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

Reduced-order modeling of large-scale network systems

Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics, which pose challenges to network management and operation. This chapter provides an overview of reduced-order modeling techniques that are developed recently for simplifying complex dynamical networks. In the first part, clustering-based approaches are reviewed, which aim to reduce the network scale, i.e., find a simplified network with a fewer number of nodes. The second part presents structure-preserving methods based on generalized balanced truncation, which can reduce the dynamics of each subsystem.Comment: Chapter 11 in the book Model Order Reduction: Volume 3 Application

Ensemble Kalman Methods With Constraints

Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it

Vibration Modelling and Control Experiments for a Thin-Walled Cylindrical Rotor with Piezo Patch Actuation and Sensing

This paper describes a dynamic model formulation and control experiments concerning the vibration behaviour of a thin-walled cylindrical rotor with internal piezoelectric patch transducers. Model development, validation and controller design procedures were undertaken for an experimental rotordynamic system comprising a tubular steel rotor (length 0.8 m, diameter 0.166 m and wall-thickness 3.06 mm) supported by two radial active magnetic bearings. Analytical solutions for mode shapes and natural frequencies for free vibration were first derived using a shell theory model, and these used to construct a speed-dependent parametric model for the rotor structure, including piezo patch actuators and sensors. The results confirm that the developed shell theory model can accurately capture the rotating frame dynamics and accounts correctly for frequency splitting from Coriolis effects. The model is also shown to be suitable for active controller design and optimization. Model-based H2 feedback control using the rotor-mounted actuators and sensors is shown to achieve vibration suppression of targeted flexural modes, both with and without rotation

Non-Bloch-Siegert-type power-induced shift of two-photon electron paramagnetic resonances of charge-carrier spin states in an OLED

We present Floquet theory-based predictions and electrically detected magnetic resonance (EDMR) experiments scrutinizing the nature of two-photon magnetic resonance shifts of charge-carrier spin states in the perdeuterated $\pi$-conjugated polymer poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylene vinylene] (d-MEH-PPV) under strong magnetic resonant drive conditions (radiation amplitude $B_1$ ~ Zeeman field $B_0$). Numerical calculations show that the two-photon resonance shift with power is nearly drive-helicity independent. This is in contrast to the one-photon Bloch-Siegert shift that only occurs under non-circularly polarized strong drive conditions. We therefore treated the Floquet Hamiltonian analytically under arbitrary amplitudes of the co- and counter-rotating components of the radiation field to gain insight into the nature of the helicity dependence of multi-photon resonance shifts. In addition, we tested Floquet-theory predictions experimentally by comparing one-photon and two-photon charge-carrier spin resonance shifts observed through room-temperature EDMR experiments on d-MEH-PPV-based bipolar injection devices [i.e., organic light emitting diode structures (OLEDs)]. We found that under the experimental conditions of strong, linearly polarized drive, our observations consistently agree with theory, irrespective of the magnitude of $B_1$, and therefore underscore the robustness of Floquet theory in predicting nonlinear magnetic resonance behaviors.Comment: 22 pages, 5 figure

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

Quantum communication tasks

Quantum theory is one of the most important theories in modern physics, yet the physical principles underlying the theory are anything but clear. Nonclassical features, such as entanglement, are often attributed as the key phenomena that make quantum theory special. However, the difference between classical and quantum systems can already be detected by observing the behavior of single systems in various communication setups. This thesis is based on the original publications I–IV. A key concept throughout is that of a communication task, by which we mean a description of conditional probabilities in a prepare-and-measure scenario. These conditional probabilities are conveniently collected into row-stochastic matrices, which we call communication matrices. The concept of a communication task was introduced in Publication II where we also studied a preorder on the set of communication matrices. We called this preorder the ultraweak matrix majorization and refined the concept in Publication III. A key motivation for introducing this preorder was that the set of communication matrices is closed with respect to the ultraweak matrix majorization. Additionally, ultraweak matrix majorization can be used to give a physical characterization of which communication tasks are harder to implement than others. We also studied monotone functions of the ultraweak preorder. By studying the different monotones it becomes possible to define different notions of dimension for operational theories. These dimensions each characterize the properties of given operational theories and we are able to capture some key differences between classical and quantum state spaces. While the preorder of ultraweak matrix majorization is a major part of this thesis, some concrete communication tasks are also studied. One of the main studied communication tasks is antidistinguishability, which plays an important role in the study of the foundations of quantum mechanics. We were able to provide a new algebraic condition for an arbitrary set of quantum states to be antidistinguishable in Publication I. We also apply the theory of ultraweak matrix majorization to antidistinguishability in the third chapter of this thesis, where we show that the set of all communication matrices is not convex for classical or quantum state spaces in any dimension. The other communication tasks studied in this thesis are communication of partial ignorance, studied in Publication II, and partial-ignorance communication tasks which was the topic of Publication IV. Both of these communication tasks can be seen as communication tasks between two parties, where one party is trying to communicate which choices the other party should avoid. A key observation for these tasks is that they lie between distinguishability and antidistinguishability. Some novel analysis is presented for both of these tasks in the final chapter of this thesis. The quantum implementation for one of the partial-ignorance communication tasks can be shown to break the principle of noncontextuality, thus proving that quantum mechanics holds a contextual advantage in the given task when compared to classical operational theories