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Full-Text Articles in Physical Sciences and Mathematics
Reduced Order Models For Beam-Wave Interaction In High Power Microwave Sources, Lokendra Singh Thakur
Reduced Order Models For Beam-Wave Interaction In High Power Microwave Sources, Lokendra Singh Thakur
LSU Doctoral Dissertations
We apply an asymptotic analysis to show that corrugated waveguides can be represented as cylindrical waveguides with smooth metamaterial coatings when the corrugtions are subwavelength. Here the metamaterial delivers an effective anisotropic surface impedance, effective dielectric constant, and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances of the metamaterial. For sufficiently deep corrugations, the waveguide exhibits backward wave propagation, which can be understood in the present context as a multi-scale phenomenon resulting from local resonances inside the subwavelength geometry. Our approach is well suited to numerical computation and we provide a …
Homogenization Of Nonlinear Partial Differential Equations, Silvia Jiménez
Homogenization Of Nonlinear Partial Differential Equations, Silvia Jiménez
LSU Doctoral Dissertations
This dissertation is concerned with properties of local fields inside composites made from two materials with different power law behavior. This simple constitutive model is frequently used to describe several phenomena ranging from plasticity to optical nonlinearities in dielectric media. We provide the corrector theory for the strong approximation of fields inside composites made from two power law materials with different exponents. The correctors are used to develop bounds on the local singularity strength for gradient fields inside microstructured media. The bounds are multiscale in nature and can be used to measure the amplification of applied macroscopic fields by the …
Multiscale Analysis Of Heterogeneous Media For Local And Nonlocal Continuum Theories, Bacim Alali
Multiscale Analysis Of Heterogeneous Media For Local And Nonlocal Continuum Theories, Bacim Alali
LSU Doctoral Dissertations
The dissertation provides new multiscale methods for the analysis of heterogeneous media. The first part of the dissertation treats heterogeneous media using the theory of linear elasticity. In this context, a methodology is presented for bounding the higher order moments of the local stress and strain fields inside random elastic media. Optimal lower bounds that are given in terms of the applied loading and the volume (area) fractions for random two-phase composites are presented. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. The second part of …
Multiscale Strain Analysis, Timothy Donald Breitzman
Multiscale Strain Analysis, Timothy Donald Breitzman
LSU Doctoral Dissertations
The mathematical homogenization and corrector theory relevant to prestressed heterogeneous materials in the linear-elastic regime is discussed. A suitable corrector theory is derived to reconstruct the local strain field inside the composite. Based on this theory, we develop an inexpensive numerical method for multi scale strain analysis within a prestressed heterogeneous material. The theory also provides a characterization of the macroscopic strength domain. The strength domain places constraints on the homogenized strain field which guarantee that the actual strain in the heterogeneous material lies inside the strength domain of each material participating in the structure.