Computing parametrized solutions for plasmonic nanogap structures

The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the confinement of light to small regions, typically several orders of magnitude smaller than the incident wavelength. The accurate prediction of these resonances entails several challenges. Small geometric variations in the plasmonic structure may lead to large variations in the electromagnetic field responses. Furthermore, the material parameters that characterize the optical behavior of metals at the nanoscale need to be determined experimentally and are consequently subject to measurement errors. It then becomes essential that any predictive tool for the simulation and design of plasmonic structures accounts for fabrication tolerances and measurement uncertainties. In this paper, we develop a reduced order modeling framework that is capable of real-time accurate electromagnetic responses of plasmonic nanogap structures for a wide range of geometry and material parameters. The main ingredients of the proposed method are: (i) the hybridizable discontinuous Galerkin method to numerically solve the equations governing electromagnetic wave propagation in dielectric and metallic media, (ii) a reference domain formulation of the time-harmonic Maxwell's equations to account for geometry variations; and (iii) proper orthogonal decomposition and empirical interpolation techniques to construct an efficient reduced model. To demonstrate effectiveness of the models developed, we analyze geometry sensitivities and explore optimal designs of a 3D periodic annular nanogap structure.Comment: 28 pages, 9 figures, 4 tables, 2 appendice

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Twisted Real Structures in Noncommutative Geometry

Twisted real structures are a generalisation of real structures for spectral triples which are motivated as a way to implement the conformal transformation of a Dirac operator without needing to twist the noncommutative 1-forms. Taking inspiration from this example, in this thesis, we study further applications of twisted real structures, in particular those pertaining to commutative or almost-commutative geometries. We investigate how a reality operator can implement a noncommutative Clifford algebra Morita equivalence bimodule and find that the corresponding real structure on a commutative spectral triple must be twisted. We also investigate how the presence of a twisted real structure affects the implementation of the C*-algebra self-Morita equivalence bimodule which gives the gauge transformations of a spectral triple and find that the twist operators must be tightly constrained to yield meaningful physical action functionals. The form of the resulting action functionals suggests that the twist operator may implement a Krein structure, which often appears in pseudo-Riemannian generalisations of spectral triples. Thus we further investigate if twisted real structures can implement Wick rotations, and though we do not find a fully satisfactory construction, our preliminary attempts are encouraging and suggest that the possibility cannot yet be ruled out. Lastly we identify from the literature that the twisted spectral triple for kappa-Minkowski space admits a reality operator which gives a twisted real structure. This indicates that twisted real structures are compatible with twisted spectral triples as had been previously conjectured, opening up a whole new range of potential applications

Comparative Analysis of H2 and H∞ Robust Control Design Approaches for Dynamic Control Systems

This paper discusses using H2 and H∞ robust control approaches for designing control systems. These approaches are applied to elementary control system designs, and their respective implementation and pros and cons are introduced. The H∞ control synthesis mainly enforces closed-loop stability, covering some physical constraints and limitations. While noise rejection and disturbance attenuation are more naturally expressed in performance optimization, which can represent the H2 control synthesis problem. The paper also applies these two methodologies to multi-plant systems to study the stability and performance of the designed controllers. Simulation results show that the H2 controller tracks a desirable closed-loop performance, while the H∞ controller guarantees robust stability for the closed-loop system. The validation of the techniques is demonstrated through the robust and performance gamma index, where the H∞ controller achieved a robust gamma index of 0.8591, indicating good robustness and the H2 controller achieved a performance gamma index of 2.1972, indicating a desirable performance. The robust control toolbox of MATLAB is used for simulation purposes. Overall, the paper shows that selecting a suitable, robust control strategy is crucial for designing effective control systems, and the H2 and H∞ robust control approaches are viable options for achieving this goal

Aspects of Symmetry, Topology and Anomalies in Quantum Matter

In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum systems including symmetry-protected topological states and topologically ordered states. Chapter 1. Introduction. Chapter 2. Geometric phase, wavefunction overlap, spacetime path integral and topological invariants. Chapter 3. Aspects of Symmetry. Chapter 4. Aspects of Topology. Chapter 5. Aspects of Anomalies. Chapter 6. Quantum Statistics and Spacetime Surgery. Chapter 7. Conclusion: Finale and A New View of Emergence-Reductionism. (Thesis supervisor: Prof. Xiao-Gang Wen)Comment: Ph.D. thesis, MIT, Dept. of Physics. Defended and submitted in May 2015. Citable URI: http://dspace.mit.edu/handle/1721.1/99285 Partially based on arxiv:1212.4863, arXiv:1306.3695, arxiv:1307.7480, arXiv:1310.8291, arXiv:1403.5256, arXiv:1404.7854, arXiv:1405.7689, arXiv:1408.6514, arXiv:1409.3216. With refinement. 250 page

Deep material networks for efficient scale-bridging in thermomechanical simulations of solids

We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations