Stability-preserving model reduction for linear and nonlinear systems arising in analog circuit applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 221-229).Despite the increasing presence of RF and analog components in personal wireless electronics, such as mobile communication devices, the automated design and optimization of such systems is still an extremely challenging task. This is primarily due to the presence of both parasitic elements and highly nonlinear elements, which makes simulation computationally expensive and slow. The ability to generate parameterized reduced order models of analog systems could serve as a first step toward the automatic and accurate characterization of geometrically complex components and subcircuits, eventually enabling their synthesis and optimization. This thesis presents techniques for reduced order modeling of linear and nonlinear systems arising in analog applications. Emphasis is placed on developing techniques capable of preserving important system properties, such as stability, and parameter dependence in the reduced models. The first technique is a projection-based model reduction approach for linear systems aimed at generating stable and passive models from large linear systems described by indefinite, and possibly even mildly unstable, matrices. For such systems, existing techniques are either prohibitively computationally expensive or incapable of guaranteeing stability and passivity. By forcing the reduced model to be described by definite matrices, we are able to derive a pair of stability constraints that are linear in terms of projection matrices.(cont.) These constraints can be used to formulate a semidefinite optimization problem whose solution is an optimal stabilizing projection framework. The second technique is a projection-based model reduction approach for highly nonlinear systems that is based on the trajectory piecewise linear (TPWL) method. Enforcing stability in nonlinear reduced models is an extremely difficult task that is typically ignored in most existing techniques. Our approach utilizes a new nonlinear projection in order to ensure stability in each of the local models used to describe the nonlinear reduced model. The TPWL approach is also extended to handle parameterized models, and a sensitivity-based training system is presented that allows us to efficiently select inputs and parameter values for training. Lastly, we present a system identification approach to model reduction for both linear and nonlinear systems. This approach utilizes given time-domain data, such as input/output samples generated from transient simulation, in order to identify a compact stable model that best fits the given data. Our procedure is based on minimization of a quantity referred to as the 'robust equation error', which, provided the model is incrementally stable, serves as up upper bound for a measure of the accuracy of the identified model termed 'linearized output error'. Minimization of this bound, subject to an incremental stability constraint, can be cast as a semidefinite optimization problem.by Bradley Neil Bond.Ph.D

Parameterized model order reduction for nonlinear dynamical systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 67-70).The presence of several nonlinear analog circuits and Micro-Electro-Mechanical (MEM) components in modern mixed signal System-on-Chips (SoC) makes the fully automatic synthesis and optimization of such systems an extremely challenging task. The research presented in this thesis concerns the development of techniques for generating Parameterized Reduced Order Models (PROMs) of nonlinear dynamical systems. Such reduced order models could serve as a first step towards the automatic and accurate characterization of geometrically complex components and subcircuits, eventually enabling their synthesis and optimization. This work combines elements from a non-parameterized trajectory piecewise linear method for nonlinear systems with a moment matching paramneterized technique for linear systems. Exploiting these two methods one can create four different algorithms or generating PROMs of nonlinear systems. The algorithms were tested on three different systems: a MEM switch and two nonlinear analog circuits. All three examples contain distributed strong nonlinearities and possess dependence on several geometric parameters.(cont.) Using the proposed algorithms, the local and global parameter-space accuracy of the reduced order models can be adjusted as desired. Models call be created which are extremely accurate over a narrow range of parameter values. as well as models which are less accurate locally but still provide adequate accuracy over a much wider range of parameter values.by Bradley N. Bond.S.M

Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions

Abstract—In this paper we present several results concerning the stabilization of piecewise-linear reduced order models. We include proofs of internal and external stability for models whose system matrices possess special structures. We then introduce a new projection scheme, and a new set of weighting functions which allow us to extend some of these results to piecewise-linear systems comprised of arbitrary matrices, at least one of which is Hurwitz. Included are an algorithm for creating switching piecewise-linear reduced models comprised of globally exponentially stable systems, and stable simulation results for a system which produces unstable results when using the standard TPWL method. I

Hubble Space Telescope Imaging of Lyman Alpha Emission at z=4.4

We present the highest redshift detections of resolved Lyman alpha emission, using Hubble Space Telescope/ACS F658N narrowband-imaging data taken in parallel with the Wide Field Camera 3 Early Release Science program in the GOODS CDF-S. We detect Lyman alpha emission from three spectroscopically confirmed z = 4.4 Lyman alpha emitting galaxies (LAEs), more than doubling the sample of LAEs with resolved Lyman alpha emission. Comparing the light distribution between the rest-frame ultraviolet continuum and narrowband images, we investigate the escape of Lyman alpha photons at high redshift. While our data do not support a positional offset between the Lyman alpha and rest-frame ultraviolet (UV) continuum emission, the half-light radii in two out of the three galaxies are significantly larger in Lyman alpha than in the rest-frame UV continuum. This result is confirmed when comparing object sizes in a stack of all objects in both bands. Additionally, the narrowband flux detected with HST is significantly less than observed in similar filters from the ground. These results together imply that the Lyman alpha emission is not strictly confined to its indigenous star-forming regions. Rather, the Lyman alpha emission is more extended, with the missing HST flux likely existing in a diffuse outer halo. This suggests that the radiative transfer of Lyman alpha photons in high-redshift LAEs is complicated, with the interstellar-medium geometry and/or outflows playing a significant role in galaxies at these redshifts.Comment: Submitted to the Astrophysical Journal. 11 pages, 10 figure

Star formation in 30 Doradus

Using observations obtained with the Wide Field Camera 3 (WFC3) on board the Hubble Space Telescope (HST), we have studied the properties of the stellar populations in the central regions of 30 Dor, in the Large Magellanic Cloud. The observations clearly reveal the presence of considerable differential extinction across the field. We characterise and quantify this effect using young massive main sequence stars to derive a statistical reddening correction for most objects in the field. We then search for pre-main sequence (PMS) stars by looking for objects with a strong (> 4 sigma) Halpha excess emission and find about 1150 of them over the entire field. Comparison of their location in the Hertzsprung-Russell diagram with theoretical PMS evolutionary tracks for the appropriate metallicity reveals that about one third of these objects are younger than ~4Myr, compatible with the age of the massive stars in the central ionising cluster R136, whereas the rest have ages up to ~30Myr, with a median age of ~12Myr. This indicates that star formation has proceeded over an extended period of time, although we cannot discriminate between an extended episode and a series of short and frequent bursts that are not resolved in time. While the younger PMS population preferentially occupies the central regions of the cluster, older PMS objects are more uniformly distributed across the field and are remarkably few at the very centre of the cluster. We attribute this latter effect to photoevaporation of the older circumstellar discs caused by the massive ionising members of R136.Comment: 15 pages, 12 figures. Accepted for publication in The Astrophysical Journa

Using H-alpha Morphology and Surface Brightness Fluctuations to Age-Date Star Clusters in M83

We use new WFC3 observations of the nearby grand design spiral galaxy M83 to develop two independent methods for estimating the ages of young star clusters. The first method uses the physical extent and morphology of Halpha emission to estimate the ages of clusters younger than tau ~10 Myr. It is based on the simple premise that the gas in very young (tau < few Myr) clusters is largely coincident with the cluster stars, is in a small, ring-like structure surrounding the stars in slightly older clusters (e.g., tau ~5 Myr), and is in a larger ring-like bubble for still older clusters (i.e., ~5-10 Myr). The second method is based on an observed relation between pixel-to-pixel flux variations within clusters and their ages. This method relies on the fact that the brightest individual stars in a cluster are most prominent at ages around 10 Myr, and fall below the detection limit (i.e., M_V < -3.5) for ages older than about 100 Myr. These two methods are the basis for a new morphological classification system which can be used to estimate the ages of star clusters based on their appearance. We compare previous age estimates of clusters in M83 determined from fitting UBVI Halpha measurements using predictions from stellar evolutionary models with our new morphological categories and find good agreement at the ~95% level. The scatter within categories is ~0.1 dex in log tau for young clusters (10 Myr) clusters. A by-product of this study is the identification of 22 "single-star" HII regions in M83, with central stars having ages ~4 Myr.Comment: 33 pages, 10 figures, 3 tables; published in March Ap

Progressive star formation in the young galactic super star cluster NGC 3603

Early release science observations of the cluster NGC3603 with the WFC3 on the refurbished HST allow us to study its recent star formation history. Our analysis focuses on stars with Halpha excess emission, a robust indicator of their pre-main sequence (PMS) accreting status. The comparison with theoretical PMS isochrones shows that 2/3 of the objects with Halpha excess emission have ages from 1 to 10 Myr, with a median value of 3 Myr, while a surprising 1/3 of them are older than 10 Myr. The study of the spatial distribution of these PMS stars allows us to confirm their cluster membership and to statistically separate them from field stars. This result establishes unambiguously for the first time that star formation in and around the cluster has been ongoing for at least 10-20 Myr, at an apparently increasing rate.Comment: 10 pages, 8 figures, accepted for publication in The Astrophysical Journa

Hubble Space Telescope WFC3 Early Release Science: Emission-Line Galaxies from Infrared Grism Observations

We present grism spectra of emission-line galaxies (ELGs) from 0.6-1.6 microns from the Wide Field Camera 3 on the Hubble Space Telescope. These new infrared grism data augment previous optical Advanced Camera for Surveys G800L 0.6-0.95 micron grism data in GOODS-South from the PEARS program, extending the wavelength covereage well past the G800L red cutoff. The ERS grism field was observed at a depth of 2 orbits per grism, yielding spectra of hundreds of faint objects, a subset of which are presented here. ELGs are studied via the Ha, [OIII], and [OII] emission lines detected in the redshift ranges 0.2<z<1.4, 1.2<z<2.2 and 2.0<z<3.3 respectively in the G102 (0.8-1.1 microns; R~210) and G141 (1.1-1.6 microns; R~130) grisms. The higher spectral resolution afforded by the WFC3 grisms also reveals emission lines not detectable with the G800L grism (e.g., [SII] and [SIII] lines). From these relatively shallow observations, line luminosities, star-formation rates, and grism spectroscopic redshifts are determined for a total of 48 ELGs to m(AB)~25 mag. Seventeen GOODS-South galaxies that previously only had photometric redshifts now have new grism-spectroscopic redshifts, in some cases with large corrections to the photometric redshifts (Delta(z)~0.3-0.5). Additionally, one galaxy had no previously-measured redshift but now has a secure grism-spectroscopic redshift, for a total of 18 new GOODS-South spectroscopic redshifts. The faintest source in our sample has a magnitude m(AB)=26.9 mag. The ERS grism data also reflect the expected trend of lower specific star formation rates for the highest mass galaxies in the sample as a function of redshift, consistent with downsizing and discovered previously from large surveys. These results demonstrate the remarkable efficiency and capability of the WFC3 NIR grisms for measuring galaxy properties to faint magnitudes and redshifts to z>2.Comment: Accepted for publication in AJ. Updated to include referee comments. Updated sample using improved reduction contains 23 new galaxies (Table 1; Figures 2 & 3

Anatomy of a post-starburst minor merger: a multi-wavelength WFC3 study of NGC 4150

(Abridged) We present a spatially-resolved near-UV/optical study of NGC 4150, using the Wide Field Camera 3 (WFC3) on board the Hubble Space Telescope. Previous studies of this early-type galaxy (ETG) indicate that it has a large reservoir of molecular gas, exhibits a kinematically decoupled core (likely indication of recent merging) and strong, central H_B absorption (indicative of young stars). The core of NGC 4150 shows ubiquitous near-UV emission and remarkable dusty substructure. Our analysis shows this galaxy to lie in the near-UV green valley, and its pixel-by-pixel photometry exhibits a narrow range of near-UV/optical colours that are similar to those of nearby E+A (post-starburst) galaxies. We parametrise the properties of the recent star formation (age, mass fraction, metallicity and internal dust content) in the NGC 4150 pixels by comparing the observed near-UV/optical photometry to stellar models. The typical age of the recent star formation (RSF) is around 0.9 Gyrs, consistent with the similarity of the near-UV colours to post-starburst systems, while the morphological structure of the young component supports the proposed merger scenario. The RSF metallicity, representative of the metallicity of the gas fuelling star formation, is around 0.3 - 0.5 Zsun. Assuming that this galaxy is a merger and that the gas is sourced mainly from the infalling companion, these metallicities plausibly indicate the gas-phase metallicity (GPM) of the accreted satellite. Comparison to the local mass-GPM relation suggests (crudely) that the mass of the accreted system is around 3x10^8 Msun, making NGC 4150 a 1:20 minor merger. A summation of the pixel RSF mass fractions indicates that the RSF contributes about 2-3 percent of the stellar mass. This work reaffirms our hypothesis that minor mergers play a significant role in the evolution of ETGs at late epochs.Comment: 28 pages, 2 tables, accepted for publication in Ap

The Hubble Space Telescope Wide Field Camera 3 Early Release Science data: Panchromatic Faint Object Counts for 0.2-2 microns wavelength

We describe the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) Early Release Science (ERS) observations in the Great Observatories Origins Deep Survey (GOODS) South field. The new WFC3 ERS data provide calibrated, drizzled mosaics in the UV filters F225W, F275W, and F336W, as well as in the near-IR filters F098M (Ys), F125W (J), and F160W (H) with 1-2 HST orbits per filter. Together with the existing HST Advanced Camera for Surveys (ACS) GOODS-South mosaics in the BViz filters, these panchromatic 10-band ERS data cover 40-50 square arcmin at 0.2-1.7 {\mu}m in wavelength at 0.07-0.15" FWHM resolution and 0.090" Multidrizzled pixels to depths of AB\simeq 26.0-27.0 mag (5-{\sigma}) for point sources, and AB\simeq 25.5-26.5 mag for compact galaxies. In this paper, we describe: a) the scientific rationale, and the data taking plus reduction procedures of the panchromatic 10-band ERS mosaics; b) the procedure of generating object catalogs across the 10 different ERS filters, and the specific star-galaxy separation techniques used; and c) the reliability and completeness of the object catalogs from the WFC3 ERS mosaics. The excellent 0.07-0.15" FWHM resolution of HST/WFC3 and ACS makes star- galaxy separation straightforward over a factor of 10 in wavelength to AB\simeq 25-26 mag from the UV to the near-IR, respectively.Comment: 51 pages, 71 figures Accepted to ApJS 2011.01.2