DOCSLIB.ORG

Investigation of Cosmic Microwave Background Anomalies with Multipole Vectors Marvin Pinkwart

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Investigation of Cosmic Microwave Background Anomalies with Multipole Vectors Marvin Pinkwart Master Thesis Investigation of Cosmic Microwave Background Anomalies with Multipole Vectors ∗ Marvin Pinkwart [email protected] Date of Submission: 14.11.2016 FacultySubmitted of Physics to the Bielefeld University Supervisor and First Referee: Prof. Dr. Dominik Schwarz Second Referee: Prof. Dr. Gernot Akemann ∗ http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2013/03/planck_cmb/12583930- 4-eng-GB/Planck_CMB.jpg ≤ l ≤ Abstract In this thesis we investigate breakingalm of isotropy in the Cosmic Microwave Background on the angular range 2 49. For this purposel we use thousand ensembles of Gaussian and isotropic random in order to receive thousand ensembles of random multipole vectors. Each multipole is represented by multipole vectors which rotate rigidly with the temperature fluctuations. We use four different statistics considering theS multipolel vectors:| l;i · | ;S l | l;i × l;j · | l l l − i ( ) i<j ( ) ( ) 1 1 X 5 2 X S (l) = v |D l;i · l;j(|);S = l (v v ) D| l;i × l;j · l;k |: l l − ( 1) l l − l − i<j ( ) ( ) i<j<k ( ) ( ) ( ) 3 2 X 4 6 X ( ) = v v ( ) = (v v ) v S S ( 1) ( 1)( 2) S S 1 5 3 4 and measure correlation with an outer direction D; and measure intra- multipole correlation. We find< the likelihoods for intra-multipoleS S correlation not to be remarkable, except for the map received by the SEVEM cleaning algorithm, while the 1 5 number of low likelihoods ( 10%) – if considering , and the Cosmic Dipole as well as the Galactic Center as the direction D only – is much higher than one would expect. SEVEM deviates from the other three maps in this regard as well with the Galacticl ; l and Ecliptic Poles impacting it the most. Despite the unusual high number of lower≤ l ≤ likelihoods we do not find a clustering of low likelihoods in some angular patch 1 2 [ ] except for the unusual alignment of multipole vectors with the Cosmic Dipole at 2 4. Kurzfassung≤ ≤ In dieser Arbeit untersuchen wir Isotropiebrechungalm im Kosmischen Mikrowellenhinter- grund in dem Winkelbereich 2 2 49. Zu diesem Zweckel verwenden wir tausend Ensembles Gaußscher und isotroper Zufalls- , um tausend Ensembles von Zufalls- multipolvektoren zu erhalten. Jeder Multipol wird durch Multipolvektoren repräsen- tiert, welche starr mit den Temperaturfluktuationen rotieren. Wir benutzen vier unter- schiedlicheS l Statistiken| l;i · bezüglich| ;S l der Multipolvektoren:| l;i × l;j · | l l l − i ( ) i<j ( ) ( ) 1 1 X 5 2 X S (l) = v |D l;i · l;j(|);S = l (v v ) D| l;i × l;j · l;k |: l l − ( 1) l l − l − i<j ( ) ( ) i<j<k ( ) ( ) ( ) 3 2 X 4 6 X ( ) = v v ( ) = (v v ) v S S ( 1) ( 1)( 2) S S 1 5 3 4 und messen die Korrelation mit einer äußeren Richtung D; und messen Intramultipolkorrelationen. Es stellt sich heraus, dass die Wahrscheinlichkeiten für die gemessenen Intramultipolkorrelationen,< abgesehenS S von der mit dem SEVEM-Algorithmus hergestellten Karte, nicht beachtenswert klein sind, während die Anzahl der geringen 1 5 Wahrscheinlichkeiten ( 10%), wenn man nur , und den kosmischen Dipol, sowie das galaktische Zentrum betrachtet, viel größer ist als man erwarten würde. Auch in diesem Hinblick unterscheidet sich SEVEM von den anderen drei Karten, denn auf SEVEM haben der galaktische und der ekliptische Pol den größten Einfluss.l ; l Trotz der hohen Anzahl an geringen Wahrscheinlichkeiten finden wir keine andere Anhäufung 1 2 von geringen≤ l Wahrscheinlichkeit≤ in einem gewissen Winkelbereich [ ] abgesehen von der ungewöhnlichen Ausrichtung der Multipolvektoren am kosmischen Dipol im Bereich 2 4. Table of Contents Page Table of Contents viii List of Figures x List of Tables xi Conventions and Abbreviations xii I. Introduction 1 II. The Universe 3 II.1. Isotropic Universe / ΛCDM . 4 II.1.1. Isotropy . 4 II.1.2. Friedmann Equations and Solutions . 7 II.1.3. Spatial Part and Full Metric . 9 II.2. Short History of the Universe . 11 II.2.1. Age of the Universe . 11 II.2.2. Contributions of Different Energies . 12 II.2.3. Thermal History . 13 II.3. Problems of ΛCDM . 15 II.3.1. Horizon Problem . 15 II.3.2. Flatness Problem/Entropy Problem . 15 II.3.3. Structure Formation Problem . 16 II.4. Inflation . 16 II.4.1. Idea . 17 II.4.2. Small Field vs. Large Field . 18 II.4.3. Resolution of ΛCDM-Problems . 18 III. The CMB 21 III.1. General Properties . 22 v Table Of Contents III.2. Era of Decoupling . 23 III.2.1. Hydrogen Formation . 24 III.2.2. Transition to Transparency . 25 III.3. Linear Perturbation Theory . 26 III.3.1. Gauges . 27 III.3.2. Helicity Decomposition . 28 III.3.3. Evolution Equations . 29 III.4. Generation of Perturbations/Initial Conditions . 30 III.5. From Initial Conditions to Recombination . 33 III.6. Black Body Spectrum . 34 III.7. CMB Statistics and Angular Spectrum . 35 III.7.1. General Properties and Definitions . 35 III.7.2. Ergodicity and Cosmic Variance . 39 III.7.3. Isotropy vs. Gaussianity . 40 III.7.4. Theoretical Description of The Angular Spectrum 41 IV. Multipole Vectors 45 IV.1. Maxwell’s Multipole Vectors and Sylvester’s Theorem . 45 IV.2. Tensorial Approach . .a .lm . 48 IV.2.1. Mathematical Derivation . 48 IV.2.2. Explicit Calculation of MPVs from ’s . 50 IV.3. Algebraic Approach . 51 IV.3.1. Proof of Sylvester’s Theorem . 51 IV.3.2. ComputationSO ; R of MPVsSL .; C . 53 IV.4. Majorana Sphere Approach . 55 IV.4.1. From (3 ) to (2 ) . 55 IV.4.2. Majorana Vectors . 56 IV.4.3. Application to Sylvester’s Theorem . 60 IV.5. Probability Distribution . 61 IV.5.1. Properties andl Assumptions; ; . 61 IV.5.2. Derivation of the Full Joint PDF . 63 IV.5.3. Special Cases = 1 2 3 . 66 IV.5.4. MPVs, the Gaussian Analytic Function and Ran- dom Matrix Theory . 68 IV.6. Further Remarks and Summary . 70 IV.6.1. Remarks . 70 IV.6.2. Summary . 71 vi Investigation of CMB Anomalies with Multipole Vectors - Marvin Pinkwart Table Of Contents V. Observed Large Scale CMB Anomalies 73 V.1. Types of Anomalies . 73 V.1.1. Lack of Correlation . 74 V.1.2. Hemispherical Asymmetry . 75 V.1.3. Parity Asymmetry . 75 V.1.4. Cold Spot . 75 V.1.5. Low Multipole Alignment Using MPVs . 75 V.2. Possible Explanations . 76 VI. ESA Planck Mission 79 VI.1. General Information . 79 VI.2. Full Sky Maps . 82 VI.2.1. HEALPix . 82 VI.2.2. General . 85 VI.2.3. Foreground Cleaned CMB Temperature Maps . 85 VI.3. 2015 Results . .l . 90 VII. Planck 2015 MPV CMB Anomalies Up to = 49 93 VII.1. Statistics Used . 93 VII.2. Numerical Method . .a .lm . 97 VII.2.1. Receiving MPVs from Planck Maps . 98 VII.2.2. Calculating MPVs for Random . 100 VII.2.3. p-Values and Likelihoods . 102 VII.2.4. Remark . 104 VII.3. Results . 105 VII.3.1. Distribution of MPVs . 105 VII.3.2. Qualitative Behaviour of Statistics and Appar- ent Similarity of Maps . 106 VII.3.3. SEVEM . 109 VII.3.4. Absence of Intra-Multipole Anomalies . 110 VII.3.5. Outer Correlations . 112 VII.3.6. Cumulative Behaviour . 115 VIII. Conclusion and Outlook 117 Appendices 121 A. Spherical Harmonics 122 A.1. Definition and Properties . 122 Investigation of CMB Anomalies with Multipole Vectors - Marvin Pinkwart vii SO L S Table Of Contents 2 2 A.2. Basis Functions of (3) on ( ) (Multipole Decom- position) . 123 B. Differential Geometry and General Relativity 125 C. Statistics 128 C.1. Bayesian Analysis . 128 C.2. Gaussian Random Variables . 129 C.3. Change of Variables . 130 D. Data 131 E. Plots 132 References 135 viii Investigation of CMB Anomalies with Multipole Vectors - Marvin Pinkwart List of Figures II.1. Distribution of galaxies measured by the 2dF Galaxy Redshift Survey . 5 II.2. Hubble length for different energy contributions . 12 II.3. Thermal History of the Universe. 14 III.1. CMB Intensity spectrum . 22 III.2. CMB Temperature Map . 23 III.3. CMB Angular Band Power Spectrum . 38 IV.1. Visualisation of relationship between distributions . 62 IV.2. 2-point density:l MPV vs. uniform . 68 IV.3. Multipole Vectors and spherical harmonics for different angular scales . ....................... 72 V.1. Lack of Correlation . 74 V.2. Angular Scales Compared to Hubble Scale . 77 VI.1. Planck Mission Timeline . 79 VI.2. Planck Scan Strategy . 81 VI.3. HEALPix pixelation scheme . 83 VI.4. HEALPix NESTED and RING ordering in Mollweide projection . 83 VI.5. Comparison of Full Sky Maps . 86 l; b VII.1. MPVs in Mollweide View . 105 VII.2. MPVs in ( )-plane . 106 VII.3. Outer statistics - All maps, Dipole . 107 VII.4. Inner statistics - All maps . 108 VII.5. Full likelihood plotted for all maps and the Galactic Pole.109 VII.6. Abundance of likelihoods - SEVEM . 110 VII.7. Abundance of inner likelihoods - all . 111 VII.8. Abundance of outer likelihoods - all . 112 VII.10. Odd modes vs. even modes . 113 ix List of Figuresχ VII.9. Outer Likelihood, NILC, Dipole2 and Center . 114 VII.11. Cumulative p-values and . 115 E.1. Full likelihood plotted for all maps and the Galactic Pole.132 E.2. Abundance of likelihoods - SEVEM - Zoom . 133 E.3. Inner likelihood of COMMANDER. 133 E.4. NILC - full and inner likelihood . 134 x Investigation of CMB Anomalies with Multipole Vectors - Marvin Pinkwart List of Tables l D.1. List of NILC MPVs up to = 5 . 131 xi c h kB − ; ; ; (1)Conventions We set = = = 1. and Abbreviations t η (2) We use the mostly plus convention for the metric signature ( 1 1 1 1).
Load more

Recommended publications
  • Rcosmo: R Package for Analysis of Spherical, Healpix and Cosmological Data Arxiv:1907.05648V1 [Stat.CO] 12 Jul 2019
    CONTRIBUTED RESEARCH ARTICLE 1 rcosmo: R Package for Analysis of Spherical, HEALPix and Cosmological Data Daniel Fryer, Ming Li, Andriy Olenko Abstract The analysis of spatial observations on a sphere is important in areas such as geosciences, physics and embryo research, just to name a few. The purpose of the package rcosmo is to conduct efficient information processing, visualisation, manipulation and spatial statistical analysis of Cosmic Microwave Background (CMB) radiation and other spherical data. The package was developed for spherical data stored in the Hierarchical Equal Area isoLatitude Pixelation (Healpix) representation. rcosmo has more than 100 different functions. Most of them initially were developed for CMB, but also can be used for other spherical data as rcosmo contains tools for transforming spherical data in cartesian and geographic coordinates into the HEALPix representation. We give a general description of the package and illustrate some important functionalities and benchmarks. Introduction Directional statistics deals with data observed at a set of spatial directions, which are usually positioned on the surface of the unit sphere or star-shaped random particles. Spherical methods are important research tools in geospatial, biological, palaeomagnetic and astrostatistical analysis, just to name a few. The books (Fisher et al., 1987; Mardia and Jupp, 2009) provide comprehensive overviews of classical practical spherical statistical methods. Various stochastic and statistical inference modelling issues are covered in (Yadrenko, 1983; Marinucci and Peccati, 2011). The CRAN Task View Spatial shows several packages for Earth-referenced data mapping and analysis. All currently available R packages for spherical data can be classified in three broad groups. The first group provides various functions for working with geographic and spherical coordinate systems and their visualizations.
    [Show full text]
  • From Stargazing to Space Travel Our Brief History Into Space
    From Stargazing to Space Travel Our brief history into space Science in the News Elaine Garcia Angela She November 4th, 2015 Why do we care? Gives us perspective • What did our forefathers think of the Heavens? • Why did they think that? • How did theories change throughout time? Gives us purpose • Mystery drives inquiry and discovery. Important Lessons were Learned and will Continue to be Discovered! Keywords Astrologyl – The study and interpretation of the movements and positions of celestial bodies in relation to Earth and Earthly affairs. Astronomy – The study of physical objects in space: gas, dust, stars, planets, moons, comets, and other non-Earthly mass and phenomena. • Astrophysics – The study of the physical nature and energy of cosmic mass. • Cosmology – A branch of study that theorizes about the origin and nature of the universe. Outline 1. Star Gazing • Theories about why, where, and how 2. Star Studying • Technology to study the unknown 3. Star Reaching • Demo on space exploration Outline 1. Star Gazing • Theories about why, where, and how 2. Star Studying • Technology to study the unknown 3. Star Reaching • Demo on space exploration What are stars’ purpose? Are they the actions, moods, or warnings of celestial beings? Star Worship Is their existence independent and separated from Earth’s existence and purpose? Star Navigation and Measurement Millennia of Lessons 570 BC 384 BC 276 BC 1600 O 1750+ BC 427 BC 310 BC 90 1700 Millennia of Lessons The earliest records of astronomical observations and mathematics. 1750+ BC Greek Rule Zeus King of Gods Hera Queen of Gods Poseidon God of the Sea Hades God of the Underworld Helios The Sun God Ares God of War Aphrodite Goddess of Love Eros God of Love Athena Goddess of Wisdom Hephaestus God of Fire/Forge Wikicommons.com What season is it? Zodiac surrounds the Earth, noting the Seasons Wikicommons.com Millennia of Lessons The earliest records of astronomical observations and mathematics.
    [Show full text]
  • Rhodri Evans
    Rhodri Evans The Cosmic Microwave Background How It Changed Our Understanding of the Universe Astronomers’ Universe More information about this series at http://www.springer.com/series/6960 Rhodri Evans The Cosmic Microwave Background How It Changed Our Understanding of the Universe 123 Rhodri Evans School of Physics & Astronomy Cardiff University Cardiff United Kingdom ISSN 1614-659X ISSN 2197-6651 (electronic) ISBN 978-3-319-09927-9 ISBN 978-3-319-09928-6 (eBook) DOI 10.1007/978-3-319-09928-6 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: : 2014957530 © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law.
    [Show full text]
  • Measuring Inflation with CLASS
    Measuring Inflation with CLASS by Dominik Gothe A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy. July 2015 Baltimore, Maryland c Dominik Gothe All rights reserved Abstract Using the Cosmology Large Angular Scale Surveyor (CLASS), we will measure the po- larization of the Cosmic Microwave Background (CMB) to constrain inflationary theory. The gravitational waves generated during the inflationary epoch imprinted specific polar- ization patterns – quantifiable by tensor-to-scalar ratio r – onto the CMB, which CLASS is designed to detect. Furthermore, we will be able to make assertions about the energy scale during inflation by discovering the features of the polarization power spectrum, providing a probe into physics of energy scales not conceivable in particle-accelerator physics. CLASS is a unique ground based experiment with extensive consideration given to mitigating sys- tematic uncertainties. A brief introduction into inflationary cosmology and review of current scientific results will be presented in the light of the upcoming measurements with the newly built CLASS de- tector. I will detail some of my technical contribution to the construction of this telescope. I have conducted my research under the advise of Prof. Bennett. Additionally the thesis was reviewed by Prof. Marriage, Prof. Kamionkowski, Prof. Chuss, and Prof. Strobel. ii Acknowledgments I would like to thank my wife, friends, members of the Johns Hopkins community, my mentors, teachers, supervisors, and dissertation committee. The CLASS project receives support from the National Science Foundation Division of Astronomical Sciences under Grant Numbers 0959349 and 1429236. iii Contents I Physics of the Origin of the Universe 1 1 Introduction to the Big Bang Framework .
    [Show full text]
  • Aerocenecampusreader FINAL
    With Contributions by: Pete Adey ……………….............................Aaron Schuster, The Cosmonaut of the Erotic Future Sasha Engelmann……………………………………….The Cosmic Flight of the Aerocene Gemini Harriet Hawkins………………………………………………………………Imagine… Geoaesthetics Sam Hertz……………………………………………………………………………….The Floating Ear Bronislaw Szerszynski………………………………………………………………Planetary Mobilities Derek McCormack……………………..Sounding: Echoes and Thresholds of Atmospheric Media Andreas Philippopoulos-Mihalopoulos……………........................Withdrawing from Atmosphere Nick Shapiro……………………………………………………………Tim Choy, Air’s Substantiations And from the cosmos of the late Steven Vogel………………………………..Life in Moving Fluids Concept, Edit & Design: Sasha Engelmann and Karina Pragnell Cover Design and Drawings by Irin Siriwattanagul Aerocene Campus NOVEMBER 26, 2016 | EXHIBITION ROAD, LONDON Aerocene comes to Exhibition Road for a multidisciplinary artistic project co-produced by the members of the Exhibition Road Cultural Group, gathering together 17 prestigious cultural and scientific institutions in London, among them, the Serpentine Galleries, Imperial College London, the Natural History Museum, the Science Museum, the Royal Geographical Society, the Victoria and Albert Museum, and the Goethe Institute. How can we hack the Anthropocene to create the Aerocene? The first Aerocene Campus is an open invitation to explore, extend and imagine the Aerocene Epoch through the sculpture of the Aerocene Explorer. The Campus asks how community- driven practices with the Aerocene Explorer can inform environmental, social and mental ecologies in post-Anthropocenic worlds. On November 26th, experts from a wide range of disciplines will gather together for a full day of provocation, discussion, collaboration and 'hacking' to experiment with the Aerocene Explorer and to co-create the Aerocene epoch. To hack is to creatively overcome the limitations of a system, to improve or subvert the intentions of its original form in a spirit of playfulness and exploration.
    [Show full text]
  • MONMOUTH County
    NJ DEP - Historic Preservation Office Page 1 of 20 New Jersey and National Registers of Historic Places Last Update: 9/28/2021 MONMOUTH County Asbury Park City MONMOUTH County Arbutus Cottage (ID#5455) 508 Fourth Avenue Aberdeen Township NR: 8/18/2015 (NR Reference #: 15000003) Freehold and Atlantic Highlands Railroad Historic District (ID#4835) SR: 12/16/2014 Railroad right-of-way from Monmouth, Matawan Borough to Monmouth, (a.k.a. Stephen Crane House, Florence Hotel) Freehold Borough SHPO Opinion: 6/30/2008 Asbury Park Casino and Carousel (ID#1951) See Main Entry / Filed Location: Lake Avenue at the Boardwalk MONMOUTH County, Matawan Borough COE: 1/11/1990 Asbury Park Convention Hall (ID#1952) Garden State Parkway Historic District (ID#3874) Ocean Avenue Entire Garden State Parkway right-of-way NR: 3/2/1979 (NR Reference #: 79001512) SHPO Opinion: 10/12/2001 SR: 12/28/1978 See Main Entry / Filed Location: CAPE_MAY County, Lower Township Asbury Park Post Office (ID#1953) 801 Bangs Avenue New York and Long Branch Railroad Historic District (ID#4354) SR: 1/31/1986 DOE: 6/21/1984 SHPO Opinion: 8/20/2004 (Thematic Nomination of Significant Post Offices) See Main Entry / Filed Location: MIDDLESEX County, Perth Amboy City Asbury Park Railroad Station (ID#1954) 111 Main Street Allenhurst Borough SHPO Opinion: 10/24/1977 (Demolished c. 1978) Allenhurst Residential Historic District (ID#4963) Roughly Bounded by the Atlantic Ocean, Main Street, Cedar Grove Asbury Park Commercial Historic District (ID#3992) Avenue, Hume Street and Elberon Avenue Roughly bounded by 500, 600, 700 bloks., of Bond St., Cookman & NR: 6/18/2010 (NR Reference #: 10000353) Mattison Aves.
    [Show full text]
  • Refueling the Magic Furnace: Kilonova 2017 Rewrites the Story of Element Origins
    Refueling the Magic Furnace: Kilonova 2017 Rewrites the Story of Element Origins Barry Wood University of Houston Abstract For more than half a century, we have understood element creation in the stars—described in Marcus Chown’s colorful image as “the magic furnace.” From 1958 until 2017, supernova explosions were thought to be the primary site of element creation above Iron, No. 26 on the Periodic Table. This assumption was radically overturned with the August 17, 2017, arrival of signals from a catastrophic collision of neutron stars. This paper traces the history of element-creation science leading to the striking discoveries attending “Kilonova 2017” that now call for a rewriting of the nucleosynthesis chapter of Big History. Correspondence | Barry Wood, [email protected] Citation | Wood, B. (2018) Refueling the Magic Furnace: Kilonova 2017 Rewrites the Story of Element Origins. Journal of Big History, II(3); 1 - 15. DOI | http://dx.doi.org/10.22339/jbh.v2i3.2300 Introduction Beginning at 24 Hertz, it gradually rose over 100 Pangea had recently broken up . North America and seconds to several hundred Hertz—indicating the Europe were slowly drifting apart inspiraling of two massive bodies about to detonate . the Himalayas had not yet appeared . tropical in a cataclysmic collision. Following 3,000 cycles, the jungles harbored enormous predatory dinosaurs that GW signal came to an abrupt end at 12:41:04.4 UTC would roam the earth for another 65 million years . (Coordinated Universal Time). Almost immediately mammals the size of housecats kept to the shadows . (1.74 seconds later) a two-second gamma-ray burst .
    [Show full text]
  • Thesis Is Submited in Partial Fulfilment of the Requirements for the Award of the Degree of Doctor of Philosophy of the University of Portsmouth
    Techniques for Cosmological Analysis of Next Generation Low to Mid-Frequency Radio Data Michael Tarr Department of Technology THE THESIS IS SUBMITED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY OF THE UNIVERSITY OF PORTSMOUTH May 2018 Declaration Whilst registered as a candidate for the above degree, I have not been registered for any other research award. The results and conclusions embodied in this thesis are the work of the named candidate and have not been submitted for any other academic award. This dissertation contains 51,523 words not including appendices, bibliography, footnotes, tables and equations, and has 68 figures. Michael Tarr May 2018 Acknowledgements First, I would like to give my most sincere thanks to David. It goes without saying that I can not imagine having completed this work without you. Your enthusiasm and belief in me has been a constant source of motivation from day one to the eleventh hour. You are an inspiration and model of a perfect superior. I cannot overstate how much I appchiate your effort, and I am eternally grateful. My love and thanks also to my parents, who have provided nothing but loving support, despite all my whims and phases. I can only hope it was all worth it to find something I have finally stuck with. Thanks should also go to Xan and Matthew, for taking precious time away from their own research to indulge my pet machine learning project. I owe you both and hope to always be friends. Rebecca1, save the final thanks for you.
    [Show full text]
  • The Evolution of the Universe
    The Evolution of the Universe edited by David L. Alles Western Washington University e-mail: [email protected] Last Updated 2013-7-14 Note: In PDF format most of the images in this web paper can be enlarged for greater detail. 1 “If being educated means having an informed sense of time and place, then it is essential for a person to be familiar with the scientific aspects of the universe and know something of its origin and structure.” Project 2061, American Association for the Advancement of Science ---------------------------- "The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy."—Steven Weinberg Steven Weinberg is winner of the Nobel Prize in Physics in 1979, and author of the book "The First Three Minutes". 2 Introduction Science at the beginning of the twenty-first century can make some bold, yet simple observations: 1) the universe has evolved; 2) we are a result of that evolution. “We are the first generation of human beings to glimpse the sweep of cosmic history, from the universe's fiery origin in the Big Bang to the silent, stately flight of galaxies through the intergalactic night.” (National Research Council) Order in the Universe Cosmology is the study of the evolution of the universe from its first moments to the present. In cosmology the most fundamental question we can ask is: Does our universe have intelligible regularities that we can understand—is it ordered? This question lies at the heart of the scientific revolution beginning in the sixteenth century.
    [Show full text]
  • Physics 403 Systematic Effects and Experimental Design
    Physics 403 Systematic Effects and Experimental Design Segev BenZvi Department of Physics and Astronomy University of Rochester Statistical Uncertainties Frequentist: how much would a result fluctuate upon repetition of the measurement? Implies some knowledge/assumptions about PDFs... Example We countp photons ! Poisson distribution. For N = 150, N ± N ≈ 150 ± 12. Note: we assumed N^ = N. Example Time from a digital clock ! Uniform distribution. E.g., t = 23 s with 1 s resolution, var (t) = (b − a)2=12 = 1=12, so t = 23 ± 0:3 s Example Efficiency of a detector ! Binomial distribution. Record 45 out of 60 particles: ^ = 45=60 = 0:75, var (^) = (1 − )=N, so = 0:75 ± 0:06 Segev BenZvi (UR) PHY 403 2 / 24 I A neglected effect is a mistake, not an uncertainty[2] I Some confusion is caused by the term systematic error, because an “error” in common language means a mistake (implying fault or incompetence), while we mean an uncertainty Systematic effects is a general category which includes effects such as background, selection bias, scanning efficiency, energy resolution, angle resolution, variation of counter efficiency with beam position and energy, dead time, etc. [3] Usually expressed in form like this A = 10:2 ± 1:2 (stat) ± 2:3 (sys) Statistical vs. Systematic Uncertainties So what is a systematic uncertainty? I “Systematic error: reproducible inaccuracy introduced by faulty equipment, calibration, or technique.” [1] I Who agrees with this? Segev BenZvi (UR) PHY 403 3 / 24 Statistical vs. Systematic Uncertainties So what is a systematic uncertainty?
    [Show full text]
  • Master Plan Reexamination Report 2010
    il IJ LJ HOLMDELTOWNSHIPCOMMITTEE Mayor SerenaDiMaso iJ DeputyMayor PatrickImpreveduto Larry Fink i,n RoccoPascucci JanetBerk ll 2OlOPLANNINGBOARDMEMBERS ll PeterNelson, Chairman (Scenic Byways) GregBuontempo, Vice Chairman DerekDailey (HEC Member) Mayor SerenaDiMaso (ClassI) SamFasciano CommitteemanPat Impreveduto(Class III) JohnMioduszewski (Class II) RobertReina JohnScagnelli JerryAllocco, Alternate #1 ThomasKing, Alternate#2 (OSAC) 2010PlanninsBoardProfessionals BonnieHeard, P.E., Board Engineer ChesterPloussas, Lisowsky Partnership, LLP , SpecialConsulting Engineer JenniferBeahm, PP/AICP, Board Planner CME, SpecialConsulting Planners Martin Pfleger,Esq. Board Attorney Rick DeNoia,Esq., Special Consulting Attorney ',,'|1 ij ,* ij il. iJ |j i,j, t.l i t i.-i t: t': !; IIr. Extent to which Problemsand Objectiveshave beenReduced or Increased... ...............16 IV. SignificantChanges in the assumptions,policies and objectives........ ..... ............ .. ..17 Land 1. 2. 3. Issuesof Concern. 22 4. Zoning Changessince the adoption of the 2004Master Plan....... .. .........2 5 J. ApplicableState and CountyP|ans........ .............,....26 6. AdjacentMunicipalities....,....... .. .. ...... ..29 B. EconomicDevelopment......... ..... .......34 1. Economictrends and prospects......... .... .......................34 2. Existing Characteristicsof Holmdel's Labor Force..........................37 3. EconomicDevelopment Opportunities and Constraints......... ........39 4 FiscalConsiderations... .... .......40 iJ tJ C. ,* , Topography, Slopesand
    [Show full text]
  • Antenna Technology
    First Edition, 2012 ISBN 978-81-323-3025-7 © All rights reserved. Published by: Research World 4735/22 Prakashdeep Bldg, Ansari Road, Darya Ganj, Delhi - 110002 Email: [email protected] Table of Contents Chapter 1 - Dipole Antenna Chapter 2 - Horn Antenna Chapter 3 - Radio Telescope Chapter 4 - Parabolic Antenna Chapter 5 - Antenna (Radio) Chapter 6 - Television Antenna Chapter 7 - Radio Masts and Towers Chapter 8 - Omnidirectional Antenna & Directional Antenna Chapter 1 Dipole Antenna A schematic of a half-wave dipole antenna that a shortwave listener might build. A dipole antenna is a radio antenna that can be made of a simple wire, with a center-fed driven element. It consists of two metal conductors of rod or wire, oriented parallel and collinear with each other (in line with each other), with a small space between them. The radio frequency voltage is applied to the antenna at the center, between the two conductors. These antennas are the simplest practical antennas from a theoretical point of view. They are used alone as antennas, notably in traditional "rabbit ears" television antennas, and as the driven element in many other types of antennas, such as the Yagi. Dipole antennas were invented by German physicist Heinrich Hertz around 1886 in his pioneering experiments with radio waves. Electric fields (blue) and magnetic fields (red) radiated by a dipole antenna Elementary doublet An elementary doublet is a small length of conductor (small compared to the wavelength ) carrying an alternating current: Here is the angular frequency (and the frequency), and is , so that is a phasor. Note that this dipole cannot be physically constructed because the current needs somewhere to come from and somewhere to go to.
    [Show full text]