[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

Integrated optical devices based on liquid crystals embedded in polydimethylsiloxane flexible substrates

The contribution of this thesis is to find possible solutions for the creation of interconnections and optical switches to be used in microoptofluidic systems in the frame of the research activities of the Optoelectronic laboratory of the Department of Information Engineering, Electronics and Telecommunications (DIET). The main goal is to explore a new technology for integrated optic based on a low cost technology to produce low driving power devices. Optofluidics is the science which links the field of photonics with microfluidics, for the creation of innovative and state-of-the-art devices. Liquid crystals (LC) can be used for optofluidic applications because they have the possibility to change without external mechanical actions, the average direction of the molecules through the application of electric fields, reorienting the crystal molecules in such a way as to alter their optical properties [1-2]. The research on LC is more than a century old, but only since the ‘80s of the past century these materials were employed in various fields, from flat panel displays used for televisions, tablets, and smartphones, to biomedical and telecommunication applications [3-5]. The results reported in this thesis include simulation, design and preliminary fabrication of optofluidic prototypes based on LC embedded in polydimethylsiloxane (PDMS) channels, defined as LC:PDMS, with co-planar electrodes to control LC molecular orientation and light propagation. Fabrication techniques which were used include microelectronic processes such as lithography, sputtering, evaporation, and electroplating. The simulations were performed through the combined use of COMSOL Multiphysics® and BeamPROP®. I used COMSOL Multiphysics® to determine the positioning of the molecules in a LC:PDMS waveguide. The LC are the core through which light propagates in a PDMS structure. In addition to these simulations, I used COMSOL Multiphysics® to determine the orientation of the LC under the effect of an electric field [6-7] to create low-power optofluidic devices [8], [11]. I used BeamPROP® to explore the optical propagation of various optical devices such as: optical couplers, the zero gap optical coupler, and a multimodal interferometer. All these devices have been simulated through various combinations of geometries which will be extensively explained in the following chapters. The fabrication of prototypes was made in the Microelectronic Technologies laboratory of DIET. The optofluidic prototypes that I designed could be used in interconnection systems on biosensing devices for chemical or biological applications [10-11], wearable [12], or lab on chips [13], which are increasingly being applied in many research fields [14]. Many of these devices need to interface with electronics for processing signals coming from the interaction between the device with molecules, liquids or other biological substances. Moreover it is necessary to create flexible and biocompatible interfaces, whose features are not guaranteed in classic metal tracks. As it will be clear in the first chapter, metal interconnections must be designed with spatial, energy and throughput restrictions. To develop the optofluidic prototypes, I chose to use a combination of two materials for their commercial availability and ease of use: E7 and 5CB LC produced by Merck® as the transmissive medium and PDMS Sylgard 184 produced by Dow Corning® for the cladding [15-16]. The molecules of the LC are anisotropic, whose shape is elongated like that of a cigar. Under appropriate temperature conditions these molecules retain a state of aggregation in which, while retaining some mechanical properties of the fluids, they have the characteristics of crystals such as birefringence or x-ray reflection. These properties are due to two factors that characterize the various phases of LC: the orientational and positional order that vary according to the temperature. E7 was used in its nematic mesophase. The material used for the cladding of my prototypes was PDMS, a thermosetting polymer, flexible, biocompatible, economical, easy to work, and suitable for the creation of optical and optofluidic devices due to its transparency. The thesis is organized in six chapters whose contents are briefly outlined below: • In the first chapter there is a brief description of optofluidics and the transport phenomena of the liquids in the microchannels. The essential parameters for a correct interpretation of the behavior of the materials in the devices will be defined. Some examples of microfluidic devices, Optofluidic Optical Components (OOC) will be mentioned. • In the second chapter, LC’s will be presented, along with their general characteristics and their behavior in the presence of electric fields. An overview of integrated optic devices based on LC will be reported. • In the third chapter the experimental results will be presented concerning the fabrications and the technologies used to obtain electro-optical LC:PDMS waveguides. • The fourth chapter will be dedicated to a brief description of COMSOL Multiphysics® and BeamPROP® simulators, and the implementation of the model of LC channels in PDMS both in 2D and 3D. Also a brief description of Monte Carlo simulations based on Lebwohl-Lasher potential will be mentioned. • In the fifth chapter an LC:PDMS optical directional coupler and the most significant results will be described. • The sixth chapter is dedicated to the multimodal interferometer and its field of application, the theory behind this device and the results obtained from the simulations using the BeamPROP® • In the conclusion, a brief recap of the results obtained in this thesis and future developments will be presented

An optimization framework for adaptive higher-order discretizations of partial differential equations on anisotropic simplex meshes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 271-281).Improving the autonomy, efficiency, and reliability of partial differential equation (PDE) solvers has become increasingly important as powerful computers enable engineers to address modern computational challenges that require rapid characterization of the input-output relationship of complex PDE governed processes. This thesis presents work toward development of a versatile PDE solver that accurately predicts engineering quantities of interest to user-prescribed accuracy in a fully automated manner. We develop an anisotropic adaptation framework that works with any localizable error estimate, handles any discretization order, permits arbitrarily oriented anisotropic elements, robustly treats irregular features, and inherits the versatility of the underlying discretization and error estimate. Given a discretization and any localizable error estimate, the framework iterates toward a mesh that minimizes the error for a given number of degrees of freedom by considering a continuous optimization problem of the Riemannian metric field. The adaptation procedure consists of three key steps: sampling of the anisotropic error behavior using element-wise local solves; synthesis of the local errors to construct a surrogate error model based on an affine-invariant metric interpolation framework; and optimization of the surrogate model to drive the mesh toward optimality. The combination of the framework with a discontinuous Galerkin discretization and an a posteriori output error estimate results in a versatile PDE solver for reliable output prediction. The versatility and effectiveness of the adaptive framework are demonstrated in a number of applications. First, the optimality of the method is verified against anisotropic polynomial approximation theory in the context of L2 projection. Second, the behavior of the method is studied in the context of output-based adaptation using advection-diffusion problems with manufactured primal and dual solutions. Third, the framework is applied to the steady-state Euler and Reynolds-averaged Navier-Stokes equations. The results highlight the importance of adaptation for high-order discretizations and demonstrate the robustness and effectiveness of the proposed method in solving complex aerodynamic flows exhibiting a wide range of scales. Fourth, fully-unstructured space-time adaptivity is realized, and its competitiveness is assessed for wave propagation problems. Finally, the framework is applied to enable spatial error control of parametrized PDEs, producing universal optimal meshes applicable for a wide range of parameters.by Masayuki Yano.Ph.D

Fluctuation-induced interactions and nonlinear nanophotonics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 293-329).We present theoretical and numerical methods for studying Casimir forces and nonlinear frequency conversion in nanophotonic media consisting of arbitrary geometries and materials. The first section of the thesis focuses on the study of various geometry-enabled resonant effects leading to strong nonlinear interactions. The starting point of this work is a coupled-mode theory framework for modeling a wide range of resonant nonlinear frequency-conversion processes in general geometries, ameliorating the need for repeated and expensive finite-difference time-domain simulations. We examine the predictions of the theory for two particular nonlinear processes: harmonic generation and difference-frequency generation. Our results demonstrate strong enhancement of nonlinear interactions at a "critical" input power leading to 100% frequency conversion, among many other interesting dynamical effects. Using a quantum-mechanical description of light, based on cavity quantum electrodynamics, similar enhancement effects are demonstrated at the single-photon level, leading to the possibility of achieving all-optical switching of a single signal photon by a single gating photon in a waveguide-cavity geometry consisting of pumped four-level atoms embedded in a cavity. Finally, we describe how one may tailor the geometry of certain materials to enhance their nonlinear susceptibilities by exploiting a consequence of the Purcell effect. The second section of the thesis, the main contribution of this work, presents a new formulation for studying Casimir forces in arbitrary geometries and materials that directly exploits efficient and well-developed techniques in computational electromagnetism. To begin with, we present the step-by-step conceptual development of our computational method, based on a well-known stress tensor formalism for computing Casimir forces. A proof-of- concept finite-difference frequency-domain implementation of the stress-tensor method is described and checked against known results in simple geometries. Building on this work, we then describe the basic theoretical ingredients of a new technique for determining Casimir forces via antenna measurements in tabletop experiments. This technique is based on a (derived) correspondence between the complex-frequency deformation of the Casimir frequency-integrand for any given geometry and the real-frequency classical electromagnetic response of the same geometry, but with dissipation added everywhere. This correspondence forms the starting point of a numerical Casimir solver based on the finite-difference time-domain method, which we describe and then implement via an off-the-shelf time-domain solver, requiring no modifications. These numerical methods are then used to explore a wide range of geometries and materials, of various levels of complexity: First, a four-body piston-like geometry consisting of two cylinders next to adjacent walls, which exhibits a non-monotonic lateral Casimir force (explained via ray optics and the method of images); Second, a zipper-like, glide-symmetric structure that leads to a net repulsive force arising from a competition between attractive interactions. Finally, we examine a number of geometries consisting of fluid-separated objects and find a number of interesting results. These include: stable levitation and suspension of compact objects, dispersion-induced orientation transitions, and strong non-zero temperature Casimir effects.by Alejandro Rodriguez-Wong.Ph.D

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Supercomputing in Aerospace

Topics addressed include: numerical aerodynamic simulation; computational mechanics; supercomputers; aerospace propulsion systems; computational modeling in ballistics; turbulence modeling; computational chemistry; computational fluid dynamics; and computational astrophysics

13th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, CA, March 17-21, 1997, Conference Proceedings Volumes I & II

Includes Volumes 1 &