Efficient Localization of Discontinuities in Complex Computational Simulations

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches

A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of "continuous" matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities

AN INVESTIGATION OF ON-CHIP ANTENNA CHARACTERISTICS RELATED TO ENERGY HARVESTING APPLICATIONS

The way a certain antenna operates is highly dependent on the dielectric medium in which it is placed. Dielectric media can be characterized by their dielectric constant, which is also called relative permittivity. When no electric field is applied, the positive and negative charges of the dielectric molecules are evenly distributed. Application of an electric field disrupts this balance and results in the creation of dipoles. The number of dipoles that are created is proportional to the permittivity of the dielectric. Permittivity is a measure of the sensitivity of the material to an applied electric field. Stated another way, permittivity is a measure of how much energy can be stored in the electric field.This thesis reports the research on several types of on-the-chip antennas such as a rectangular spiral and a rectangular patch. The characteristics of these antennas that are useful to Energy Harvesting are analyzed and the effects of permittivity changes in the dielectrics surrounding the antenna are studied

Functionalized hyperbranched polymers via olefin metathesis

Hyperbranched polymers are highly branched, three-dimensional macromolecules which are closely related to dendrimers and are typically prepared via a one-pot polycondensation of AB_(n≥2) monomers.^1 Although hyperbranched macromolecules lack the uniformity of monodisperse dendrimers, they still possess many attractive dendritic features such as good solubility, low solution viscosity, globular structure, and multiple end groups.^1-3 Furthermore, the usually inexpensive, one-pot synthesis of these polymers makes them particularly desirable candidates for bulk-material and specialty applications. Toward this end, hyperbranched polymers have been investigated as both rheology-modifying additives to conventional polymers and as substrate-carrying supports or multifunctional macroinitiators, where a large number of functional sites within a compact space becomes beneficial

DNA-Mediated Electrochemistry

The base pair stack of DNA has been demonstrated as a medium for long-range charge transport chemistry both in solution and at DNA-modified surfaces. This chemistry is exquisitely sensitive to structural perturbations in the base pair stack as occur with lesions, single base mismatches, and protein binding. We have exploited this sensitivity for the development of reliable electrochemical assays based on DNA charge transport at self-assembled DNA monolayers. Here, we discuss the characteristic features, applications, and advantages of DNA-mediated electrochemistry