properties of optimal solutions to transform variational inequality constraints into partial differential equation constraints and devised an active-set method which allowed us to solve the optimization problems using the adjoint approach. We extended our approach to evolution problems with constraints on the trajectory of the state variable, such as the irreversibility condition in fracture mechanics. We implemented a gradient descent algorithm …
Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang
Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang
LSU Doctoral Dissertations
We investigate the spectrum of regular quantum-graph trees, where the edges are endowed with a Schr\"odinger operator with self-adjoint Robin vertex conditions. It is known that, for large eigenvalues, the Robin spectrum approaches the Neumann spectrum. In this research, we compute the lower Robin spectrum. The spectrum can be obtained from the roots of a sequence of orthogonal polynomials involving two variables. As the length of the quantum tree increases, the spectrum approaches a band-gap structure. We find that the lowest band tends to minus infinity as the Robin parameter increases, whereas the rest of the bands remain positive. Unexpectedly, …