General Physics I: Classical Mechanics
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Relativistic Dynamics
Chapter 4 Relativistic dynamics We have seen in the previous lectures that our relativity postulates suggest that the most efficient (lazy but smart) approach to relativistic physics is in terms of 4-vectors, and that velocities never exceed c in magnitude. In this chapter we will see how this 4-vector approach works for dynamics, i.e., for the interplay between motion and forces. A particle subject to forces will undergo non-inertial motion. According to Newton, there is a simple (3-vector) relation between force and acceleration, f~ = m~a; (4.0.1) where acceleration is the second time derivative of position, d~v d2~x ~a = = : (4.0.2) dt dt2 There is just one problem with these relations | they are wrong! Newtonian dynamics is a good approximation when velocities are very small compared to c, but outside of this regime the relation (4.0.1) is simply incorrect. In particular, these relations are inconsistent with our relativity postu- lates. To see this, it is sufficient to note that Newton's equations (4.0.1) and (4.0.2) predict that a particle subject to a constant force (and initially at rest) will acquire a velocity which can become arbitrarily large, Z t ~ d~v 0 f ~v(t) = 0 dt = t ! 1 as t ! 1 . (4.0.3) 0 dt m This flatly contradicts the prediction of special relativity (and causality) that no signal can propagate faster than c. Our task is to understand how to formulate the dynamics of non-inertial particles in a manner which is consistent with our relativity postulates (and then verify that it matches observation, including in the non-relativistic regime). -
OCC D 5 Gen5d Eee 1305 1A E
this cover and their final version of the extended essay to is are not is chose to write about applications of differential calculus because she found a great interest in it during her IB Math class. She wishes she had time to complete a deeper analysis of her topic; however, her busy schedule made it difficult so she is somewhat disappointed with the outcome of her essay. It was a pleasure meeting with when she was able to and her understanding of her topic was evident during our viva voce. I, too, wish she had more time to complete a more thorough investigation. Overall, however, I believe she did well and am satisfied with her essay. must not use Examiner 1 Examiner 2 Examiner 3 A research 2 2 D B introduction 2 2 c 4 4 D 4 4 E reasoned 4 4 D F and evaluation 4 4 G use of 4 4 D H conclusion 2 2 formal 4 4 abstract 2 2 holistic 4 4 Mathematics Extended Essay An Investigation of the Various Practical Uses of Differential Calculus in Geometry, Biology, Economics, and Physics Candidate Number: 2031 Words 1 Abstract Calculus is a field of math dedicated to analyzing and interpreting behavioral changes in terms of a dependent variable in respect to changes in an independent variable. The versatility of differential calculus and the derivative function is discussed and highlighted in regards to its applications to various other fields such as geometry, biology, economics, and physics. First, a background on derivatives is provided in regards to their origin and evolution, especially as apparent in the transformation of their notations so as to include various individuals and ways of denoting derivative properties. -
Winter Constellations
Winter Constellations *Orion *Canis Major *Monoceros *Canis Minor *Gemini *Auriga *Taurus *Eradinus *Lepus *Monoceros *Cancer *Lynx *Ursa Major *Ursa Minor *Draco *Camelopardalis *Cassiopeia *Cepheus *Andromeda *Perseus *Lacerta *Pegasus *Triangulum *Aries *Pisces *Cetus *Leo (rising) *Hydra (rising) *Canes Venatici (rising) Orion--Myth: Orion, the great hunter. In one myth, Orion boasted he would kill all the wild animals on the earth. But, the earth goddess Gaia, who was the protector of all animals, produced a gigantic scorpion, whose body was so heavily encased that Orion was unable to pierce through the armour, and was himself stung to death. His companion Artemis was greatly saddened and arranged for Orion to be immortalised among the stars. Scorpius, the scorpion, was placed on the opposite side of the sky so that Orion would never be hurt by it again. To this day, Orion is never seen in the sky at the same time as Scorpius. DSO’s ● ***M42 “Orion Nebula” (Neb) with Trapezium A stellar nursery where new stars are being born, perhaps a thousand stars. These are immense clouds of interstellar gas and dust collapse inward to form stars, mainly of ionized hydrogen which gives off the red glow so dominant, and also ionized greenish oxygen gas. The youngest stars may be less than 300,000 years old, even as young as 10,000 years old (compared to the Sun, 4.6 billion years old). 1300 ly. 1 ● *M43--(Neb) “De Marin’s Nebula” The star-forming “comma-shaped” region connected to the Orion Nebula. ● *M78--(Neb) Hard to see. A star-forming region connected to the Orion Nebula. -
Title of the Paper
Variable Star and Exoplanet Section of Czech Astronomical Society and Planetarium Ostrava Proceedings of the 51st Conference on Variable Stars Research Planetarium Ostrava, Ostrava, Czech Republic 1st November - 3rd November 2019 Editor-in-chief Radek Kocián Participants of the conference OPEN EUROPEAN JOURNAL ON VARIABLE STARS November 2020 http://oejv.physics.muni.cz ISSN 1801-5964 DOI: 10.5817/OEJV2020-0208 TABLE OF CONTENTS Modeling of GX Lacertae ........................................................................................................................................ 5 Cataclysmic variable CzeV404 Her ......................................................................................................................... 8 On the spin period variability in intermediate polars ............................................................................................. 11 Photometric and spectroscopic observation of symbiotic variables at private observatory Liptovská Štiavnica ... 18 Outburst activity of flare stars 2014 – 2019 ........................................................................................................... 29 2 OPEN EUROPEAN JOURNAL ON VARIABLE STARS November 2020 http://oejv.physics.muni.cz ISSN 1801-5964 DOI: 10.5817/OEJV2020-0208 INTRODUCTION The Variable Star and Exoplanet Section of the Czech Astronomical Society organized traditional autumn conference on research and news in the field of variable stars. The conference was held in a comfortable space of Ostrava Planetarium. In addition -
Time-Derivative Models of Pavlovian Reinforcement Richard S
Approximately as appeared in: Learning and Computational Neuroscience: Foundations of Adaptive Networks, M. Gabriel and J. Moore, Eds., pp. 497–537. MIT Press, 1990. Chapter 12 Time-Derivative Models of Pavlovian Reinforcement Richard S. Sutton Andrew G. Barto This chapter presents a model of classical conditioning called the temporal- difference (TD) model. The TD model was originally developed as a neuron- like unit for use in adaptive networks (Sutton and Barto 1987; Sutton 1984; Barto, Sutton and Anderson 1983). In this paper, however, we analyze it from the point of view of animal learning theory. Our intended audience is both animal learning researchers interested in computational theories of behavior and machine learning researchers interested in how their learning algorithms relate to, and may be constrained by, animal learning studies. For an exposition of the TD model from an engineering point of view, see Chapter 13 of this volume. We focus on what we see as the primary theoretical contribution to animal learning theory of the TD and related models: the hypothesis that reinforcement in classical conditioning is the time derivative of a compos- ite association combining innate (US) and acquired (CS) associations. We call models based on some variant of this hypothesis time-derivative mod- els, examples of which are the models by Klopf (1988), Sutton and Barto (1981a), Moore et al (1986), Hawkins and Kandel (1984), Gelperin, Hop- field and Tank (1985), Tesauro (1987), and Kosko (1986); we examine several of these models in relation to the TD model. We also briefly ex- plore relationships with animal learning theories of reinforcement, including Mowrer’s drive-induction theory (Mowrer 1960) and the Rescorla-Wagner model (Rescorla and Wagner 1972). -
Správa O Činnosti Organizácie SAV Za Rok 2017
Astronomický ústav SAV Správa o činnosti organizácie SAV za rok 2017 Tatranská Lomnica január 2018 Obsah osnovy Správy o činnosti organizácie SAV za rok 2017 1. Základné údaje o organizácii 2. Vedecká činnosť 3. Doktorandské štúdium, iná pedagogická činnosť a budovanie ľudských zdrojov pre vedu a techniku 4. Medzinárodná vedecká spolupráca 5. Vedná politika 6. Spolupráca s VŠ a inými subjektmi v oblasti vedy a techniky 7. Spolupráca s aplikačnou a hospodárskou sférou 8. Aktivity pre Národnú radu SR, vládu SR, ústredné orgány štátnej správy SR a iné organizácie 9. Vedecko-organizačné a popularizačné aktivity 10. Činnosť knižnično-informačného pracoviska 11. Aktivity v orgánoch SAV 12. Hospodárenie organizácie 13. Nadácie a fondy pri organizácii SAV 14. Iné významné činnosti organizácie SAV 15. Vyznamenania, ocenenia a ceny udelené organizácii a pracovníkom organizácie SAV 16. Poskytovanie informácií v súlade so zákonom o slobodnom prístupe k informáciám 17. Problémy a podnety pre činnosť SAV PRÍLOHY A Zoznam zamestnancov a doktorandov organizácie k 31.12.2017 B Projekty riešené v organizácii C Publikačná činnosť organizácie D Údaje o pedagogickej činnosti organizácie E Medzinárodná mobilita organizácie F Vedecko-popularizačná činnosť pracovníkov organizácie SAV Správa o činnosti organizácie SAV 1. Základné údaje o organizácii 1.1. Kontaktné údaje Názov: Astronomický ústav SAV Riaditeľ: Mgr. Martin Vaňko, PhD. Zástupca riaditeľa: Mgr. Peter Gömöry, PhD. Vedecký tajomník: Mgr. Marián Jakubík, PhD. Predseda vedeckej rady: RNDr. Luboš Neslušan, CSc. Člen snemu SAV: Mgr. Marián Jakubík, PhD. Adresa: Astronomický ústav SAV, 059 60 Tatranská Lomnica http://www.ta3.sk Tel.: 052/7879111 Fax: 052/4467656 E-mail: [email protected] Názvy a adresy detašovaných pracovísk: Astronomický ústav - Oddelenie medziplanetárnej hmoty Dúbravská cesta 9, 845 04 Bratislava Vedúci detašovaných pracovísk: Astronomický ústav - Oddelenie medziplanetárnej hmoty prof. -
Contents Sisukord
Contents Sisukord Eessõna ................................... 8 Foreword.................................. 9 1 Ülevaade 10 1.1 Uurimisteemad ja grandid ..................... 10 1.1.1 Sihtfinantseeritavad teadusteemad ............ 10 1.1.2 Eesti Teadusagentuuri grandid .............. 10 1.1.3 Euroopa Liidu 7. raamprogrammi projektid ...... 11 1.1.4 Euroopa kosmoseagentuuri Euroopa koostööriikide programmi projektid .................... 11 1.1.5 Euroopa Liidu struktuuritoetused ............ 11 1.1.6 COST projektid ....................... 13 1.1.7 Muud projektid ja lepingud ................ 13 1.2 Töötajad ............................... 14 1.3 Tunnustused ............................. 15 1.4 Eelarve ................................ 17 1.5 Aparatuur ja seadmed ....................... 18 1.6 Teadusnõukogu töö ......................... 19 1.7 Suhted avalikkusega ........................ 20 1.8 Tänuavaldused ........................... 23 2 Summary 24 2.1 Researchprojectsandgrants. 24 2.1.1 Targetfinancedprojects . 24 2.1.2 EstonianResearchCouncilgrants . 24 2.1.3 The European Commission 7th Framework Program- meprojects ......................... 25 2.1.4 European Space Agency Programme for European CooperatingStates . 25 2.1.5 FinancingfromtheEUStructuralFunds. 25 2.1.6 COSTprojects........................ 27 2.1.7 Someotherprojectsandcontracts . 27 2.2 Staff.................................. 28 2.3 Awards................................ 29 2.4 Budget ................................ 31 2.5 Instrumentsandfacilities . 32 3 2.6 ScientificCouncil -
Lie Time Derivative £V(F) of a Spatial Field F
Lie time derivative $v(f) of a spatial field f • A way to obtain an objective rate of a spatial tensor field • Can be used to derive objective Constitutive Equations on rate form D −1 Definition: $v(f) = χ? Dt (χ? (f)) Procedure in 3 steps: 1. Pull-back of the spatial tensor field,f, to the Reference configuration to obtain the corresponding material tensor field, F. 2. Take the material time derivative on the corresponding material tensor field, F, to obtain F_ . _ 3. Push-forward of F to the Current configuration to obtain $v(f). D −1 Important!|Note that the material time derivative, i.e. Dt (χ? (f)) is executed in the Reference configuration (rotation neutralized). Recall that D D χ−1 (f) = (F) = F_ = D F Dt ?(2) Dt v d D F = F(X + v) v d and hence, $v(f) = χ? (DvF) Thus, the Lie time derivative of a spatial tensor field is the push-forward of the directional derivative of the corresponding material tensor field in the direction of v (velocity vector). More comments on the Lie time derivative $v() • Rate constitutive equations must be formulated based on objective rates of stresses and strains to ensure material frame-indifference. • Rates of material tensor fields are by definition objective, since they are associated with a frame in a fixed linear space. • A spatial tensor field is said to transform objectively under superposed rigid body motions if it transforms according to standard rules of tensor analysis, e.g. A+ = QAQT (preserves distances under rigid body rotations). -
Physics Study Sheet for Math Pre-Test
AP Physics 1 Summer Assignments Dear AP Physics 1 Student, kudos to you for taking on the challenge of AP Physics! Attached you will find some physics-related math to work through before the first day of school. The problems require you to apply math concepts that were covered in algebra and trigonometry. Bring your completed sheets on the first day of school. Please familiarize yourself with the following websites. https://phet.colorado.edu/en/simulations/category/physics We will use this website extensively for physics simulations. These websites are good resources for physics concepts: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html http://www.thephysicsaviary.com/APReview.html http://www.physicsclassroom.com/ http://www.learnapphysics.com/apphysics1and2/index.html https://openstax.org/subjects/science This website provides free online textbooks with links to online simulations. Finally, you will need a graph paper composition notebook on the first day of class. This serves as your Lab Notebook. I look forward to learning and teaching with you in the fall! Find time to relax and recharge over the summer. I will be checking my district email, so feel free to contact me with any questions and concerns. My email address is [email protected]. 1 Physics Study Sheet for Math Algebra Skills 1. Solve an equation for any variable. Solve the following for x. ay a) v + w = x2yz c) bx 2 1 1 21y b) d) x 32 x 32 2. Be able to reduce fractions containing powers of ten. 2 3 10 4 10 a) 10 b) 103 106 3. -
Spectral Observations of AG Draconis During Quiescence and Outburst (1993–1995)
Astron. Astrophys. 347, 151–163 (1999) ASTRONOMY AND ASTROPHYSICS Spectral observations of AG Draconis during quiescence and outburst (1993–1995) M.T. Tomova and N.A. Tomov National Astronomical Observatory Rozhen, P.O. Box 136, BG-4700 Smolyan, Bulgaria ([email protected]) Received 30 July 1998 / Accepted 1 February 1999 Abstract. High and intermediate resolution observations of the depends on the nebula’s velocity field, which on its side is deter- blue and the Hα spectral regions of the symbiotic star AG Dra mined by the components’ interaction. That is why investigation at quiescence and during an active phase in 1994 and 1995 of the interaction in the symbiotic stars is of prime importance were performed. Variationsof profiles, fluxes and radial velocity for understanding their nature. data of a number of emission lines are investigated. The width The star AG Dra (BD +67◦922) is a known symbiotic (FWHM) of all of these lines was very large at times close to the system with high galactic latitude, large barycentric velocity 1 1994 light maximum. The emission measure of the surrounding γ = 148 km s− and a relatively early spectral type (K). Its nebula was also calculated using Balmer continuum emission photometric− period is about 550d (Meinunger 1979; Skopal on the basis of U photometric observations from the literature. 1994). The consistency of this period with the orbital period It turned out that at the times of the 1994 and 1995 visual light of the binary is confirmed by radial velocity variations of the maxima the emission measure has increased by a factor of 15 cool primary component, measured by Garcia & Kenyon (1988), and 8 respectively, compared with its quiescent maximal value. -
Quantum Theory, Quantum Mechanics) Part 1
Quantum physics (quantum theory, quantum mechanics) Part 1 1 Outline Introduction Problems of classical physics Black-body Radiation experimental observations Wien’s displacement law Stefan – Boltzmann law Rayleigh - Jeans Wien’s radiation law Planck’s radiation law photoelectric effect observation studies Einstein’s explanation Quantum mechanics Features postulates Summary Quantum Physics 2 Question: What do these have in common? lasers solar cells transistors computer chips CCDs in digital cameras Ipods superconductors ......... Answer: They are all based on the quantum physics discovered in the 20th century. 3 “Classical” vs “modern” physics 4 Why Quantum Physics? “Classical Physics”: developed in 15th to 20th century; provides very successful description “macroscopic phenomena, i.e. behavior of “every day, ordinary objects” o motion of trains, cars, bullets,…. o orbit of moon, planets o how an engine works,.. o Electrical and magnetic phenomena subfields: mechanics, thermodynamics, electrodynamics, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” 5 --- William Thomson (Lord Kelvin), 1900 Why Quantum Physics? – (2) Quantum Physics: developed early 20th century, in response to shortcomings of classical physics in describing certain phenomena (blackbody radiation, photoelectric effect, emission and absorption spectra…) describes microscopic phenomena, e.g. behavior of atoms, photon-atom scattering and flow of the electrons in a semiconductor. -
Stars and Their Spectra: an Introduction to the Spectral Sequence Second Edition James B
Cambridge University Press 978-0-521-89954-3 - Stars and Their Spectra: An Introduction to the Spectral Sequence Second Edition James B. Kaler Index More information Star index Stars are arranged by the Latin genitive of their constellation of residence, with other star names interspersed alphabetically. Within a constellation, Bayer Greek letters are given first, followed by Roman letters, Flamsteed numbers, variable stars arranged in traditional order (see Section 1.11), and then other names that take on genitive form. Stellar spectra are indicated by an asterisk. The best-known proper names have priority over their Greek-letter names. Spectra of the Sun and of nebulae are included as well. Abell 21 nucleus, see a Aurigae, see Capella Abell 78 nucleus, 327* ε Aurigae, 178, 186 Achernar, 9, 243, 264, 274 z Aurigae, 177, 186 Acrux, see Alpha Crucis Z Aurigae, 186, 269* Adhara, see Epsilon Canis Majoris AB Aurigae, 255 Albireo, 26 Alcor, 26, 177, 241, 243, 272* Barnard’s Star, 129–130, 131 Aldebaran, 9, 27, 80*, 163, 165 Betelgeuse, 2, 9, 16, 18, 20, 73, 74*, 79, Algol, 20, 26, 176–177, 271*, 333, 366 80*, 88, 104–105, 106*, 110*, 113, Altair, 9, 236, 241, 250 115, 118, 122, 187, 216, 264 a Andromedae, 273, 273* image of, 114 b Andromedae, 164 BDþ284211, 285* g Andromedae, 26 Bl 253* u Andromedae A, 218* a Boo¨tis, see Arcturus u Andromedae B, 109* g Boo¨tis, 243 Z Andromedae, 337 Z Boo¨tis, 185 Antares, 10, 73, 104–105, 113, 115, 118, l Boo¨tis, 254, 280, 314 122, 174* s Boo¨tis, 218* 53 Aquarii A, 195 53 Aquarii B, 195 T Camelopardalis,